Physiology of intracellular calcium buffering

Abstract

Calcium signaling underlies much of physiology. Almost all the Ca²⁺ in the cytoplasm is bound to buffers, with typically only ∼1% being freely ionized at resting levels in most cells. Physiological Ca²⁺ buffers include small molecules and proteins, and experimentally Ca²⁺ indicators will also buffer calcium. The chemistry of interactions between Ca²⁺ and buffers determines the extent and speed of Ca²⁺ binding. The physiological effects of Ca²⁺ buffers are determined by the kinetics with which they bind Ca²⁺ and their mobility within the cell. The degree of buffering depends on factors such as the affinity for Ca²⁺, the Ca²⁺ concentration, and whether Ca²⁺ ions bind cooperatively. Buffering affects both the amplitude and time course of cytoplasmic Ca²⁺ signals as well as changes of Ca²⁺ concentration in organelles. It can also facilitate Ca²⁺ diffusion inside the cell. Ca²⁺ buffering affects synaptic transmission, muscle contraction, Ca²⁺ transport across epithelia, and the killing of bacteria. Saturation of buffers leads to synaptic facilitation and tetanic contraction in skeletal muscle and may play a role in inotropy in the heart. This review focuses on the link between buffer chemistry and function and how Ca²⁺ buffering affects normal physiology and the consequences of changes in disease. As well as summarizing what is known, we point out the many areas where further work is required.

CLINICAL HIGHLIGHTS.

• Intracellular calcium controls the function of all organs in the body.

• Most of the intracellular calcium is not free; rather, it is bound to calcium buffers. This affects the amplitude and time course of intracellular calcium transients.

• Disordered intracellular calcium regulation is linked to many pathological conditions. Abnormal calcium buffering, as opposed to changes in transmembrane fluxes, has been suggested as a primary pathological mechanism.

• For example, in common conditions such as atrial fibrillation and heart failure, altered intracellular calcium buffering is thought to contribute to proarrhythmic behavior.

• In rarer genetic conditions such as hypertrophic cardiomyopathy, altered calcium buffering caused by mutations in contractile proteins is thought to promote abnormal contraction time course and increased incidence of arrhythmias. Initial studies suggest that drugs targeting the abnormal calcium buffering may improve contraction kinetics and reduce arrhythmias.

• In neurons, calcium-binding proteins contribute to the regulation of electrical excitability and short-term synaptic plasticity.

• Altered neuronal expression of calcium-binding proteins has been reported in the context of neurological diseases including dementia, epilepsy, and ataxia, but whether this is the primary cause or a consequence of abnormal neural function is less established.

• This review introduces the readership of Physiological Reviews to the basic chemistry of calcium buffers and discusses how this relates to their function in both health and disease. Although modulation of intracellular calcium buffering may represent a promising novel therapeutic route, challenges such as the complex interdependence of calcium signaling and the need for tissue-specific interventions need to be addressed in future research.

1. INTRODUCTION

The importance of Ca²⁺ ions in regulating cell and tissue function is well established. Life begins with an increase of intracellular calcium concentration ([Ca²⁺]_i) at the moment of fertilization (1). Cell death (apoptosis) is also accompanied by a Ca²⁺ signal (2). In between, the function of virtually every cell and tissue is controlled or influenced by changes of [Ca²⁺]_i, and many important diseases involve disorders of Ca²⁺ signaling (for reviews see, e.g., Refs. 3–10). This Ca²⁺-dependent regulation is mediated by Ca²⁺ ions binding to proteins and thereby changing their structure and function. However, a consequence of this binding is that changes in cytoplasmic free Ca²⁺ are strongly constrained or “buffered,” with typically only ∼1% being free and ionized at resting [Ca²⁺]_i. The chemistry of ionic buffering was first described with respect to the hydrogen ion (H⁺) in the early twentieth century and quantified initially by Koppel and Spiro (11) (see also Ref. 12) and subsequently by van Slyke (13). One of the first physiological indications of Ca²⁺ buffering, noted >70 years ago, was that intracellular Ca²⁺ is relatively immobile (14). Subsequent work on the squid axon led to the concept that most cytoplasmic Ca²⁺ is bound to Ca²⁺-binding molecules rather than being freely ionized (15), and similar conclusions have been reached for other tissues.

This buffering function of Ca²⁺-binding molecules means that not only the amplitude but also the time course of changes of [Ca²⁺]_i may depend as much on the properties of the Ca²⁺ buffers as on the magnitude of the underlying Ca²⁺ fluxes. As described in this review, Ca²⁺ buffers are essential regulators for such important and diverse functions as muscle contraction, neuronal excitability and synaptic facilitation, epithelial transport, and killing of bacteria. The effects of buffers are not restricted to the cytoplasm but also extend to endoplasmic reticulum (ER), mitochondrial, and nuclear Ca²⁺.

Much is now known about the molecules that buffer Ca²⁺ and how their chemical properties determine this buffering. For many tissues, however, the quantitative contribution of the various potential buffers still remains to be established. Buffers differ in the affinity and speed with which they bind and release Ca²⁺ ions, and this binding can also be affected by other ions such as Mg²⁺ and protons. It is therefore important to understand how functional properties of Ca²⁺ buffers relate to their structure and chemistry. Some Ca²⁺ buffers are mobile, and binding to these can accelerate the rate at which Ca²⁺ diffuses within the cytoplasm. Another important and underappreciated issue concerns the factors that determine the strength or power of Ca²⁺ buffering. For example, how does buffering depend on the Ca²⁺ concentration and the affinity of the buffer for Ca²⁺, and how is it different for buffers that bind more than one Ca²⁺ in a cooperative manner?

As well as being physiologically important, experimentally added Ca²⁺ buffers have been used to control Ca²⁺ concentrations and probe cellular mechanisms of Ca²⁺ handling. Ca²⁺-sensitive fluorescent indicators used to measure [Ca²⁺]_i are Ca²⁺ buffers and accordingly alter Ca²⁺ signaling.

Despite its importance, buffering is much less well understood than are many other aspects of Ca²⁺ signaling. In this review, we first consider the chemistry of Ca²⁺ buffering and the factors that determine the extent and speed of buffering. We emphasize the importance of the quantitative properties of buffering, deriving these from physicochemical principles and simplifying assumptions to describe general relationships. We show how the physiology of cells as diverse as epithelial cells, neurons, and muscle and immune cells is shaped by the chemistry of Ca²⁺ buffering and how a given buffer can be used to control the function of diverse tissues. Finally, there is much that is still not understood about buffering, and we highlight new directions for research.

2. CHEMISTRY OF Ca²⁺ BUFFERING

In aqueous solution, Ca²⁺ ions electrostatically form a solvation sphere with 6–10 water molecules (16). Chelation is the process of replacing two or more of these water molecules with dative covalent bonds between the Ca²⁺ ion and a ligand molecule and is the mechanism through which Ca²⁺ ions in solution bind to both small synthetic molecules and various Ca²⁺-binding proteins. In biological environments, the energetically optimum coordination of water around Ca²⁺ is 7, with 5 points arranged almost in a planar pentagon and 2 on an orthogonal plane creating a pentagonal bipyramid (17) (FIGURE 1). Most synthetic and biological chelators replace 6 or 7 of the water molecules with a chelation structure. Molecules interact directly with Ca²⁺ via electronegative points on the ligand molecule, typically negatively charged oxygen on a carboxylate group, the electronegative carbonyl group, or the lone pair of electrons of amino or histidyl groups (18) (FIGURE 2). Synthetic or natural Ca²⁺-binding molecules present an array of these electronegative residues to form a clawlike structure around each Ca²⁺ ion. The dative covalent bonds can form on each of the X, Y, and Z planes around the ion, thereby excluding most of the water molecules in the solvation sphere (17, 18).

FIGURE 1.

Pentagonal bipyramid arrangement of water around the Ca²⁺ ion in aqueous solution. In the chelation process, each water molecule is replaced by an organic residue that has an electronegative pole to support a dative covalent bond with Ca²⁺. The common groups that participate in chelation are shown with the electronegative poles designated.

FIGURE 2.

Examples of chelate structures. A: the small molecule EDTA adapted from Ref. 19, with permission from Fibres and Textiles in Eastern Europe. B: the EF-hand domain in terms of the helix-loop-helix structure (left) and the detail of the chelation site for the canonical form (right). Adapted from Ref. 17, with permission from Biochemical Journal. C: the proposed reaction scheme for the polymerization of calsequestrin (CSQ). Ca²⁺ ions are denoted as yellow balls in A–C; adapted from Ref. 20, with permission from Journal of Biological Chemistry.

2.1. Kinetics and Affinity

$$\mathrm{Ca}+\mathrm{B}\underset{{\mathrm{k}}_{\mathrm{off}}}{\overset{{\mathrm{k}}_{\mathrm{on}}}{\rightleftharpoons }}\mathrm{CaB}$$ reaction 1

The simplest Ca²⁺ binding scheme is described in reaction 1. More complicated reactions, involving cooperative binding to multiple sites or competition with other ions are considered below. Here, Ca²⁺ binds to the buffer (B) with a rate constant k_on (in M⁻¹·s⁻¹) and dissociates with rate constant k_off (in s⁻¹). As described in sect. 3, for a total buffer concentration, [B]_Tot, the equilibrium concentration of Ca²⁺ bound to buffer, [CaB], will be given by

$$[\mathrm{CaB}]={[\mathrm{B}]}_{\mathrm{Tot}}\mathrm{\hspace{0.17em}·\hspace{0.17em}}\frac{{\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{i}}}{K_{\mathrm{d}}+{\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{i}}}$$ (1)

The equilibrium dissociation constant is given by K_d = k_off/k_on. In chemistry, it is more customary to describe the association reaction of reaction 1 with an association constant (K_a = k_on/k_off). However, K_a has units of M⁻¹, and its inverse, the K_d, is easier to appreciate as it is equivalent to the concentration of free Ca²⁺ at which 50% of the buffer has Ca²⁺ bound. Interestingly, almost regardless of the structure, the rate of Ca²⁺ binding to a buffer is generally rapid and close to the diffusion limit of 10³ to 10⁴ µM⁻¹·s⁻¹ (10⁹ to 10¹⁰ M⁻¹·s⁻¹) in aqueous media (21). Such rates are technically difficult to measure and involve measurements on isolated proteins/molecules under chemical conditions that are far from physiological. Dissociation rate constants and equilibrium constants are easier to measure accurately, and therefore very fast association rate constants are often calculated as the ratios of k_off over K_d. Values of K_ds vary greatly across a range of chelation structures, with low-affinity buffers resulting from structures with high k_off values.

2.2. Competition with Mg²⁺ and Protons

A mechanism that is frequently involved in lowering the affinity of a buffer is a decreased effective k_on of the chelation/association reaction due to sequestering of the free buffer by other competing cations. As discussed below and illustrated in reactions 2A and 2B, if Mg²⁺ or protons are bound to a buffer, these ions must dissociate before Ca²⁺ can bind. This additional step slows down the overall rate constant for the Ca²⁺-binding reaction and therefore decreases the “apparent” affinity of the buffer under these conditions. For some buffers (for example ATP), even in the presence of Mg²⁺ or H⁺, Ca²⁺ binding is still rapid, whereas for others the slowing is profound (TABLE 1).

$${\text{Ca}}^{\text{2}+}+\text{BMg}\underset{{\text{k}}_{\text{off},\text{Mg}}}{\overset{{\text{k}}_{\text{on},\text{Mg}}}{\mathrm{\leftrightharpoons }}}{\text{Mg}}^{\text{2}+}+{\text{Ca}}^{\text{2}+}+\text{B}\hspace{0.17em}\underset{{\text{k}}_{\text{off},\mathrm{Ca}}}{\overset{{\text{k}}_{\text{on},\mathrm{Ca}}}{\mathrm{\rightleftharpoons }}}\text{CaB}+{\text{Mg}}^{\text{2}+}$$ reaction 2A

$${\text{Ca}}^{\text{2}+}+\text{BH}\underset{{\text{k}}_{\text{off},\text{H}}}{\overset{{\text{k}}_{\text{on},\text{H}}}{\mathrm{\leftrightharpoons }}}{\text{H}}^{+}+{\text{Ca}}^{\text{2}+}+\text{B}\hspace{0.17em}\underset{{\text{k}}_{\text{off},\text{Ca}}}{\overset{{\text{k}}_{\text{on},\text{Ca}}}{\mathrm{\rightleftharpoons }}}\text{CaB}+{\text{H}}^{+}$$ reaction 2B

Table 1.

Examples of K_d and rate constants (both measured and apparent), for buffers which have a significant affinity for Mg²⁺ and or H⁺ in addition to Ca²⁺

Buffer	Kd, μM	kon, µM−1·s−1	koff, s−1	Kd,app, µM (pH 7.2, 1 mM Mg2+)	kon,app, µM−1·s−1 (pH 7.2, 1 mM Mg2+)
EDTA	2.5 × 10-5 a	2,500a	0.7a	15.7a	0.06a
EGTA	1 × 10-5 b	2,500c	0.5d	0.18c	2.7d
BAPTA	0.17d	450d	79d	0.176d	440d
ATP	170l	150k	30,000k	2,496l	12l
PV	0.012e,g	100e,g	1e,f	0.16g	6.2
CB-D28k	0. 312i,h	110i,h	34h	0.434i	78i
Isolated skeletal TnC	3.3j	157j	342j	5.9j	45j

The listed measured equilibrium constants (K_d) and rate constants k_on and k_off values apply to Ca²⁺ binding to the buffer in the presence of a range of conditions including very low H⁺ and Mg²⁺ concentrations. The apparent equilibrium constants (K_d,app) were taken from measured values at 1 mM Mg²⁺, pH 7.2. The rate constants k_on,app were estimated under those conditions based on measured k_off values. Note that parvalbumin (PV), calbindin-D28k (CB-D28k), and Troponin-C (TnC) have multiple Ca²⁺ binding sites, and the k_on values represent the highest measured at a single site unless the dissociation constants are identical. The parameters for a single ligand can come from different studies: the measured K_d does not equal the expected ratio of the rate constants. ^aRef. 22, 25°C, no added Mg²⁺; ^bRef. 23; ^cRef. 24, 35°C, no added Mg²⁺; ^dRef. 25, 22°C, no added Mg²⁺; ^eRef. 26, whiting (fish) protein, k_on is highest of two binding sites, ∼20°C, no added Mg²⁺; ^fRef. 27, bovine chromaffin cells, K_d and k_off at 20°C, 0.14 mM Mg²⁺; ^gRef. 28, bullfrog skeletal muscle, K_d values for Ca²⁺ and Mg²⁺ (∼90 μM) [note that another study found a 2-fold lower value for K_d(Mg) ∼40 μM (29)]; ^hRef. 30, recombinant protein, highest k_on of 2 binding sites, 20°C, no added Mg²⁺; ⁱRef. 31, recombinant human protein, highest K_d value of 4 binding sites, 20°C; ^jRef. 32, isolated TnC in the absence and presence of 3 mM Mg²⁺; ^kRef. 33, measured in solution at 20°C in 0.1 M KCl, from a compilation of stability constants; ^lRef. 34, rate constants based on measurements in free solution but corrected for intracellular conditions.

The equilibria describing the reactions between protons, Mg²⁺, and Ca²⁺ with a buffer can be expressed by modifying Eq. 1 such that

$$[\mathrm{CaB}]={[\mathrm{B}]}_{\mathrm{Tot}}\mathrm{\hspace{0.17em}·\hspace{0.17em}}\frac{{\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{i}}}{K_{\mathrm{d},\mathrm{app}}+{\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{i}}}$$ (2)

where

$$K_{\mathrm{d},\mathrm{app}}=K_{\mathrm{d},\mathrm{Ca}}\mathrm{\hspace{0.17em}·\hspace{0.17em}}\left(1+\frac{{\left[\mathrm{M}{\mathrm{g}}^{2+}\right]}_{\mathrm{i}}}{K_{\mathrm{d},\mathrm{Mg}}}+\frac{{\left[{\mathrm{H}}^{+}\right]}_{\mathrm{i}}}{K_{\mathrm{d},\mathrm{H}}}\right)$$ (3)

K_d,Ca, K_d,Mg, and K_d,H are the equilibrium dissociation constants, for Ca²⁺, Mg²⁺, and H⁺, respectively, such that K_d,Ca = k_off,Ca/k_on,Ca, K_d,Mg = k_off,Mg/k_on,Mg, and similarly for H⁺.

In other words, as [Mg²⁺]_i or [H⁺]_i increases, the apparent K_d for Ca²⁺ increases. Equations 2 and 3 quantify the extent to which H⁺- or Mg²⁺-bound forms of the buffer will affect the overall Ca²⁺ equilibration position. The apparent equilibrium constant (K_d,app) can be used to calculate the apparent association rate constant k_on,app = k_off/K_d,app using the measured dissociation rate constant (k_off), which only involves Ca²⁺ and the buffer and is therefore unaffected by Mg²⁺ or H⁺. Some examples of measurements that demonstrate the reduction of the rate constant are given in TABLE 1 and discussed in sects. 2.3 and 2.5. It should be noted that the numbers presented come from many different studies, not necessarily performed at the same temperature, pH, and ionic strength and using material from different sources. Therefore, one cannot expect quantitative agreement in all cases. As will become apparent in subsequent sections, uncertainty about Ca²⁺ binding under physiological conditions makes it difficult to predict the properties of Ca²⁺ buffering from the known concentrations of buffers, and it will be important to address this in future work.

2.3. Small Synthetic Molecule Ca²⁺ Buffers

Small synthetic molecule buffers have many uses in experimental biology, forming the basis of many Ca²⁺-indicator dyes (35, 36), and are used for determining or altering the free Ca²⁺ concentration of solutions (35, 37, 38). In addition, “caged” Ca²⁺ chelators can change their affinity for Ca²⁺ upon photolytic exposure to light, thereby either releasing (39–41) or chelating (42) Ca²⁺ ions. Furthermore, understanding how the different chelation structures of the small synthetic molecules correlate with changes in affinity, selectivity, and kinetics helps explain the range of properties of the various Ca²⁺-binding molecules seen in nature. The kinetics and equilibria of Ca²⁺ binding depend on the structure of the ligand relative to the ionic radius of the cation. In the case of ethylenediaminetetraacetic acid (EDTA; FIGURE 2A), the ligand structure chelates Ca²⁺ but also accommodates Mg²⁺, an abundant intracellular divalent cation with a smaller ionic radius and a larger solvated radius. Although the affinity of EDTA for Mg²⁺ is 100-fold lower than for Ca²⁺ cytosolic levels of Mg²⁺ are >1,000-fold higher, and thus Mg²⁺ binding dominates over Ca²⁺ in an intracellular environment. Under these conditions, buffering or binding Ca²⁺ inevitably involves displacement of bound Mg²⁺, and therefore the complete reaction scheme incorporates Mg²⁺ dissociation/association (reaction 2A). As discussed in sect. 2.2, this feature, together with the effect of H⁺ binding, reduces the affinity (by ∼400,000 fold) and slows the overall kinetics of Ca²⁺ buffering. Furthermore, Ca²⁺ binding to EDTA releases Mg²⁺ from the buffer molecule and potentially increases the free Mg²⁺ level. In turn, buffering by EDTA will depend on Mg²⁺, which is buffered by free ATP²⁻ and therefore depends on the metabolic state of the cell.

The related ligand ethylene glycol-bis(β-aminoethyl ether)-N,N,N′,N′-tetraacetic acid (EGTA) has a higher selectivity for Ca²⁺ over Mg²⁺ (10,000 fold) because of a longer backbone between the two amino groups that is more suited to chelate the larger ionic radius of Ca²⁺. Therefore, Mg²⁺ binding is minimal and interferes less with the Ca²⁺ buffering action. This means that k_on of Ca²⁺ binding to the unprotonated form of EGTA approaches the diffusion limit of 10³ to 10⁴ µM⁻¹·s⁻¹ (24). However, at neutral pH, >98.5% of EGTA is in the diprotonated form, with protons bound to the two amino groups that participate in chelation, and this form of the molecule has a much-reduced ability to bind Ca²⁺, with a K_d ∼10^5.6 times greater than in the absence of protons and therefore not significantly contributing to chelation. Significant amounts of the unprotonated form are only available to bind Ca²⁺ metal ions after the dissociation of protons (reaction 2B) (25); thus the effective k_on for Ca²⁺ binding is ∼100-fold less than the diffusion limit because of the additional steps of proton dissociation as part of the chelation reaction. This property not only slows buffering but also makes it steeply pH dependent, and for every Ca²⁺ ion that binds to EGTA approximately two H⁺ ions are released (23). In consequence, EGTA-containing solutions will acidify upon addition of Ca²⁺. Therefore, solutions should be pH adjusted after adding Ca²⁺, and EGTA-loaded cells should be strongly pH buffered to avoid pH changes upon Ca²⁺ influx. It should be noted that around pH 7.2 a titration error of only 0.1 pH units will cause a 50–80% error in the apparent K_d of EGTA (23, 43, 44).

In contrast to EDTA and EGTA, for which the rate of Ca²⁺ binding is limited by the need for Mg²⁺ or protons to dissociate, 1,2-bis(2-aminophenoxy) ethane-N,N,N′,N′-tetraacetic acid (BAPTA) has fast Ca²⁺ binding kinetics at neutral pH (35). This molecule combines a high selectivity for Ca²⁺ over Mg²⁺ arising from the optimum backbone length and a low affinity for protons on the two amine groups, allowing it to be relatively unaffected by the Mg²⁺ concentration and pH of the solution. Ca²⁺ binding can therefore occur without any significant exchanges with Mg²⁺ or H⁺, and this explains the fast k_on for Ca²⁺ association (>10² µM⁻¹·s⁻¹) (25). It is worth emphasizing that the intrinsic rate of Ca²⁺ binding by BAPTA is actually lower than for EDTA and EGTA (TABLE 1). It is the lack of competition with H⁺ or Mg²⁺ that ensures an effective fast binding rate under physiological conditions.

2.4. Small Biological Molecule Ca²⁺ Binding

A range of small-molecule ligands is endogenous to the cellular environment. One example is that of humic and fulvic acids, comprising a mixture of many different molecules resulting from the breakdown of organic matter, which buffer a range of environmental divalent cations including Ca²⁺, Cd²⁺, and Pb²⁺, with the K_d of humic acid for Ca²⁺ being of the order of 1 mM at neutral pH (45, 46). In biological systems, individual amino acids such as l-arginine and l-lysine have significant single-site Ca²⁺ affinities, whereas di- and tripeptides, e.g., Gly-Glu, bind Ca²⁺ with chelation structure and K_ds (0.1–1 µM) similar to synthetic chelators such as EGTA and BAPTA (47). These Ca²⁺-peptide complexes may have a biological function, for example facilitating Ca²⁺ transport across the intestinal epithelium (48).

2.4.1. Histidyl dipeptides, including carnosine.

Another function of Ca²⁺ binding to dipeptides is suggested by studies of the histidyl dipeptides (HDPs, e.g., carnosine) in striated muscle (49). Although possessing a relatively low Ca²⁺ affinity (K_d ∼1 mM) (50, 51), the very high intracellular levels (10–20 mM) mean that these dipeptides may bind significant amounts of intracellular Ca²⁺. However, there is uncertainty over the apparent Ca²⁺ affinity of carnosine under physiological conditions, in particular over the role of an amino group with a pK of ∼9 (50), which will be protonated at normal intracellular pH. If this is involved in chelation, Ca²⁺ binding will be negligible at normal pH (34). However, a recent study suggests that carnosine does bind Ca²⁺ with millimolar affinity at pH 7.2 (52). That carnosine can bind Ca²⁺ at physiological pH is also suggested by the observation that acidification from 7.3 to 6.7 results in the release of Ca²⁺ ions from carnosine in a mock intracellular solution (49). This pH sensitivity is, however, greater than what would be expected from measured binding constants (52). Given the high intracellular concentration of carnosine and its potential importance as a buffer, it is essential to address these issues.

2.4.2. ATP.

Another important biological small-molecule buffer is ATP; this is almost entirely bound to Mg²⁺ under physiological conditions. The molecule also binds Ca²⁺ with a low affinity relative to intracellular Ca²⁺ concentrations [K_d ∼ 0.2 mM (33)], but the high intracellular concentration of ATP (∼5 mM) makes it a significant Ca²⁺ buffer in many cell types (34). Most importantly, the fact that ATP is freely diffusible enables it to facilitate diffusion of Ca²⁺ (see sects. 4.5, 6.3, 7.6, and 9.2).

2.4.3. Inorganic phosphate.

$\mathrm{P}{\mathrm{O}}_4^{3\mathrm{-}}$ is in equilibrium with $\mathrm{HP}{\mathrm{O}}_4^{2\mathrm{-}}$ and ${\mathrm{H}}_2\mathrm{P}{\mathrm{O}}_4^{\mathrm{-}}$, with the relative proportions being sensitive to pH. All forms have the ability to bind Ca²⁺ (33). At normal intracellular pH (∼7.0) the apparent K_d for Ca²⁺ binding is ∼16 mM, so for [Ca²⁺]_i ≤ 100 nM, the total Ca²⁺ bound to 1 mM phosphate will be ≤10 nM. In other words, phosphate makes a negligible contribution to cytoplasmic Ca²⁺ binding but may be more relevant to Ca²⁺ buffering in mitochondria (sect. 2.6.2.1) or organelles with higher [Ca²⁺] such as sarcoplasmic reticulum (SR), endoplasmic reticulum, and the nuclear envelope.

2.4.4. Other intracellular anions including gluconate.

Intracellular anions include intracellular proteins (see above) and the phosphate and carbonyl groups of lipids in the inner leaflet of the plasma membrane (53, 54), as well as a series of small-molecular weight anions, the relative concentration of which varies depending on cell type. A surface array of negative charges represented by the phospholipids of the inner surface of the plasma membrane is thought to influence the physical chemistry of Ca²⁺ in cells in two ways: 1) by contributing to intracellular buffering, which can be approximated by a contribution to global cytoplasmic binding (54) [such a role of negative surface charges has featured in models of intracellular Ca²⁺ binding (55)], but its contribution to bulk Ca²⁺ buffering is estimated to be small, and 2) electrostatic interactions between Ca²⁺ and the surface of fixed negative charges may create a layer of 2- to 3-nm depth with a higher Ca²⁺ concentration than bulk concentration (56). This may influence the apparent affinity of Ca²⁺ binding to proteins within the membrane. Again, the influence on bulk buffering will be small apart from regions of the cell where the relative surface area of membrane to cytoplasmic volume is very high, e.g., the diadic/triadic clefts in striated muscle. Under these circumstances, in the presence of significant transmembrane Ca²⁺ fluxes, Ca²⁺ binding to nearby surface membranes may be a significant factor in determining the extent and time course of free Ca²⁺.

The inorganic anions include Cl⁻, $\mathrm{N}{\mathrm{O}}_2^{\mathrm{-}}$, $\mathrm{N}{\mathrm{O}}_3^{\mathrm{-}}$, ${\mathrm{H}}_2\mathrm{P}{\mathrm{O}}_4^{\mathrm{-}}$/$\mathrm{HP}{\mathrm{O}}_4^{2\mathrm{-}}$, and $\mathrm{S}{\mathrm{O}}_4^{2\mathrm{-}}$ and the organic anions include amino acids and dipeptides, all of which associate via various forms of electrostatic interactions with the cations of the intracellular medium including Ca²⁺ and Mg²⁺ ions (57). Replicating this complex range of anions in mock intracellular solutions can be difficult, and unphysiological levels of some anions can have effects on intracellular processes, e.g., higher than normal intracellular chloride concentrations inhibit G protein-related reactions (58). Gluconate has become a popular choice for the major anion of pipette solutions in whole cell patch-clamp studies on neurons. Although earlier work had not assigned any Ca²⁺-binding capacity to this compound (59), a subsequent study (60) demonstrated low-affinity Ca²⁺ binding with a K_d of 57 mM. As shown in sect. 9.4, this cannot be neglected given the relatively high concentrations of this anion in pipette-filling solutions.

2.5. Structural Ca²⁺-Binding Motifs in Proteins

The reader is referred to several review articles on the general subject of Ca²⁺-binding proteins (CBPs) (61–64). Most proteins can bind Ca²⁺ at two types of sites: the electronegative sites of salt bridges and the hydrogen bonds formed between carbonyl/carboxylate side chains and an amino/imidazole residue of nearby amino acids. These interactions form loose chelate structures that bind ionized Ca²⁺ and Mg²⁺ with a range of low affinities such that the relationship between Ca²⁺ binding and concentration is approximately linear even at the millimolar levels of ionized Ca²⁺ in the extracellular space, as in the case of serum albumin (65). However, such low-affinity interactions produce little Ca²⁺ binding at cytoplasmic Ca²⁺ concentrations. At rest, intracellular [Ca²⁺] is ∼2,000- to 20,000-fold lower than extracellular, and in the presence of millimolar levels of Mg²⁺, specific Ca²⁺ binding requires precise chelate structures for selectivity and affinity. Within eukaryotes, the Ca²⁺-binding motifs of intracellular CBPs conform to a limited set of designs, discussed below in this section; variants of each form with different Ca²⁺ binding characteristics allow their use in a range of intracellular processes.

2.5.1. Ca²⁺ buffering by the EF-hand domain.

The EF hand is a helix-loop-helix motif that generates a chelation structure in the loop segment (FIGURE 2B); many CBPs contain multiple paired EF-hand domains allowing the structure to interact with intracellular Ca²⁺ over a specific concentration range. Ca²⁺ binding to an EF-hand domain changes the tertiary structure. A commonly applied distinction is between CBPs acting solely as buffers with little conformational change upon Ca²⁺ binding and those acting as signaling molecules (“Ca²⁺ sensors”). Although this distinction is not always justified (66), for some CBPs such as parvalbumin (PV; Ref. 565) and calbindin-D_9k (CB-D9k), which function primarily as buffers or to facilitate Ca²⁺ diffusion, Ca²⁺ binding-induced conformational changes can be small. In contrast, many EF-hand proteins undergo large changes of tertiary structure on binding Ca²⁺, thus altering the properties of the protein containing the EF hand. This mechanism is used to control the activity of proteins in many aspects of cellular function including cell mitosis, movement, sensory function, and molecular memory. Examples include Ca²⁺ binding to the Troponin-C (TnC) subunit causing major structural changes in striated muscle thin filament proteins, thereby allowing cross-bridge activity and contraction, and Ca²⁺ binding to calmodulin (CaM), which exposes specific hydrophobic structures allowing binding to corresponding sites on the regulatory domain of CaM kinase, displacing the autoinhibitory domain and activating this enzyme. For instance, Ca²⁺/calmodulin kinase II (CaMKII) and its activation by Ca²⁺ are essential for induction of long-term synaptic plasticity and memory formation (67). The S100 protein group is a large family (25 to date) of related proteins with 2 EF-hand motifs/protein. As reviewed previously (68), their role is varied, with some entirely acting inside the cell, some with both intracellular and extracellular actions, and others with a purely extracellular role. Inside the cell, S100 proteins generally endow Ca²⁺ sensitivity to cellular processes; for example, the abovementioned CB-D9k is also known as S100G (68). Interestingly, some of the S100 proteins bind Zn²⁺, Cu²⁺, and Mn²⁺ at the interface of S100 dimers, i.e., sites distinct from the EF motifs. The sequestering or buffering of these transition metal ions modulates biological pathways; for example, Mn²⁺ binding by extracellular S100 proteins is thought to be responsible for aspects of “nutritional immunity” (see Ref. 69 for review and sect. 11).

The canonical EF motif structure has a 12-residue loop containing the amino acids aspartate and glutamate that commonly provides 4 carbonyl and 2 carboxylate groups for coordination to Ca²⁺; the seventh coordination site is provided by a water molecule hydrogen-bonded to the carboxylate of the aspartate at residue 9 (17). This structure was first discovered in PV almost 50 years ago (70), and >4,400 EF motif structures have since been identified in >1,600 proteins (71). When incorporated into a protein, the EF-hand motif exists in closely associated pairs that are not identical in structure; binding in one motif can influence the binding of the partner, resulting in cooperative Ca²⁺ binding characteristics (see sect. 3.3). CaM (72) and CB-D9k (73) are well-documented examples of this phenomenon. The two EF-hand motifs are positioned such that the Ca²⁺-binding domains face each other and in such proximity that the bound Ca²⁺ ions are only 10 Å apart (17). EF hands can have high affinities for Ca²⁺ even under intracellular conditions. For example (TABLE 1), CB-D28k has a measured K_d in the absence of Mg²⁺ of ∼0.12 µM (30, 31), which increases to ∼0.24 µM at intracellular Mg²⁺ levels.

2.5.1.1. Mg²⁺ binding by the ef domain.

For the reasons outlined above, Mg²⁺ would be expected to bind to the EF-hand motif (74). Since the canonical EF motif structure has a K_d for Mg²⁺ in the millimolar range, ∼50% of binding sites have Mg²⁺ bound at resting levels of [Ca²⁺]_i. There are two forms of site-selective interactions between Ca²⁺, Mg²⁺, and the EF hand, which render the respective sites as either 1) Ca²⁺-selective or 2) “Ca/Mg” sites.

1) Ca²⁺-selective sites: The coordination of Mg²⁺ involves only four residues on the NH₂-terminal loop region; none of the residues in the COOH-terminal section of the loop normally participates. With this type of interaction, Mg²⁺ binding acts to stabilize the apo state (without Ca²⁺ bound), the inactive form of the EF motif. In contrast, Ca²⁺ binding recruits both NH₂- and COOH-terminal regions of the loop and activates the motif. Therefore, as with EDTA, the presence of intracellular Mg²⁺ will slow Ca²⁺ binding and decrease its affinity at those sites (75, 76). There are other potential consequences of Mg²⁺ binding: if it is to one site of a pair of adjacent EF sites, Mg²⁺ binding can act cooperatively to enhance Ca²⁺ binding to the other site (75, 77). Therefore, the effects of Mg²⁺ binding to the COOH-terminal section of these Ca²⁺-selective sites are complex, and the consequences for the Ca²⁺ sensitivity of the proteins with canonical EF-hand sites have yet to be fully explored (76, 77).

2) Ca/Mg sites: In some noncanonical forms of the EF-hand motif, the sequences in the loop region form a smaller chelate structure that engages both NH₂-terminal and COOH-terminal regions when either Ca²⁺ or Mg²⁺ is bound, and therefore both ions activate the motif; these sites are classified as Ca/Mg sites. In many instances, there is little unbound buffer, and at low intracellular Ca²⁺ levels (100 nM), the majority of the sites have either Ca²⁺ or Mg²⁺ bound. This chronically activated EF-hand domain is important for protein shape (i.e., structural sites). This is the case for the EF-hand domains of sites III and IV in striated muscle TnC, the so-called “nonspecific sites.” Both are Ca/Mg sites and, in the resting/inactive muscle, are almost fully occupied with Ca²⁺ (∼49%) or Mg²⁺ (49%) (78, 79). Sustained increases of cytoplasmic Ca²⁺ will slowly displace the bound Mg²⁺ on sites III and IV, accounting for the slow kinetics of Ca²⁺ buffering (for discussion see Refs. 80–82). One of the best-characterized Ca/Mg sites is that on PV, where the slow Ca²⁺ binding and Mg²⁺ dissociation have important consequences for skeletal muscle physiology and synaptic function and plasticity (see sects. 7.2, 9.4, and 9.5).

Both the Ca/Mg and Ca²⁺-selective sites bind Mg²⁺, but only in the former does this binding mimic that of Ca²⁺ binding. Thus, in both Ca/Mg and Ca²⁺-selective EF-hand domains, Mg²⁺ will slow the kinetics of Ca²⁺ binding and reduce affinity. Interestingly, Mg²⁺-bound states are often not included in computational models of Ca-EF hand interactions (83–86), although it has been observed that Mg²⁺ is bound to the Ca²⁺-selective sites of troponin-C and may slow Ca²⁺ binding and thence the development of force (87).

Approximately 80 different subfamilies of EF-hand domains have been recognized (88). Insertions, deletions, and substitutions in the loop region chelation site are believed to be the cause of the range of Ca²⁺ affinities that these EF-hand structure variants display, ranging from a K_d of ∼10⁻⁹ M seen in some CBPs such as PV to K_d values close to 10⁻³ M in the CREC, a group of ER-based proteins (89) (see sect. 2.6.1.1). A systematic study of the various EF-hand chelation structures and associated Ca²⁺ affinities across a range of EF-hand domain sequences is lacking, preventing the prediction of affinity from structure alone (89).

Almost one-third of known EF-hand structures do not bind Ca²⁺ (88), supposedly because of changes in the amino acid composition of the loop region including the substitution of the amino acids with oxygen-containing side chains. A well-documented example of a nonbinding EF-hand motif is that of site I in the striated muscle protein troponin-C. In the fast-twitch skeletal form both sites I and II bind Ca²⁺, whereas in the cardiac and slow-twitch forms only site II can do so. It has been suggested that site I cannot bind Ca²⁺ because of the disruption of the chelation site by an insertion (V28) and two key Ca²⁺-binding amino acid substitutions (D29L and D31A) (90).

2.5.1.2. h⁺ influence on ef-hand buffering of ca²⁺.

As mentioned above, some small-molecule Ca²⁺ chelators have a steep dependence on pH due to the direct involvement of amino groups (with pK_a close to neutral pH) in the coordination of Ca²⁺. In contrast, the chelation structure of EF-hand domains uses only the carboxylate groups on glutamate and aspartate residues to coordinate Ca²⁺. The amino groups on other residues do not participate directly in chelation. These carboxylate groups have a pK_a of ∼2 and would therefore be expected to be fully dissociated at normal intracellular pH. Hydrogen ions, however, can form a loose association by bridging carboxylate and carbonyl groups of adjacent residues. The shared H⁺ has a pK_a of ∼6.2, close to the physiological pH range, and is thought to be one of the main causes of pH dependence of Ca²⁺ binding (91) and for the stoichiometry of ∼1 H⁺ released per Ca²⁺ bound to an EF-hand domain at neutral pH (92). This interaction between Ca²⁺ and protons also means that a decrease of pH will release Ca²⁺ from the EF hand, and this has been suggested to account for the acid-induced increase of [Ca²⁺]_i seen in cardiac muscle (49, 93).

2.5.2. Buffering due to cytosolic Ca²⁺ binding to P-type ATPases.

The P-type transport ATPases constitute a family of proteins involved in the pumping of cations including Ca²⁺ across plasma membranes using a binding and translocation process. Although they are included in some models of Ca²⁺ dynamics in myocytes (e.g., Ref. 80), it is often overlooked that, in addition to their role in active transport, the chelation sites of these proteins contribute to the static intracellular Ca²⁺ buffering component of the cell (94). The two main forms of Ca²⁺ pumps in mammalian cells are the sarco(endo)plasmic reticulum Ca²⁺-ATPase (SERCA) and the plasma membrane Ca²⁺ ATPase (PMCA) (for reviews see Refs. 6, 95). These pumps are further divided into isoforms (SERCA1–3 and PMCA1-4), with alternative splicing generating ∼15–20 variants. The two types of Ca²⁺ pumps have a common general structure composed of E1 and E2 conformational states. The E1 state binds Ca²⁺ on the cytosolic side, and the E2 state releases Ca²⁺ on the intraluminal (SERCA) or extracellular (PMCA) side (96, 97). As part of the Ca²⁺ pump cycle, the Ca²⁺ binding to SERCA follows a sequential cooperative reaction scheme involving the two binding sites. It can be described by a Hill slope of 1.9 and a K_app ∼0.4 µM (see sect. 3.3). The two individual sites have quite different K_d values (20 nM and 8.3 µM, respectively) (98). The cooperative Ca²⁺ binding has consequences for the Ca²⁺ buffer characteristics of SERCA, reducing its buffer contribution at lower [Ca²⁺]_i (see sect. 3.3). The buffer characteristics of SERCA interact with its function as a pump (94, 99, 100), leading to paradoxical consequences of altering SERCA expression. For example, increased expression of SERCA increases the Ca²⁺ content of the ER/SR and therefore the amount released on stimulation, but the accompanying increased cytoplasmic buffer power may limit the rise in free Ca²⁺ levels and curtail the peak of the Ca²⁺ transient (99, 101).

In contrast to SERCA, PMCA pumps bind only one Ca²⁺ per cycle/ATP with a K_d of ∼1 µM (102). Because of this simpler reaction scheme, the PMCA has a different [Ca²⁺]-buffer power relationship (see sect. 3.3). As with SERCA, the pump turnover complicates the analysis of the overall buffer function of the PMCA. Its peripheral location and a relatively limited PMCA expression mean that the direct contribution to buffering may be small compared to the role in control of local subplasmalemma Ca²⁺ levels within cells (103).

2.5.3. Ca²⁺ binding by the C2 domain.

The conserved domain 2 (C2) is another Ca²⁺ binding motif that endows Ca²⁺ sensitivity to a series of membrane-targeted signaling molecules that include membrane receptors, kinases, G proteins, and various synaptic proteins. The numbers of different C2 and EF-hand designs are comparable in eukaryotes (104). Although less studied in terms of the physical chemistry of Ca²⁺ binding than the EF-hand domain, the C2 domains are found in a range of signaling pathways including kinases that phosphorylate membrane proteins, vesicle-targeting proteins, enzymes that modify signaling phospholipids, transmembrane pore proteins, and Ca²⁺ sensors for neurotransmitter and hormone release. A C2 domain is made up of ∼140 amino acids and typically forms a three-loop structure that links two β-sheets (105), chelating normally two and sometimes three Ca²⁺ using carboxylates and carbonyl residues in adjacent regions of two loops with relatively low affinity. Binding of the second Ca²⁺ within a C2 site usually shows strong cooperativity and generates a steep Ca²⁺ dependence and a switchlike response to increased intracellular Ca²⁺ (105). The Ca²⁺ levels required to activate C2-dependent signaling tend to be higher than those for common EF-hand domain motifs (106–108). The overall lower affinity for Ca²⁺ and Mg²⁺ implies that the low-affinity C2 domains do not have significant Ca²⁺ or Mg²⁺ bound under resting conditions. The high-affinity C2 domain on the common PKC isoforms has a K_d of 1–5 µM compared to ∼20 µM on the second C2 domain (107). In summary, the C2 domains represent a chelation design used in various signaling proteins that require [Ca²⁺]_i in the micromolar or tens of micromolar range to activate. These concentrations of free Ca²⁺ are observed in the cytoplasm of skeletal muscle during a tetanus but otherwise are typically seen only within local Ca²⁺ domains, for instance near open Ca²⁺ channels at active zones of synapses (109) (see sects. 4.7.2 and 9.4). Therefore, C2 domains do not contribute substantially to overall Ca²⁺ buffering power but respond to local Ca²⁺ signals that are shaped by the actions of Ca²⁺ flux and other dominant buffers.

2.5.4. Ca²⁺ binding to annexins.

Another common Ca²⁺ binding site that is distinct from EF-hand and C2-protein domains is the endonexin fold seen in the Annexin group of proteins (110, 111). This large group is expressed across many species and has the general property of mediating Ca²⁺-sensitive phospholipid binding that allows increased cytoplasmic Ca²⁺ to mediate events such as membrane fusion. Twelve types of annexins are expressed in mammalian cells, and although their intracellular roles have not been fully explored, their low expression levels and generally low Ca²⁺ affinity means they do not participate in intracellular Ca²⁺ buffering or diffusion (110, 111).

2.6. Ca²⁺ Buffering in Organelles

2.6.1. ER and SR Ca²⁺ buffers.

A major role of the endoplasmic and sarcoplasmic reticulum is to release Ca²⁺ ions into the cytoplasm through inositol trisphosphate (IP₃) and ryanodine receptors (RyRs), respectively. The free Ca²⁺ concentration in the ER and SR is typically between 100 µM and 1 mM (112–115), i.e., 1,000 to 10,000 times greater than that in the cytoplasm, thereby requiring different Ca²⁺ buffers, which are discussed below in this section.

2.6.1.1. ef-hand buffers.

Reticulocalbin (44 kDa) was identified as a CBP of the ER lumen containing six EF hands (116, 117). Subsequent work showed the existence of a class of such proteins, the CREC family comprising also Calumenin, ER Ca²⁺-binding protein of 55 kDa, and Calumenin 1 (see Refs. 89, 118 for reviews). Calumenin (37 kDa) (119) binds Ca²⁺ with a low affinity (K_d ∼600 µM) at seven EF-hand sites (120). Binding of Ca²⁺ results in major changes of structure, from disordered at low Ca²⁺ to alpha-helical at higher (121). These proteins may also regulate the activity of other proteins including RyR1 in skeletal muscle (122) and SERCA2 in cardiac muscle (123). Another lumen-resident protein is Stromal Interacting Molecule (STIM 1 and 2). This uses an EF hand-based Ca²⁺ sensor to detect the decrease of luminal Ca²⁺ associated with ER-mediated Ca²⁺ release. Ca²⁺ free STIM interacts with the plasma membrane Ca²⁺ release-activated calcium channel protein ORAI1 to increase Ca²⁺ influx into the cell, a process known as store-operated calcium entry (SOCE) (see Ref. 124 for review). Because the concentration of these proteins is low in comparison to those discussed in sect, 2.6.1.2, they will not play a major role in buffering Ca²⁺ in the ER lumen (117).

2.6.1.2. calreticulin, calnexin, and calmegin.

The bulk of endoplasmic reticulum Ca²⁺ buffering results from proteins with structures very different from those discussed in the previous section. Calreticulin [CRT, molecular weight (MW) 46,000] is predominantly an ER luminal CBP and molecular chaperone that promotes protein folding but also has many other functions (125). There are three distinct regions in the protein: the N globular domain, the P-arm domain, and the C domain. None of these sites conforms to EF-domain or C2 protein configurations. The N domain binds Zn²⁺ and participates in chaperone interactions. The proline-rich P arm is key to the protein folding function and contains a single Ca²⁺ binding domain with a K_d of ∼1–10 µM (126). At the high Ca²⁺ concentration of the ER lumen, this site is normally fully Ca²⁺ bound and crucial for the tertiary structure of the protein. Finally, the COOH terminal of the protein ends in a region containing highly acidic residues (35 glutamate and aspartate residues out of 50), and this region can bind up to 25 Ca²⁺ ions per molecule with a K_d of ∼1 mM (for reviews see Refs. 125, 127). The degree to which the binding reactions involve cooperative interactions is not clear. The chelation mechanism uses two acidic groups on Asp and Glu residues to bind to Ca²⁺ with a k_on close to the diffusion limit (∼10³ µM⁻¹·s⁻¹) and a rapid k_off (∼10⁶ s⁻¹). CRT accounts for ∼50% of the Ca²⁺ buffering within the ER. Ca²⁺ binding to the COOH-terminal sites not only buffers Ca²⁺ but also alters the structure of this region, which in turn alters the affinity of CRT for interacting proteins (chaperones) within the ER (125, 128). Through this mechanism, the intra-ER Ca²⁺ concentration modulates the types of proteins processed (129). Measurements of free Ca²⁺ concentration within the lumen of the ER with targeted sensors suggest a maximal concentration of 300–400 µM (113, 114). The minimal Ca²⁺ concentration when the ER is depleted has not been accurately measured, as few studies have used luminal indicators with appropriate sensitivities, but concentrations lower than 5–10 µM may destabilize the tertiary structure of CRT by dissociation of Ca²⁺ from the high-affinity structural site. The ER also contains two structurally related proteins, calnexin and calmegin. These differ from calreticulin in that they are membrane bound (see Ref. 130 for review). Interestingly, in calnexin the Ca²⁺ binding C domain is exposed to the cytoplasm (131) (for review see Ref. 125), raising the possibility that a single molecule can buffer Ca²⁺ on both sides of the ER membrane.

2.6.1.3. calsequestrin.

The related protein calsequestrin (CSQ; MW 44,000) is the main Ca²⁺ buffer in skeletal, cardiac, and smooth muscle sarcoplasmic reticulum and comprises two isoforms (CSQ1 and CSQ2). Aspects specific to skeletal muscle function are considered in sect. 7.5. Analogous to CRT, CSQ has a limited number (2 or 3) of high-affinity Ca²⁺ binding sites; occupancy of these is key to the tertiary structure of the CSQ monomer. However, most Ca²⁺ binding occurs at multiple low-affinity binding sites arising from the numerous aspartate and glutamate residues particularly on the COOH-terminal but also the NH₂-terminal end of the monomer. These acidic groups can bind >40 Ca²⁺ ions per molecule, with K_d values ranging from 0.1 to 10 mM (132). The isoform CSQ2, present in slow-twitch skeletal, cardiac, and smooth muscle, has a modified COOH terminal and binds up to 20 Ca²⁺ ions per molecule (133). As with CRT, the coordination of Ca²⁺ by these low-affinity sites is via pairs of acidic resides binding a single Ca²⁺. An aspect unique to CSQ is the process through which Ca²⁺ binding to the monomer allows CSQ to polymerize and generate a structure with further Ca²⁺ binding sites (FIGURE 2C). This is a cooperative process, as described in sect. 3.3. In both skeletal (134) and cardiac (135, 136) muscle, in addition to buffering SR Ca²⁺, CSQ2 can interact with the RyR and thereby provide a mechanism for luminal Ca²⁺ controlling RyR opening. It can therefore be challenging to separate the consequences of CSQ2-RyR interactions from Ca²⁺ buffering effects.

Mg²⁺ can also bind to CSQ. However, evidence suggests that, unlike many chelation interactions, the Mg²⁺ binds at sites distinct from Ca²⁺ (137). The two sites interact such that Ca²⁺ binding to CSQ displaces a fraction of bound Mg²⁺ (137). In common with other CBPs that involve carbonyl-carboxylate interactions, a proton can bridge between these two residues in the absence of Ca²⁺ (pK_a ∼6.2). Therefore Ca²⁺ binding to CSQ will displace significant amounts of protons (137, 138) and may change intraluminal pH, influencing other processes including SERCA and the Ca²⁺ release channel.

2.6.2. Buffering in other organelles.

The reader is referred to an earlier review for a discussion of this area (139). Here we provide brief comments on mitochondria and the nucleus.

2.6.2.1. mitochondria.

Regulation of mitochondrial matrix [Ca²⁺] ([Ca²⁺]_mito) is important since it regulates various mitochondrial enzymes, and thus ATP production (140, 141). The introduction of Ca²⁺-sensitive indicators targeted to the mitochondrial matrix has suggested that [Ca²⁺]_mito is normally similar to cytoplasmic [Ca²⁺]_i, ∼100 nM (142, 143). As previously reviewed (144), there is controversy as to the extent to which mitochondrial matrix Ca²⁺ responds to brief changes of cytoplasmic Ca²⁺. For example, in cardiac muscle, some studies have reported that the cytoplasmic Ca²⁺ transients result in beat-to-beat changes of [Ca²⁺]_mito (145–147), whereas other work has reported little or no change of [Ca²⁺]_mito in response to fluctuations of cytoplasmic [Ca²⁺]_i (148). Even when [Ca²⁺]_mito transients are observed, they can decay very slowly (142), such that stimulation at normal rates results in a maintained increase of [Ca²⁺]_mito with little or no beat-to-beat fluctuations (see Ref. 9 for review). There are two explanations for this slow decay of [Ca²⁺]_mito: 1) a low activity of the mitochondrial sodium/calcium exchange (NCLX) that pumps Ca²⁺ out of the mitochondria (149) and 2) a high mitochondrial matrix buffer power. This emphasizes the need to quantify mitochondrial Ca²⁺ buffer power.

Most measurements have been made in isolated mitochondria, often at [Ca²⁺]_mito greater than those thought to occur physiologically (see below); and they may be susceptible to changes resulting from mitochondrial isolation. One such study found that total Ca²⁺ concentration was ∼1,000 times greater than free in heart mitochondria (150). High Ca²⁺ buffer powers were also found in heart and liver mitochondria (151). Another study reported a value of up to ∼150,000, indicating a total mitochondrial Ca²⁺ concentration of the order of 100 mM (152). These high levels of total Ca²⁺ are thought to exist mainly as calcium phosphate crystals (153), in which case the relevance of such buffering will depend critically on the kinetics of crystal formation and dissolution. A more recent study on isolated mitochondria used changes in the free Ca²⁺ of the external fluid to calculate Ca²⁺ fluxes into and out of mitochondria and compared this with changes of [Ca²⁺]_mito (154). Modeling of the data (155) suggested two classes of buffers. One was tentatively attributed to phospholipids and metabolites. The other was estimated to bind Ca²⁺ in a cooperative manner and was suggested to involve annexins acting as “nucleation factors” to promote binding of Ca²⁺ with phosphate. Another study on isolated guinea pig heart mitochondria found that phosphate is a significant buffer at elevated mitochondrial Ca²⁺ but that some, unidentified, mitochondrial buffer contributes at lower [Ca²⁺]_mito levels (156).

Work on intact cells found that the change of [Ca²⁺]_mito during a cardiac cytoplasmic Ca²⁺ transient was 2–10 nM (157). The authors pointed out that if the mitochondrial Ca²⁺ buffering power was 100 (similar to that of cytoplasm) the magnitude of the measured changes of [Ca²⁺]_mito is consistent with the calculated contribution of mitochondria to Ca²⁺ removal from the cytoplasm (158). More precise measurements are required, but it is difficult to imagine how total mitochondrial Ca²⁺ can be measured in intact cells. Another obvious question relates to whether the mitochondrial Ca²⁺ buffering power is identical in cells from all tissues.

Given the challenges involved in direct measurements of mitochondrial Ca²⁺ buffering, estimating it from the known composition of the matrix is a useful alternative. One suggested contributor is inorganic phosphate (for review see Ref. 159). Considering the binding constants of the various forms of phosphate (33), and assuming a total matrix phosphate concentration of 1 mM, then at 100 nM [Ca²⁺]_mito the contribution to buffer power will be only 1.5. There is also ∼5 mM ATP present, which will provide a buffer power of 7.2. This is greater than the expected buffer power of 3.6 for the cytoplasm of cardiac muscle (see TABLE 5) because of the more alkaline pH (8.0) in mitochondria. Thus, the anticipated Ca²⁺ buffer power of the mitochondria is considerably lower than that of cytosol, and it is not obvious how the known buffers can account for some of the above measurements. Further work is required to determine the identity of mitochondrial Ca²⁺ buffers.

Table 5.

Contributions of various compounds to calcium buffering in cardiac muscle

Buffer	Conc, µM	Kapp, µM	Hill Slope	Binding Sites	βi(Ca) 0.1 μM (ss)	βi(Ca) 0.2 μM (ss)	βi(Ca) 1.0 μM (ss)	βi(Ca) 10 μM (ss)	βi(ΔCa) 0.1–1.0 μM (in)	βi(ΔCa) 0.1–1.0 μM (ss)	βi(ΔCa) 0.1–10 μM (in)	βi(ΔCa) 0.1–10 μM (ss)	Ref.
Calmodulin	6	2.7/12.7	1.8/1.9	4	0.6	1.0	2.8	0.7	2.0	2.0	1.6	1.6	187
SERCA	48	0.60	1.9	2	56.8	89.5	36.3	0.1	73.9	73.9	9.3	9.3	98
TnC (reg)	70	0.60	1	1	85.7	65.6	16.4	0.4	37.5	37.5	5.7	5.7	78
Carnosine	10,000	1,350.00	1	1	7.4	7.4	7.4	7.3	7.4	7.4	7.3	7.4	49
ATP	5,000	2,496	1	1	2.0	2.0	2.0	2.0	2.0	2.0	1.9	2.0	33
Myosin	70	9.10	1	2	15.1	14.7	12.5	3.5	0.5	13.7	0.1	7.3	78
TnC (nonspec)	70	0.10	1	2	349.9	157.2	11.9	0.1	2.3	64.5	0.2	7.0	78
Total					517	338	89	14	126	201	26	40

From left to right: cytoplasmic concentration; K_app; Hill slope (n); no. of binding sites; steady-state (ss) buffer power (β_i) at 0.1, 0.2, 1.0, and 10 µM Ca²⁺, calculated with Eq. 8 or 16; and the buffer power for a change in calcium concentration ([Ca²⁺]) [β(ΔCa)] for 0.1–1 µM and 0.1–10 μM Ca²⁺, calculated from the change in Ca²⁺ binding (Eq. 5 or 15). To indicate the relative contributions of the fast and slow buffers, we show both instantaneous buffer power (in, assuming equilibration of Ca²⁺ binding but no change in the Mg²⁺ binding state) and steady-state buffer power (ss, assuming equilibrium at both Ca²⁺ and Mg²⁺ sites). The value of the Hill slope for the regulatory Troponin-C (TnC) site is taken from isolated TnC (78) and ignores the influence of possible cross-bridge interactions (sect. 3.3).SERCA, sarco(endo)plasmic reticulum Ca²⁺-ATPase.

2.6.2.2. nucleus.

One might expect the Ca²⁺ buffering of the nucleus to be different from that of cytoplasm. For example, troponin, which is a major cytoplasmic buffer in striated muscle, is absent from the nucleus and cannot contribute to buffering there. Some work has produced results consistent with lower Ca²⁺ buffering in the nucleus than in cytoplasm. For example, Ca²⁺ puffs, which are mediated by Ca²⁺ release from the ER through IP₃ receptors and occur near the nuclear membrane, spread further in the nucleus than in the cytoplasm (160). Similar results have been seen for Ca²⁺ released from Golgi (161). The apparent diffusion coefficient for Ca²⁺ is similar in nucleus and cytoplasm (162, 163). It should, however, be noted that there is no simple relationship between Ca²⁺ diffusion and buffering: Mobile buffers can increase while fixed buffers decrease diffusion. Electron microprobe measurements have reported a higher concentration of total Ca²⁺ in the nucleus compared with the cytoplasm (164). Assuming that the free Ca²⁺ concentration is the same in both regions, this would imply greater Ca²⁺ buffering in the nucleus. The highest total Ca²⁺ concentrations were found in areas occupied by heterochromatin (condensed DNA). This is interesting, given that high (∼1 mM) Ca²⁺ has been reported to be bound to DNA and that this binding alters the structure of DNA (165). Separate studies on isolated chromosomes suggest that Ca²⁺ binding alters chromosome structure during mitosis (166). It should, however, be noted that the nuclear envelope, which contains high total Ca²⁺, invaginates the nucleus as the so-called “nucleoplasmic reticulum” (167, 168). It is possible that Ca²⁺ in this structure contributes to the high total Ca²⁺ measurements from the nucleus, whereas in the nuclear lumen total Ca²⁺ content and buffering power may in fact be lower.

The work described above does not provide quantitative measurements of nuclear Ca²⁺ buffering. Another approach is to look for differences in the concentrations of candidate Ca²⁺ buffers between nucleus and cytoplasm. For example, a study on smooth muscle cell lines derived from human aorta and jejunum characterized the distribution of various S100A proteins (see sect. 2.5.1). S100A2 and A6 were found mainly in the nucleus, whereas A1 and A4 were largely in the cytosol (169). The effects of increasing nuclear Ca²⁺ buffering have been studied in cultured hippocampal neurons by targeting parvalbumin to the nucleus. This decreased the rise of nuclear Ca²⁺ produced by electrical stimulation but had no effect on the cytoplasmic [Ca²⁺]_i. A functional consequence of increased nuclear Ca²⁺ buffering was a change of cell morphology, in particular decreased dendrite length and complexity (170, 171). Work on human eggs and preimplantation embryos found that various CBPs including calreticulin and calsequestrin were distributed in the cytoplasm but not evident in the nucleus (172).

3. QUANTIFICATION OF BUFFER POWER

The degree of Ca²⁺ buffering can be defined as “buffer power.” This is illustrated for the case of a simple buffer in FIGURE 3. For a total buffer concentration [B]_Tot, bound Ca²⁺ ([CaB]) and free Ca²⁺ ([Ca²⁺]) are described by Eq. 1 above.

FIGURE 3.

Dependence of buffer power on Ca²⁺. A, a: bound Ca²⁺ as a function of intracellular calcium concentration ([Ca²⁺]_i). The black curve represents binding to a simple buffer according to Eq. 1, with an equilibrium dissociation constant (K_d) of 0.5 µM (vertical dotted line). Total buffer concentration ([B]_Tot) is 100 µM. The red line is a fit to the initial part of the curve with a slope of [B]_Tot/K_d. b: Buffer power as a function of [Ca²⁺]_i. B: similar to A but for a buffer with a K_d of 2 µM (dotted line). The dashed curve in Bb shows the buffer power-[Ca²⁺]_i relationship of the buffer in A superimposed for comparison. The gray shaded regions in all panels represent the [Ca²⁺]_i range from 100 nM (resting [Ca²⁺]_i) to 300 nM. For a [Ca²⁺]_i transient covering this range, buffer power is predicted to decrease by 44% (arrowheads, from 139 to 78) for the K_d of 0.5 µM (A) and by 17% (arrowheads, from 45 to 38) for the K_d of 2.0 µM (B).

The total Ca²⁺ concentration ([Ca²⁺]_Tot) is given by the sum of free and bound:

$${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Tot}}=\left[\mathrm{C}{\mathrm{a}}^{2+}\right]+\left[\mathrm{Ca}\mathrm{B}\right]$$ (4)

$${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Tot}}=\left[\mathrm{C}{\mathrm{a}}^{2+}\right]+{\left[\mathrm{B}\right]}_{\mathrm{Tot}}\mathrm{\hspace{0.17em}·\hspace{0.17em}}\frac{\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}{K_{\mathrm{d}}+\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}$$ (5)

Buffer power has been defined by relating changes of either total or bound Ca²⁺ to those of free. In the former case it is quantified [by analogy with the original definition of pH buffering (11, 13)] as the ratio of the change in total to that of free concentration (d[Ca²⁺]_total/d[Ca²⁺]_free), which is often (including this article) represented by the symbol β and is commonly used in experimental muscle physiology.

By differentiating Eq. 5 with respect to [Ca²⁺] at constant K_d one obtains

$$\beta \left(\mathrm{Ca}\right)=\frac{\mathrm{d}{\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Tot}}}{\mathrm{d}\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}=1+{\left[\mathrm{B}\right]}_{\mathrm{Tot}}\mathrm{\hspace{0.17em}·\hspace{0.17em}}\frac{K_{\mathrm{d}}}{{\left(\left[\mathrm{C}{\mathrm{a}}^{2+}\right]+K_{\mathrm{d}}\right)}^2}$$ (6)

A slightly different definition of buffer power, often referred to in the neuroscience literature as differential Ca²⁺-binding ratio (173) and customarily designated as κ, describes the buffering by individual buffers or groups of buffers. It is the ratio of the change in bound to that of free (d[Ca²⁺]_bound/d[Ca²⁺]_free).

$$\kappa \left(\mathrm{Ca}\right)=\frac{\mathrm{d}\left[\mathrm{CaB}\right]}{\mathrm{d}\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}={\left[\mathrm{B}\right]}_{\mathrm{Tot}}\mathrm{\hspace{0.17em}·\hspace{0.17em}}\frac{K_{\mathrm{d}}}{{\left(\left[\mathrm{C}{\mathrm{a}}^{2+}\right]+K_{\mathrm{d}}\right)}^2}$$ (7)

That there are two definitions is largely a consequence of differences in experimental approaches. In many studies on muscle, changes of [Ca²⁺]_i are compared with total changes of Ca²⁺ as measured from Ca²⁺-specific ionic currents. This corresponds to the buffer power, as defined by β (Eq. 6). In contrast, in the neuroscience literature buffer power is often measured by the “added buffer approach” (see below), which does not invoke total changes in Ca²⁺ but rather a comparison of effects of an endogenous buffer with those of a known buffer, usually that of a Ca²⁺-indicator dye. It should be noted (cf. Eqs. 6 and 7) that β is equal to 1 + κ. Therefore, for values of β or κ commonly measured in physiology (>20) there is very little difference between the two values.

As expressed in Eq. 6, β contains contributions from both free Ca²⁺ and Ca²⁺ bound to buffer (respectively, the first and second terms on the right-hand side). In the remainder of this review, it will be convenient to quantify the contribution to buffering of particular buffers. We therefore define β_i as the contribution to buffering provided by the ith buffer.

$${\mathrm{\beta }}_i\left(\mathrm{Ca}\right)={\left[\mathrm{B}\right]}_{\mathrm{Tot}}\mathrm{\hspace{0.17em}·\hspace{0.17em}}\frac{K_{\mathrm{d}}}{{\left(\left[\mathrm{C}{\mathrm{a}}^{2+}\right]+K_{\mathrm{d}}\right)}^2}$$ (8)

The contributions of the n buffers can then be summed and added to 1 (representing free Ca²⁺) to give the overall value of β:

$$\beta \left(\mathrm{Ca}\right)=1+\sum _{i=1}^n{\beta }_i\left(\mathrm{Ca}\right)$$ (9)

Likewise, κ can be annotated with a subscript i when individual buffers are considered, such as in Eq. 29 below. β_i is identical to κ_i, and in this article, which aims to bring together literature across physiology, the terms are used interchangeably depending on the context.

3.1. Effects of Ca²⁺ Concentration on Buffer Power

Equation 8 shows that the buffer power contribution is greatest at very low [Ca²⁺]_i, where it can be approximated by ([B]_Tot/K_d), illustrated by the red lines that are tangents to the binding curves of FIGURE 3. As shown in FIGURE 3, bottom, as [Ca²⁺]_i increases more buffer has Ca²⁺ bound and its contribution to buffer power declines eventually to a value very close to zero at high [Ca²⁺], when effectively all binding sites are occupied. Expressed as a multiple of [B]_Tot/K_d, buffer power decreases from 1 at 0 [Ca²⁺] to 0.44 when [Ca²⁺] = 0.5 × K_d and 0.25 when [Ca²⁺] = K_d. When [Ca²⁺] rises to 2 × K_d, buffer power falls to 0.11.

If [Ca²⁺] changes over a finite but small range (≪K_d), β_i can be taken as constant and calculated at the average level of [Ca²⁺]_i. Therefore, relating changes in total Ca²⁺ bound, ΔCaB, to those of free Ca²⁺, Δ[Ca²⁺]:

$$\beta i\left(\mathrm{\Delta Ca}\right)=\frac{\Delta \mathrm{CaB}}{\Delta \left[\mathrm{C}{\mathrm{a}}^{2+}\right]}$$ (10)

For larger values of Δ[Ca²⁺], β_i can be replaced by (174)

$$\kappa \text{′}={\beta }_i\left(\mathrm{\Delta Ca}\right)={\left[\mathrm{B}\right]}_{\mathrm{Tot}}·\frac{K_{\mathrm{d}}}{\left({\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_1+K_{\mathrm{d}}\right)·\left({\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_2+K_{\mathrm{d}}\right)}$$ (11)

Here, [Ca²⁺]₁ and [Ca²⁺]₂ are [Ca²⁺] values before and after the addition of Ca²⁺ ions to a buffer system as in TABLE 5 and TABLE 6. For more complex reaction mechanisms, β_i(ΔCa) can be calculated from the binding curves as shown in FIGURE 3 and FIGURE 5.

Table 6.

Contributions of various compounds to calcium buffering in skeletal muscle, fast-twitch fibers, and slow-twitch fibers in the mouse

Buffer	Conc, µM	Kapp, µM	Hill Slope	Binding Sites	βi(Ca) 50 nM (ss)	βi(Ca) 2.0 μM (ss)	βi(Ca) 20 μM (ss)	βi(ΔCa) 50 nM-2.0 μM (in)	βi(ΔCa) 50 nM-2.0 μM (ss)	βi(ΔCa) 50 nM-20 μM (in)	βi(ΔCa) 50 nM-20 μM (ss)	Ref.
Fast-twitch fibers
SERCA1a	120	0.30	1.9	2	283.8	5.9	0.0	115.9	115.9	11.6	11.6	98
TnC (reg)	120	1.30	1	2	171	28.7	0.7	70.0	70.0	10.8	10.9	84
Carnosine	10,000	1,350	1	1	7.4	7.4	7.2	7.4	7.4	7.2	7.3	49
Parvalbumin	75	0.14	1	2	574	4.7	0.1	4.6	51.9	0.5	5.5	83
ATP	8,000	2,496	1	1	3.2	3.2	3.2	3.2	3.2	2.9	3.2	33
Myosin	120	9.10	1	2	26.1	17.7	2.6	0.4	21.5	0.0	8.2	78
TnC (nonspec)	120	0.10	1	2	1,060	5.5	0.1	1.6	76.6	0.2	8.0	78
Total					2,125	73	14	203	347	33	55
Slow-twitch fibers
SERCA2a	48	0.60	1.9	2	31.9	7.6	0.0	44.3	44.3	4.8	4.8	98
TnC (reg)	120	1.30	1	1	86	14.3	0.3	35.0	35.0	5.4	5.4	84
Carnosine	10,000	1,350	1	1	7.4	7.4	7.2	7.4	7.4	7.2	7.3	49
Parvalbumin	7.5	0.14	1	2	57	0.5	0.0	0.5	5.2	0.0	0.6	83
ATP	5,000	2,496	1	1	2.0	2.0	2.0	2.0	2.0	1.8	2.0	33
Myosin	120	9.10	1	2	26.1	17.7	2.6	0.4	21.5	0.0	8.2	78
TnC (nonspec)	120	0.10	1	2	1,060	5.5	0.1	1.6	76.6	0.2	8.0	78
Total					1,270	55	12	91	192	19	36

From left to right: cytoplasmic concentration; K_app; Hill slope (n); no. of binding sites; steady-state (ss) buffer power [β_i(Ca)] at 0.05, 2, and 20 µM Ca²⁺ (calculated with Eq. 8 or 16); and the buffer power for a change in [Ca²⁺] [β_i(ΔCa)] for 0.05–2 µM and 0.05–20 μM Ca²⁺, calculated from the change in Ca²⁺ binding (Eq. 5 or 15). steady-state binding (ss) was calculated based on equilibrium at both Ca²⁺ and Mg²⁺ sites. Instantaneous buffer power (in) was calculated assuming equilibration of Ca²⁺ binding but no change in the Mg²⁺ binding state in order to indicate the relative extent of the fast and slow buffers. SERCA, sarco(endo)plasmic reticulum Ca²⁺-ATPase; TnC, Troponin-C.

FIGURE 5.

Dependence of buffer power on intracellular calcium concentration [Ca²⁺]_i for buffers with cooperative Ca²⁺ binding. A and B: bound Ca²⁺ (top) and buffer power (bottom), both as a function of [Ca²⁺]. All buffers are present at a concentration giving a total of 100 µM binding sites and have a [Ca²⁺] at which half the binding sites are occupied (K_app) of 0.5 µM. A: cooperative binding described by the Hill equation with values of Hill slope (n) of 1.0, 1.25, 1.5, and 2.0. B: comparison of higher values of n (4 and 8) with 1 and 2.

Does the dependence of buffer power on Ca²⁺ concentration have any physiological significance? One can speculate that a high buffer power at low [Ca²⁺] will stabilize the low resting levels of cytosolic Ca²⁺ whereas at elevated [Ca²⁺]_i a smaller increase in total Ca²⁺ is required to produce a given rise of [Ca²⁺]_i, and this may be energetically advantageous. Evidently, an increase of resting [Ca²⁺]_i will decrease buffer power (but see sect. 3.3.1 for discussion of cooperative buffers). This has two consequences. 1) As discussed in the context of skeletal muscle and nerve physiology (sects. 7.4 and 9.5), an initial increase of [Ca²⁺]_i will decrease buffer power such that a subsequent identical increase of total Ca²⁺ will increase [Ca²⁺]_i more, thereby contributing to phenomena such as synaptic facilitation (175–178) and muscle contraction (82, 84, 179). 2) As discussed in sect. 7.1, some of the variation of buffer power reported for a given tissue may reflect the range of [Ca²⁺]_i over which it was measured. In experimental studies, it is important to investigate whether changes of buffer power arise from alteration of the properties of the buffer or, alternatively, are a consequence of changes of [Ca²⁺]_i. For example, a measured decrease of buffer power could be a consequence of either a change in the concentration or properties of buffers or, alternatively, an increase of resting [Ca²⁺]_i.

3.2. Effects of Buffer K_d

The total buffering produced by a given concentration of any buffer is fixed, and changing K_d simply shifts the range of [Ca²⁺] over which buffering occurs. This is exemplified in FIGURE 3, bottom, for two buffer species with fourfold different K_d values. Whereas the maximum β is four times larger for the high-affinity buffer (FIGURE 3A), β decreases more rapidly with increasing [Ca²⁺] compared to the low-affinity buffer (FIGURE 3B). FIGURE 4A shows buffer power (β) as a function of K_d at various values of [Ca²⁺]. At each [Ca²⁺], increasing K_d first increases and then decreases buffer power for that buffer (82, 180). As K_d decreases below an optimal value, the buffer becomes increasingly saturated with Ca²⁺ and its ability to buffer is decreased. As K_d increases above the optimum, less Ca²⁺ binds for a given increase of [Ca²⁺] and, again, buffer power falls. Buffer power for an individual buffer is therefore zero at both limiting low and high values of K_d. This relationship can be seen in the contour plot of FIGURE 4B and can be examined by differentiating Eq. 8 with respect to K_d at constant [Ca²⁺]:

$$\frac{\mathrm{d}{\beta }_i}{\mathrm{d}{K}_{\mathrm{d}}}={\left[\mathrm{B}\right]}_{\mathrm{Tot}}\mathrm{\hspace{0.17em}·\hspace{0.17em}}\frac{\left(\left[\mathrm{C}{\mathrm{a}}^{2+}\right]-K_{\mathrm{d}}\right)}{{\left(\left[\mathrm{C}{\mathrm{a}}^{2+}\right]\mathrm{+}{K}_{\mathrm{d}}\right)}^3}$$ (12)

FIGURE 4.

The dependence of buffer power on equilibrium dissociation constant (K_d) and calcium concentration ([Ca²⁺]). A: 3-dimensional (3-D) plot showing buffer power (z-axis) as a function of K_d at the various [Ca²⁺] values indicated. A buffer concentration of 100 µM was assumed. Note that at each [Ca²⁺] buffer power increases and then decreases with increasing K_d. B: contour plot showing buffer power as a function of K_d (x-axis) and [Ca²⁺] (y-axis). The horizontal dashed red line shows how buffer power changes with K_d at constant [Ca²⁺].

For a given [Ca²⁺], the maximum buffer power (β_i,max) of an individual buffer will occur when $\frac{\mathrm{d}{\beta }_i}{\mathrm{d}{K}_{\mathrm{d}}}=0$ and therefore K_d = [Ca²⁺]. At this value of [Ca²⁺], substitution into Eq. 8 shows that the maximum buffer power will be given by

$${\beta }_{i,\max }=\frac{{\left[\mathrm{B}\right]}_{\mathrm{Tot}}}{4\mathrm{\hspace{0.17em}·\hspace{0.17em}}{K}_{\mathrm{d}}}\hspace{0.17em}$$ (13)

Therefore, the lower the K_d, the greater the maximum buffer power (cf. FIGURE 3, bottom). One important issue concerns the effect that a given change of K_d will have. Consider a case when a physiological or pathological change increases buffer K_d from K_d,1 to K_d,2. From Eq. 8 the buffer power will be identical when

$$\frac{K_{\mathrm{d},1}}{{\left(\left[\mathrm{C}{\mathrm{a}}^{2+}\right]+K_{\mathrm{d},1}\right)}^2}=\frac{K_{\mathrm{d},2}}{{\left(\left[\mathrm{C}{\mathrm{a}}^{2+}\right]+K_{\mathrm{d},2}\right)}^2}$$

This is satisfied when [Ca²⁺] equals the geometric mean of the two values of K_d, i.e.,

$$\left[\mathrm{C}{\mathrm{a}}^{2+}\right]=\sqrt{K_{\mathrm{d},1}\mathrm{\hspace{0.17em}·\hspace{0.17em}}{K}_{\mathrm{d},2}}$$ (14)

For example, when comparing β_i for various [Ca²⁺] for the two buffers exemplified in FIGURE 3, it is seen that their buffer power is identical at [Ca²⁺] = $\sqrt{0.\text{5 }\mu \mathrm{M\times 2}\mathrm{.0 }\mu \mathrm{M}}$ = 1 μM (FIGURE 3Bb). Below this level of [Ca²⁺] the increase of K_d from 0.5 to 2 µM will decrease buffer power, and above it buffer power will increase. As illustrated below (see FIGURE 10 and sect. 4.3), changes of buffer K_d are predicted to have complicated effects on the kinetics of decay of the [Ca²⁺] transient, depending on whether the level of [Ca²⁺] is below or above the geometric mean of the K_ds.

FIGURE 10.

Predicted effects of changing the buffer affinity and amount of Ca²⁺ released on the decay of intracellular calcium concentration ([Ca²⁺]_i). A: effects of K_d. Model similar to that of FIGURE 7 except that the buffer had different K_d values, as indicated. As for FIGURE 7, the buffer is assumed to bind Ca²⁺ instantaneously. a: [Ca²⁺]_i. b: Normalized [Ca²⁺]_i. c: Instantaneous rate constant of decay. d: Buffer power. A portion of the records at expanded timescale is displayed on right. Note the expanded vertical scale on the right graph of d. B: effects of changing the amount of Ca²⁺ released. The same saturating buffer (K_d = 500 nM) was used throughout. The increase of total cytoplasmic Ca²⁺ was changed from 25 (black) to 50 (red) µM.

3.3. Buffers with Cooperative Ca²⁺ Binding

Above, we have described the features of simple interactions between Ca²⁺ ions and small buffer molecules and the independent binding of Ca²⁺ ions to larger molecules. Frequently, however, Ca²⁺ binding to multiple sites on a protein is either positively or negatively cooperative: binding one Ca²⁺ ion enhances or diminishes the affinity of an adjacent site during a subsequent binding step. This type of interaction is commonly seen with Ca²⁺ binding to buffers such as EF-hand proteins and Ca²⁺ pump proteins. Both sequential and independent schemes can be summarized by reactions 3A and 3B:

$${\text{CaB}}_a\mathrm{▂}{\text{B}}_b\stackrel{K_{\text{d}(a)}}{\rightleftharpoons }{\text{B}}_a\mathrm{▂}{\text{B}}_b+\text{ Ca}$$ reaction 3A

$${\text{B}}_a\mathrm{▂}{\text{B}}_b\text{Ca}\stackrel{K_{\text{d}(b)}}{\rightleftharpoons }\hspace{0.17em}{\text{B}}_a\mathrm{▂}{\text{B}}_b+\text{ Ca}$$ reaction 3B

B_a and B_b are two sites on the same protein with individual affinities described by K_d(a) and K_d(b). When two binding sites are in close proximity, the binding of Ca²⁺ to an array of negative charges may be expected to reduce the chances of a second Ca²⁺ binding purely on the basis of electrostatics, thus causing negative cooperativity (17). The fact that positive cooperativity is commonly seen in adjacent Ca²⁺ binding sites means the effect of favorable structural changes evoked by binding of the first Ca²⁺ ion must outweigh the electrostatic effects. Cooperative Ca²⁺ binding may also arise from interactions between linked protein molecules, for example in the case of Troponin-C (TnC), where binding of Ca²⁺ to one TnC will change the structure of the thin filament and increase binding to other TnC proteins bound to adjacent sites on the thin filament (32, 181, 182).

In many cases, the properties of the individual binding sites are unknown and the cooperative binding can be usefully approximated by reaction 4.

$$n\text{Ca }+\text{ B}\hspace{0.17em}\rightleftharpoons \hspace{0.17em}{\text{BCa}}_n$$ (reaction 4)

As discussed previously (183), this can be described mathematically by the Hill equation (Eq. 15) (184). Note that in Eqs. 15–28 we abbreviate [Ca²⁺] to Ca for simplicity:

$$\frac{\mathrm{BC}{\mathrm{a}}_n}{{\left[\mathrm{B}\right]}_{\text{Tot}}}=\frac{\mathrm{C}{\mathrm{a}}^n}{K_{\mathrm{app}}^n+\mathrm{C}{\mathrm{a}}^n}$$ (15)

Here, K_app is the concentration of Ca²⁺ at which half the binding sites are occupied. n is the Hill slope, which represents the degree of cooperativity, with a value of 1 meaning no cooperativity. For a molecule with two sites that bind Ca²⁺ cooperatively, K_app and n can be calculated from the individual dissociation constants [K_d(a) and K_d(b)] as follows (185): $K_{\mathrm{app}}\mathrm{=}\sqrt{K_{\mathrm{d}(a)}\mathrm{\hspace{0.17em}·\hspace{0.17em}}{K}_{\mathrm{d}(b)}}$ and $n\mathrm{=2/}\left(\mathrm{1+}\sqrt{K_{\mathrm{d}(a)}/K_{\mathrm{d}(b)}}\right)$. In the special case where K_d(b) ⪢ K_d(a), it can be seen that n approaches 2. We have used this method to calculate values of K_app and n in TABLE 2.

Table 2.

Examples of individual K_d values from pairs of EF-hand domains in different Ca²⁺ binding proteins along with the associated K_app value and the Hill slope

Buffer Name	Ka, µM	Kb, µM	Kapp, µM	Hill Slope	Ref.
CB-D28K	0.41	0.24	0.31	1.1	30
CB-D9k	0.31	0.15	0.21	1.2	186
CR	2.8	0.068	1.38	1.5	185
CaM (COOH terminus)	28	0.26	2.7	1.8	187
CaM (NH2 terminus)	193	0.79	12.7	1.9	187
SERCA	8.3	0.02	0.41	1.9	98

K_a represents the equilibrium constant for the initial binding and K_b the equilibrium constant created by the cooperative interaction. CalbindinD9k (CB-D9k) has 1 pair of Ca²⁺-binding EF-hand motifs and calretinin (CR) and calbindinD28k (CB-D28K) have 2 pairs; the values listed apply to both pairs in that molecule. Note that CR has an additional functional EF-hand site that is not described here. The pairs of EF-hand domains situated at the COOH- and NH₂-terminal ends of calmodulin (CaM) are shown separately. SERCA, sarco(endo)plasmic reticulum Ca²⁺-ATPase.

Ca²⁺ binding domains can exist in pairs, and in many CBPs multiple pairs of domains exist. The structure and therefore function of these domains are not identical; some differ to the extent that Ca²⁺ cannot bind to one of the pairs of sites, in other domains Mg²⁺ or Ca²⁺ can bind and engage (Ca/Mg sites), and in others Mg²⁺ can bind but not activate the site (Ca²⁺-selective sites). In the case of some well-studied CBPs such as calmodulin (4 EF sites) (72), calretinin (5 EF sites) (185), and calbindin-D_9k (2 EF sites) (186), the cooperativity is between the two adjacent EF-hand domains. TABLE 2 shows examples of several CBPs and the varying extent of cooperativity that has been measured. Detailed information on all individual Ca²⁺ binding sites in a single protein is only available for a few members of the large family of CBPs. More commonly, only general descriptions of Ca²⁺ binding in terms of the Hill K_app and slope value have been reported, and we now consider cooperative buffering in these terms.

3.3.1. The effects of cooperativity on buffer power.

The effects of a cooperative Ca²⁺ binding scheme on the relationship between free [Ca²⁺], Ca²⁺ binding, and buffer power are shown in FIGURE 5. As the Hill slope (n) value increases, so does the steepness of the dependence of bound on free Ca²⁺ (FIGURE 5, top). An instructive comparison is between n values of 1.0 and 1.25 (FIGURE 5A). The difference in the binding curves (FIGURE 5A, top) would be difficult to distinguish experimentally, at least with the techniques applied to intact cells and tissues. However, it has marked effects on the dependence of buffer power on [Ca²⁺] (FIGURE 5A, bottom).

The effects of cooperative binding on Ca²⁺ buffering have been considered previously (188). Here, we calculate the buffer power as a function of [Ca²⁺] by differentiating Eq. 15:

$${\beta }_i\left(\mathrm{Ca}\right)=\frac{\mathrm{dCaB}}{\mathrm{dCa}}={[\mathrm{B}]}_{\text{Tot}}·\frac{n·K_{\mathrm{app}}^n·\mathrm{C}{\mathrm{a}}^{n-1}}{{\left(K_{\mathrm{app}}^n+\mathrm{C}{\mathrm{a}}^n\right)}^2}$$ (16)

The dependence of the buffer power on [Ca²⁺] can be shown by differentiating β_i with respect to [Ca²⁺] to obtain

$$\frac{\mathrm{d}{\beta }_i}{\mathrm{dCa}}={[\mathrm{B}]}_{\mathrm{Tot}}·\frac{n·K_{\mathrm{app}}^n·\mathrm{C}{\mathrm{a}}^{n-2}·\left[\left(n-1\right)·K_{\mathrm{app}}^n-\left(n+1\right)·\mathrm{C}{\mathrm{a}}^n\right]}{{\left(K_{\mathrm{app}}^n+\mathrm{C}{\mathrm{a}}^n\right)}^3}$$ (17)

When dβ_i/dCa = 0, buffer power (β) will have a maximum value, which will be obtained at a value of [Ca²⁺] given by

$${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{i}}={\left(\frac{n-1}{n+1}\right)}^{1/n}\mathrm{\hspace{0.17em}·\hspace{0.17em}}{K}_{\mathrm{app}}$$ (18)

Consistent with Eq. 8, this predicts for n = 1 that the highest buffer power is obtained at zero [Ca²⁺]. In contrast, when the buffer is cooperative (n > 1), buffer power is low at low [Ca²⁺] and peaks at intermediate [Ca²⁺], before decreasing to zero at higher [Ca²⁺] (188) (FIGURE 5). Two other conclusions can be derived from FIGURE 5: 1) An increase of n reduces the range of [Ca²⁺] over which buffering occurs. Since the total amount of Ca²⁺ bound is unaffected, this means that the maximum buffer power is greatest at higher values of n. Indeed, for n = ∞ (not shown), the buffer power curve will have an infinitely high and narrow peak. 2) The value of [Ca²⁺] at which the maximum buffer power is obtained increases with n, approaching a value of K_app at high n.

As regards the dependence of buffer power on K_app, one can differentiate Eq. 16 with respect to K_app and obtains

$$\frac{\mathrm{d}{\beta }_i}{\mathrm{d}{K}_{\mathrm{app}}}={\left[\mathrm{B}\right]}_{\mathrm{Tot}}·n^2·\mathrm{C}{\mathrm{a}}^{n-1}·K_{\mathrm{app}}^{n-1}\frac{\left(\mathrm{C}{\mathrm{a}}^n-K_{\mathrm{app}}^n\right)}{{\left(K_{\mathrm{app}}^n+\mathrm{C}{\mathrm{a}}^n\right)}^3}$$ (19)

For a given [Ca²⁺]_i, the maximum buffer power is obtained when this derivative is equal to zero. Irrespective of the value of n, this occurs when K_app = [Ca²⁺]. Substituting into Eq. 16 and expressing as buffer power (β) gives

$${\beta }_{i,\max }=\frac{{\left[\mathrm{B}\right]}_{\mathrm{Tot}}·n}{4·K_{\mathrm{app}}}$$ (20)

In other words, the maximum buffer power (at [Ca²⁺]_i = K_app) is proportional to n. For the simple case of n = 1 (no cooperativity), this reduces to Eq. 13.

It can also be shown that Eq. 14 holds for cooperative buffers. If K_app increases from K_app,1 to K_app,2, there will be no change of buffer power at a [Ca²⁺] given by the geometric mean ($\sqrt{K_{\mathrm{app},1}\mathrm{\hspace{0.17em}·\hspace{0.17em}}{K}_{\mathrm{app},2}}$).

A good example of the effects of cooperativity on buffer power is provided by calsequestrin (CSQ). At [Ca²⁺] < 50 µM, CSQ exists as monomers; an increase of free Ca²⁺ causes binding to acidic residues at the NH₂ terminal and COOH terminals, changing their tertiary structure allowing NH₂-to-NH₂ terminal and COOH-to-COOH terminal region binding. This results initially in the formation of dimers, then as [Ca²⁺] increases tetramers, and at the highest Ca²⁺ concentration (above ∼5 mM) polymers. Recent work suggests that CSQ forms polymers of helically arranged CSQ monomers (138). This change in tertiary structure exposes further binding sites on the outer surface and the water-filled lumen of the helix. This highly cooperative reaction scheme means that, unlike the case of a noncooperative buffer, the buffer power of CSQ increases with Ca²⁺ binding. As shown in FIGURE 6, buffer power calculated from published data on Ca²⁺ binding to CSQ (133) shows a complex relationship between luminal Ca²⁺ concentration and Ca²⁺ buffer power as a consequence of the multiphasic and cooperative binding curve. The extent and kinetics of this reaction are not fully understood. There are no values for n in the literature, but a value of 10 has been used in modeling (189), and values of 5–9 fit the data of Park et al. (133) (see FIGURE 6). The properties of CSQ are discussed more fully in the context of skeletal muscle (sect. 7.5).

FIGURE 6.

Ca²⁺ dependence of buffering by calsequestrin (CSQ). The data points featured are measurements of Ca²⁺ binding to CSQ at different free calcium concentration ([Ca²⁺]) by Park et al (133). The solid black line represents a multiple summed sigmoidal relationship that best fit the data. The red line is the buffer power calculated from the black fit. Note that the multiphasic steep relationship results in limited epochs of Ca²⁺ buffer power over the range of luminal [Ca²⁺] expected.

For the different CBPs listed in TABLE 2, the cooperativity arises from the interaction between the two adjacent EF-hand domains on the same protein or, in the case of the binding sites on SERCA, from a sequential reaction scheme. For Ca²⁺ binding to isolated fast-twitch skeletal TnC, the adjacent EF-hand domains (sites I and II) have distinct K_d values (affinity of site II is ∼10 fold higher than that of site I) as a consequence of sequential cooperative binding (32, 190), i.e., Ca²⁺ binding to site II is necessary to generate the higher-affinity structure of site I. Note that slow-twitch skeletal and cardiac TnC binds Ca²⁺ only to site II, as site I is nonfunctional (181). Therefore, the cooperativity of Ca²⁺ binding to slow-twitch/cardiac TnC observed when TnC is bound to the troponin-thin filament-myosin complex (191) is a consequence of long-range effects of Ca²⁺ TnC binding transmitted through the thin filament to adjacent TnC sites. Other examples of sequential cooperative schemes can be seen in intraorganelle proteins such as calreticulin and calsequestrin, which can bind up to 20 Ca²⁺ ions per molecule (see sects. 2.6.1 and 7.5).

As mentioned above, detailed kinetic parameters for cooperative Ca²⁺ binding exist only for a few CBPs. A study of Ca²⁺ binding to calretinin revealed two pairs of sites with cooperative interactions and a single independent site (185). The cooperative sites consisted of a low-affinity rapid binding and a higher-affinity slower binding site. A protein with such kinetically heterogeneous sites will maintain rapid Ca²⁺ binding kinetics across a wide range of baseline Ca²⁺ concentrations, a feature not possible in simpler buffer systems (185). This unusual buffer feature is consistent with the experimental observation that calretinin modifies the time course of the IP₃-evoked Ca²⁺ transient in ways that cannot be reproduced by either BAPTA or EGTA (192) and illustrates the importance of understanding other intracellular Ca²⁺ buffers in detail to fully appreciate the functional consequences of buffer action.

4. THE EFFECTS OF Ca²⁺ BUFFER PROPERTIES ON Ca²⁺ SIGNALING

4.1. Effects of Buffers on [Ca²⁺]_i

It is important to consider the roles that Ca²⁺ buffers play in the regulation of cytoplasmic Ca²⁺ concentration ([Ca²⁺]_i). Buffers decrease the change of [Ca²⁺]_i produced by a given flux of Ca²⁺. A similar effect can be produced by transport of Ca²⁺ into organelles, and the combined effects have been referred to as “muffling” (193). In this review, however, we are concerned primarily with physicochemical buffering as opposed to transport into and out of intracellular organelles. It is important to note that, in contrast to the use of the term “buffer” in chemistry, Ca²⁺ buffers cannot alter the steady-state level of [Ca²⁺]_i in an intact cell. At steady state, the level of [Ca²⁺]_i reflects a simple balance between Ca²⁺ entry and efflux at the surface membrane (194–196), whereas buffers are equilibrated with Ca²⁺ according to their K_d. A caveat applies to whole cell patch-clamp recordings during which the intracellular medium is connected to a large volume of buffered pipette solution, which can influence the steady state [Ca²⁺]_i. What buffering does under normal cellular conditions is to slow down and decrease the effects of changes of total Ca²⁺ on changes in free Ca²⁺. FIGURE 7 simulates the changes in free Ca²⁺ resulting from a bolus of Ca²⁺ entering the cytoplasm. [Ca²⁺]_i increases in a steplike fashion and subsequently decays back to its basal value. It is assumed that Ca²⁺ is removed from the cytosol by a plasma membrane Ca²⁺ pump with activity proportional to [Ca²⁺]_i. Four scenarios are shown, for β_i equal to 25, 50, 100, or 200. In all cases, it is assumed that Ca²⁺ binds instantaneously to the buffer and that diffusion of Ca²⁺ and buffer across the volume of interest is rapid. Higher buffer power strongly attenuates the rise of free [Ca²⁺]_i. Equally important is the prominent slowdown of the decay, since the pump will have to remove not only free Ca²⁺ but also the Ca²⁺ that is dissociating from buffers while free Ca²⁺ decays back to baseline values. Decay time constant τ and inverse of the peak amplitude (A⁻¹) are plotted as a function of β_i in FIGURE 7, B and C, respectively. These plots illustrate that the fraction by which the decay is slowed is identical to that by which the amplitude is reduced (see also sect. 4.7.1.1 and Eqs. 30–32). If Ca²⁺ removal is a linear function of [Ca²⁺]_i, then the area under the curve (time integral A × τ) and correspondingly the time-averaged [Ca²⁺]_i during the transient will be unaffected by the presence of buffers (FIGURE 7D). The effects of experimental alteration of buffer power on Ca²⁺ transients are illustrated in FIGURE 12, FIGURE 16B, and FIGURE 21A (see also sect. 9.7 for a discussion of the effects of changing the concentration of the buffer calretinin on the changes of [Ca²⁺]_i). The impact of buffering on processes regulated by [Ca²⁺]_i will depend on the activation mechanisms of these processes. For a process that is activated linearly with [Ca²⁺]_i, the presence of a buffer will not alter the cumulative effect of Ca²⁺ transients. If the Ca²⁺-regulated process has a steep supralinear dependence on [Ca²⁺]_i, then increased buffering will decrease the end effect, since high Ca²⁺ concentrations are ablated. On the other hand, a process with a saturating Ca²⁺ dependence will actually be enhanced by the presence of a buffer, since the latter attenuates the amplitudes of the [Ca²⁺]_i transients, thereby preventing saturation of the Ca²⁺-dependent process, while prolonging the duration of Ca²⁺ action.

FIGURE 7.

Simulation of the effects of altering buffer power (β_i) on amplitude and decay of a cytosolic intracellular calcium concentration ([Ca²⁺]_i) transient. A: [Ca²⁺]_i is controlled by a constant Ca²⁺ leak into the cell that is balanced by a Ca²⁺ pump with an activity equal to γ × [Ca²⁺]_i where γ = 1,000 s⁻¹. At 20 ms, 10 µmol of Ca²⁺ was added per liter of cytosol. The 4 traces denote simulations performed with the buffer powers indicated. A very low-affinity buffer was assumed. Note that increasing β_i decreases the amplitude and slows the decay of the transient. The area under the [Ca²⁺]_i transient above resting [Ca²⁺]_i of 100 nM is unchanged (see also Eqs. 30–32). B–D: predicted dependence on β_i of decay time constant τ (B); reciprocal of the [Ca²⁺]_i transient amplitude A (C); and the product A × τ (D). Symbols represent the respective values for the sample traces in A with corresponding colors. The lines in B and C intersect with the x-axis at a value of β_i of −1.

FIGURE 12.

Effects of exogenous buffers on cardiac myocytes. A: fast buffer. Top: measurements of intracellular calcium concentration [Ca²⁺]_i; from left to right: control cell; after loading with the photolabile Ca²⁺ chelator nitr-5; after flash photolysis of nitr-5. Bottom: averaged, normalized traces. B: slow buffer. Top: recordings from a cell loaded with NP-EGTA before (left) and after (right) flash photolysis. Bottom: normalized traces. Figures redrawn from Ref. 199, with permission from Biophysical Journal.

FIGURE 16.

Estimating cytosolic Ca²⁺ buffering power by competition of endogenous with added exogenous buffers. A: somatic intracellular calcium concentration ([Ca²⁺]_i) transients recorded in a cerebellar Purkinje neuron either shortly (top) or 18 min (middle) after establishing whole cell configuration with 500 µM fura-2 in the patch pipette. Bottom: the progressive loading of the cell with the dye. Amplitudes and decay kinetics of [Ca²⁺]_i transients are resistant to fura-2 loading via a patch pipette. Modified from Ref. 443, with permission from Journal of Physiology. B: similar experiment as in A performed in a calyx of Held nerve terminal. a: Loading of the terminal with 100 µM fura-2 monitored with the fluorescence at the isosbestic excitation wavelength (top). Fluorescence signals at 385-nm excitation (F₃₈₅; middle) and corresponding AP-evoked [Ca²⁺]_i transients (bottom) are shown for 3 time points after establishing whole cell configuration (top; filled circles). With increasing dye concentration, [Ca²⁺]_i transients decrease in amplitude and decay more slowly (cf. FIGURE 7). b: Decay time constant τ (top) and inverse of the peak amplitude A⁻¹ (bottom) plotted as a function of the fura-2 Ca²⁺-binding ratio ${\kappa }_{\mathrm{B}}^{\mathrm{\prime }}$ (exogenous buffer power) for various time points during dye loading. Regression lines through the τ and A⁻¹ plots yield extrapolated y-axis intercepts for τ and A⁻¹ at ${\kappa }_{\mathrm{B}}^{\mathrm{\prime }}$ = 0 (no added buffer). Negative x-axis intercepts represent estimates for 1 + ${\kappa }_{\mathrm{S}}^{\mathrm{\prime }}$ (endogenous buffer power). Modified from Ref. 440, with permission from Biophysical Journal. C: similar as in B except that Ca²⁺ influx was triggered by short trains of action potential (AP)-like depolarizations, a low-affinity dye was used, and plotted decay constants represent pooled data obtained from several terminals loaded with 3 different dye concentrations. Each data cluster corresponds to 1 of the 3 fura-6F concentrations. Modified from Ref. 248, with permission from Journal of Physiology.

FIGURE 21.

Endogenous Ca²⁺ buffers shape the time course of intracellular calcium concentration ([Ca²⁺]_i) transients in dendrites and spines. A: [Ca²⁺]_i transients evoked by single action potentials (APs), measured in the proximal dendrites of cortical pyramidal neurons that lack expression of parvalbumin (PV), CB-D28k, and calretinin (CR) and therefore exhibit a low endogenous Ca²⁺-binding ratio, somatically loaded with either 20, 80, 125, or 250 µM fura-2. Gray areas represent the integral A × τ, the product of peak amplitude A and time constant τ fitted to the decay, which is similar under all recording conditions. Modified from Ref. 441, with permission from Biophysical Journal. B: slow and biphasic decay kinetics of [Ca²⁺]_i transients in dendritic shafts (top) and spines (bottom) of cerebellar Purkinje cells. The superimposed continuous lines represent double-exponential fits to the decay. The dashed lines represent an assumed resting [Ca²⁺]_i of 45 nM. Insets show the fits with their corresponding fast (red) and slow (blue) components. In the spine, the fit yielded a similar slow component but a much larger fast component, likely reflecting fast efflux of Ca²⁺ from the spine into the dendrite. Modified from Ref. 510, with permission from Journal of Physiology.

For these conclusions to be quantitatively correct, it has to be assumed that the on and off rate constants are infinitely fast such that bound and free Ca²⁺ are always in equilibrium, that diffusion of buffers and Ca²⁺ across the cellular dimensions is rapid, and that buffering power is constant over the relevant range of changes in [Ca²⁺]_i (see sects. 4.2 and 4.7.1).

4.1.1. Effects of buffers on the calculations of fluxes.

Fluxes of Ca²⁺ across cell membranes are often estimated by measuring the resulting changes of [Ca²⁺]_i, and it is often overlooked that changes of Ca²⁺ buffering will alter the change of [Ca²⁺]_i produced by a given flux. For example, an increase of buffer power will attenuate the increase of [Ca²⁺]_i produced by a given influx of Ca²⁺ through a membrane Ca²⁺ channel. Furthermore, the activities of Ca²⁺ removal processes are often assessed from the time constant of decay of [Ca²⁺]_i. However, as shown in FIGURE 7, A AND B, this time constant is also affected by Ca²⁺ buffering. This raises the possibility that an increase of the time constant of decay of [Ca²⁺]_i could result from an increase of buffering as opposed to a decrease of pumping (197). Given these issues, it is best to calculate Ca²⁺ fluxes from changes of total Ca²⁺ estimated from the buffer properties and changes of [Ca²⁺]_i (80, 197).

4.2. Effects of Buffer Kinetics

It is important to distinguish between instantaneous and steady-state buffering. As shown in reaction 1, a simple buffer can be characterized by binding (k_on) and unbinding (k_off) rate constants, which determine the time over which buffering occurs. FIGURE 8A shows the response of both free and bound Ca²⁺ to a step increase of total [Ca²⁺] for buffers with a similar K_d but different rate constants. For simplicity we assume that there is no pumping of Ca²⁺ and therefore changes of [Ca²⁺]_i are determined solely by Ca²⁺ binding to and Ca²⁺ unbinding from the buffer. The resulting time courses of total, free, and bound Ca²⁺ are shown for a slow (EGTA) and a fast (BAPTA) buffer. In both cases, all added Ca²⁺ initially appears as free Ca²⁺. As Ca²⁺ progressively binds to the buffer, [Ca²⁺]_i decreases, and this occurs more quickly with the faster buffer. Finally, in the case of BAPTA, [Ca²⁺]_i approaches a steady state within a few milliseconds, at which it is in equilibrium with the bound state according to Eq. 1. EGTA is sufficiently slow that [Ca²⁺]_i is still declining at the end of the period shown. Two further points are worth noting: 1) The transient overshoot of [Ca²⁺]_i will only occur if the rise of total Ca²⁺ is very fast relative to k_on; if slower, the fast phase of decay of free Ca²⁺ will be obscured. 2) Even if the fast phase of decay does occur, the ability to detect it will require a fast Ca²⁺ indicator and a fast acquisition rate.

FIGURE 8.

Effects of buffer kinetics. A: response to a bolus of total Ca²⁺. a: Total Ca²⁺ was increased by 10 µM. b: Free calcium concentration ([Ca²⁺]_free). c: Ca²⁺ bound to buffer. Simulations are shown for both EGTA (black solid lines) and BAPTA (red dashed lines). Note the transient overshoot of intracellular [Ca²⁺] ([Ca²⁺]_i) for both buffers, the decay of which is scarcely apparent at this timescale for the case of EGTA. B, a: a transient rise of [Ca²⁺]_i was imposed. b and c: The calculated change of Ca²⁺ bound to BAPTA (b) and EGTA (c). The solid lines in d and e show hysteresis plots of bound Ca²⁺ plotted as a function of free Ca²⁺ calculated from the responses shown in b and c, respectively. The arrows indicate the direction of time. The dashed lines show the steady-state relationship between free and total Ca²⁺.

It is also instructive to see how Ca²⁺ binding to a buffer tracks a rise of free [Ca²⁺]. Comparison of FIGURE 8, Bb AND Bc, shows that binding to even the fast buffer BAPTA lags slightly behind free Ca²⁺ and the lag is much greater for EGTA. The hysteresis curves (FIGURE 8, Bd AND Be) plot bound as a function of free Ca²⁺, both for the rise and fall of [Ca²⁺]. For BAPTA, the hysteresis curve only deviates markedly from the steady-state relationship during the very fast rise of free [Ca²⁺]. In contrast, for the slower buffer EGTA, there is a marked difference between the instantaneous and steady-state relationships throughout. FIGURE 8Be also shows that less Ca²⁺ is bound at a given free [Ca²⁺] during the transient compared to the steady state (when bound and free Ca²⁺ are in equilibrium), indicating that EGTA buffers more weakly than BAPTA during a transient.

As discussed in sects. 2.2 and 2.5.1.1, most slow kinetics arise not from intrinsically slow kinetics of Ca²⁺ binding but rather from the time it takes for Mg²⁺ or H⁺ to dissociate, making binding sites available for Ca²⁺. If [Ca²⁺]_i increases, free Ca²⁺ can quickly bind only to free buffer, which may be a small fraction of the total. By mass action, the resulting decrease in concentration of the free buffer will decrease the concentration of the Mg²⁺- or H⁺-bound forms, thereby regenerating free buffer for Ca²⁺ to bind to. Thus, the steady-state buffering is much greater than the instantaneous one. The speed at which this occurs is limited by the rate at which the competing ions dissociate. This can result in two phases of Ca²⁺ binding: rapid binding to the free buffer and delayed binding to that which had Mg²⁺ bound. This is illustrated in FIGURE 9, which also shows how a slow buffer (here PV as an example) and a Ca²⁺ pump combine to promote relaxation of [Ca²⁺]_i. The results should be compared with the simulation of FIGURE 7 for fast buffering. The simulation illustrated by the black solid line in FIGURE 9 assumes a total concentration of 500 µM PV. Initially, only 25 µM PV is free, with 205 and 270 µM, respectively, bound to Ca²⁺ (FIGURE 9B) and Mg²⁺ (FIGURE 9C). The addition of 150 µM total Ca²⁺ results in a rise of [Ca²⁺]_i (FIGURE 9A), leading to a rapid increase of Ca²⁺-bound PV (FIGURE 9B) (over the period indicated by i), as Ca²⁺ binds to available free PV. The kinetics of this increase are determined by the binding and dissociation rate constants of Ca²⁺ with PV. This is accompanied by an initial rapid fall of [Ca²⁺]_i. A slower phase (ii) then ensues when Mg²⁺ dissociates from Mg²⁺-bound PV (FIGURE 9C) in exchange for Ca²⁺ binding (FIGURE 9B). There is also a decrease of free PV (not shown). On a longer timescale, beyond the period shown, the concentrations of all species will return to the initial levels. Such biphasic decays have been demonstrated when PV was added to adrenal chromaffin cells (27) and also recorded in cardiac muscle when slow buffers were added to the cytoplasm (198, 199).

FIGURE 9.

Comparison of a slow Ca²⁺ buffer with a Ca²⁺ pump. All simulations use a slow buffer, here taken to be parvalbumin (PV) at the concentrations indicated (500 or 1,000 µM). Steady-state intracellular calcium concentration ([Ca²⁺]_i) was controlled by a leak flux opposed by a pump. Pump rate is given by pump·[Ca²⁺]_i, where the rate constant of pump (units of s⁻¹) is defined in the key. The leak was adjusted to give a resting [Ca²⁺]_i of 100 nM in all cases. Total Ca²⁺ was increased by 150 µM at 20 ms. A: [Ca²⁺]_i. B: Ca²⁺ bound to buffer. C: Mg²⁺ bound to buffer. D: Ca pump rate. The fast and slow phases of Ca²⁺ binding are denoted by i and ii. Note that the data for 1,000 µM PV case are off the top of the range shown in B and C.

FIGURE 9 also serves to compare the effects of PV with those of a Ca pump. The red dashed lines show the effects of reducing the pump to 1%. [Ca²⁺]_i still decreases, and this is accompanied by larger changes of bound Mg²⁺ and Ca²⁺ indicating that PV is compensating for the loss caused by the pump. The two final simulations show that either increasing PV (dotted blue lines) or the pump (green solid lines) can accelerate the slow decay component of [Ca²⁺]_i to similar levels, with the former resulting in more Ca²⁺ binding to PV and the latter in less. FIGURE 9D indicates the effects on pump activity, which are discussed in more detail in sect. 7.2.

4.3. Effects of K_d and Ca²⁺ Dependence of Buffering

The influence of buffer K_d on Ca²⁺ signaling can be appreciated from FIGURE 10A, which shows a simulation of the effects of adding the same amount of Ca²⁺ to the cytoplasm in the presence of fast buffers with different values of K_d. The effect of buffer K_d on the decay depends on the fact that (see sects. 3.1. and 3.2) buffer power is sensitive to both K_d and cytosolic [Ca²⁺]_i. In contrast to the simulations of FIGURE 7, where buffer power was assumed to be constant (Δ[Ca²⁺]_i ≪ K_d), the decays of [Ca²⁺]_i are not single exponentials as shown (FIGURE 10Ab) by the curves intersecting. This is emphasized in FIGURE 10Ac, which plots the instantaneous rate constant of decay of [Ca²⁺]_i. For a simple exponential decay this would be constant. However, the instantaneous rate constants of all [Ca²⁺]_i transients shown are initially high and then decrease. This is caused by the buffer saturation and, consequently, decreased buffer power at high [Ca²⁺]_i (FIGURE 10Ad). Thus, a given rate of Ca²⁺ pumping results in a faster fall of [Ca²⁺]_i. Such saturation of Ca²⁺ buffers has been suggested to account for the initial rapid decay of the caffeine-evoked Ca²⁺ transient in ventricular myocytes (197). As evident from the normalized traces (FIGURE 10Ab) and especially the instantaneous rate constants, the buffer with the highest affinity (K_d = 0.25 µM) causes a faster initial decay of the [Ca²⁺]_i transients than do the others, because of the greater binding of Ca²⁺ and consequent decrease of buffer power at the peak (FIGURE 10Ad). As [Ca²⁺]_i approaches resting levels, buffer power of the high-affinity buffer increases and the Ca²⁺ transient decays more slowly. In other words, for a given amount of Ca²⁺ added to the cytoplasm, increasing the affinity of the buffer causes stronger buffer saturation and produces a [Ca²⁺]_i decay that crosses over with the lower-affinity cases (see sects. 6.2.2–6.2.5 for other practical consequences in cardiac muscle).

FIGURE 10B demonstrates the predictions for increasing the amount of added Ca²⁺. Doubling the Ca²⁺ release into the cytosol results in a larger Ca²⁺ transient (FIGURE 10Ba), which initially decays much faster because of buffer saturation (FIGURE 10Bb). Once again, it is clear from the plot of instantaneous rate constants (FIGURE 10Bc) that the decays are not single exponentials. However, this might not be apparent in real, noisy data, and it would be all too easy to assume that the larger transient decays more quickly because of enhanced Ca²⁺ pumping as opposed to buffer saturation.

4.4. The Effects of Cooperative Buffers

As shown above, for noncooperative buffers buffer power decreases as [Ca²⁺]_i increases. In contrast, for a cooperative buffer, buffer power will first increase but then decrease once [Ca²⁺]_i rises above an optimal concentration (FIGURE 5). FIGURE 11 demonstrates that this may have marked effects on Ca²⁺ signaling. The black traces show a simulation (similar to that of FIGURE 10A) for a noncooperative buffer (n = 1). The red trace shows the prediction for a cooperative buffer (n = 2). Here the peak value of [Ca²⁺]_i is greater than the level at which maximum buffering occurs, resulting in an increase of buffer power. As [Ca²⁺]_i falls toward the level at which peak buffer power occurs, buffer power increases further and this is accompanied by a decrease of the instantaneous rate constant of decay of [Ca²⁺]_i. However, as [Ca²⁺]_i decays below the level of peak buffering, buffer power decreases and the rate constant of decay will increase. Therefore, in contrast to a simple buffer, where for large Ca²⁺ transients the instantaneous rate constant of decay is expected to decrease as [Ca²⁺]_i falls, a slowing followed by acceleration should be observed. It should, however, be noted that the kinetics of decay of the Ca transient will also be affected by the dependence of Ca²⁺ pumping on [Ca²⁺]_i.

FIGURE 11.

The effect of a cooperative buffer on the decay of intracellular calcium concentration [Ca²⁺]_i. Model similar to FIGURE 10. The buffer had a K_app of 0.5 µM. Traces show the predicted effects of values of Hill coefficient (n) of 1 (black solid lines) and 2 (red dashed lines). A: [Ca²⁺]_i. B: normalized [Ca²⁺]_i. C: instantaneous rate constant of decay. D: buffer power.

4.5. The Influence of Buffering on the Diffusion of Ca²⁺

Diffusion of Ca²⁺, i.e., the ability of the ion to move along its concentration gradient, is affected by interactions of solvated Ca²⁺ with the components in the medium. A striking physiological example of the ability of Ca²⁺ buffers to enhance diffusion is that of the calbindin proteins, which facilitate Ca²⁺ diffusion across epithelial cell layers (200) (see sect. 10). Often, the bulk of cytoplasmic Ca²⁺ buffering is from fixed structures, i.e., cytoskeleton, membranes, contractile proteins, and pumps on organelles, which will not contribute to the diffusive flux of Ca²⁺ (173, 201). Therefore, even if mobile cytoplasmic Ca²⁺ buffers only make a small contribution to the total cellular buffer power, they can have a large role in diffusion (174, 202–204). The exact contribution will depend on the relative diffusion coefficient of the Ca²⁺ bound forms and on their buffering power (see Eq. 29). An estimate for the diffusion coefficient (D) can be obtained from the known dependence of D on molecular weight (M) as described by a simplified form of the Stokes–Einstein equation (D ∝ 1/M^r); r can be measured empirically and is 0.33–0.40 over a wide range of M (205, 206). In this review, we use a value of 0.33.

Kinetic considerations aside, intracellular Ca²⁺ buffers will affect Ca²⁺ diffusion in two distinct ways: 1) for any cytosolic influx/efflux event, buffers will reduce the free Ca²⁺ concentration gradient generated and therefore the rate of intracellular diffusion and 2) the reduction in diffusive flux of Ca²⁺ due to a lower free Ca²⁺ concentration gradient may be offset by a contribution to diffusion by the Ca²⁺-bound form of the buffer; the magnitude of this component will depend on the value of the diffusion coefficient of the complex and the concentration gradient of the bound Ca²⁺ (178, 202, 204).

Specifically, the flux of free Ca²⁺ due to diffusion is described by the Fick equation.

$$J_{\mathrm{Ca}}=-D_{\mathrm{Ca}}\mathrm{\hspace{0.17em}·\hspace{0.17em}}\frac{\mathrm{dCa}}{\mathrm{d}x}$$ (21)

where D_Ca is the diffusion coefficient of free Ca²⁺ and dCa/dx is its concentration gradient.

The flux of bound Ca²⁺ is similarly

$$J_{\mathrm{CaB}}=-D_{\mathrm{CaB}}\mathrm{\hspace{0.17em}·\hspace{0.17em}}\frac{\mathrm{dCaB}}{\mathrm{d}x}$$ (22)

where D_CaB is the diffusion coefficient of Ca²⁺ bound to buffer and dCaB/dx is its concentration gradient.

The total flux is

$$J_{\mathrm{Ca}(\mathrm{total})}=J_{\mathrm{Ca}}+J_{\mathrm{CaB}}=-D_{\mathrm{Ca}}·\frac{\mathrm{dCa}}{\mathrm{d}x}-D_{\mathrm{CaB}}·\frac{\mathrm{dCaB}}{\mathrm{d}x}$$ (23)

Henceforth, we assume that Ca²⁺ binding and dissociation are fast enough such that the local bound and free Ca²⁺ are in equilibrium; therefore dCaB/dx can be replaced by the product of dCa/dx (the free Ca²⁺ gradient) and dCaB/dCa (the buffer power), resulting in

$$J_{\mathrm{CaB}}=-D_{\mathrm{CaB}}·\frac{\mathrm{dCa}}{\mathrm{d}x}·\frac{\text{dCaB}}{\mathrm{dCa}}$$ (24)

which can be rewritten as follows:

$$J_{\mathrm{CaB}}=-D_{\mathrm{CaB}}·\frac{\mathrm{dCa}}{\mathrm{d}x}·{\mathrm{\beta }}_i\left(\mathrm{Ca}\right)$$ (25)

Dividing Eq. 25 by Eq. 21 gives the relative contribution made by the flux of bound compared to free Ca²⁺ to diffusion as

$$\frac{J_{\mathrm{CaB}}}{J_{\mathrm{Ca}}}=\frac{D_{\mathrm{CaB}}}{D_{\mathrm{Ca}}}\mathrm{\hspace{0.17em}·\hspace{0.17em}}{\text{β}}_i\left(\mathrm{Ca}\right)$$ (26)

This means that buffers make the biggest fractional contribution to Ca²⁺ diffusion when they also buffer Ca²⁺ most strongly (β_i,max). For a simple noncooperative buffer, where the binding is described by a single dissociation constant (K_d), we can substitute from Eq. 8 for β_i(Ca) to give

$$\frac{J_{\mathrm{CaB}}}{J_{\mathrm{Ca}}}=\frac{D_{\mathrm{CaB}}}{D_{\mathrm{Ca}}}·{\left[\mathrm{B}\right]}_{\mathrm{Tot}}·\frac{K_{\mathrm{d}}}{{\left(\mathrm{Ca}+K_{\mathrm{d}}\right)}^2}$$ (27)

More generally, including cooperative buffers, we substitute from Eq. 16:

$$\frac{J_{\mathrm{CaB}}}{J_{\mathrm{Ca}}}=\frac{D_{\mathrm{CaB}}}{D_{\mathrm{Ca}}}·{\left[\mathrm{B}\right]}_{\mathrm{Tot}}·\frac{n·K_{\mathrm{app}}^n·\mathrm{C}{\mathrm{a}}^{n-1}}{{\left(K_{\mathrm{app}}^n+\mathrm{C}{\mathrm{a}}^n\right)}^2}$$ (28)

Hence, noncooperative buffers contribute most to Ca²⁺ diffusion at low [Ca²⁺] (Eq. 27). As [Ca²⁺] reaches high levels, the buffer will become saturated [β(Ca) = 0], there will be no gradient of CaB, and therefore no contribution to net diffusion. In contrast, for cooperative buffers, their contribution to Ca²⁺ diffusion will be low at both very low and high [Ca²⁺] and greatest at a value of [Ca²⁺] given by Eq. 18. As regards the dependence on K_d, for noncooperative buffers their contribution to diffusion will be largest when K_d = [Ca²⁺]_i (Eq. 13) (207), and a similar condition holds for cooperative buffers (Eq. 20).

Equations 21–28 describe the local fluxes contributed by individual Ca²⁺-binding components of the cytosol. When confronted with the problem of solving the spatiotemporal pattern of diffusion of several interacting components, this can, of course, be accomplished by numerical integration (see sect. 4.7). For certain limiting cases, however, simple analytical solutions can be derived, which often provide a more intuitive understanding of the processes involved.

Thus, for the case of small changes in [Ca²⁺] around low values, where the buffering power of all Ca²⁺-binding species is constant, the “apparent diffusion coefficient” for Ca²⁺ (D_app) can be calculated as

$$D_{\mathrm{app}}=D_{\mathrm{Ca}}·\frac{1+\sum \left({\kappa }_i·D_i/D_{\mathrm{Ca}}\right)}{1+\sum {\kappa }_i}$$ (29)

where the sums extend over all Ca²⁺-binding species (178, 202). The use of κ in Eq. 29 reflects the original papers, but the equation could equally well be written in terms of β_i (sect. 3).

This equation provides an intuitive understanding in the sense that in the numerator the individual terms of the sum specify contributions of the respective buffers to Ca²⁺ mobility, normalized by the sum of Ca²⁺ binding ratios of all species, irrespective of whether they are mobile or stationary.

TABLE 3 gives values for some important mobile intracellular buffers. The respective relative diffusion constant (D_i/D_Ca), appearing in Eqs. 26–29, is given in the table for each buffer. One major contributor to D_app is ATP, which is present at 5–8 mM in virtually all cell types (34, 203). ATP binds Ca²⁺, Mg²⁺, and H⁺ and, despite its relatively low Ca affinity (K_d of ∼1 mM), because of its high concentration it can nevertheless bind significant amounts of intracellular Ca²⁺ (sect. 2.4.2). This and its low molecular weight mean that the diffusive flux carried by Ca-ATP will be greater than that due to free Ca²⁺ (see TABLE 3 and Eq. 27). This contribution will be larger in cytoplasmic regions close to channels/exchangers where Ca²⁺ influx can increase the local [Ca²⁺] to higher levels, which will saturate higher-affinity buffers. Striated muscle cells also contain high concentrations (up to 20 mM) of histidyl dipeptides (HDPs) such as carnosine (211, 212), and, subject to the concerns about Ca²⁺ binding at physiological pH (sect. 2.4.1), these may also contribute to Ca²⁺ diffusion.

Table 3.

Predicted effects of various mobile Ca²⁺ buffers on diffusion of Ca²⁺

	Mol Weight, g	Relative Diffusion Constant	Conc, µM	Kapp, µM	Hill Slope	Binding Sites	Ca-Bound, µM	β(Ca)	Relative Flux
Free calcium	40	1.00	0.1					1	1
Calmodulin	16,700	0.14	20a	2.7/12.7b	1.8/1.9	4	0.05	0.49	0.09
ATP	525	0.43	7,000c	2,496d	1	1	0.28	2.80	1.20
Carnosine	226	0.56	10,000e	1,350e	1	1	0.74	7.41	4.18
CB-D9k	10,000	0.16	60f	0.21g	1.2	2	34.9	148.6	48.0
CB-D28k	28,000	0.12	60f	0.31h	1.1	4	53.7	114.6	52.8
EGTA	380	0.48	100	0.18i	1	1	35.7	230	109.2
Fura-2	636	0.40	100	0.3j	1	1	25.0	188	75.3
GCAMP	50,000	0.10	10	0.32k	3	4	11.8	86.2	32.8

From left to right: molecular (atomic) weight (MW); diffusion constant relative to Ca²⁺, calculated as (40/MW)^0.33; concentration of buffer; K_app; Hill slope; no. of Ca²⁺ binding sites per molecule; concentration of bound Ca²⁺; buffer power (from Eq. 8 or 16); diffusion flux relative to that of Ca²⁺, calculated at free Ca²⁺ of 0.1 µM (from Eq. 27 or 28). N.B. The concentration for carnosine applies to striated muscle and that for calbindinD9K (CB-D9k) and CalbindinD28K (CB-D28k) to Ca²⁺-transporting epithelia, the concentrations for EGTA, fura-2, and GCAMP represent typical values under experimental conditions. The CaM data represent both the COOH- and NH₂-terminal sites. All compounds bind 1 Ca²⁺ per molecule except: CaM, 4; CB-D9K, 2; CB-D28K, and 4; GCAMP, 4. The values come from Refs. 208 (a), 187 (b), 34 (c), 33 (d), 49 (e), 209 (f), 186 (g), 30 (h), 24 (i), 25 (j), and 210 (k). Note that the table shows a value of 3 for the Hill coefficient of GCAMP but a range of K_ds is found for different variants from 1 to 3 (210). These values were used to calculate K_app. For noncooperative buffers, this was the apparent K_d at pH 7.0 and 1 mM Mg²⁺; for cooperative buffers, it was calculated as in TABLE 2. Buffers listed in italics are synthetic molecules used in research.

The low intracellular concentration and large molecular weight of Ca²⁺-signaling molecules such as annexin and CaM mean that their contributions to diffusive flux are small (TABLE 3). For CaM, the inferred diffusion coefficient (20–30 µm²/s) (203, 204) is approximately what would be anticipated from its molecular weight (∼17,000). The calbindins (CB-D9k and CB-D28k) at nominal cytoplasmic concentrations of 300 µM make a significant contribution to diffusive flux. Interestingly, the lower diffusion coefficient of the larger 28k form is offset by being able to bind four Ca²⁺ compared to the two Ca²⁺ binding sites on the 9k form (see TABLE 3). It is useful to compare the calbindins with CaM. The molecular weights and therefore diffusion constants are of the same order. The much greater contribution to Ca²⁺ diffusion of the calbindins arises from two factors: 1) The concentration of the calbindins in epithelia is three times greater than that of CaM. 2) More importantly, the higher affinity of the calbindins means that at lower values of [Ca²⁺]_i the buffer power of calbindin, and therefore its contribution to diffusion, is much greater. Finally, the effects of Ca²⁺ indicators to promote intracellular Ca²⁺ diffusion are illustrated by the inclusion of fura-2 and the protein indicator GCaMP in TABLE 3 (note the very high relative fluxes of EGTA and fura-2, which at the assumed concentrations dominate diffusion; see also sect. 4.6).

A mechanism through which a relatively immobile Ca²⁺ buffer can enhance net Ca²⁺ diffusion has been suggested to apply in the case of the intra-SR buffer CSQ (213). CSQ polymers within the SR may mediate enhanced Ca²⁺ diffusion from a distal region of the polymer to a region next to the SR Ca²⁺ channel via the “jumping” of Ca²⁺ ions from binding site to site without going through the aqueous phase, which in a linear polymer would form a “Ca²⁺ wire.” This theory is based on the well-known physical process of diffusion on an adsorptive surface (214) and may enhance net diffusion by 10- to 100-fold. There is, however, no direct evidence that this process features in intra-SR Ca²⁺ diffusion.

4.5.1. Linkage between diffusion of calcium and protons.

Buffer-mediated diffusion of Ca²⁺ may also be linked to that of protons, since many buffers can bind both ions. This was originally proposed for calbindin-mediated transport, where it was suggested that protons might facilitate Ca²⁺ binding resulting in a coupled cotransport of Ca²⁺ and protons (207). However, there is no evidence to suggest that protons increase Ca²⁺ binding, and, indeed, the opposite is more likely, as ∼1 H⁺ is released when Ca²⁺ binds to an EF-hand domain (see sect. 2.6.1.2). It is therefore likely that calbindin-mediated Ca²⁺-facilitated diffusion results in countertransport of protons. More recently, competition of H⁺ and Ca²⁺ for binding to ATP and carnosine has been suggested to produce a countertransport of Ca²⁺ and protons in cardiac cells. Acidifying a region of a cell resulted in an increase of [Ca²⁺]_i in that region. This was explained by the buffers shuttling protons away from this region and returning with Ca²⁺ bound (49).

4.6. Effects of Exogenous Buffers on Ca²⁺ Signaling

The use of small-molecule intracellular Ca²⁺ indicators will increase Ca²⁺ buffering and thus decrease the amplitude of [Ca²⁺]_i transients and alter their kinetics (174, 215) (sect. 4.1). The magnitude of the effect will depend on both the concentration and K_d of the indicator. An important requirement for [Ca²⁺]_i fluorimetry, therefore, is to keep the concentration of indicators low, preferably much lower than that of endogenous buffers. The low molecular weight of fura-2 and its high buffer power at low [Ca²⁺]_i (as a consequence of its high affinity) require extremely low concentrations of this indicator for unperturbed measurement of [Ca²⁺]_i signals (204). The low K_d means that this problem lessens at higher [Ca²⁺]_i as buffer power falls. Equally, however, the accuracy of measuring [Ca²⁺]_i falls at higher [Ca²⁺]_i as the indicator saturates. If the indicator is loaded via a patch pipette, then its concentration is known. Most studies, however, use the membrane-permeant acetoxymethyl (AM) ester form, and the cytosolic concentration is therefore unknown. TABLE 3 shows the effects of a typical 100 µM dye concentration. At 0.1 µM [Ca²⁺]_i, there is a significant contribution to buffer power. Lower-affinity indicators will produce less buffering. However, as [Ca²⁺]_i increases, the contribution to buffering of low-affinity indicators will be greater than that of high-affinity indicators (FIGURE 3).

Exogenously applied slow buffers have been used for a variety of purposes in physiological experiments. In muscle, Ca²⁺ release from the SR has been studied as Ca²⁺ “spikes” by using a fast fluorescent Ca²⁺ indicator in combination with a higher concentration of the slow Ca²⁺ buffer EGTA (198). The slow buffer keeps [Ca²⁺]_i low so the fast indicator will be mainly in the low-fluorescence state. When Ca²⁺ is released, [Ca²⁺]_i will briefly and locally reach high levels and thereby be detected by the fluorescent indicator before Ca²⁺ is bound to EGTA. The amplitude of the spike of [Ca²⁺]_i then gives a measure of the release flux (198, 216, 217). Similarly, so-called “puffs” of local elevated [Ca²⁺]_i, released from the endoplasmic reticulum by IP₃, have been studied in various cell types (218–220). Local domains of elevated [Ca²⁺] in the vicinity of Ca²⁺ channel clusters were analyzed at ribbon synapses in auditory hair cells by both Ca²⁺ imaging and computational approaches (221–223). Ca²⁺ signals due to the opening of single voltage-gated Ca²⁺ channels could be resolved by total internal reflection fluorescence (TIRF) microscopy (224). A careful balance of fast low-affinity indicator dyes and slow high-affinity buffers (usually EGTA) is required for optimum resolution (see sect. 4.7.2 for a detailed discussion of local [Ca²⁺]_i domains).

The buffering effect of Ca²⁺ indicators can also be used to advantage. In the extreme case of a large excess of indicator, changes in [Ca²⁺]_i will be very small, but since the indicator binds essentially all the Ca²⁺ changes in fluorescence at the Ca²⁺-dependent wavelength of an indicator dye will be proportional to fluxes and can be used for quantitative determination of Ca²⁺ fluxes through ion channels (173, 225–227).

Exogenous buffers will also affect Ca²⁺ diffusion. As mentioned above, mobile endogenous buffers contribute only ∼20% of the total cytoplasmic buffer power, so added Ca²⁺ indicators will increase the relative concentration of mobile buffers within the cytosol and therefore alter physiological Ca²⁺ gradients and fluxes (174, 203, 204). Although generally present at concentrations (∼50 µM) lower than those of endogenous buffers, these indicators, mostly derivatives of BAPTA, have relatively high affinity (K_d 0.3–1 µM) and therefore their contribution to buffer power and thence Ca²⁺ diffusion may increase to levels that match or exceed that of endogenous mobile buffers, thereby increasing the diffusion of Ca²⁺ and attenuating intracellular Ca²⁺ gradients. This is analogous to the very large influence of low-molecular weight metabolites such as ATP (sect. 2.4.2) on D_app of Ca²⁺ (Eq. 29) in cells that contain only low levels of endogenous mobile CBPs. Therefore, and as indicated in TABLE 3, only by ensuring low cytoplasmic indicator concentrations (<10 µM) or using indicators with a low diffusion coefficient can experimenters hope to preserve physiological intracellular Ca²⁺ gradients while measuring intracellular Ca²⁺ signals with high-affinity Ca²⁺ dyes. Genetically encoded Ca²⁺ indicators of the GCaMP family (228), which are derivatives of GFP, have a MW of ∼ 50,000 and therefore diffuse considerably more slowly (TABLE 3). Nevertheless, at least at resting [Ca²⁺]_i, they are predicted to make a significant contribution to Ca²⁺ buffering and to interfere with physiological processes (215, 229). In practice, there is a compromise between avoiding excessive additional mobile buffer, while having adequate signal to noise. Efforts are being made to develop more sensitive and brighter protein-based probes (230, 231), which, because of their high MW, may preserve the endogenous diffusion properties better than conventional Ca²⁺ indicators. An alternative approach is to use dextran-coupled dyes (220, 232). Furthermore, Ca²⁺ indicators can be targeted to structures within the cell (233, 234), thereby becoming immobile. However, as immobile buffers they may still retard Ca²⁺ diffusion according to studies of diffusion in cytoplasm (235) because of their contribution in the denominator of Eq. 29.

Studies on the influence of Ca²⁺-indicator dyes and other small Ca²⁺-binding molecules on D_app of Ca²⁺ have shown that this very much depends on the presence of endogenous buffers. With a MW of ∼400, the diffusion coefficient of indicators would be ∼50% of that of free Ca²⁺ (200–220 µm²/s). Thus, one would expect D_app to be near 100 µm²/s if the indicator dye were the dominating buffer. If, on the other hand, an immobile low-affinity buffer with a buffering power of ∼20 (236) were present as the only buffer, D_app would be expected to be around 200/20 = 10 µm²/s. Measured or inferred values are often in between these values. In rod photoreceptor cells, for instance, D_app was found to be only ∼15 µm²/s (236), pointing toward a small contribution of the mobile indicator or else a lower buffering power of the fixed buffer. A detailed Ca²⁺ imaging and modeling study on atrial myocytes (203) concluded that because of the presence of immobile buffers the apparent diffusion coefficient would be as low as 4.25 μm²/s if diffusion were not accelerated by the presence of indicator dyes and ATP. An imaging study of Ca²⁺ diffusion within nerve axons (204) measured D_app for a range of different indicator concentrations and extrapolated to zero indicator. This yielded an upper bound for D_app of <16 µm²/s (see also sect. 4.7.3). Estimates of D_app in skeletal muscle (237) as well as cardiac muscle (238) were in a similar range of 15–30 µm²/s. Such low values are only obtained, however, if care is taken to use as low indicator concentrations as possible, unless endogenous buffers dominate. Otherwise, the relatively mobile indicators speed up Ca²⁺ diffusion. The study of Gabso et al. (204), for instance, concluded that D_app is increased by more than a factor of 3 by 100 µM fura-2. In contrast, the low-affinity indicator CaGreen 5N increases D_app by only twofold when used at even twice the concentration (200 µM). This was calculated for the case of nerve axons of cultured Aplysia neurons, which have a low abundance of endogenous buffers. Higher concentrations of endogenous mobile and immobile buffers reduce the influence of Ca²⁺-indicator dyes on D_app. Furthermore, immobile buffers may be heterogeneously distributed in subregions of the cell cytoplasm in some of which large Ca²⁺ gradients are generated. A good example is in muscle, where the major Ca²⁺ buffer, TnC, is only found in the myofilament compartment.

4.7. Modeling of Spatiotemporal Gradients

Quantitative solutions to the combined problem of binding of Ca²⁺ to several buffers and diffusion in a realistic geometry can only be obtained by numerical computation. Early work by Roberts (239) on the [Ca²⁺]_i patterns generated by Ca²⁺ influx through arrays of Ca²⁺ channels in saccular hair cells provided important insights into the interaction between Ca²⁺ channels and Ca²⁺-activated K⁺ channels. This sparked major efforts for the development of software platforms to handle such calculations. Both stochastic tools such as MCell (https://mcell.org/) (240) and deterministic approaches, e.g., CalC (https://web.njit.edu/~matveev/calc.html) (241) have become available. These tools and custom-made software have been used to simulate signals generated by arrays of voltage-dependent Ca²⁺ channels (222, 242–244) and so-called Ca²⁺ sparks or Ca²⁺ puffs (218–220, 245–247). Such calculations provide a complete picture of the complex features, which arise by the combination of buffering and diffusion in a specific geometric environment. They may include the kinetics of Ca²⁺ binding to and dissociation from several ligands. However, images and graphs produced by these software tools are often snapshots that convey limited intuitive understanding. Therefore, it is worthwhile considering approximate solutions to the problem, which are valid for certain limiting scenarios (178). One of these, the so-called “single compartment model” (SCM) considers the case that the structure of interest is small enough that diffusional equilibration in a given compartment is fast on the timescale of interest. Thus, the SCM considers homogeneous concentrations throughout, and mobility of buffers is not an issue. This assumption was made for many of the equations and features discussed so far.

Another limiting case is the so-called “rapid buffer approximation” (RBA), which considers timescales that are long enough that all binding/dissociation reactions are at equilibrium, while there may still be diffusional gradients within the structure of interest. Equation 29, which allows one to calculate an apparent diffusion coefficient, D_app, is an example for the rapid buffer approximation. With the additional assumption of linearity of the buffer, the so-called “linear buffer approximation” (LBA), predictions such as those by Eq. 29 become very simple but are restricted to [Ca²⁺]_i smaller than the K_d of the ligand with the highest affinity.

4.7.1. Approximations for special cases.

Here we describe the assumptions and the use of approximate calculations for the special cases listed above.

4.7.1.1. the single compartment model.

For small structures on the order of a few micrometers, such as small cell bodies and longitudinally homogeneous dendrites, [Ca²⁺] gradients equilibrate on the timescale of 20 ms according to the Stokes–Einstein equation, assuming D_app = 200 µm²/s. The single compartment model (SCM) is typically applied to describe time courses of small global [Ca²⁺]_i transients elicited by action potentials (APs) in presynaptic boutons, dendritic spines, small cell bodies of neurons, and endocrine cells, such as adrenal chromaffin cells. Although the latter have diameters up to 15 µm, a detailed quantitative analysis of [Ca²⁺]_i gradients found that such gradients elicited by short episodes of Ca²⁺ influx largely dissipated within 25 ms (163). The SCM is also applicable to striated muscle cells made up of many identical sarcomeres, each of which can be modeled as a single compartment. Together with the assumption of linearity and rapid equilibration (see the LBA and RBA discussed below), the SCM predicts that [Ca²⁺]_i transients have a rapid rise with an amplitude proportional to the total amount of Ca²⁺ influx and an exponential decay according to

$${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_i\left(t\right)=\text{Δ}{\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_i\mathrm{\hspace{0.17em}·\hspace{0.17em}exp}\left(-t/{\tau }_{\mathrm{Ca}}\right)$$ (30)

with

$$\text{Δ}{\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_i=\frac{q_{\mathrm{Ca}}}{2F·\mathrm{v}·(1+\sum {\kappa }_i)}$$ (31)

where q_Ca is the charge carried by the Ca²⁺ influx, F is the Faraday constant, and v is the accessible volume of the compartment (174). The sum of the denominator in Eq. 31 extends over all Ca²⁺ buffers. The time constant τ_Ca is given by

$${\tau }_{\mathrm{Ca}}=\frac{1+\sum {\kappa }_i}{\gamma }$$ (32)

with γ representing the relationship between the Ca²⁺ extrusion (pump) mechanism and [Ca²⁺]_i (Refs. 174, 248; see also a graphical representation of these equations in FIGURE 3). It is readily seen that the time integral of [Ca²⁺]_i(t), the product of amplitude Δ[Ca²⁺]_i and time constant τ_Ca, is independent of buffering (q_Ca/(2F·v·γ).

4.7.1.2. the rapid buffer approximation.

Most Ca²⁺ buffers of interest have relatively fast binding kinetics (sect. 2.1), with the exception of PV, a CBP with high expression in skeletal muscle and certain neuron types (sects. 7.2 and 9.2), and the exogenous buffers EGTA and EDTA. For studying cellular properties on the millisecond to second timescale, it is, therefore, often convenient to assume that [Ca²⁺]_i is at equilibrium with all buffers (201, 249–254). This approximation misses, of course, some very interesting kinetic features caused by slow buffers, but it simplifies computations enormously (178). In particular in combination with the LBA, discussed below, some important features of buffering and diffusion can be understood intuitively on the basis of very simple equations, such as Eq. 30–32. But the rapid buffer approximation (RBA) can also be extended by including buffer saturation, which expands its range of applications (202). Furthermore, extensions for the case of buffers with two binding sites have been described (188, 241).

4.7.1.3. the linear buffer approximation.

As stated by Eq. 8, the buffer power β of a given ligand with dissociation constant K_d is nearly constant for [Ca²⁺]_i ≪ K_d. For small [Ca²⁺]_i transients around resting values and in the range of a few hundred nanomolar, neglecting buffer saturation may be acceptable and proves helpful in understanding the changes in [Ca²⁺]_i dynamics induced by the presence of buffers. This implies that changes in [Ca²⁺]_i are proportional to changes in total [Ca²⁺] (178, 255–257). Furthermore, Ca²⁺ signals caused by various processes add linearly—as long as the resulting summed response stays well below the K_d of the buffer with the highest affinity. Exploiting these properties, the aggregate signal and expected neurotransmitter release has been calculated for various arrays of Ca²⁺ channels, which becomes particularly simple in the presence of millimolar concentrations of EGTA (Refs. 255, 256, 258, 259; see also sect. 4.7.2 on local domains). As noted above, the linear buffer approximation (LBA) is reasonable for the small changes of [Ca²⁺]_i that typically occur in neurons. For example, from Eq. 8, assuming a buffer K_d of 0.75 µM, the buffer power at a peak [Ca²⁺] of 200 nM will be 71% of that at 50 nM resting [Ca²⁺]_i. In contrast, with the same K_d, the buffer power at the very much higher peak of a cardiac Ca²⁺ transient (1 µM) will be only 24% of that at a resting [Ca²⁺]_i of 100 nM, and the approximation would be problematic (see also FIGURE 3).

The LBA, together with the RBA, leads to simple equations like Eq. 29 for the apparent diffusion coefficient. It was used to describe the diffusional spread in cylindrical (178, 204) and spherical (163) structures. Together with RBA and applied to a single compartment, it leads to a simple description (Eqs. 30–32) of exponentially decaying small [Ca²⁺]_i transients, as frequently observed in neurons.

4.7.2. Local domains.

Many Ca²⁺-dependent processes are triggered very locally by single-molecule events. Prominent examples are the release of neurotransmitters upon the opening of one or only few voltage-dependent Ca²⁺ channels and the generation of “sparks” of [Ca²⁺]_i in muscle due to opening of RyR-operated channels in the SR. Numerical simulations have shown that such local domains, often called “microdomains” or “nanodomains,” of elevated [Ca²⁺]_i rise within microseconds, stay elevated as long as Ca²⁺ channels are open, and decay equally rapidly after channel closure (178, 239, 246, 256, 257, 260–266). Mobile buffers are particularly efficient in shaping such local domains, since diffusion across the small dimensions of these domains is very rapid, such that when buffer binds Ca²⁺ it is rapidly replaced by free buffer. A particularly simple scenario emerges in the presence of slow buffers, such as EGTA (256, 262, 263) or PV (267). Because of their slow Ca²⁺ binding and rapid diffusional replacement they can “penetrate” the local domain without significant changes in their free concentration, [B]₀. Where [B]₀ is high enough, such that its local value does not change appreciably with respect to the bulk [B]₀, the buffer constitutes a spatially and temporally uniform sink, leading to a differential equation with a particularly simple solution for Δ[Ca²⁺](r), the steady-state increment in [Ca²⁺]_i at distance r from the channel mouth (262):

$$\text{Δ}\left[\mathrm{C}{\mathrm{a}}^{2+}\right](r)=\frac{i_{\mathrm{Ca}}}{4\pi Fr{D}_{\mathrm{Ca}}}·\exp \left(-r/\lambda \right)$$ (33)

where i_Ca is the single-channel calcium current, F is the Faraday constant, and λ is the length constant of the domain, which is given by

$$\lambda =\sqrt{D_{\mathrm{Ca}}/\left(k_{\mathrm{on}}\mathrm{\hspace{0.17em}·\hspace{0.17em}}{\left[\mathrm{B}\right]}_0\right)}$$ (34)

Here, k_on is the apparent Ca²⁺ binding rate constant of the buffer (178, 262). The time constant, τ, of rise and decay of the local domain is given by

$$\tau =1/\left(k_{\mathrm{on}}\mathrm{\hspace{0.17em}·\hspace{0.17em}}{\left[B\right]}_0\right)$$ (35)

These equations hold for the case when the slow buffer is the dominating one. They do not consider stationary buffers. In the presence of stationary, very fast-binding low-affinity buffers, for which the RBA and the LBA apply, a steady-state solution for free [Ca²⁺]_i very similar to that in the absence of stationary buffers is obtained. The characteristic time constant, however, has to be increased by a factor of 1 + κ_s (268), where κ_s is the sum of values for all such stationary buffers. It should be noted that in general diffusion is slowed down in the presence of stationary buffers. Nevertheless, the diffusion coefficient appearing in Eqs. 33 and 34 is that of free Ca²⁺, since the equations describe the steady state for which fixed buffers are in equilibrium with free Ca²⁺. Therefore, the rates that represent binding and dissociation of Ca²⁺ to/from fixed buffers in the respective differential equations cancel each other. Values for λ and τ × (κ_s + 1) for various concentrations of EGTA and PV, assuming κ_s = 21, are given in TABLE 4 (248). These are meant to provide an “order-of-magnitude” idea about the extent and dynamics of local domains in the presence of a dominating slow buffer.

Table 4.

The dependence of length constant and time constant of local [Ca²⁺] domains

Buffer Conc, mM	λEGTA, µm	τEGTA, ms	λPV, µm	τPV, ms
1	0.22	5.02	0.27	7.10
2	0.16	2.51	0.19	3.55
5	0.10	1.00	0.12	1.42
10	0.07	0.50	0.084	0.71
20	0.05	0.25	0.060	0.35

Length constant (λ) and time constant (τ) for EGTA and parvalbumin (PV) were calculated, using Eqs. 34 and 35 under the following assumptions: diffusion coefficient of free Ca²⁺ (D_Ca) = 220 µm²/s; apparent association rate constants k_on,app = 4.38 µM⁻¹·s⁻¹ for EGTA (248) and k_on,app = 3.1 µM⁻¹·s⁻¹ for PV at a Mg²⁺ concentration of 1 mM. For the calculation of k_on,app, we assumed 1 binding site per molecule to be relevant for the buildup and decay of the local intracellular calcium concentration ([Ca²⁺]_i) domains with k_on = 103 µM⁻¹·s⁻¹ (27). Time constants were further multiplied by a factor of 22 to include the effects of a fast, immobile buffer with a buffering power of 21 (248).

Equation 33 provides intuitive insight: The term $\frac{i_{\mathrm{Ca}}}{4\pi Fr{D}_{\mathrm{Ca}}}$ represents the solution in the absence of buffers and reflects diffusion of Ca²⁺ from a point source in homogeneous medium. The effect of the slow buffer at steady state is exclusively contained in the length constant, where it appears as the so-called “buffer product” k_on × [B]₀. The diffusion coefficient of the slow buffer does not appear in these equations, since it is assumed that diffusion is fast enough to secure a constant concentration of free buffer within the domain. These approximations do not depend on the RBA and LBA but, importantly, on the assumption regarding nondepletion of free slow buffer. Clearly, the slow buffer is not at equilibrium with [Ca²⁺]_i within that domain. Nevertheless, local domains in the presence of sufficiently high concentrations of free slow buffer superimpose linearly as long as their combined Ca²⁺ load does not deplete free buffer (see also sect. 9.4).

The validity of these conclusions about local domains has been confirmed by solving the underlying equations analytically (269) and by numerical computation (270). In these calculations, several buffer species were included and it was shown that very close to the site of entry Ca²⁺ ions are first captured by the buffer with the highest buffer product (k_on × [B]₀). This was ATP, which was assumed to be present at a free concentration of 0.17 mM. However, as a low-affinity buffer, ATP rapidly releases Ca²⁺ again. During cycles of binding and unbinding from ATP, buffers with lower buffer product can capture Ca²⁺. If they are of higher affinity, they will retain the Ca²⁺ ions for longer times, while moving away from the Ca²⁺ source. In the end, the buffer species with the highest affinity will carry the bulk of Ca²⁺, according to equilibrium conditions. The resulting spatial profile of the local domain decays multiexponentially, unless the buffer with the highest affinity also has the highest buffer product. Numbers given in TABLE 4 assume that this is the case for EGTA and PV, respectively.

The influence of small organic molecules with low affinity but higher buffer product on the properties of local domains has largely been neglected in the literature so far, despite their important role in shaping these domains and likely consequences for physiological processes (see sect. 9.4 and Ref. 60 on the effect of gluconate on neurotransmitter release).

4.7.3. Diffusion in a cylinder.

Elongated cells or subcellular compartments such as axons, dendrites, cardiac myocytes, and muscle fibers often have narrow diameters such that diffusional gradients along their cross section are small because of rapid equilibration. However, gradients may be very pronounced longitudinally. In this case, the spread of Ca²⁺ along the longitudinal axis can be conveniently described by simple analytical expressions, Additionally, if both rapid buffer approximation (RBA) and linearity of buffers (LBA) are assumed, the transport of Ca²⁺ along the cylinder will follow the classical one-dimensional diffusion equation with D_app according to Eq. 29 (178, 202, 204). If a leak of Ca²⁺ across the cylinder wall is considered, the same simplifying assumptions (RBA and LBA) lead to an equation analogous to that for propagation of voltage in a leaky cable (268). Using this simplified formalism, Gabso et al. (204) attempted to measure D_app in largely intact axons of the snail Aplysia. They locally injected, via a microelectrode, boluses of Ca²⁺ into uniform lengths of axons, which had previously been loaded with defined concentrations of indicator dyes. Analyzing images of Ca²⁺ spread as a function of position and time after injection, they found that the local [Ca²⁺]_i elevation had a Gaussian shape, which spread and decayed rapidly. According to theory, the square of the half-width of that Gaussian should be proportional to the time since the Ca²⁺ injection and the apparent diffusion coefficient, D_app. This allowed evaluation of buffering power and D_app for various concentrations of the indicator dye. To obtain estimates for the case of an unperturbed cell, the results were extrapolated to zero indicator dye. This yielded values for D_app (<16 µm²/s) and for κ_s (<60). Unfortunately, only upper bounds could be provided in this analysis, since the extrapolation depended very much on the measurements with the lowest indicator concentrations, which were very noisy. The finding that D_app is much smaller than D_Ca points toward the presence of fixed buffers that retard diffusion. On the other hand, the upper bound (16 µm²/s) is higher than the lowest possible value, D_Ca/(κ_s + 1) = 223 µm²/s/61 ≈ 3.7 µm²/s, which would be expected if all endogenous buffers were immobile. Thus, it can be concluded that mobile buffers must also be present.

In the light of the above considerations, we now turn to the role of buffers in specific instances of physiology and pathology. Most of the quantitative work has been carried out in nerve and muscle, but, although there are tissue-specific differences in buffering, the general principles will apply throughout.

5. THE RED BLOOD CELL

Red blood cells differ from all other cell types in that their total Ca²⁺ content is unmeasurably low. In human red blood cells the Ca²⁺ content extractable by ionophores and chelator treatments amounts to <1 μmol/(L packed cells) (271). Most mammalian red blood cells contain no organelles, making it simpler to measure their cytoplasmic buffering than is the case in many other cell types. An early study measured Ca²⁺ binding at relatively high levels of Ca²⁺ (20 µM to 1.4 mM) in suspensions of freeze-thawed red blood cells. A K_d of ∼0.3 mM was reported (272). Subsequent work measured Ca²⁺ buffering in lysed red blood cells (thereby preserving any contribution from cellular contents) and found a linear dependence of bound on free Ca²⁺, over the range 0.1 to 3 mM, with bound and free Ca²⁺ being approximately equal. When the cell constituents were removed by dialysis, all the bound Ca²⁺ was lost, suggesting that cell membranes do not contribute appreciably to buffering (273). Because these studies were performed at Ca²⁺ levels much greater than normal cytoplasmic, higher-affinity buffers would have been saturated and their contribution would have been overlooked.

Buffering was measured in intact red blood cells by controlling intracellular free Ca²⁺ with an ionophore (A23187) while measuring total intracellular Ca²⁺ with ⁴⁵Ca (274). Again, total Ca²⁺ was proportional to free with a buffer power of only 2–3. A subsequent study (275) measured buffering at [Ca²⁺]_i levels as low as 100 nM and again found a linear (nonsaturable) binding, attributed to binding to hemoglobin and other proteins, with bound Ca²⁺ equal to ∼35% of free, a very low buffer power. In addition, there was evidence of a saturable buffer with K_d of ∼8 µM and maximum capacity of ∼100 µM, thereby contributing a buffer power of ∼12 at 100 nM [Ca²⁺]_i. A tentative suggestion for the identity of this component was calpromotin, now known as Peroxiredoxin 2, a major antioxidant (276). CaM was also considered, but its concentration is too low to account for more than a small fraction. It should, however, be noted that the saturable buffer was identified by subtracting the nonsaturable component from the total, and, as pointed out by the authors, this limited the precision of the estimation. Importantly, no evidence was found for high-affinity buffers with K_d values below 1 µM. This contrasts with the tissues reviewed in subsequent sections, where the major buffer power is provided by buffers with such low K_ds.

The low Ca²⁺ buffering of the red blood cell has been suggested to be physiologically important as it means that small Ca²⁺ fluxes can produce large changes of [Ca²⁺]_i. Given the very limited metabolic reserves of this cell, minimizing these fluxes, and the consequent demand for ATP to pump Ca²⁺ out of the cell, is important for the economy of the cell. Human red cells have a programmed circulatory life span of ∼120 days (277). As the cells deform when traversing capillaries, the mechanosensitive PIEZO1 channels of the cell membrane (278, 279) become transiently activated, allowing brief episodes of Ca²⁺ influx. The low calcium buffering power of the cells allows this minimal Ca²⁺ influx to elevate [Ca²⁺]_i sufficiently to activate Ca²⁺-sensitive K⁺ channels, leading to progressive KCl and water loss. This explains the physiological mechanism behind the progressive increase in the density of aging red cells in the circulation and highlights the important role of low Ca²⁺ buffering by minimizing the magnitude and maximizing the speed of the leak-restorative Ca²⁺ fluxes by the Ca²⁺ pump during each capillary transit (280–282).

The low buffer power of the red blood cell contrasts with the much higher values (by a factor of 10–100 fold) in the cells and tissues considered in subsequent sections. A major aim of these sections is to identify the substances responsible for this difference of buffering and the physiological roles of the greater buffering.

6. CARDIAC MUSCLE

Each heartbeat is activated by a systolic increase of [Ca²⁺]_i, derived from Ca²⁺ entry via the L-type Ca²⁺ channel and by Ca²⁺ release from the sarcoplasmic reticulum through the ryanodine receptor (RyR). The amplitude of this free Ca²⁺ transient is of the order of 1 µM and results from an increase of total cytoplasmic [Ca²⁺] of ∼100 µM. Changes of the size of the Ca²⁺ transient are the major factor regulating contraction strength (see Ref. 81 for review). For the heart to work as a pump it must also relax during diastole; Ca²⁺ is lowered back to resting levels via a combination of uptake back into the SR via SERCA and pumping out of the cell (largely via Na/Ca exchange, NCX). Ca²⁺ buffers will therefore affect both the amplitude and rate of decay of the Ca²⁺ transient.

6.1. Measurements of Buffer Power in Cardiac Muscle

There are many direct measurements of Ca²⁺ buffering in intact myocytes that can be compared with the measured concentrations of potential buffers. Initial estimates were obtained from Ca²⁺ titration of isolated myofilaments indicating that these alone could contribute a buffering power of at least 10 (283). Similar studies on cardiac homogenates gave a value of 70 (284), and work on permeabilized myocytes showed that cytoplasmic Ca²⁺ buffering could be represented by a buffer with a K_d of 0.42 µM at a concentration of 78 µM as well as a lower-affinity component (285). The higher-affinity component would contribute a buffer power of ∼120 at 0.1 µM [Ca²⁺]_i. Subsequent studies have measured cytoplasmic buffering in intact cells by comparing changes of [Ca²⁺]_i measured with a fluorescent indicator to those of total Ca²⁺ calculated from the integral of a membrane current. One approach uses the L-type Ca²⁺ current activated by depolarizing pulses (286, 287). A related technique applies caffeine to release Ca²⁺ from the SR. The Ca²⁺ is then pumped out of the cell largely by the electrogenic Na/Ca exchange (NCX), and integrating the NCX current gives a measure of the change of total Ca²⁺ (254). This method requires correction for that fraction of Ca²⁺ that is transported by the electroneutral PMCA. In rat ventricular myocytes, the L-type Ca²⁺ current method provided a K_d of 0.96 µM and a B_max of 123 µM (287) whereas the NCX method gave 0.49 µM and 149 µM, respectively. Various sources of errors need to be considered when comparing these values. First, the cytoplasmic volume must be measured to convert the measured total change of Ca²⁺ to a concentration. Second, the accuracy depends on that of the measurement of [Ca²⁺]_i. There are at least two potential problems: 1) Calibrating the measured fluorescence signals in terms of absolute [Ca²⁺]_i requires knowledge of the minimum and maximum fluorescence as well as the K_d of the indicator dye (36), and these values can be affected by the cytoplasmic environment (288–292). Although this is a particular problem for single-wavelength indicators such as the Fluo family, it is not trivial even for ratiometric indicators. Indeed, the Fluo indicators have the advantage that fluorescence is essentially zero in the absence of Ca²⁺, meaning that calibration only requires knowledge of the maximum fluorescence and K_d. The literature shows a range of values assumed for even the most used indicators (288–292). 2) Accurate calculation of the K_d of the buffer requires measurements over a wide range of [Ca²⁺]_i, certainly much greater than the K_d value. That this is not always possible complicates, for example, establishing whether buffering is cooperative. Indeed, many cardiac buffer curves can be fit reasonably well by a linear regression. It would also be useful to make measurements at values of [Ca²⁺]_i below the normal resting level. These issues should not, however, affect measurement of the buffer power over the range of [Ca²⁺]_i studied, which implies that such measurements are probably most useful for comparing buffering between two conditions. Absolute values need to be treated with caution, a problem when trying to compare with the measured concentrations of cellular CBPs.

[Ca²⁺]_i in the bulk cytoplasm in cardiac muscle is generally in the range 0.1 to 1 µM. The major buffers in cardiac muscle are listed in TABLE 5. This follows from previous compilations (81, 294). For simplicity, we ignore the modest contributions from the sarcolemmal binding sites. The top five rows of TABLE 5 show the faster buffers and the lower two rows the slower (see sect. 6.1.3). At 0.1 µM [Ca²⁺]_i, the total buffer power provided by the faster buffers is predicted to be ∼140, in reasonable agreement with the experimental values reviewed above. Importantly, the bulk of the buffering is provided by immobile buffers, with the mobile buffers (calmodulin, carnosine, and ATP) contributing <10%.

The effects of experimentally altering Ca²⁺ buffering in cardiac muscle are shown in FIGURE 12 (199). Here, buffering was first increased by adding a photolabile Ca²⁺ chelator. Buffering was then decreased by photolysis. As expected from FIGURE 7, the fast buffer nitr-5 decreases the amplitude and slows the kinetics of the Ca transient (FIGURE 12A). In contrast (FIGURE 12B), the slow buffer NP-EGTA results in a biphasic decay (cf. FIGURE 8 and FIGURE 9).

6.1.1. Contribution of TnC and SERCA.

As shown in TABLE 5, TnC is expected to be the major buffer at diastolic levels of [Ca²⁺]_i. As discussed in sect. 2.5.1.1, TnC has two classes of Ca²⁺ binding sites: 1) the regulatory Ca²⁺ site, which has a K_d of ∼0.6 µM, and 2) a pair of nonspecific “Ca²⁺/Mg²⁺” sites with a much lower K_d for both Ca²⁺ (0.003 µM) and Mg²⁺ (3.3 µM) (discussed in sect. 6.1.3). At diastolic Ca²⁺ levels, these sites bind significant amounts of Ca²⁺ and Mg²⁺. Experimental studies have investigated the effects of increasing the binding affinity of the regulatory sites of TnC with a single amino acid substitution (L48Q). With an adenoviral technique, ∼20% of the TnC in a rat heart was replaced. As expected, this increased myocyte contraction but did not alter the rate of decay of the [Ca²⁺]_i transient (295), suggesting little effect on buffering. There are two possible explanations. 1) If TnC accounts for slightly less than 50% of total buffering (TABLE 5), then 20% replacement will decrease total buffering by only 10%, resulting in only a small effect on the decay of the [Ca²⁺]_i transient. 2) A decrease of K_d will increase buffering at low and decrease it at high [Ca²⁺]_i (Eq. 14), leading to a mixed effect on relaxation. Although both factors will presumably contribute, the importance of the former is supported by a subsequent study expressing a higher concentration of the same mutation in mice myocytes (50% replacement) resulting in slowing of the decay of the [Ca²⁺]_i transient (296). A recent study has emphasized the importance of TnC in buffering by comparing buffering and Ca²⁺ handling in myocytes from the right and left ventricle of rat hearts. This showed a lower buffer power in the right ventricle that was associated with, and suggested to result from, lower expression of TnC (297). The other major contribution to buffering is expected to come from binding to SERCA (94). Direct evidence for a role of SERCA in buffering comes from the observation that inhibiting it with thapsigargin decreases buffer power by 16% in mouse ventricular myocytes (298).

6.1.1.1. cooperative buffering.

The cooperative nature of Ca²⁺ binding to some buffers has not generally been considered in cardiac Ca²⁺ buffering. SERCA binds Ca²⁺ cooperatively, and this would be expected to produce a bimodal dependence on [Ca²⁺]_i of the buffer power contributed by fast buffers, with buffer power being low at both low and high [Ca²⁺]_i (TABLE 5). This contrasts with the simple hyperbolic buffer curves shown in the literature, where buffer power decreases with increasing [Ca²⁺]_i (180, 254, 287, 297, 299, 300). It is therefore possible that TABLE 5 overestimates the contribution of cooperative buffers. Equally, the experimental studies may have insufficient accuracy to resolve sigmoidal binding curves. A limitation of these studies is the lack of data below the normal resting [Ca²⁺]_i of ∼100 nM, and it will be important to obtain this. As pointed out in sect. 3.3, despite having only one regulatory site TnC may also show cooperativity due to interactions along the thin filament. Such effects would be expected to be different between isotonic and isometric contractions (sect. 6.2.3) and, given the lack of detailed information, are ignored in TABLE 5.

6.1.2. The role of other fast buffers.

TABLE 5 shows that the buffer power provided by both SERCA and TnC falls as [Ca²⁺]_i increases to micromolar levels. During Ca²⁺ release, the Ca²⁺ concentration in the dyads may reach levels of up to 100 µM (55). Even at 10 µM [Ca²⁺]_i, the combined contribution of TnC and SERCA is predicted to produce a buffer power of only 0.5. This raises the question as to what, if anything, provides buffering at this high [Ca²⁺]_i. TABLE 5 suggests that total fast buffer power is ∼10, contributed largely by CaM, ATP, and carnosine. In other words, these buffers, which make only a modest fractional contribution to buffering at diastolic and systolic levels, may be important during Ca²⁺ release. Not only will they buffer Ca²⁺, but ATP and carnosine will accelerate its diffusion away from the release sites (TABLE 3). However, as mentioned in sect. 2.4.1, there is controversy as to whether carnosine buffers Ca²⁺ appreciably under physiological conditions. More work is required to investigate carnosine’s buffering role and the extent to which this may be altered, for example, in heart failure and other disease.

6.1.3. The role of “slow” buffers.

Above, we have ignored the slower buffers, including the nonspecific or Ca²⁺/Mg²⁺ sites on TnC as well as Ca²⁺ binding to myosin. The nonspecific sites on TnC are present at twice the concentration of the regulatory sites and have a high affinity for Ca²⁺ with an apparent K_d for Ca²⁺ (in the presence of 1 mM Mg²⁺) of ∼100 nM (78, 79, 301). This means that they are ∼50% occupied by Ca²⁺ and contribute a buffer power of ∼350 at a diastolic level of Ca²⁺ of 100 nM. However, the relevance of this buffer power will depend on the kinetics and, specifically, on whether appreciable binding occurs during a [Ca²⁺]_i transient. This is illustrated by the difference between the instantaneous and steady-state values of buffer power in TABLE 5. Two experimental studies have provided very different measurements as exemplified by values for k_off of 0.33 s⁻¹ (78) and 0.032 s⁻¹ (79). This 10-fold difference in Ca²⁺ unbinding kinetics results in different predictions for the time course of Ca²⁺ occupancy of the sites as shown in FIGURE 13 (78, 79, 301). The faster kinetics predict some beat-to-beat change of bound Ca²⁺ and therefore buffering during the Ca²⁺ transient. In contrast, the slower kinetics result in essentially no beat-to-beat changes but a gradual increase of bound Ca²⁺ at higher frequencies. Either kinetic may lead to significant problems in the interpretation of experimental studies. For example, maneuvers that increase the time-averaged level of [Ca²⁺]_i will result in a slow loading of these sites (82). This will occur when stimulation is resumed after a quiescent period (FIGURE 13) or during the application of many agents that increase systolic [Ca²⁺]_i. On cessation of stimulation, the Ca²⁺ gradually dissociating from these slow buffers is expected to keep both cytoplasmic and SR Ca²⁺ concentrations elevated for a period. The subsequent gradual decrease of [Ca²⁺]_i might erroneously be ascribed to movements of Ca²⁺ across SR or surface membranes. We are unaware of work investigating this possibility. The other major Ca²⁺ binding site on the myofilaments, which can also bind Mg²⁺, is on myosin, with a high apparent K_d for Ca²⁺ of ∼9 µM. As shown in FIGURE 13, Ca²⁺ binding to myosin is also slow, and the high K_d predicts that the amount of Ca²⁺ bound, even during repetitive stimulation, is modest and is unlikely to make a major contribution to total buffer power.

FIGURE 13.

Simulation of Ca²⁺ binding to slow sites in cardiac muscle. The model simulates the effects of cytoplasmic Ca²⁺ transients. Traces show (from top to bottom) intracellular calcium concentration ([Ca²⁺]_i); Ca²⁺ bound to the regulatory site of Troponin-C (TnC); Ca²⁺ bound to the nonspecific sites on TnC, comparing rate constants taken from Refs. 78, 301 (solid) and Ref. 79 (dashed); Ca²⁺ binding to myosin. Note the different vertical scales for TnC and myosin binding. The model shows the effect of (from left to right) a single stimulus; 1-Hz stimulation; and 2-Hz stimulation. The free Ca²⁺ transient was modeled with an instantaneous increase from 0.1 to 0.8 µM followed by an exponential decay (time constant 0.2 s).

6.1.4. SR buffers.

The above section has concentrated on the cytoplasmic buffers. The major Ca²⁺ buffer in the SR is calsequestrin, CSQ2. As well as acting as a buffer, it also interacts with triadin and junctin in regulating the RyR (302). The Ca²⁺ buffering properties of the SR have been measured in rabbit ventricular myocytes by measuring free SR [Ca²⁺] with Fluo-5N and estimating changes of total SR [Ca²⁺] from the corresponding changes of total cytoplasmic Ca²⁺ (as assessed from changes of [Ca²⁺]_i and cytoplasmic buffering). The buffering could be represented by a single buffer present at a concentration of 2.5 mM with a K_d of ∼0.6 mM (Ref. 303; see also Ref. 293). Even at very low [Ca²⁺], this would give a buffer power of only ∼4. With a loaded SR (typical free [Ca²⁺] of ∼1 mM) there will be 1.6 mM bound Ca²⁺. Two points are worth emphasizing: 1) The buffer power of the SR is much less than that of the cytoplasm. 2) The low buffer power means that complete removal of the major buffer (CSQ2) only decreases total Ca²⁺ by ∼60% and significant Ca²⁺ release from the SR can occur in the absence of CSQ2. Indeed, the CSQ2 knockout (KO) mouse shows normal cardiac contractility, and the loss of CSQ2 is compensated for by an increase of SR volume (304). As discussed in sects. 3.3.1 and 7.5, in skeletal muscle the binding of Ca²⁺ is cooperative and promoted by polymerization of CSQ2. In contrast, there is no evidence for cooperativity in the cardiac measurements (303). Although this may simply reflect a lack of sufficiently precise data, it is also possible that the low concentration of CSQ2 decreases the probability of polymerization. Further work is required to look for such cooperativity. Increasing the amount of CSQ2 prolongs Ca²⁺ release from the SR, an effect attributed to maintaining free SR content (305). Some mutations have been shown to decrease Ca²⁺ binding capacity (306). A decrease in CSQ2 concentration or mutations results in abnormal Ca²⁺ release from the SR, and this is one of the causes of the inherited arrhythmia syndrome CPVT (catecholaminergic polymorphic ventricular tachycardia) (307). At least in transgenic mouse models, removal of CSQ2 leads to a compensatory increase of another ER/SR Ca²⁺-binding protein, calreticulin (308). Calsequestrin is discussed more extensively in the context of skeletal muscle (sect. 7.5).

6.2. Factors Affecting Cardiac Calcium Buffering

Cardiac contraction is controlled by the amplitude of the systolic Ca²⁺ transient, which is generally assumed to be regulated by the size of the Ca²⁺ fluxes into and out of the cytoplasm. An important, and unresolved, issue is the extent to which changes of the amplitude of the [Ca²⁺]_i transient seen in both physiology and disease may also result from changes of Ca²⁺ buffering as opposed to those of Ca²⁺ fluxes. In other words, is Ca²⁺ buffering constant over time? We now consider some of the factors that may alter buffering. These include changes of [Ca²⁺]_i as well as of the properties of the buffers.

6.2.1. Calcium concentration.

As discussed above (sect. 3.1) and also previously (82, 309, 310), for noncooperative buffers the available buffer power is affected by the level of [Ca²⁺]_i, tending to decrease as [Ca²⁺]_i increases (see TABLE 5). This will have two consequences: 1) An increase of diastolic [Ca²⁺]_i will decrease buffer power. This raises the possibility that the positive inotropic effects of maneuvers that increase diastolic [Ca²⁺]_i such as increased stimulation rate (311–313) and the application of cardiac glycosides (314) include a contribution from decreased Ca²⁺ buffering. Direct experimental work is required to assess this. The decreased buffer power at elevated [Ca²⁺]_i also complicates comparing buffer power between different animals, for example in the context of heart failure versus control. It is important to exclude the possibility that changes of buffer power are simply a consequence of differences of diastolic [Ca²⁺]_i as opposed to alterations of the buffer properties. This is not helped by the relative paucity of absolute measurements of diastolic [Ca²⁺]_i in different species (for review see Ref. 315). 2) More generally, Ca²⁺ concentration-dependent changes in Ca²⁺ buffer power are predicted to contribute to shaping the time course of [Ca²⁺]_i transients as suggested in sect. 4.3 and FIGURE 10 and FIGURE 11. For example, the fact that the rate constant of decay of the Ca²⁺ transient increases with the amplitude of the transient is at least in part due to decreased buffering at increased [Ca²⁺]_i (316). Another example is the initial rapid phase of the decay of the [Ca²⁺]_i transient, which can be explained by the decreased buffer power at elevated [Ca²⁺]_i since a given rate of total Ca²⁺ removal by SERCA produces a larger fall of [Ca²⁺]_i (197).

6.2.2. Phosphorylation of buffers.

A further question is whether the properties of cardiac cytoplasmic Ca²⁺ buffers can vary at fixed [Ca²⁺]_i. The apparent K_ds for Ca²⁺ of the two major buffers (SERCA and TnC) are regulated by phosphorylation [of phospholamban and troponin I (TnI), respectively], raising the possibility that this will also affect buffering. An experimental study, however, found no effect of beta adrenergic stimulation on Ca²⁺ buffering (298), and it was suggested that this resulted from the fact that, while phosphorylation of phospholamban increases the Ca²⁺ affinity of SERCA phosphorylation of troponin decreases its affinity, with the net result being no change. It should, however, be noted that previous work has not explicitly considered that the effects of changes of buffer K_d are expected to depend on the level of [Ca²⁺]_i (sect. 3.2). It is possible that the lack of change of buffer power could reflect a smearing of opposite effects above and below the value of [Ca²⁺]_i where changing K_d has no effect. Precise measurements of buffer power over a broader range of [Ca²⁺]_i are required.

6.2.3. Effects of muscle length.

One special feature of TnC is that its location on the myofilaments makes it potentially sensitive to force development, with an increase of force increasing the affinity of Ca²⁺ binding. Direct measurements of [Ca²⁺]_i in cat papillary muscles showed that rapid stretches and releases resulted in transient decreases and increases of [Ca²⁺]_i consistent with Ca²⁺ being taken up by or released from TnC, respectively (317, 318). A maintained increase of muscle length was found to accelerate the initial rate of decay of the [Ca²⁺]_i transient and slow down the final phase, with both effects attributed to increased affinity of Ca²⁺ binding to troponin (319, 320). This is consistent with the analysis in sect. 3.2 and the simulations of FIGURE 10 illustrating that increased buffer affinity decreases buffering at higher [Ca²⁺]_i but increases it at lower [Ca²⁺]_i. The former effect will accelerate the initial decay and the latter prolong the final phase (see also Ref. 321). Stretch has previously been reported to increase Ca²⁺ release from the SR (322). A recent study showed that the rise of [Ca²⁺]_i was increased by the actomyosin inhibitor blebbistatin (sect. 6.2.5), suggesting that, in the absence of blebbistatin, stretch increases the binding affinity of TnC, thereby attenuating the rise of [Ca²⁺]_i (323).

6.2.4. Effects of pH on cardiac Ca²⁺ buffering.

As mentioned in sect. 2.5.1.2, changes of pH may significantly affect Ca²⁺ binding to buffers, either because of direct competition between protons and Ca²⁺ for binding sites or via effects on the tertiary structure of the buffers. An example is the decrease of Ca²⁺ binding to troponin produced by acidification (324). This interaction provides a potential mechanism linking changes of intracellular pH to those of [Ca²⁺]_i. It is important to consider the relative magnitude of the effects on intracellular pH and [Ca²⁺]_i. For example, a displacement of 20 µM total Ca²⁺ from TnC and its one-to-one replacement by protons will elevate [Ca²⁺]_i by 200 nM (given a Ca²⁺ buffer power of 100). In contrast, the typical intracellular pH buffer power is 30 mM per pH unit (325), so the absorption of 20 µM protons would be expected to change intracellular pH by 0.02/30 ≈ 0.0007 pH units. Although the change of [Ca²⁺]_i would be easily measurable, that of pH would not. An acid-induced increase of [Ca²⁺]_i has been measured in cardiac muscle (93, 194). However, as pointed out previously (82, 326) and in sect. 4.1, buffers cannot change the steady-state level of [Ca²⁺]_i and one would expect that the Ca²⁺ ions released would be pumped out of the cell, thereby restoring [Ca²⁺]_i. In this context, it is worth noting that effects of protons on various membrane channels including acid-sensing ion channels (ASICs) and TRPV channels have been shown to contribute to changes of [Ca²⁺]_i in rat ventricular myocytes (327) and that protons also affect NCX activity (328). A further complication arises from the finding that changes of intracellular pH of the order of 0.4 pH units do not produce measurable changes of buffer power (329). Again, this may be a consequence of the fact that the direction of the effect of a given change of K_d on buffer power is opposite at high and low [Ca²⁺]_i (see sect. 3.2). A resolution of this issue will require further studies measuring buffer power as a function of both [Ca²⁺]_i and pH.

6.2.5. Effects of modulators of actin-myosin interactions.

Given the importance of TnC to buffering, it would not be surprising if modulating Ca²⁺ binding directly or via interaction with other sarcomeric proteins affected buffering. Compounds such as EMD57033 are contractile sensitizers that increase TnC’s apparent affinity for Ca²⁺. In mouse ventricular myocytes, EMD57033 had no effect on B_max but decreased the buffer K_d (180). A recent study investigated its effects on Ca²⁺ buffering in cardiac myocytes derived from human induced pluripotent stem cells (iPSCs). Again, there was no effect on B_max, and the K_d decreased from ∼0.47 to 0.25 µM (300). This was accompanied by a slowing of the decay of the [Ca²⁺]_i transient. The authors also calculated the rate of decrease of total Ca²⁺ from the measured buffering, which was unaffected by the drug, consistent with the conclusion that the slowing of decay of free Ca²⁺ is due to buffering. Strictly speaking (see sect. 3.2), one would expect the decrease of K_d to only increase buffer power at [Ca²⁺]_i below the geometric mean of the K_ds (here 0.34 µM), with decreased buffering and therefore a faster decay of [Ca²⁺]_i above this level. It would therefore be interesting to study the effect of EMD57033 over a wider range of [Ca²⁺]_i. The effects of such contractile sensitizers are of more than academic interest, as members of this group such as levosimendan (330) and omecamtiv mecarbil (331) have been developed for use in heart failure.

In contrast, other drugs decrease actin-myosin interactions, and one example is the myosin ATPase activity inhibitor blebbistatin (332). This can decrease the apparent affinity for Ca²⁺ to activate force (333, 334). One might therefore expect that it would lower the affinity for Ca²⁺ buffering by TnC, but we are unaware of any direct measurements. Whereas blebbistatin is simply an experimental tool, another inhibitor, mavacamten (see Ref. 335 for review), has been developed as a treatment for hypertrophic cardiomyopathy (336). As mentioned in sect. 6.4, mavacamtem decreases the affinity for Ca²⁺ activating contraction (337), and it is therefore also important to characterize its effects on Ca²⁺ buffering.

6.3. Ca²⁺ Buffers and Ca²⁺ Diffusion in Cardiac Muscle

As discussed in sect. 4.5, mobile Ca²⁺ buffers accelerate the diffusion of Ca²⁺. The major cardiac Ca²⁺ buffers, SERCA and TnC, are immobile, and the best-characterized mobile buffers are CaM and ATP. As we have seen above, the contribution of CaM to diffusion of Ca²⁺ is negligible, particularly since the majority of CaM is bound. With the values of TABLE 3, the flux of Ca²⁺ carried by Ca-ATP will be ∼1.4 times that of free Ca²⁺ over a wide range of [Ca²⁺]_i, thereby making a significant contribution. It is also worth noting that there is up to 20 mM carnosine and other histidyl dipeptides in cardiac muscle (211). As mentioned in sect. 2.4.1, there is controversy as to their degree of Ca²⁺ binding, but, if significant, these will also contribute greatly to Ca²⁺ diffusion.

What effect will such Ca²⁺ diffusion mediated by mobile buffers have? As discussed below for skeletal muscle (sect. 7.6), diffusion is required for Ca²⁺ ions to move from the sarcoplasmic reticulum release sites to the TnC on the myofilaments (34, 338), and therefore the mobile buffers, in particular ATP, will accelerate activation of the myofilaments. We are unaware of any experimental evidence in cardiac muscle, and it will be important to obtain this. This effect of mobile buffers will promote cardiac contractility. Set against this, however, is the fact that excitation-contraction coupling depends on local Ca²⁺ release, observed as Ca²⁺ sparks. Larger [Ca²⁺]_i transients result from the summation of closely spaced individual Ca²⁺ sparks (339). These sparks are spatially independent, and this is important for controlling cardiac contractility in a stable way (340). Increasing Ca²⁺ diffusion will potentially increase the spatial extent of Ca²⁺ sparks and remove this independence. One consequence of loss of spatial independence of sparks is the generation of propagating Ca²⁺ waves. These are not seen normally but occur under conditions where Ca²⁺ spark frequency (341) and leak from the SR are increased, because of either an increase of SR Ca²⁺ content or alterations in the properties of the RyR (for review see Ref. 342). Modeling has suggested that such waves can propagate by a “fire-diffuse-fire” mechanism. Importantly, the speed of propagation of the waves is proportional to the apparent diffusion constant for Ca²⁺ (343) and would therefore be expected to be increased by mobile buffers. In particular, at least for IP₃-induced Ca²⁺ waves, for a given buffer concentration calculations suggest that the more mobile the buffer, the faster the wave propagation velocity (344). Another modeling study predicted that Ca²⁺ waves are more likely to appear at low cytoplasmic buffer concentrations and that, at a given buffer concentration, the higher the K_d for the buffer the more likely are waves (345). At least at low [Ca²⁺]_i, high K_d and low buffer concentration will both decrease buffer power, suggesting that increased buffering decreases wave occurrence. It would be useful to extend this modeling to consider mobile buffers.

6.4. Ca²⁺ Buffering in Cardiac Disease

Several studies have examined whether Ca²⁺ buffering changes in cardiac disease. One example is atrial fibrillation, the most common cardiac arrhythmia (346). When this was simulated with rapid electrical pacing in rabbits, a large (2- to 3-fold) increase of buffer power was observed that was attributed to decreased phosphorylation of TnI decreasing the K_d for Ca²⁺ binding to TnC (299). This was accompanied by (and suggested to cause) a failure of the Ca²⁺ release to propagate from the periphery to the interior of the cell. A threefold decrease of K_d would increase buffer power by the same factor at low [Ca²⁺]_i (sect. 3.1). At higher [Ca²⁺]_i, however, buffer power would increase by less and would be expected to decrease above a [Ca²⁺]_i given by the geometric mean of the K_ds in control and rapid pacing. This effect on propagation could be mimicked by the addition of BAPTA to increase buffering. Addition of EGTA similarly stops propagation in normal feline atrial myocytes (347). It should be noted that the waves occur because atrial myocytes from small animal species contain relatively few transverse tubules and therefore Ca²⁺ release initially occurs at the periphery where the SR and surface membrane are in contact (348). However, atrial myocytes from larger species, including human, have a more complete network of t tubules, and Ca²⁺ release also occurs in the center of the cell, making excitation-contraction coupling less dependent on Ca²⁺ waves (349–351). This may impact on the broader relevance of this decreased wave propagation mechanism in atrial fibrillation. A decrease of buffer power was seen in a sheep model of atrial fibrillation, where it was suggested to facilitate the spread of Ca²⁺ release and thereby maintain fibrillation (352). Also in sheep atrium, rapid pacing to induce heart failure decreased buffer power (353). In contrast, a recent study found no difference in Ca²⁺ buffering between myocytes taken from human atrium with or without postoperative atrial fibrillation (354). The origin of these disparate findings is unclear and may be in part due to the different species and models studied. Further work is required to resolve this and also the possibility that changes of diastolic [Ca²⁺]_i may have contributed.

Many studies have shown that heart failure is associated with increased Ca²⁺ sensitivity of the contractile machinery, possibly as a result of decreased phosphorylation of troponin I (334, 355–357) or myosin binding protein C (358, 359). It is therefore surprising that direct measurements have found that ventricular Ca²⁺ buffering is unaffected by heart failure (360, 361). Two factors need to be considered: 1) Increased Ca²⁺ sensitivity does not necessarily imply increased affinity for Ca²⁺, as it is possible that events downstream from changes in Ca²⁺ binding are augmented, giving an apparent increase of Ca²⁺ affinity. 2) An increase of Ca²⁺ affinity of buffers will increase buffering at low [Ca²⁺]_i but decrease it at higher (sect. 3.2). Measuring buffer power over the whole range of [Ca²⁺]_i will average out these changes and result in no apparent change of buffer power. More detailed measurements are therefore required.

In humans, hypertrophic cardiomyopathy (HCM) frequently results from mutations in thin filament proteins including troponin and tropomyosin (362). Mutations in these and other proteins are also associated with dilated cardiomyopathy (DCM) (363). Many of the HCM mutations have been shown to increase the affinity of Ca²⁺ binding, whereas those producing DCM decrease it (364). Troponin mutations associated with HCM slow the decay and decrease the amplitude of the [Ca²⁺]_i transient (180, 365). These effects could result from an increase of buffer power due to the increased affinity, although, as pointed out previously (180), buffer power would only be expected to increase at low [Ca²⁺]_i (in the range of [Ca²⁺]_i below the geometric mean of the K_ds). The myosin inhibitor mavacamtem decreased the apparent Ca²⁺ affinity of such HCM mutations and reversed the slowing of the decay of the [Ca²⁺]_i transient (337), and it is therefore possible that these effects also result from normalization of buffering. However, buffering was not measured. The increase of buffering and therefore of total Ca²⁺ in HCM has been suggested to increase Ca²⁺ loading of the SR and thence increased arrhythmogenic Ca²⁺ release during diastole, partly accounting for the increased arrhythmia burden (180). The link between increased Ca²⁺ binding and arrhythmias is supported by the fact that those mutations that have the greatest effect on Ca²⁺ binding are also the most arrhythmogenic (333). A modeling study has, however, questioned whether increasing Ca²⁺ sensitivity does promote arrhythmias in human HCM (366). Increased buffering also leads to shortening and triangulation of the AP (333), findings that were reproduced in both work on cardiac myocytes derived from human iPSCs (367) and computer simulations (368). It was suggested that the AP shortening results from the increased Ca²⁺ buffering decreasing the amplitude of the Ca²⁺ transient and thence the inward NCX current, which contributes to maintaining the normal AP plateau (367). Such electrophysiological alterations can also be arrhythmogenic. A significant factor that predisposes to arrhythmias is that of electrical alternans (a condition in which the AP duration alternates on a beat-to-beat basis). This is often accompanied by alternation in the amplitude of contraction and the underlying Ca²⁺ transient (for recent review see Ref. 369) and is a particular issue when the alternation is inhomogeneous throughout the ventricle (370). It is therefore interesting to note that HCM mutants can increase the probability of such electrical alternans (367). Modeling has also indicated that changes of Ca²⁺ affinity would be expected to affect the likelihood of alternans (371), with an increase of Ca²⁺ sensitivity increasing alternans in the atrium (368).

The study referred to in sect. 6.2.5 on iPSC-derived cardiomyocytes compared control cells with those derived from patients with a troponin T mutation leading to DCM. The mutation was associated with increased affinity of Ca²⁺ buffering (K_d = 0.32 µM in mutant vs. 0.40 µM in control), with no effect on maximum buffer power (300). It is worth noting (see sect. 3.2) that with these values of K_d buffer power will only be increased in a range of [Ca²⁺]_i below ∼0.35 µM. At higher [Ca²⁺]_i, the mutant troponin will have a lower buffer power. The decreased buffer K_d was accompanied by increased occurrence of alternans, and this link was reinforced by showing that the myofilament Ca²⁺ sensitizer EMD57033 increased both buffering and alternans. This contrasts with the suggestion (above) that DCM mutations have lower affinity. It may be accounted for by the decreased phosphorylation of troponin I leading to increased affinity of Ca binding found in iPSC-derived cardiomyocytes (372). Nevertheless, this change of buffering was associated with increased occurrence of alternans, suggesting a link between altered Ca²⁺ handling and the arrhythmias seen in DCM.

7. SKELETAL MUSCLE

The intracellular Ca²⁺ signals in skeletal muscle control body movements lasting from <1 s to many minutes. Excitation-contraction (EC) coupling is the process whereby an action potential (AP) lasting only a few milliseconds generates a twitch with a duration of hundreds of milliseconds. Most movements are initiated by a short volley of APs (20–50 Hz) in a motor neuron innervating a group of skeletal muscle fibers, resulting in a train of skeletal muscle APs and tetanic contraction (373). There are two main subtypes of skeletal muscle fibers, fast and slow twitch. This distinction is based on the kinetics of contraction, and different muscles have predominantly one or the other fiber type. Muscles involved with posture are generally slow twitch and are more energetically efficient than the predominantly fast twitch involved in rapid limb movements (374, 375). A skeletal muscle AP triggers a pulse of Ca²⁺ release from the SR of ∼1-ms duration at rates of 200 µM/ms (34, 376) (for review see Ref. 84). SERCA-mediated Ca²⁺ uptake then returns the released Ca²⁺ back to the SR over ∼100 ms. The timescale of the release event is comparable to the half-time of Ca²⁺ binding to TnC, ∼1.5 ms (84), and therefore the Ca²⁺-TnC interaction does not reach equilibrium during a twitch (see also FIGURE 14 and Ref. 377). As demonstrated by [Ca²⁺]_i measurements and computational models, the kinetics and relative affinities of the cytoplasmic buffers determine the rapid and sustained contractile responses to the [Ca²⁺]_i signal (83, 84). It is important to note that the levels of [Ca²⁺]_i reached in skeletal muscle [up to ∼20 µM (84)] are considerably greater than those in cardiac muscle.

FIGURE 14.

The role of buffers in skeletal muscle. A: changes of free and bound Ca²⁺ during a twitch in a mouse fast-twitch fiber. Records show (from top to bottom) rate of release of Ca²⁺ from sarcoplasmic reticulum (SR); changes of total calcium concentration (Δ[Ca_T]); [Ca-parvalbumin (PV)]; [Ca-Troponin-C (TnC)]; [Ca-ATP]; Ca²⁺ bound to the indicator (furaptra) (CaD); and intracellular [Ca²⁺] ([Ca²⁺]_i). Note that [Ca²⁺]_i decays more quickly than total; [Ca-TnC] falls while [Ca-PV] is still increasing. B: changes during tetanic stimulation. Traces show (from top to bottom) rate of release of Ca²⁺; total [Ca²⁺]; [Ca-TnC]; and [Ca²⁺]_i. Note that the release flux and increase of total [Ca²⁺] on the second stimulus is much less than on the first, but the change of [Ca²⁺]_i is almost comparable. Figure taken from Ref. 377, with permission from the Journal of Physiology.

7.1. Skeletal Muscle Ca²⁺ Buffers

Several methods have been used to obtain direct measurements of Ca²⁺ buffering in skeletal muscle. An early approach used frog skeletal muscle fibers with the ends cut to allow control of the intracellular environment. Buffer power was increased by raising the concentration of the Ca²⁺ indicator Antipyrylazo III (APIII) (378). As expected, the higher the concentration of indicator, the slower the decay of [Ca²⁺]_i. Extrapolating this relationship to zero indicator suggested that ∼25% of the cytoplasmic Ca²⁺ was free, with the remainder bound to endogenous buffers, giving a rather low value of ∼4 for buffer power. The authors pointed out that the accuracy of this method was limited by the accuracy of the estimate of the Ca²⁺ affinity of the indicator, although it is not clear that this could reconcile this low buffer power with the higher ones discussed below. In later work using the same technique, a higher buffer power of 16 was obtained (379), and this was suggested to have a significant contribution from TnC. Another study (on intact fibers) used the Ca²⁺ indicator Arsenazo III at high concentrations such that the bulk of the Ca²⁺ release from the SR would be bound to the indicator (225). This allowed a minimum estimate of the Ca²⁺ release from the SR of ∼100 µM. With a lower indicator concentration, the rise of free [Ca²⁺]_i was found to be ∼4 µM. This would suggest a buffer power of ∼25, but, as mentioned, the estimate of SR content is a minimum estimate so that the actual buffer power could have been up to ∼37.

Most research into the effects of Ca²⁺ buffers on Ca²⁺ signaling and contraction in skeletal muscle has used concentrations and affinities of the buffers found in biochemical studies (e.g., Ref. 78). The main intracellular Ca²⁺ buffers for fast- and slow-twitch fibers are listed in TABLE 6. Such lists have been used in studies designed to investigate the interrelationship between Ca²⁺ fluxes from the sarcoplasmic reticulum and the resulting contraction (83, 84, 225, 376). As well as giving information about the steady-state contributions to buffer power of the various buffers, TABLE 6 also gives values for the average buffer power on increasing [Ca²⁺]_i from a resting value of 50 nM to either 2.0 or 20 µM. Two values are given, “instantaneous” and “steady state.” The former assumes that the fast buffers such as TnC and SERCA will have reached equilibrium with [Ca²⁺]_I, whereas the latter (higher) value assumes that all buffers are equilibrated. Note that the contribution of the slower buffers will be much greater during a tetanus compared to a single twitch.

The concentrations of the Ca²⁺ binding sites on the major fast buffers (TnC and SERCA) are greater than in cardiac muscle (TABLE 5). In contrast, the buffer powers reviewed above in skeletal muscle are lower than in cardiac muscle. This is partly a consequence of the much higher levels of [Ca²⁺]_i in skeletal muscle and the consequent buffer saturation. For example, TABLE 6 shows that, in fast-twitch fibers, the buffer contribution produced by the sum of SERCA and the regulatory sites on TnC is 455 at 50 nM [Ca²⁺]_i but only 0.7 at 20 µM [Ca²⁺]_i. Another study, on frog skeletal muscle, used depolarizing pulses to activate the L-type Ca²⁺ current. Ca²⁺ release from the SR was inhibited with EGTA so that the observed increase of [Ca²⁺]_i could be assumed to originate from the Ca²⁺ current. The change of total Ca²⁺ (calculated from the integral of the current) was then compared with the measured free [Ca²⁺]_i. With this approach, a high buffer power of ∼150–190 was calculated (380). This study was performed over a lower range of [Ca²⁺]_i (<1 µM) than occurs during twitches and tetani, and this (TABLE 6) would contribute to a larger buffer power. Two complications should be noted. 1) There will be a contribution of ∼14 from the Ca²⁺ indicator (again APIII), and 2) in these experiments the muscle also contained 1 mM EGTA, which will make a major contribution to buffering. As mentioned above, there is still controversy about the buffer role of carnosine and other HDPs under physiological conditions. As previously reviewed (381), carnosine, the major member of the HDP family, has many biological roles including acting as an antioxidant and intracellular pH buffer. In skeletal muscle, it sensitizes contraction to activation by Ca²⁺ (382) but may also have a role as a mobile calcium buffer analogous to that of ATP (338).

7.2. The Role of Parvalbumin

The cytoplasmic CBP parvalbumin is an example of a pure buffer: a protein with apparently no role in skeletal muscle other than to shape the intracellular Ca²⁺ signal and thereby influence function (61). It also plays an important role as a buffer in many neurons (see sect. 9.2). The PVs are a group of small acidic proteins (MW 11,000–12,000) with three EF-hand motifs, two of which can bind Ca²⁺ at cytoplasmic Ca²⁺ concentrations There are two major forms, α-PV and β-PV, arising from separate genes; the PVβ group includes the protein oncomodulin (see Ref. 383 for review). In the α form of PV (present in mammalian skeletal muscle), the two EF-hand motifs have similar binding affinities, are Ca²⁺/Mg²⁺ sites, and do not show significant cooperativity (29, 83, 384). PV is present at higher concentrations in smaller compared with larger mammals and, in a given species, in fast- compared with slow-twitch fibers (385). The conversion by high-intensity exercise of fast- to slow-twitch fibers is accompanied by a decrease of PV concentration (386). In humans, only very low levels of PV are expressed in both fiber types, and it is only found in the intrafusal fibers (muscle spindles); the reason for this difference is not known (385). Increase of PV concentration by direct gene transfer accelerates mechanical relaxation (387).

The EF hands of PV bind Mg²⁺ ions in competition with Ca²⁺. The dissociation constant of Mg²⁺ is ∼10⁴ times greater than that for Ca²⁺, but since cytoplasmic free Mg²⁺ levels are ∼10⁴ times higher than Ca²⁺, PV binds comparable amounts of the two ions, leaving only a small amount of PV unbound even in a relaxed muscle. Using the values of TABLE 6 for fast-twitch fibers, at rest ([Ca²⁺]_i = 0.05 µM) 68% of PV will have Mg²⁺ bound, 26% is Ca²⁺ bound, and 6% remains unbound. This unbound fraction will contribute to rapid buffering; the time course of the larger subsequent buffering by Ca²⁺ binding to the Mg²⁺ sites will depend on the rate constant of dissociation of Mg²⁺ [k_off,Mg = 3 s⁻¹ (34)] as the subsequent Ca²⁺ association rate constant is rapid [k_on,Ca = 42 µM⁻¹·s⁻¹, equivalent to a pseudo-first-order rate constant of 42 s⁻¹ at 1 µM Ca²⁺ (83)]. Despite being a slow buffer, the buffer capacity of PV is significant, particularly in the case of some fast-twitch muscles. This is illustrated in TABLE 6, in the form of the calculation of an “instantaneous” (in) versus “steady-state” (ss) buffer power for mouse skeletal muscle fibers.

The role of PV in mechanical relaxation depends on the fact that it binds Ca²⁺ slowly via the Mg²⁺ exchange mechanism such that binding continues when [Ca²⁺]_i decreases and Ca²⁺ dissociates from TnC (87). The relaxation of [Ca²⁺]_i and contraction therefore reflects a sequential mechanism: Ca²⁺ is initially bound to TnC and is then taken up by PV before being removed by SERCA into the SR (see Ref. 388 for review). Binding of Ca²⁺ to PV allows [Ca²⁺]_i to decrease quickly at the end of the SR release phase as the slow displacement of Mg²⁺ from PV provides a buffer in addition to SR Ca²⁺ uptake and therefore accelerates the decrease in cytoplasmic Ca²⁺ (83, 376). As shown in FIGURE 14A, as Ca²⁺ dissociates from TnC, it binds to PV (377). Under experimental conditions, PV can promote full mechanical relaxation, albeit at a slow rate, even when SERCA is virtually completely inhibited (389). This can also be seen in the simulation of FIGURE 9D. This additional boost to Ca²⁺ removal will only occur at the end of a twitch or brief tetanus; longer tetani will cause increased Ca²⁺ binding to PV as it displaces bound Mg²⁺, leading to saturation of PV (83, 390, 391, 564). This explains why PV is expressed at higher concentrations in fast-twitch muscle in smaller mammals (see sect. 7.3). For example, in rat skeletal muscle the faster relaxation of a twitch compared to that after a long tetanus is more prominent in fast- compared with slow-twitch fibers (390), consistent with the presence of PV in the former but not the latter (385).

Adding EGTA, a slow buffer, can also accelerate the rate of [Ca²⁺]_i decay (392). A subsequent study characterized [Ca²⁺]_i transients accompanying tetani in mouse fast- and slow-twitch muscle fibers. Slow-twitch muscle fibers show a stimulus-to-stimulus increase of [Ca²⁺]_i during the initial phase of the tetanus. Such a staircase is absent in fast-twitch fibers. Addition of the exogenous buffer EGTA to a slow-twitch fiber virtually abolished this staircase and made the [Ca²⁺]_i time course resemble that of a fast-twitch fiber (393). Although alternative mechanisms exist to explain this data, these findings are consistent with the role of PV in shaping the fast-twitch Ca²⁺ transient, and measurements and simulations confirm this mechanism (377).

The high concentration of PV in fast-twitch fibers of small mammals enhances relaxation in an energetically efficient manner. A decrease of [Ca²⁺]_i produced by binding to PV does not consume ATP (see sect. 4.2). ATP is required subsequently as SERCA eventually lowers [Ca²⁺]_i, leading to Ca²⁺ dissociation from PV. However, the peak SERCA rate is much lower than would be the case in the absence of PV (FIGURE 9 and Ref. 394). This role of PV comes at the price of a higher buffer power at resting [Ca²⁺]_i (0.05 µM; TABLE 6), which would in part explain the higher Ca²⁺-storage capacity of the SR in fast-twitch fibers as larger Ca²⁺ release is required to achieve comparable loading of the contractile proteins (225). This distinction between rapid and slow effects of PV is also relevant to neurons (see sects. 9.4–9.6). Related to this, the lower temperature dependence of PV kinetics compared to those of SERCA increases the relative contribution of PV to relaxation at lower temperatures (388, 395). As pointed out in sect. 7.7, modification of PV to increase the affinity for Mg²⁺ would decrease the concentration of free PV and therefore the buffering during Ca²⁺ release. It would, however, also decrease the ability to buffer Ca²⁺ during relaxation, and it is possible that the existing values represent an optimum balance between effects during Ca²⁺ release and relaxation. This is supported by recent data from an inducible mouse PV knockout that showed increased peak twitch and tetanic Ca²⁺ acutely in fast-twitch fibers (396) such that short-term fatigue was reduced, despite the slower rate of the early phase of decay of the intracellular Ca²⁺ signal at the end of a tetanus while longer-term fatigue was unaffected. This work contrasts with earlier work that showed greater long-term fatigue in a constitutive PV knockout model and parallel increases in mitochondrial volume and elevated resting [Ca²⁺]_i (397).

There are several significant cytoplasmic Ca²⁺/Mg²⁺ buffers in skeletal muscle, but PV shows the greatest difference between the instantaneous and steady-state buffer power at Ca²⁺ concentrations normally achieved during tetani. As shown in TABLE 6, in fast-twitch fibers the steady-state contributions of the TnC nonspecific (Ca²⁺/Mg²⁺) sites and of myosin are much less than provided by PV. In slow-twitch fibers (TABLE 6) these sites may play a larger role, but we can find no experimental data testing this.

Finally, an interesting example of the importance of PV is provided by the woodpecker, which drums its beak against a tree at a rate of almost 20 s⁻¹. The neck muscles responsible for this drumming have much higher PV concentrations than both other skeletal muscle in the woodpecker and in the neck muscles of nondrumming species (398).

7.3. Differences in Buffering between Fast-Twitch and Slow-Twitch Fibers

The calculated buffer power differs considerably between fiber types because of differences in expression of proteins associated with Ca²⁺ signaling and contraction. (399). TABLE 6 lists the levels of the major cellular buffers found in small mammals such as mice (83, 84) and shows a much higher buffer power in fast- compared to slow-twitch fibers at both 0.05 and 2.0 µM [Ca²⁺]_i. The greater concentration of SERCA in fast-twitch fibers corresponds to a larger SR Ca²⁺ store in this fiber type and the higher number of SR Ca²⁺ release sites compared with slow-twitch fibers (84). This arrangement generates a larger Ca²⁺ release during E-C coupling and along with the cooperative binding of Ca²⁺ at two sites on TnC (compared to only a single site in slow twitch), generating a faster rate of contraction in fast fibers. As discussed in sect. 7.2, the major contributor to intracellular buffering at [Ca²⁺]_i values normally achieved during tetani (up to 20 µM) is PV, which is expressed at ∼10-fold higher levels in fast-twitch compared with slow-twitch fibers (385). The Ca²⁺ binding and buffer powers due to PV for the two fiber types are shown in FIGURE 15 and illustrate the minimal additional Ca²⁺ binding and Ca²⁺ buffering attributable to PV both immediately after SR Ca²⁺ release (instantaneous) and during sustained (>200 ms) tetani (steady state) in slow-twitch muscle fibers. This contrasts with the very large additional binding and the associated buffer power that operates in mouse fast-twitch muscle with 10-fold higher concentrations of PV (see TABLE 6).

FIGURE 15.

Theoretical parvalbumin (PV) buffer and Ca²⁺ binding curves in mouse skeletal muscle. A and B: buffer power [β(ΔCa)] and the change in total Ca²⁺ binding to PV assuming a resting (initial) Ca²⁺ of 50 nM. Black lines (dashed and solid) show the buffer power for a range of changes in free Ca²⁺ (Δfree[Ca²⁺]) that is normally experienced during a tetanus. The dashed black lines represent the initial buffer power (before dissociation of Mg²⁺ from PV), corresponding to the initial 20–30 ms [“instantaneous” values, in β_i(ΔCa)]. The solid black lines show steady-state values calculated assuming the equilibrium of Ca²⁺ and Mg²⁺ with PV that would be approached during tetani lasting >200 ms [“steady-state” values, ss β_i(ΔCa)]. Red lines and right axis represent the concentration of Ca²⁺ bound to PV at the instantaneous time point (in ΔBound [Ca²⁺]) and that during the steady state (ss ΔBound [Ca²⁺]).

7.4. The Role of Buffer Saturation in Tetanic Contraction

Another example of the physiological consequences of buffer kinetics for muscle function involves the Ca²⁺ binding events at the start of a tetanic contraction. As shown in FIGURE 14B, the initial SR Ca²⁺ release from the first in a train of action potentials (APs) raises total cytoplasmic Ca²⁺ by ∼350 µM, resulting in an increase of free [Ca²⁺]_i of ∼20 µM. Free and total [Ca²⁺] as well as Ca²⁺ bound to TnC then begin to decay as a result of SR reaccumulation by SERCA; however, [Ca²⁺]_i is still elevated at the time of the next stimulus (∼20 ms later). Since the SR Ca²⁺ content is decreased (not shown), this AP results in a smaller increase of total cytoplasmic Ca²⁺. However, this smaller SR Ca²⁺ release will be added on top of an already elevated [Ca²⁺]_i with the majority of high-affinity Ca²⁺ binding sites being occupied. This occupancy reduces the cytoplasmic Ca²⁺ buffer power considerably, and although the second SR Ca²⁺ release is much smaller than the first, it is still sufficient to raise [Ca²⁺]_i to a peak value almost as high as that produced by the first AP, maintaining an almost maximal Ca²⁺ binding to TnC (84, 179, 400). It should be noted that the slow kinetics of PV means that it does not substantially influence the time course of [Ca²⁺]_i during such high-frequency stimulation. The interval between consecutive APs is critical. Too short intervals will attenuate APs and SR Ca²⁺ release. Too long intervals will allow the free Ca²⁺ concentration to decay sufficiently to decrease Ca²⁺ binding to TnC, and therefore contraction will not be maintained (179). The net effect is that a train of APs in skeletal muscle generates an immediate (<10 ms) increase in contractile activity that is sustained at close to maximal levels for the duration of the tetanic train. This effect of buffer saturation is analogous to that seen for buffer saturation-induced synaptic facilitation (sect. 9.5).

This principle also explains the benefit of doublet or triplet firing patterns recorded commonly in motor neurons of fast mammalian skeletal muscle fibers (373, 401). The first two or three APs are separated by shorter intervals (e.g., 5 ms) compared with the intervals in the rest of the train (e.g., 30 ms) (402). The doublet/triplet pattern of motor neuron firing ensures a rapid step change in contractile activity and sustained force response during a brief tetanic response (179) by sustaining [Ca²⁺]_i for the initial 10–15 ms.

It has been suggested that cytoplasmic Ca²⁺ buffering may have significant effects on the level of [Ca²⁺]_i reached during a tetanus (see Ref. 400 for review). For example, acidosis decreases force while increasing [Ca²⁺]_i, and both effects can be attributed, at least in part, to decreased binding of Ca²⁺ to troponin (403). In this context, it is worth emphasizing an important difference between these effects and what would be expected in cardiac muscle. Ca²⁺ fluxes across the sarcolemma are small in skeletal muscle, so a decrease of Ca²⁺ binding to buffers would be expected to produce an increase of [Ca²⁺]_i that will be maintained for longer than would be the case in the heart. Another mechanism by which altered buffering may be involved in fatigue has been proposed. The increase of cytoplasmic phosphate concentration, as a result of breakdown of phosphocreatine, has been suggested to increase the SR phosphate concentration, leading to precipitation of Ca phosphate in the SR and a reduction of Ca²⁺ release (404, 405). It should, however, be noted that changes of metabolites have a variety of other effects on Ca²⁺ handling (see Ref. 406 for review).

7.5. The Role of Calsequestrin

The concentration of free Ca²⁺ in the SR ([Ca²⁺]_SR) of skeletal muscle is ∼300–600 µM (112, 407, with considerable Ca²⁺ also bound to CSQ (for review see Ref. 213). The major isoform in skeletal muscle is CSQ1 (408). The properties of SR Ca²⁺ buffering have been studied in intact frog skeletal muscle fibers in which the ends were cut to allow incorporation of indicators into the cytoplasm and SR. A high concentration of EGTA was added for two reasons: 1) to suppress changes of cytoplasmic [Ca²⁺]_i, allowing the added Ca²⁺ indicator (tetramethylmurexide) to measure changes of [Ca²⁺]_SR uncontaminated by those of cytoplasmic [Ca²⁺]_i (409), and 2) Ca²⁺ released from the SR will bind to cytoplasmic EGTA releasing protons. The resulting change of intracellular pH gives a measure of the change of total SR Ca²⁺ concentration (256). This method gave a value (in frog skeletal muscle) of 670 µM for free and 17.1 mM for total SR Ca²⁺ with ∼30 mM CSQ. It was concluded that ∼95% of the Ca²⁺ released from the SR came from that bound to CSQ as opposed to free Ca²⁺. The SR buffering could be fit with a Hill coefficient of 3.0, indicating pronounced cooperativity of Ca²⁺ binding (cf. sect. 3.3). A subsequent study measured SR Ca²⁺ buffering in mouse skeletal muscle by comparing changes of free SR Ca²⁺ with those of calculated total Ca²⁺ assessed from changes of [Ca²⁺]_i measured with a cytoplasmic indicator (410). This provided an average SR buffer power of 157. Measurements in myocytes of CSQ knockout mice showed that buffer power was reduced to 25%, indicating that CSQ is the major SR Ca²⁺ buffer. The SR Ca²⁺ buffer curve could be fit with a Hill coefficient of 3.52, again indicating cooperative binding. As discussed in sect. 3.3, the cooperativity of Ca²⁺ binding has been associated with polymerization of CSQ. This was investigated in intact skeletal muscle by using fluorescence recovery after bleaching (FRAP) to measure the diffusion of CSQ in the SR. Depleting the SR of Ca²⁺ increased the diffusion coefficient, indicating depolymerization (411). The cooperative nature of Ca²⁺ binding to CSQ has been suggested to have important physiological consequences (411, 412).

It is not simple to relate the biophysical properties of SR Ca²⁺ buffering to the known biochemical properties of CSQ (410). During Ca²⁺ release from the SR, the decrease of free [Ca²⁺] from ∼1 mM to 50 µM will cause depolymerization of the CSQ filament and a reduction in the available binding sites and therefore potentially buffer power (20, 132). Whereas the on and off rate constants of Ca²⁺ binding to the individual chelation sites are relatively rapid, the kinetics of the polymerization-depolymerization processes, which would determine the overall buffer kinetics, are unknown. Estimates of dimerization kinetics have been derived from the analysis of records of [Ca²⁺]_SR signals from smooth muscle (189). More direct measurements are required, particularly since it is uncertain what degree of CSQ polymerization occurs within the SR lumen of different muscle types. EM images of the terminal cisternae of skeletal muscle show extensive branching networks of CSQ suggesting a high degree of polymerization (213, 413). However, the estimate of the maximum [Ca²⁺]_SR in skeletal and cardiac muscle is ∼1 mM. Based on biochemical measurements, this concentration would only result in CSQ dimers and not higher-order polymers (132, 133). It is, of course, possible that the Ca²⁺ sensitivity of polymerization is affected by cellular constituents absent in biochemical studies. Furthermore, the law of mass action would suggest that the higher CSQ concentration found in fast-twitch SR compared to that used in the biochemical studies would favor polymer formation. The degree of polymerization may also be expected to be affected by the CSQ concentration, something that has yet to be studied in detail.

If CSQ did not buffer Ca²⁺ cooperatively, it would have its lowest buffer power at high [Ca²⁺]_SR (FIGURE 3). Release of a given amount of Ca²⁺ would result in a large decrease of [Ca²⁺]_SR, thereby increasing buffer power and decreasing the release flux. In contrast, the high buffer power of the cooperative CSQ buffer maintains [Ca²⁺]_SR and thence Ca²⁺ release (213). Direct measurements of [Ca²⁺]_SR have shown the occurrence of abrupt rises of [Ca²⁺]_SR attributed to depolymerization of CSQ and therefore release of bound Ca²⁺ (411, 414). These papers also advanced an explanation for muscle fatigue with the idea that a decrease of [Ca²⁺]_SR would (because of the cooperative nature of Ca²⁺ buffering) decrease the buffer power and thereby the Ca²⁺ release. In this context it is noteworthy that mutations in CSQ that alter polymerization and reduce Ca²⁺ binding have been associated with disease, including malignant hyperthermia and vacuole aggregate myopathy (415–417).

7.6. Diffusion of Ca²⁺ in Skeletal Muscle

The release of Ca²⁺ from the terminal cisternae of the SR results in a high local, cytoplasmic Ca²⁺ signal (376). To enable contraction, this Ca²⁺ must diffuse from the terminal cisternae of the SR, located near the Z lines (418), to bind to TnC molecules, located along most of the sarcomere, at a distance of up to 1 µm away. Modeling studies suggested that Ca²⁺ diffusion is accelerated by binding to ATP (34). An experimental study using frog skeletal muscle fibers compared the rise time of [Ca²⁺]_i at the release sites (Z line) with that in the middle of the sarcomere (M line). The latter lagged by 2–3 ms, and these relative kinetics could be explained by a model including diffusion of CaATP (338). The situation may be different in mammalian skeletal muscle, where the Ca²⁺ release triads reside at the A-I border as opposed to the Z line (419), placing them closer to the TnC and thereby decreasing the diffusion distance and the need for acceleration of Ca²⁺ diffusion by mobile buffers. Note that skeletal muscle contains significant amounts of the mobile buffer carnosine (212) (cf. sect. 2.4.1). Subject to current uncertainties about its Ca²⁺ binding, this may also aid Ca²⁺ diffusion.

7.7. The Role of Buffers in Skeletal vs. Cardiac Muscle

The above sections emphasize an important difference between the role of buffers in these two types of striated muscle. There are four important roles of Ca²⁺ buffers in skeletal muscle: 1) SR Ca²⁺ buffering by CSQ limits the fall of Ca²⁺ that occurs during Ca²⁺ release from the SR. 2) Mobile buffers help transfer Ca²⁺ ions from the SR release sites to the myofibrils. 3) Buffering by PV accelerates relaxation. 4) Buffer saturation increases the rise of [Ca²⁺]_i during a tetanus. In contrast, in cardiac muscle only the first two of these occur. Furthermore, the degree of SR Ca²⁺ buffering by CSQ is considerably greater in skeletal compared with cardiac muscle, perhaps reflecting a higher concentration of CSQ (409). Functionally, the difference may reflect the fact that depletion of the cardiac SR on a single beat does not matter as the SR is refilled before the next beat. Indeed, the decrease of free Ca²⁺ may contribute to closing of RyRs and thence termination of Ca²⁺ release (420). In contrast, the SR will gradually deplete during a tetanus in skeletal muscle, and the higher CSQ content will minimize this.

Other differences between buffering in cardiac versus skeletal muscle do not result from the differences in the buffers expressed but rather from the time course and concentration range of [Ca²⁺]_i. As discussed above, the higher peak [Ca²⁺]_i in skeletal muscle will result in decreased buffer power due to saturation, and the prolonged rise of [Ca²⁺]_i during a tetanus will increase contributions from slow buffers.

The role of PV to accelerate relaxation in skeletal muscle contrasts with the fact that Ca²⁺ buffers slow relaxation of cardiac muscle. The explanation of this paradox is the slow kinetics of PV, which works in parallel with SERCA to reduce [Ca²⁺]_i in fast-twitch skeletal fibers. In particular, the kinetics of PV are sufficiently slow that it continues to take up Ca²⁺ even when [Ca²⁺]_i is declining. There is no equivalently slow buffer in cardiac muscle or slow-twitch skeletal fibers. In this context, it has been suggested that expression of a PV-like buffer in cardiomyocytes might be a useful therapeutic approach in heart failure as it could accelerate relaxation without decreasing contraction. PV binds Ca²⁺ too slowly to interfere appreciably with peak [Ca²⁺]_i in systole but would bind significant amounts of Ca²⁺ during diastolic relaxation (421, 422). It has further been shown that β-PV performs better in this respect because it binds Mg²⁺ better than α-PV (423). This will increase the concentration of the Mg²⁺-bound and decrease that of the free form of the buffer, thereby decreasing the rapid component of buffering and allowing it to accelerate relaxation with less effect on the amplitude of the systolic [Ca²⁺]_i transient and thence contractility. A similar improvement has been reported for single amino acid mutations in the α-PV EF-hand domain (424, 425).

8. SMOOTH MUSCLE

Several studies have measured the Ca²⁺ buffer power in smooth muscle by using the method described in sect. 6.1 in which cells are depolarized to activate L-type Ca²⁺ currents. The measured Ca²⁺ current and inferred total Ca²⁺ can then be compared with the rise of [Ca²⁺]_i measured with an indicator dye. The resulting value of buffer power includes contributions from both the endogenous buffers and the indicator used to measure [Ca²⁺]_i. A value of 82 was reported for toad stomach (426). A similar approach in rat portal vein myocytes gave a buffering power of 170, which, corrected for the contribution of the Ca²⁺ indicator, provided an endogenous buffering power of 114 (427). A smaller buffer power of 30–40 was reported for guinea pig urinary bladder smooth muscle cells (428). In guinea pig colonic smooth muscle cells, a much higher buffer power (∼400) was measured. This was reduced to 250 by the addition of ryanodine, suggesting that some of this apparent buffer power represented Ca²⁺ uptake into the SR (429), suggesting the lower value as the better estimate. In guinea pig coronary vascular smooth muscle cells, a buffer power of 300 was obtained, which corresponded to ∼150 when corrected for the contribution by the fluorescent indicator (430). A different study using the added buffer method (173) (sect. 9.1) provided a buffer power of 46 (431). Further research is required to clarify whether the wide range of reported buffer power values reflects real differences between the various types of smooth muscle as opposed to being a consequence of methodological differences. It is, however, worth noting that the lowest buffer power mentioned above was obtained with changes of [Ca²⁺]_i of ∼4 µM (428) whereas the other studies typically involved maximum [Ca²⁺]_i of 250–800 nM. It is therefore possible (cf. sect. 3.1) that the lowest buffer power values might result from buffer saturation. Given this, it is challenging to model buffering. A computer model of smooth muscle Ca²⁺ movements used a lumped buffer with a total concentration of 230 µM and K_d of 1 µM, equivalent to a rather high buffer power at low [Ca²⁺]_i of 230 µM/1 µM = 230 (432).

What is the origin of the measured Ca²⁺ buffering? One potential contributor is CaM, which is present at concentrations of 34 and 40 µM in guinea pig taenia coli (433) and cultured bovine tracheal cells (434), respectively. Taking 40 µM and the K_apps listed in TABLE 5 (187), one calculates a buffer power of 4 at 100 nM [Ca²⁺]_i. This value is lower than most of the buffer powers reported above. The affinity for Ca²⁺ binding increases when CaM is bound to proteins (435), and this would be expected to increase buffer power. A study using electron probe microanalysis found that the increase of total cytoplasmic Ca²⁺ accompanying a contracture produced by the combination of KCl-induced depolarization and norepinephrine was ∼235 µM (436). The authors pointed out that this was considerably greater than what might be expected to bind to CaM. They therefore suggested that Ca²⁺ must also bind to myosin and possibly other proteins. It has, however, been questioned whether myosin binds significant amounts of Ca²⁺ in the presence of cytoplasmic Mg²⁺ concentrations (see Ref. 437 for review). The reader will note that the studies referred to in this paragraph are mainly >30 years old. In their review published in 1986 (437), Sommerville and Hartshorne note, “A contemporary problem is to identify the various components of the Ca²⁺ buffer system.” It is our opinion that this problem is still “contemporary.”

A recent paper reported expression of calreticulin in endothelial cells forming myoendothelial junctions, which are important in coordinating calcium signaling between endothelium and smooth muscle. Much of the calreticulin expression was not associated with other ER markers, suggesting that it is located somewhere other than in the ER (438). Further work is required to establish whether this is present in the cytoplasm.

9. NEURONS AND NEUROENDOCRINE CELLS

As in muscle cells, Ca²⁺ ions function as the principal second messengers coupling action potential (AP) firing to diverse intracellular events, from activation of cytosolic signaling pathways to gene transcription. In addition, Ca²⁺ serves a dual neuron-specific function at chemical synapses: Ca²⁺ triggers synaptic vesicle fusion at presynaptic active zones, and Ca²⁺ is a pivotal signaling molecule controlling synaptic plasticity. The spatiotemporal characteristics of neuronal [Ca²⁺]_i transients are determined by Ca²⁺ influx, extrusion, and buffering. Ca²⁺ influx into somata, dendrites, and axon terminals occurs primarily in response to membrane depolarizations opening voltage-gated Ca²⁺ channels (VGCCs). In some neurons, Ca²⁺ influx through Ca²⁺-permeable ligand-gated channels and/or Ca²⁺ release from internal stores represent two additional routes to increase [Ca²⁺]_i. AP-induced Ca²⁺ influx is generally brief, lasting at most a few milliseconds. At glutamatergic synapses equipped with postsynaptic NMDA channels, Ca²⁺ influx can last longer owing to the slow deactivation kinetics of these channels (227, 439). Nevertheless, global cytosolic [Ca²⁺]_i transients that remain after the collapse of local Ca²⁺ domains following channel closure can outlast the duration of Ca²⁺ influx by one or two orders of magnitude. These global cytosolic [Ca²⁺]_i transients are shaped by Ca²⁺ extrusion and buffering, which differ between different neuron types and different subcellular compartments and which temporally and spatially confine Ca²⁺ signals. The manner in which neuronal [Ca²⁺]_i transients are affected by Ca²⁺ buffers is determined by three parameters: 1) their concentration in the cytosol, 2) their affinity and binding kinetics for Ca²⁺ and Mg²⁺ ions, and 3) their mobility in the cytosol.

9.1. Measuring Cytosolic Ca²⁺ Buffering in Neurons and Neuroendocrine Cells

Much work characterizing neuronal buffers has used the “added buffer approach” as originally applied to adrenal chromaffin cells (27, 174) and later extended to nerve terminals (248, 440) and dendrites of hippocampal neurons (59, 201, 441, 442). In these experiments, a whole cell recording is established on the compartment of interest, with a patch pipette containing a ratiometric Ca²⁺ indicator, usually fura-2 or one of its low-affinity analogs at a known concentration and therefore ${\kappa }_{\mathrm{B}}^{\text{′}}$ value. Either single APs are elicited or short depolarizing pulses are applied under voltage clamp at various time points while the cell is loaded with the indicator dye (FIGURE 16) (248, 440, 443). Both the amplitudes (Δ[Ca²⁺]_i) as well as the decay time constants τ_Ca,i of the resulting [Ca²⁺]_i transients are evaluated. According to the simple theory presented in Eqs. 31 and 32 (27, 174), plots of 1/A or τ against the amount of “added buffer power” allow the calculation of values for A and τ in the absence of exogenous buffers by extrapolation to zero added buffer (y-axis intercept, FIGURE 16Bb). The negative x-axis intercept of such plots is an estimate for the endogenous buffer power (1 + ${\kappa }_{\mathrm{S}}^{\text{′}}$; FIGURE 16Bb). This method is therefore a refinement of the approach using different concentrations of Antipyrylazo III in skeletal muscle (sect. 7.1 and Ref. 378). Unlike the techniques presented above for cardiac and smooth muscle (sects. 6.1 and 8), where buffer power is estimated by comparing the movement of Ca²⁺ into the cytoplasm with the change of [Ca²⁺]_i, the added buffer approach does not require knowledge of the cytoplasmic volume. However, it does not easily provide information about buffer type, its concentration, or affinity. In fact, several mobile and immobile buffer species may often contribute to the obtained buffer power estimates. The added buffer approach is typically used with small and compact cells such as adrenal chromaffin cells or with subcellular compartments of neurons such as somata or nerve terminals, for which it can be assumed that spatial [Ca²⁺]_i gradients collapse over a time span much shorter than typical values for the decay constants of [Ca²⁺]_i transients (>10 ms). The method is also suitable for cylindrical structures such as axons and dendrites under careful selection of uniform diameter, such that longitudinal gradients are minor. FIGURE 16 illustrates its use to estimate buffer power in neuronal cell bodies and nerve terminals. When it is applied to cerebellar Purkinje cells, their high endogenous buffer power results in dialysis with fura-2 having only small effects on measured [Ca²⁺]_i transients (FIGURE 16A). In contrast, much larger effects are observed (FIGURE 16, B AND C) in calyx of Held terminals because of their much lower buffer power.

As originally described (174), the results of the added buffer approach are somewhat ambiguous since it is not clear which types of endogenous buffer are being assayed. All fixed buffers are expected to be included, but mobile buffers may be washed out while the indicator dye is infused (FIGURE 17) (444). Typical buffers, with diffusion coefficients about four times smaller than that of fura-2 (TABLE 3), should be retained at the early time points of the whole cell recording and are therefore probably included. Small metabolites, however (sect. 2.4), may be washed out quickly. During extended recording periods, diffusional equilibration between pipette and cytoplasm is achieved also for larger buffer molecules such as calbindin-D28k, resulting in nearly complete washout of that mobile buffer with a time constant of ∼10 min (FIGURE 17E). At the same time gluconate⁻, often chosen as the main anion of the pipette solutions in these types of experiments, is infused together with the indicator. The gluconate anion binds Ca²⁺ weakly (60) and may well compensate for the loss of endogenous counterparts. Therefore, estimates of buffering power contributed by small low-affinity Ca²⁺ binders and determined by the original added buffer approach cannot be considered reliable. Although their contribution to the absolute value of buffering power is expected to be small, their influence on Ca²⁺ diffusion and on local domains may be substantial (see sects. 4.5. and 4.7.2). To remove this uncertainty and to focus on low-mobility and stationary buffers, Matthews, Schoch, and Dietrich (59) proposed a modification of the procedure: Instead of measuring changes in [Ca²⁺]_i during a single dye-loading experiment, several whole cell recordings are performed with different concentrations of indicator dyes in the pipette. [Ca²⁺]_i transients are elicited after dye loading is complete and mobile Ca²⁺ buffers are expected to have been washed out. Therefore, the plots of A⁻¹ and τ plots versus ${\kappa }_{\mathrm{B}}^{\text{′}}$ of the indicator, as described above, should report the buffering power of immobile and slowly mobile buffers, depending on the geometry of the cell under study and the waiting period before measurement. When applied to the calyx of Held nerve terminal, this method yielded an endogenous Ca²⁺ buffer power of 21 (248), whereas somewhat higher estimates (40–46) were obtained with the original procedure (440, 445).

FIGURE 17.

Loss of the endogenous mobile Ca²⁺ buffer CB-D28k during whole cell recordings in hippocampal dentate gyrus granule neurons (GCs). A–D: several GCs were recorded and filled with the fluorescent dye Lucifer yellow (LY) during whole cell recording episodes lasting for 30 s (A), 6 min (B), 12 min (C), or 38 min (D). Subsequently, hippocampal slices were fixed and stained for CB-D28k. Arrows indicate recorded neurons identified by their LY fluorescence. E: time course of CB-D28k loss during whole cell recordings. The CB-D28k immunofluorescence of each recorded GC was normalized to that of neighboring GCs. Modified from Ref. 444, with permission from Journal of Neuroscience.

The same problem was addressed in studies on bovine chromaffin cells (446) by “balanced dye loading.” In this approach, individual cells are preloaded with a certain concentration of fura-2, either by AM-ester loading or by dye preloading, during a brief whole cell recording episode. Subsequently, a perforated-patch recording is established, this time with a concentration of fura-2 in the pipette, which is expected to match the concentration inside the cell under study. Total Ca²⁺ buffer power, including mobile and immobile buffers, is estimated from total Ca²⁺ influx and changes in free [Ca²⁺]_i during short depolarizing voltage-clamp pulses. Once a stationary situation has been established, the perforated patch is ruptured, resulting in a whole cell configuration. Subsequent changes in buffering power are followed by repetitive application of depolarizing pulses. Experiments are considered successful if dye loading is “balanced,” meaning that total fura-2 fluorescence did not change rapidly after rupture. In that case, later changes in Ca²⁺ buffer power are interpreted as changes in endogenous buffers. No such changes were observed in some cells after “balanced loading,” indicative of little or no contribution to Ca²⁺ buffering from mobile buffers, which would have washed out. However, on a longer timescale about half of the cells displayed a partial drop in buffering power compatible with the loss of proteins of ∼7,000–20,000 molecular weight, which before their washout contributed ∼25% of the total buffering power of 40.

All versions of the added buffer approach discussed so far depend on the approximations discussed in sect. 4.7.1, employing Eqs. 30–32 for the analysis of exponentially decaying [Ca²⁺]_i transients. When studying slow buffers, such as PV, which cause biphasic decays of [Ca²⁺]_i transients, more complex stimulus patterns and analysis procedures need to be invoked (27). Various other methods for measuring Ca²⁺ buffer power, and also for titrating endogenous buffers, have been described (251, 447, 448), similar to methods typically used when studying muscle cells (sects. 6.1 and 8). With photolysis of caged Ca²⁺ compounds, K_d, Ca²⁺ binding rate constant, and Ca²⁺ binding ratio of the endogenous fixed buffer in adrenal chromaffin cells were estimated as ∼100 µM, 5.17 × 10⁸ M⁻¹·s⁻¹, and 40, respectively (449). Altogether, values of buffer power are typically in the range of 15–300; maximum values of ∼2,000 for Purkinje cell somata and dendrites were found. For a compilation of Ca²⁺ buffer powers and affinities of endogenous Ca²⁺ ligands see Refs. 173, 201. Thus, the fraction of free Ca²⁺ in the cytosol varies typically between ∼0.3% and ∼7% of total [Ca²⁺]_i at equilibrium but can be as low as 0.05%. The buffering power of fixed buffers is small but nevertheless the dominating one in many types of neurons. Higher buffering powers are primarily achieved by a higher abundance of endogenous mobile Ca²⁺ binding proteins and confer special characteristics of short-term synaptic plasticity and electrical excitability (see below).

9.2. Neuronal Expression of EF-Hand Domain Ca²⁺-Binding Proteins

In the mammalian brain, the predominant mobile Ca²⁺ buffers found in neurons are parvalbumin (PV/α-PV), calbindin-D_28K (CB-D28k), and calretinin (CR), which are members of the superfamily of EF-hand domain CBPs (sect. 2.5.1). Neurons typically express only one of these three proteins, but coexpression of combinations of two of the three EF-hand domain CBPs is also observed. Two other relevant molecules that bind Ca²⁺ rapidly and are present at high cytoplasmic concentrations in neurons, and therefore shape the spatiotemporal characteristics of local and/or global Ca²⁺ transients, are ATP (450) and CaM (451). CaM binds Ca²⁺ with faster kinetics than any of the three CBPs CR, CB-D28k, or PV (187).

The commonly applied criterion (sect. 2.5.1) that pure Ca²⁺ buffer proteins do not undergo marked conformational changes upon Ca²⁺ binding and do not interact with other proteins in a Ca²⁺-dependent way holds for PV among the family of EF-hand domain CBPs (565). In contrast, a substantial conformational change is observed upon Ca²⁺ binding to CB-D28k (31). The apparent diffusion coefficient for CB-D28k in the cytosol depends on the subcellular compartment, and an interaction of CB-D28k with myo-inositol monophosphatase has been identified in spines and dendrites of cerebellar Purkinje neurons, indicating that CB-D28k is both a Ca²⁺ buffer and a Ca²⁺-signaling molecule (452). A similar picture emerges with respect to CR: CR and P/Q-type (Ca_V2.1) VGCCs coimmunoprecipitate from mouse cerebellum homogenate. In HEK293T cells, coexpression of CR attenuates Ca²⁺-dependent inactivation (CDI) and augments Ca²⁺-dependent facilitation (CDF) of heterologously expressed P/Q-type VGCCs via a direct interaction with the α₁2.1 subunit (453). It remains to be established whether a modulation of VGCCs by CR as observed in HEK293T cells also occurs in neurons.

The expression of EF-hand domain CBPs in different brain regions has been studied extensively at the cellular and subcellular levels and in various species, once specific antibodies became available. It is the topic of several excellent reviews (454–460), and here we only summarize some key findings. PV is predominantly, but not exclusively, expressed in inhibitory interneurons of the brain. Many of these are fast-spiking GABAergic interneurons, including fast-spiking basket and chandelier cells of the neocortex and the hippocampus, fast-spiking striatal interneurons, two classes of GABAergic interneurons of the molecular layer of the cerebellum, stellate and basket cells, and many interneurons of the thalamus. PV is absent from pyramidal neurons of the neocortex and hippocampus, but it is expressed in large amounts in the output neurons of the cerebellum, the Purkinje cells, which additionally coexpress CB-D28k. PV is heavily present in somata and neuropil of the rodent auditory system, for example in auditory nerve fibers, and neurons of the spiral ganglia, the cochlear nucleus, and the inferior colliculus (461).

Prominent PV immunoreactivity is found in three types of large calyciform synaptic terminals: GABAergic terminals of interneurons in the thalamus (462) and glutamatergic endbulb of Held and calyx of Held terminals in the auditory brain stem (461). In subsets of the latter two types of auditory terminals coexpression of presynaptic CR but not CB-D28k was found (463, 464). Interestingly, the onset of PV expression in numerous classes of neurons of the auditory brain stem of mice and rats occurs relatively late and coincides approximately with the onset of hearing (461, 463).

CB-D28k is expressed in a variety of neurons, mostly interneurons, and the adult pattern of expression is in general established at birth. In the rat neocortex, CB-D28k-immunoreactive cells are predominantly found in the upper layers II and III (457). In the hippocampus, CB-D28k-immunoreactive interneurons are found in all subdivisions (465). CB-D28k is also a major Ca²⁺ buffer of hippocampal dentate gyrus granule cells and CA1 pyramidal neurons, whereas it is absent from CA3 pyramidal cells (444, 466). In the cerebellum, Purkinje cells are the only neurons expressing CB-D28k (455).

Similar to CB-D28k, CR is expressed in various interneurons of the neocortex, most abundantly in the upper layers II and III, and in specific interneurons of the hippocampus (467, 468). However, coexpression of CB-D28k and CR in individual neurons is rare (469). In the cerebellum, CR is expressed in the glutamatergic granule cells, which relay mossy fiber inputs to Purkinje cell dendrites via the parallel fiber pathway (455).

Expression of CBPs within the vertebrate retina varies among species. In the rodent, photoreceptors and bipolar cells lack expression of CBPs whereas some classes of horizontal, amacrine, and ganglion cells express one or more of CB-D28K, CR, and PV (470–472). In the rat cochlea, in situ hybridization shows exclusive expression of β-PV (oncomodulin) in outer hair cells (OHCs) whereas inner hair cells (IHCs) express both α-PV and β-PV (473). The developmental profile of PV isoform, CB-D28k, and CR expression revealed a transient β-PV expression during IHC development while the expression of CR and α-PV slightly increases. The sum of the CBP concentrations decreases in IHCs but increases in OHCs during cochlear maturation (474).

The selective expression of CBPs in distinct neuron populations of different brain areas suggests that specific functional properties of CBPs confer specific physiological properties to those neurons. This finding has been exploited experimentally to identify and/or selectively manipulate the respective neurons in situ. The availability of Cre-driver mouse lines for both PV and CR allows targeting PV- and CR-expressing neurons for genetic manipulations, including the expression of fluorescent markers, fluorophores for Ca²⁺-imaging, and channelrhodopsin and its derivatives enabling stimulation or silencing of specific neuron populations (475, 476).

9.3. Cytosolic Concentration of Ca²⁺-Binding Proteins

For some neurons and subcellular compartments, cytosolic concentrations of CBPs have been estimated either by using calibrated immunohistochemistry or via functional assays during which neurons lacking a certain CBP were loaded with recombinant protein to restore normal function.

Hippocampal dentate gyrus granule cells (hDG GCs) contain ∼40 µM CB-D28k, corresponding to ∼160 µM Ca²⁺ binding sites, as estimated by performing postrecording immunohistochemistry following whole cell dialysis with known concentrations of recombinant CB-D28k and comparing immunofluorescence intensities to that in neighboring, unperturbed neurons (444). Cytosolic CB-D28k concentrations for hippocampal CA3 stratum radiatum interneurons and CA1 pyramidal neurons were similar, with ∼47 µM and ∼45 µM, respectively (444). With a similar approach, a cytosolic PV concentration of ∼12 µM was estimated for hippocampal dentate gyrus basket cells (hDG BCs) (267). The PV concentration was variable among individual hDG BCs but similar in somata and boutons of a given cell. For cerebellar basket cell (cBC) somata, a substantially higher mean PV concentration of ∼565 µM was reported, which was also less variable among individual cBCs (267).

In other studies, the concentrations of CBPs were estimated from densities of gold particles with electron microscopic postembedding immunogold procedures. Quantification of particle densities allows for a statistical comparison of the relative levels of CBPs in somata, dendrites, dendritic spines, axons, and axon terminals. Using this approach, Kosaka et al. (477) found significantly higher levels of PV immunoreactivity in axons and axon terminals of Purkinje cells and basket cells than in their respective somata and dendrites. In contrast, CB-D28k immunoreactivity was more similar in somata, dendrites, and spines of Purkinje cells. Estimates for absolute PV concentrations were obtained by comparison to calibration curves deduced from quantitative immunogold analyses of standard PV samples. Estimated PV concentrations were 50–100 µM for Purkinje cell somata and dendrites as well as for interneuron somata and 1 mM or more in axons and axon terminals of Purkinje cells and cBCs (477), corresponding to 100–200 µM and 2 mM Ca²⁺ binding sites, respectively. Estimates for PV and CB-D28k concentrations in Purkinje cell somata were obtained more recently from calibrated immunogold tissue counts, with 116 µM and 208 µM for PV and CB-D28k, respectively (474), corresponding to 232 µM and 832 µM Ca²⁺ binding sites. In postnatal day 26 rats with fully developed hearing, cochlear inner hair cells contained one-tenth of the amount of CBPs of outer hair cells. In these latter cells, the cell body contained β-PV and CB-D28k at high levels equivalent to 5 mM Ca²⁺ binding sites. In contrast, the concentration of Ca²⁺ binding sites in inner hair cells was ∼0.5 mM and was dominated by α-PV (474).

An alternative approach for estimating CBP concentrations is based on functional assays during which normal neuronal function in neurons lacking a certain CBP, either due to genetic ablation or because of washout during whole cell dialysis, is restored by supplying exogenous buffer via the patch pipette. With such a “rescue approach,” a concentration of 1.2 mM CR was estimated for frog saccular hair cells, corresponding to ∼6 mM Ca²⁺ binding sites. The criterion for rescue was the concentration of exogenous CR required to restore the voltage dependence of activation of Ca²⁺-sensitive potassium channels to the level of that measured in perforated-patch recordings (478) (FIGURE 18A). In voltage-clamped cochlear inner hair cells (IHCs) of young (postnatal day 14–23) constitutive triple KO (α-PV^−/−CB-D28k^−/−CR^−/−) mice, a relationship between Ca²⁺ influx duration and exocytosis similar, but not identical, to that of wild type could be restored by buffer infusion via the patch pipette (223). The required mobile buffer concentrations were equivalent to ∼1 mM synthetic Ca²⁺ binding sites, half of them with kinetics as fast as BAPTA, the remainder with properties like EGTA.

FIGURE 18.

Estimating the concentration of endogenous buffers by functional rescue. A: exogenous calretinin (CR) in the pipette solution mimics the native Ca²⁺ buffer in suppressing the Ca²⁺-activated potassium channel (K_Ca) current in frog saccular hair cells. K_Ca currents normalized to the amplitude at –15 mV are plotted against membrane potential (V_m). The voltage dependence of K_Ca is similar to that seen in perforated-patch recordings if the pipette solution for whole cell recordings contains 1.2 mM CR. Modified from Ref. 478, with permission from Nature Neuroscience. B: exogenous parvalbumin (PV) in the pipette solution mimics the native Ca²⁺ buffer in accelerating the decay of action potential (AP)-triggered intracellular calcium concentration ([Ca²⁺]_i) transients. Average waveforms of AP-evoked [Ca²⁺]_i transients during presynaptic whole cell recordings in calyx of Held terminals obtained with pipette solutions supplemented with either 100 µM fura-6F, 100 µM fura-6F + 100 µM recombinant PV, 100 µM fura-6F + 100 µM EGTA, or 50 µM fura-2. The slow Ca²⁺ buffer EGTA and recombinant PV restore the fast decay of AP-evoked [Ca²⁺]_i transients. Modified from Ref. 479, with permission from Journal of Neuroscience.

Presynaptic AP-induced [Ca²⁺]_i transients in calyx of Held terminals decay with a biphasic time course when the intracellular medium is only minimally perturbed by brief dye preloading. When such transients are measured during standard whole cell recordings without added Ca²⁺ buffers, a slower monoexponential decay is observed. Ca²⁺ transient amplitudes differ only marginally between the two conditions. This finding is consistent with a washout of a mobile Ca²⁺ buffer with slow binding kinetics such as PV during whole cell recording. In agreement with this notion, AP-induced presynaptic [Ca²⁺]_i transients decayed slowly in calyx terminals of PV-deficient (PV^−/−) mice. A fast decay of AP-evoked [Ca²⁺]_i transients was restored when whole cell recordings were performed with 50–100 µM of the slow buffers EGTA or PV added to the presynaptic pipette solution, indicating that unperturbed terminals probably contain an equivalent amount of PV (479) (FIGURE 18B).

9.4. Local [Ca²⁺]_i Domains Triggering Synaptic Vesicle Fusion

Local Ca²⁺ domains that are established when VGCCs open and rapidly collapse after channel closure dominate fast Ca²⁺ signaling. They may trigger synaptic vesicle fusion and also activate Ca²⁺-sensitive potassium channels, which contribute to AP repolarization.

Immobile endogenous Ca²⁺ buffers retard diffusion and thereby prolong the time until local domains of elevated [Ca²⁺]_i reach steady state. Mobile endogenous buffers, on the other hand, accelerate the redistribution of Ca²⁺ ions and thereby reduce both the amplitude of changes of local [Ca²⁺]_i and their spatial extent. The importance of the binding rate constant k_on as a major factor determining the effect of exogenous buffers on local Ca²⁺ domains was first considered in a study on Ca²⁺-sensitive BK potassium channels in adrenal chromaffin cells (480). It was observed that EGTA is much less effective than BAPTA in blocking the activation of these channels, even though the buffers have similar equilibrium dissociation constants K_d (TABLE 1) and consequently similar steady-state buffering power (see Eqs. 33–35 and TABLE 4 for order-of-magnitude estimates of the spatial extent and kinetics of local Ca²⁺ domains). The size of the local domain depends mainly on the product of the binding rate constant k_on and the concentration of free, mobile chelator, [B]₀.

Thus, anions that are present at high concentration in the cytosol may have a strong effect on local domains, even if their equilibrium buffering power is very small, e.g., because of a very fast off-rate constant. For example, gluconate⁻, which is often infused as the main anion in patch-clamp experiments together with ATP²⁻, was found to increase the Ca²⁺ influx necessary for eliciting a given amount of transmitter release by a factor of 2.7, when comparing experiments performed with different intracellular solutions containing either gluconate⁻ and ATP²⁻ or methanesulfonate⁻, lacking Ca²⁺ binding and no ATP²⁻ (60). Other small anions, present in unperturbed cells, as discussed in sect. 2.4.4, may have similar effects on local domains.

From the perspective of intracellular Ca²⁺ sensors, the terms “nanodomain” and “microdomain” are frequently used to describe the tightness of coupling between sites of Ca²⁺ entry and the sensor. However, these terms are not precisely defined with respect to spatial distances, and the distinction is primarily based on the experimentally determined effectiveness of the slow and fast buffers EGTA and BAPTA, respectively, in uncoupling the Ca²⁺-triggered process under study from Ca²⁺ influx. Synapses in which transmitter release is sensitive to EGTA (indicative of microdomain coupling) are the calyx of Held (481) and synapses between layer 5 cortical pyramidal neurons (482) in young rats. Synapses in which release is largely insensitive to EGTA (nanodomain coupling) are the mature calyx of Held (483), inner hair cells of the cochlea (484), GABAergic hippocampal dentate gyrus BC→GC synapses (485), glutamatergic cerebellar GC→PC synapses (486), and rod bipolar cell→amacrine cell synapses of the retina (487). Numerical simulations suggest mean coupling distance of ∼100 nm and <30 nm for microdomain and nanodomain coupling, respectively (243, 445, 450, 485, 486, 488).

To base the determination of coupling distance between VGCCs and docked synaptic vesicles exclusively on the differential effectiveness of EGTA and BAPTA may be an oversimplification because processes upstream of synaptic vesicle fusion can also be Ca²⁺ dependent, for example the resupply of fusion-competent synaptic vesicles (489–492) or the balance between distinct priming states (492). Therefore, reduced synaptic strength after prolonged presynaptic whole cell dialysis with EGTA-containing pipette solution may result not only from uncoupling of the Ca²⁺ sensor for vesicle fusion but also from reduced availability of fusion-competent vesicles unless resting [Ca²⁺]_i is guaranteed to remain unchanged while changing the concentration of free chelator. This can be achieved by maintaining a fixed ratio of Ca²⁺-bound to free buffer in the recording pipettes while increasing total amount of buffer.

Relative contributions of the fast CBPs CB-D28k and CaM to buffering of AP-evoked [Ca²⁺]_i transients at presynaptic active zones were studied by numerical simulations (451). These predicted that each buffer contributes to the reduction of AP-evoked local [Ca²⁺]_i transients and resulting decrease of synaptic vesicle fusion probability. At an assumed VGCC-to-synaptic vesicle distance of 40 nm, CB-D28k caused ∼50% reduction of the synaptic vesicle fusion probability relative to control simulations without CB-D28k and CaM. CaM had a stronger inhibitory effect of ∼80% reduction, and addition of CB-D28k on top of CaM caused only a minor further reduction (∼85%). The reduction of AP-evoked fusion at synapses that contain both CB-D28k and CaM is mainly caused by fast Ca²⁺ binding to the N- and C-lobes of CaM. CB-D28k plays only secondary roles (451). At a resting [Ca²⁺]_i of 50 nM, >99.8% of CaM C-lobes are in the Ca²⁺-free apo-state.

The slow Ca²⁺ buffer PV has Ca²⁺ binding kinetics similar to EGTA. Because of its relatively high affinity for Mg²⁺, the majority of PV is Mg²⁺ bound and little PV is free at physiological cytosolic [Mg²⁺]_i (sect. 4.2). Competition with bound Mg²⁺ slows the binding of Ca²⁺ to PV in response to a cytosolic [Ca²⁺]_i increase. However, if the total cytosolic PV concentration is high, sufficient amounts of PV are not Mg²⁺ bound but free and can therefore act as a fast Ca²⁺ buffer. For example, for cerebellar BC→PC synapses, which contain on average >0.5 mM PV, 5% of the PV is free at rest, 73% is bound to Mg²⁺, and 22% is bound to Ca²⁺, when assuming resting concentrations of 40 nM free Ca²⁺ and 400 µM free Mg²⁺ (267). Thus, there is ∼30 µM of free PV available that can rapidly bind Ca²⁺ and affect peak local domain [Ca²⁺]_i. When free PV is depleted in the local domain, it is replenished both by diffusion of free PV from the periphery and from a large reservoir of Mg²⁺-bound PV, which, however, has to shed Mg²⁺ before being able to bind Ca²⁺. The Mg²⁺ binding of PV, therefore, represents a mechanism for generating new buffer (called “metabuffering”) (267), albeit on a slower timescale. This distinction between fast buffering by free PV and slower buffering following dissociation of Mg²⁺ is identical to that discussed above for skeletal muscle (sect. 7.2).

9.5. Modulation of Short-Term Plasticity by Ca²⁺ Buffers

During repetitive activation, the strength of synapses can transiently increase or decrease, resulting in synaptic facilitation or depression. Facilitating and depressing mechanisms are likely to operate simultaneously at many synapses, and the balance between the two defines magnitude and time course of changes in synaptic strength during stimulus trains. Local and global [Ca²⁺]_i signaling plays a key role in the presynaptic mechanisms of short-term plasticity (STP). Ca²⁺ buffers can affect presynaptic STP in two ways: 1) buffers shape amplitude and spatial profile of local Ca²⁺ domains triggering transmitter release, and 2) buffers determine the time course of global [Ca²⁺]_i changes, which occur in nerve terminals after diffusional equilibration after AP firing. These signals, also called “residual [Ca²⁺]_i changes,” are crucially involved in regulating STP.

The relationship between transmitter release rates and [Ca²⁺]_i is highly nonlinear, and the spatial profile of local [Ca²⁺]_i domains that build up in the vicinity of open presynaptic VGCCs after AP arrival is affected by Ca²⁺ buffers. Provided that these buffers bind Ca²⁺ fast enough, they are able to intercept incoming Ca²⁺ ions before binding to the Ca²⁺ sensor for transmitter release (see sect. 9.4). Thereby, Ca²⁺ buffers determine the [Ca²⁺]_i seen by the Ca²⁺ sensor and control synaptic vesicle fusion probability. During repetitive presynaptic AP firing, the concentration of free Ca²⁺ buffers may decrease if Ca²⁺ does not completely dissociate during interstimulus intervals or else if global [Ca²⁺]_i is transiently elevated. Such buffer saturation can lead to release facilitation because synaptic vesicles experience incrementally higher local [Ca²⁺]_i during repetitive stimulation (178, 493). Such a mechanism has been proposed to underlie facilitation at cortical synapses between multipolar bursting (MB) interneurons and pyramidal neurons (177) (FIGURE 19) and is analogous to the buffer saturation underpinning tetanic contraction in skeletal muscle (sect. 7.4). MB interneurons are CB-D28k positive, and MB→CA3 pyramidal cell synapses show pronounced paired-pulse facilitation (PPF). Washout of CB-D28k from MB interneurons during prolonged whole cell recordings increased the amplitude of the first responses and reduced PPF at MB→pyramidal cell synapses. Recordings in synapses of CB-D28k^−/− mice showed a similar pattern. CB-D28k loading into MB interneurons of CB-D28k^−/− mice via the recording pipette restored wild-type-like synaptic amplitudes and PPF (177). Taken together, these observations demonstrate that rapid Ca²⁺ binding to CB-D28k is able to reduce [Ca²⁺]_i within local domains that trigger vesicle fusion, and thus reduces synaptic strength.

FIGURE 19.

Ca²⁺ buffer saturation contributes to paired-pulse facilitation (PPF). A and B: opposite effects of changing Ca²⁺ influx on PPF in wild-type (MF, top) and CB-D28k-deficient (MF CB-KO, bottom) hippocampal MF→CA3 pyramidal cell synapses. A: excitatory postsynaptic currents (EPSCs) recorded in CA3 pyramidal cells during paired-pulse stimulation (interval 100 ms) of mossy fibers. B: paired-pulse ratios (EPSC₂/EPSC₁) normalized to those measured in 2 mM external calcium concentration ([Ca²⁺]_o). In wild-type MF→CA3 synapses (□), increasing external [Ca²⁺] increases facilitation, whereas decreasing ([Ca²⁺]_o reduces facilitation. In CB-D28k-deficient MF→CA3 synapses (●), the opposite was observed. Normalized PPFs measured at Schaffer collateral (SC)→CA1 synapses (■) are shown for comparison. Right graph illustrates a similar dependence of EPSC₁ on ([Ca²⁺]_o in all 3 synapses. Modified from Ref. 177, with permission from Neuron. C–E: a fast endogenous buffer attenuates transmitter release during the first action potential (AP). Buffer saturation during the first AP leads to higher local intracellular [Ca²⁺] ([Ca²⁺]_i) during the second AP and thereby produces PPF at MF→CA3 synapses. Upon washout of endogenous buffer, substitution with the slow buffer EGTA alters PPF whereas the fast buffer BAPTA restores PPF. C: schematic illustration of recording configurations. Presynaptic APs were elicited via stimulation in bouton-attached (left) or whole bouton (right) configuration with either EGTA or BAPTA in the pipette. The whole bouton configuration leads to rapid washout of mobile endogenous buffers from the presynaptic MF terminal. D: EPSCs recorded in a CA3 neuron while the MF bouton was first stimulated in the bouton-attached configuration (left) and subsequently in the whole bouton configuration with 100 µM EGTA in the stimulation pipette (right). E: similar experiment as shown in D but with 300 µM BAPTA in the pipette. Modified from Ref. 494, with permission from Science.

Buffer saturation also contributes to PPF and frequency facilitation at hippocampal mossy fiber (hMF)→CA3 pyramidal cell synapses (177, 494). Synaptic facilitation counteracts a potential reduction in synaptic strength caused by the consumption of synaptic vesicles during repetitive AP firing. In contrast to many other types of synapses, which show increased synaptic facilitation when lowering external [Ca²⁺] to attenuate release probability and thereby prevent synaptic vesicle exhaustion, the magnitudes of both PPF and frequency facilitation are decreased in these synapses at lower external [Ca²⁺] (177). This finding is consistent with reduced buffer saturation due to reduced presynaptic Ca²⁺ influx (FIGURE 19, A AND B). Dialysis of hippocampal mossy fiber boutons (hMFBs) with pipette solution containing 0.1 mM EGTA strongly augmented initial excitatory postsynaptic currents (EPSCs) and decreased paired-pulse ratios, whereas dialyzing 0.3 mM BAPTA into hMFBs restored amplitudes and facilitation to a pattern similar to synaptic responses generated by stimulating unperturbed hMBs (494), consistent with the loss of a mobile fast binding endogenous Ca²⁺ buffer during whole cell dialysis of the hMFB terminal (FIGURE 19, D AND E).

GABAergic synapses between cerebellar interneurons and Purkinje cells (PCs) show paired-pulse depression (PPD) in response to paired stimuli delivered at intervals between 30 and 300 ms (495). In PV^−/− mice, in synapses as well as in whole cell recordings of connected interneuron-PC pairs, the same stimulus pattern induced PPF (267, 495). Wild-type-like short-term plasticity could be restored by loading recombinant PV into presynaptic interneurons (267). Likewise, dialysis of presynaptic interneurons with 1 mM of the slow Ca²⁺ buffer EGTA rescued PPD in synapses of PV^−/− mice. EGTA and PV do not reduce markedly the peak of AP-induced [Ca²⁺]_i transients, but both accelerate their initial rate of decay. Thus, the acceleration of the Ca²⁺ decay is likely to reduce the residual [Ca²⁺]_i and hence to attenuate facilitation (495) (FIGURE 20A).

FIGURE 20.

The slow endogenous buffer parvalbumin (PV) affects the time course of presynaptic global intracellular calcium concentration ([Ca²⁺]_i) transients and thereby regulates synaptic short-term plasticity. A: absence of paired-pulse depression at GABAergic synapses between interneurons and Purkinje cells (PCs) of PV knockout (KO) mice. Inhibitory postsynaptic currents (IPSCs) in response to extracellular stimulations of GABAergic interneurons with paired stimuli (30-ms interval) were recorded in Purkinje cells of a PV^+/+ mouse (top) and a PV^−/− mouse (middle). Bottom: average paired-pulse ratios [PPR = excitatory postsynaptic current (EPSC)₂/EPSC₁] are shown as a function of interstimulus interval for PV^+/+ (circles) and PV^−/− (diamonds) mice. Modified from Ref. 495, with permission from Proceedings of the National Academy of Sciences USA. B: slower decay of PPF at glutamatergic calyx of Held synapses of PV^−/− mice. EPSCs were recorded in response to pulse pairs at 3 different interstimulus intervals (Δt) in a PV^−/− calyx of Held synapse at reduced (0.6 mM) external [Ca²⁺] (top). PPRs plotted as a function of Δt were fitted by an exponential function with a time constant of 77 ms (middle). Paired-pulse facilitation in a calyx synapse from a wild-type (PV^+/+) mouse decayed notably faster, with a time constant of 17 ms (bottom). Modified from Ref. 479, with permission from Journal of Neuroscience.

Similar observations were made at calyx of Held synapses, which show pronounced PPF at low-release probability conditions (0.6 mM external [Ca²⁺]). PPF decays with a time constant of 17 ms in synapses of wild-type mice, whereas genetic ablation of PV expression increases the time constant of decay to 77 ms. PV^+/+ and PV^−/− calyx of Held synapses show a similar magnitude of PPF when probed at an interstimulus interval of only 4 ms. However, at an interstimulus interval of 50 ms, PPF had nearly completely decayed in the wild type, whereas it was reduced to only half in PV^−/− calyx synapses (479) (FIGURE 20B). These observations are consistent with the notion that the slow Ca²⁺ buffer PV only marginally reduces the peak of residual [Ca²⁺]_i transients, because of its slow action. Nevertheless, PV binds Ca²⁺ fast enough to strongly accelerate their initial decay. In contrast to the case of calyx of Held synapses, genetic elimination of PV has only minimal effects on synaptic transmission at hippocampal BC→GC synapses, consistent with its low concentration in hBCs (267).

Cerebellar Purkinje cells (PCs), which express large amounts of CB-D28k and PV, are reciprocally connected via inhibitory synapses that show PPF during high-frequency activation. Surprisingly, PPF is not affected by the absence of either CB-D28k or PV at these GABAergic recurrent PC→PC synapses. Likewise, PPF measured in experiments on wild-type pairs of connected PCs that were dialyzed for 60–70 min with 10 mM EGTA remains unaltered compared with controls. Thus, PPF at PC→PC synapses is largely independent of the major endogenous Ca²⁺ buffers CB-D28k and PV and of the decay of residual [Ca²⁺]_i. Instead, it was proposed that PPF results from long-lived Ca²⁺-bound states of the sensor for transmitter release (496).

9.6. Modulation of Delayed Asynchronous Transmitter Release by Ca²⁺ Buffers

In many synapses, two kinetically distinct components of AP-evoked transmitter release can be distinguished: 1) synchronous release that is temporally tightly coupled to the arrival of the presynaptic AP and 2) delayed asynchronous release that can last up to hundreds of milliseconds (497, 498). The relative contributions of these components to the total release depend on synapse type and can change with repetitive synapse activation during which asynchronous release typically builds up with increasing frequency and duration of stimulus trains.

At synapses between interneurons of the cerebellar molecular layer (MLIs), the time course of global [Ca²⁺]_i determines the time course of delayed asynchronous release observed after stimulus trains (250). After 50-Hz stimulation, a barrage of asynchronous release events was observed that can last for up to ∼2.5 s after cessation of stimulation. This delayed release was strongly attenuated in PV^−/− mice. This is consistent with the postulated effect of the slow buffer PV on global [Ca²⁺]_i transients. In the presence of PV, the initial [Ca²⁺]_i decay is sped up because of Ca²⁺ binding. The subsequent unloading of Ca²⁺ from PV during the decline of global [Ca²⁺]_i generates a slowly decaying component of the [Ca²⁺]_i transient that supports delayed asynchronous release during a time window between 0.5 and 2.5 s after cessation of stimulation. In PV^−/− mice, the slow [Ca²⁺]_i transient component is absent, and delayed asynchronous release is strongly reduced.

A similar scenario was described for hippocampal mossy fiber to CA3 pyramidal cell (hMF→CA3) synapses, where brief 20-Hz EPSC trains are followed by delayed asynchronous release lasting for ∼1–2 s (499). [Ca²⁺]_i measurements in mossy fiber boutons revealed a slowly decaying time course of presynaptic global Ca²⁺. Treatment of the synapses with the membrane-permeable slow buffer EGTA-AM decreased the amplitude of delayed asynchronous release but prolonged its duration, reminiscent of what was observed in cerebellar MLI→MLI synapses of PV-expressing in comparison to PV-lacking mice (250).

Presynaptic terminals of glutamatergic endbulb→bushy cell synapses in the mammalian antero-ventral cochlear nucleus invariably express PV, but only a subset coexpress CR. Interestingly, postsynaptic neurons contacted by CR/PV-coexpressing terminals show lower rates of asynchronous release compared with those that are contacted by terminals void of presynaptic CR immunoreactivity (464). At glutamatergic calyx of Held→MNTB synapses, the magnitude of delayed asynchronous release observed after high-frequency stimulus trains strongly decreases during postnatal maturation. Developmental decrease in asynchronous release coincides with an upregulation of presynaptic CR expression, but virtually all calyces are PV immunoreactive already shortly after hearing onset (postnatal day 12) (463). Neither endbulb nor calyx terminals express CB-D28k. Whether this developmental downregulation of asynchronous release is related to differences in CR expression remains to be established. Nevertheless, these findings can be understood on the basis that CR is a fast buffer, which reduces the peak of the [Ca²⁺]_i transient. During the [Ca²⁺]_i decay, free and Ca²⁺-bound forms of CR are at equilibrium, such that Eqs. 30–32 hold. Although these equations predict that the area under the [Ca²⁺]_i transient is unchanged in the presence of the buffer (FIGURE 7D), its amplitude is reduced (FIGURE 7, A AND C). For a cooperative process, such as Ca²⁺-triggered synaptic vesicle fusion, this implies a reduction of the overall effect of the [Ca²⁺]_i transient.

Among hippocampal dentate gyrus inhibitory interneuron→principal neuron synapses, PV-expressing interneurons provide temporally precise inhibition, which is tightly synchronized to the timing of presynaptic AP firing, whereas cholecystokinin (CCK)-expressing interneurons release GABA in a less synchronized manner and exhibit prominent asynchronous release for a few hundreds of milliseconds after stimulus trains. CCK-expressing interneurons seem to lack expression of PV, CB-D28k, and CR. It is therefore conceivable that the differential expression of PV contributes to the mechanisms responsible for the ∼15-fold difference in the ratio of synchronous versus asynchronous release at these two synapses by accelerating the initial decay of AP-induced [Ca²⁺]_i transients in PV-expressing interneurons and thereby reducing the number of asynchronously released quanta immediately following presynaptic APs (500).

9.7. Modulation of Excitability, AP Firing, and Network Activity

Neuronal membrane excitability and discharge properties are determined by an interplay of various voltage- and/or Ca²⁺-sensitive ion conductances. The amount of Ca²⁺ entering per AP is controlled by the AP duration, which needs to be precisely regulated to limit Ca²⁺ influx especially during repetitive AP firing. Many cortical neurons, including hippocampal granule cells (hGCs), express large-conductance Ca²⁺-sensitive potassium channels (BK channels), which contribute to AP termination. When recorded with pipettes containing 10 mM BAPTA, AP durations in hGCs increase similarly as observed after application of BK channel blockers, indicating that BAPTA uncouples BK channels from Ca²⁺ influx. Intracellular application of 10 mM EGTA does not affect AP kinetics, because BK channels are spatially tightly coupled to VGCCs. By quantitatively analyzing the extent of AP prolongation by different intracellular BAPTA concentrations, the mean diffusional distance for Ca²⁺ ions from VGCCs to BK channels was estimated to be ∼13 nm in hGCs (501). Such tight colocalization of the two types of channels together with low Ca²⁺ sensitivity of BK channels confines the activation of BK channels to short, well-timed episodes, which is required for fast AP repolarization. It also decouples channel activation from changes in global [Ca²⁺]_i levels.

CR is the main cytosolic Ca²⁺ buffer in cerebellar granule cells (cGCs), which provide the major excitatory input to Purkinje cells via their parallel fibers. Recordings in cGCs of CR^−/− mice showed that CR-deficient cGCs exhibit briefer APs compared with cGCs of wild-type mice. They also generate repetitive spike discharge with a steeper rise in firing frequency with increasing current injections. Addition of 0.15 mM BAPTA to the patch pipette solution restored normal excitability levels in CR-deficient cGCs, indicating that 0.15 mM BAPTA effectively mimics the contribution of CR to the cytosolic Ca²⁺-buffering power in cGCs of wild-type mice. A minimal single compartment-based model of cGC AP firing, which considers voltage- and Ca²⁺-sensitive conductances as well as Ca²⁺ buffering and extrusion, supports the conclusion that larger and faster-decaying AP-induced [Ca²⁺]_i transients in CR-deficient cGCs are a consequence of reduced Ca²⁺ buffering, which enhances activation of Ca²⁺-sensitive BK potassium channels, speeds up AP repolarization, and thus produces shorter APs that enable faster discharge rates (502).

A similar modeling approach was used to study the role of the slow buffer PV for regulating the discharge properties of striatal fast-spiking (FS) interneurons (503). A conductance-based model that also includes Ca²⁺-sensitive small-conductance (SK) potassium channels and the presence of a Ca²⁺ buffer reproduces average firing frequencies and spike adaptation as observed during whole cell recordings in striatal FS interneurons in response to current injection. Higher concentrations of PV lead to elevated [Ca²⁺]_i between consecutive AP-induced [Ca²⁺]_i transients when Ca²⁺ dissociates from PV and thereby facilitate activation of the SK current. This increases the duration of the afterhyperpolarization (AHP) following each AP and thereby delays the next AP and reduces the firing frequency. Thus, variable concentrations of PV in the cytoplasm of striatal FS interneurons can modulate their intrinsic excitability and may potentially alter striatal information processing (503).

Neurons of the reticular thalamic nucleus (RTN) express high levels of PV and are characterized by low-threshold voltage-activated (LVA) Ca²⁺ currents. Based on the firing patterns observed in extracellular in vivo recordings, four types of neurons can be distinguished in the RTN: irregularly firing, medium bursting, long bursting, and tonically firing. Neurons of the medium-bursting type are more frequently observed than those of the long-bursting type in PV^−/− mice. The generation of AP bursts involves Ca²⁺ influx thorough LVA VGCCs that subsequently activates Ca²⁺-dependent SK potassium channels. It is possible that a lack of PV in RTN neurons alters SK channel activation following Ca²⁺ influx and thereby affects their firing properties (504).

Cerebellar Purkinje cells generate two types of membrane discharges: simple and complex spikes. Simple spikes occur spontaneously or are triggered synaptically by parallel fiber input, whereas complex spikes are driven by climbing fiber input. Extracellular recordings in Purkinje cells from cerebella of adult calretinin-deficient (CR^−/−) mice revealed a strongly enhanced spontaneous simple spike firing rate compared with wild-type mice, whereas mean spontaneous firing rates of complex spikes were unaltered. The duration of complex spikes was reduced in CR^−/− PCs, as was the duration of pauses in simple spike firing following spontaneous complex spikes (505). A reduced complex spike duration may decrease Ca²⁺ influx and thence activation of Ca²⁺-sensitive potassium channels, leading to shorter pauses in simple spike firing that normally follows the complex spike (505). Motor coordination is impaired in CR^−/− mice consistent with the role of the cerebellum in motor control and motor learning (506). Genetic ablation of both CR and CB-D28k (CR^−/−CB-D28k ^−/−) induces 160-Hz local field potential oscillations in the cerebellar cortex of alert mice, with PCs firing simple spikes phase-locked to the oscillations. Since the intrinsic excitability of PCs is unaltered in CR^−/−CB-D28k ^−/− mice but oscillations reversibly disappear when gap junctions or either GABA_A or NMDA receptors are blocked, these 160-Hz oscillations are likely to emerge at the network level, demonstrating that changes in intracellular Ca²⁺ buffering in specific neuron types can alter network dynamics (507).

9.8. Modulation of Ca²⁺ Signaling in Dendritic Shafts and Spines

Dendritic Ca²⁺ signaling and its modulation by Ca²⁺ buffers has been studied experimentally by dye loading into dendrites of neocortical and hippocampal pyramidal neurons, cerebellar Purkinje cells and various interneurons, as well as by numerical simulations using deterministic or stochastic approaches. Dendritic [Ca²⁺]_i transients in pyramidal neurons evoked by backpropagating APs have amplitudes of several hundreds of nanomolar and decay rapidly with time constants generally <100 ms at physiological temperature (441, 508, 509) (FIGURE 21A). Neocortical and hippocampal CA3 pyramidal neurons lack expression of PV, CR, and CB-D28K. Hippocampal CA1 pyramidal neurons are also void of PV and CR but contain ∼45 µM CB-D28K (444). For these neurons, estimates for the endogenous Ca²⁺ buffer power in dendrites ranged between 170 and 200, indicating that <1% of the total Ca²⁺ entering per AP remains free. During AP trains, [Ca²⁺]_i increases to a steady-state level that depends linearly on the firing frequency. Thus, the dendritic [Ca²⁺]_i level linearly encodes the frequency of APs in pyramidal neurons (441). Dendritic Ca²⁺ transients elicited by backpropagating APs in bitufted interneurons in layer 2/3 of the somatosensory cortex have a mean amplitude of ∼140 nM and decay with a slow time constant of ∼200 ms, consistent with their higher endogenous Ca²⁺ buffer power (∼285) compared with that of pyramidal neurons (511). [Ca²⁺]_i transients measured in dendrites of hippocampal dentate gyrus basket cells (hDG BCs) show similar kinetics, with a mean decay time constant of ∼200 ms, but have smaller amplitudes, with a mean of only ∼40 nM. The endogenous Ca²⁺ buffer power in hippocampal dentate gyrus BC dendrites is ∼200. In these neurons, Ca²⁺ buffering power was estimated both during Ca²⁺ indicator loading and under steady-state conditions up to 20 min after establishing whole cell configuration, when mobile buffers are expected to be largely washed out. The similarity of the buffering power estimates obtained under these two conditions suggests that the Ca²⁺ buffering power in proximal apical dendrites of BCs is primarily determined by buffers that are resistant to washout (512). Similarly to pyramidal cells, dendritic [Ca²⁺]_i transients in these two classes of cortical and hippocampal interneurons summate linearly during short AP bursts (511, 512) whereas dendrites of midbrain dopamine neurons of the substantia nigra exhibit a supralinear summation of single AP-evoked Ca²⁺ transients (513).

AP-induced [Ca²⁺]_i transients in dendritic spines and shafts of Purkinje cells (PCs), which contain high concentrations of PV and CB-D28k, last considerably longer than those in pyramidal cell dendrites (510, 514) (FIGURE 21B). In both compartments, [Ca²⁺]_i transients decay double exponentially with fast and slow time constants of ∼20–30 and ∼300–400 ms, respectively (510). Whereas amplitudes of the slowly decaying component are comparable for [Ca²⁺]_i transients measured in dendritic shafts and spines, amplitudes of the fast-decaying components are considerably greater in spines, which largely accounts for the higher total amplitudes of their [Ca²⁺]_i transients. To reproduce the rapid initial decay of [Ca²⁺]_i transients in spines in numerical simulations, diffusional coupling had to be assumed, allowing free Ca²⁺ as well as all Ca²⁺-bound and free buffer species to diffuse between both compartments. The simulations further suggest that 1) neither CB-D28k nor PV saturates in spines or shafts during climbing fiber-evoked Ca²⁺ transients, 2) k_on of CB’s medium-affinity binding is fast enough to reduce [Ca²⁺]_i transient peaks, and 3) slow Ca²⁺ binding to PV and CB-D28k leads to biphasic decay of [Ca²⁺]_i transients in dendritic shafts (510).

In cerebellar Purkinje cells, the functional consequences of genetic removal of one or both mobile Ca²⁺ buffers PV and CB-D28k were studied. Kinetic analysis of [Ca²⁺]_i transients in PC dendrites of CB-D28k^−/− mice (515, 516) and in spines and dendritic shafts of PCs of PV^−/− and PV^−/−CB-D28k^−/− mice (510) shows that Ca²⁺ buffers contribute to sculpting amplitude and decay of [Ca²⁺]_i transients. In CB-D28k^−/− PCs, resting [Ca²⁺]_i is unaltered but peak amplitudes of synaptically evoked dendritic [Ca²⁺]_i transients associated with complex spikes are enhanced on average by >80% compared with wild-type PCs. This is mainly due to an increase of the fast, but not the slow, decay component of [Ca²⁺]_i transients (515, 516). In PV^−/− PCs, [Ca²⁺]_i transients reach the same peak amplitudes as in wild-type animals, but the biphasic nature of the decay is less pronounced. When both PV and CB-D28k are removed (PV^−/−CB-D28k^−/−), peak amplitudes of [Ca²⁺]_i transients are about two times higher than those in wild-type PCs, and their decay is nearly monophasic (510).

9.9. Ca²⁺ Buffers in Neurological and Neurodegenerative Diseases

It was originally considered that Ca²⁺ binding proteins may exert a neuroprotective function by protecting cells against damaging effects of excessively high [Ca²⁺]_i during periods of strong activity (517). Distinct populations of neurons are selectively affected by different neurodegenerative diseases, which could be facilitated by a weakening of their Ca²⁺ buffering power because of intrinsically low or diminished expression of CBPs. Differential expression of CBPs in neuronal subpopulation could thus contribute to defining their susceptibility to disease processes. For example, motoneuron populations lost early in amyotrophic lateral sclerosis (ALS) lack CB-D28K and PV expression, whereas those damaged late or infrequently express higher levels of these CBPs (518). On the other hand, a substantial loss of neostriatal neurons containing CB-D28K has been reported for postmortem brain specimens from patients diagnosed with Huntington’s disease, indicating a selective vulnerability of these neuron populations (519). In general, the concept of CBPs primarily serving neuroprotective functions has received only limited experimental support. Rather, CBPs are essential components in neuronal Ca²⁺ homeostasis and signaling that primarily regulate the timing and spatial extent of Ca²⁺ signals. Deficiencies in one or more CBPs lead to distinct alterations in neuronal excitability and/or synaptic physiology that possibly also penetrate to the behavioral level.

Mice with genetic ablation of PV, CB-D28k, or CR expression are generally healthy and fertile and show no gross abnormalities in brain morphology (520). For example, CB-D28k^−/− mice develop normally and have a normal anatomy and synaptic connectivity with no signs of cell death. However, CB-D28k-deficient mice show motor deficits. They develop a graded cerebellar ataxia, which is correlated with marked changes in the amplitude and kinetics of synaptically mediated [Ca²⁺]_i transients, and display aberrant network activity (515). In CR^−/− mice, gross development and many morphological, biochemical, and behavioral characteristics were found to be unaffected, but these animals show a motor discoordination that worsens dramatically with age (505, 521). In addition, long-term potentiation (LTP) but not basal synaptic transmission is impaired in CR^−/− mice at synapses between the perforant pathway and granule cells in the dentate gyrus connecting entorhinal cortex with the hippocampal formation. Normal LTP can be restored in these animals by application of the GABA_A receptor antagonist bicuculline, suggesting that in CR^−/− dentate gyrus an excess of GABA release interferes with LTP induction. Thus, expression of CR contributes to the control of synaptic plasticity in mouse dentate gyrus by indirectly regulating the activity of GABAergic interneurons (522). Despite such roles of Ca²⁺ buffers in neuronal signaling, a complete absence of α-PV, CB-D28k, and CR has little impact on cochlear function and hearing when comparing distortion-product otoacoustic emissions and auditory brain stem responses between constitutive triple KO and wild-type mice (223). PV^−/− and PV^+/− mice show social behavior deficits with an autism spectrum disorder (ADS)-like phenotype including impairments in communication and repetitive and stereotyped patterns of behavior (523). This seems to relate to an absent or reduced PV expression in PV^−/− and PV^+/− mice, respectively, rather than to a loss of fast-spiking GABAergic interneurons (523).

We are unaware of human monogenic disorders causally linked to mutations in the CB-D28k, PV, or CR genes. However, altered expression of the CBPs PV, CB-D28k, or CR has been reported in the context of neurological diseases including ADS, dementia, epilepsy, and ataxia (524, 525). For example, a decrease in the levels of CB-D28K has been found in the cortex of brains of Alzheimer disease (AD) patients (526, 527). Vulnerability to AD also extends to PV-containing interneurons. A decrease in PV immunostaining was reported for parts of the entorhinal cortex when AD neuropathological markers are present. As the density of pathological markers in the entorhinal cortex becomes greater and more widespread, the decrease of PV immunostaining encompasses additional layers, even though some changes that are observed in PV-expressing interneurons may be linked to the fate of the projection neurons on which they synapse (528). AD disease-sensitive PV-containing inhibitory interneurons were further identified in the perirhinal cortex of AD patients (529). In the temporal cortex of AD patients the number of PV-immunoreactive somata was unchanged, but in layer II a decreased density of terminals of PV-expressing chandelier cells was observed, suggesting that not the interneurons themselves but only their terminals are decreased (530).

These findings raise the possibility that dysregulation of Ca²⁺ buffering power in certain neuron populations may contribute to the etiopathology. It is, however, challenging to differentiate between selective loss of neurons expressing a certain CBP and decreased protein expression. For example, for caldendrin, a member of the neuronal calcium-binding protein (nCaBP) family with rapid Ca²⁺-binding kinetics and high abundance in postsynaptic density of spine synapses, it was reported that in postmortem brains of subjects with chronic schizophrenia the number of caldendrin-immunoreactive neurons is significantly reduced in the left dorsolateral prefrontal cortex (531). Despite the reduced number of immunoreactive neurons, absolute caldendrin protein levels were elevated (532). A reduction of mRNAs encoding PV was found in the prefrontal cortex of subjects with schizophrenia. This was primarily due to a reduction in neuronal PV mRNA expression rather than a decreased density of PV mRNA-positive neurons. In contrast, the same measures of CR mRNA expression were not altered in schizophrenia (533).

10. EPITHELIA

Transport of Ca²⁺ across epithelia is important for the body’s Ca²⁺ homeostasis (for review see Ref. 534). To summarize, Ca²⁺ is absorbed by the intestine and then excreted from the body via the kidneys. Although the kidney may be a site of net Ca²⁺ loss from the body, it is important to remember that there is a balance between glomerular filtration and subsequent reabsorption, so Ca²⁺ (re)absorption occurs in both kidney and intestine. There are two routes for transepithelial Ca²⁺ transport. Some can occur via a paracellular route, through tight junctions between cells (535). Another important route involves transcellular transport with Ca²⁺ present in the lumen, entering the cell, along its electrochemical gradient, before being actively transported (by NCX and/or PMCA) at the basolateral membrane into the extracellular fluid and thence the blood.

Early work on rat duodenum found that calcium absorption comprised two components as characterized by their response to elevating luminal [Ca²⁺] and vitamin D. One was a saturating function of luminal [Ca²⁺] and was stimulated by vitamin D, whereas the other was proportional to [Ca²⁺] and independent of vitamin D (536, 537). The transport through the former pathway was found to be proportional to the concentration of a vitamin D-induced CBP (536, 538, 539). This CBP was subsequently shown to be comprised of the two calbindins (CBs) CB-D9k and CB-D28k (for review see Ref. 540). CB-D9k has two Ca²⁺ binding sites, and CB-D28k has four (30, 186) (see TABLES 2 and 3). In general, tissues only express one of the two CBs, for example CB-D9k in the duodenum and CB-D28k in the kidney.

A major challenge for the transport mechanism described above is that, to move between the apical and basolateral membranes, Ca²⁺ must traverse the cytoplasm, where [Ca²⁺]_i is very low. It was calculated that the diffusion rate of free Ca²⁺ would be ∼70 times smaller than the experimentally measured transepithelial flux (541). Therefore the role of CBs is to allow rapid diffusion of Ca²⁺ across the cytoplasm while maintaining [Ca²⁺]_i low. As pointed out previously (174, 200, 209) (see also sect. 4.5), there are two opposing factors. 1) Since CB has a larger MW than Ca²⁺, the diffusion rate of an individual Ca²⁺ bound to CB will be much slower, in proportion to the 0.33th power of the ratio of molecular weights, than that of a free Ca²⁺ ion. Calcium has an atomic weight of 40, so Ca²⁺ bound to CB-D9k will diffuse at a speed of about (40/9000)^0.33 ≈ 16% of that of free Ca²⁺. For Ca²⁺ bound to CB-D28k, the corresponding value is ∼12%. This effect is greatly outweighed by the fact that the concentration of Ca²⁺ bound to CB is much higher than that of free Ca²⁺ so the net effect is a marked increase in the rate of Ca²⁺ diffusion (≈50-fold with the values of TABLE 3). It should also be noted that free Ca²⁺ ions will bind to fixed charges in the cell, slowing their diffusion. Charge neutralization by binding to CB will thereby accelerate diffusion. We could not find measurements of the contribution of fixed buffers in epithelia, but, given the high concentration of CBs, it is probable that Ca²⁺-transporting epithelia represent a case where the majority of buffering comes from mobile rather than fixed buffers.

Evidence suggests that CB-D9k plays the major role as the CBP in the intestine. A similar mechanism involving CB is also important for renal reabsorption of Ca²⁺ in the distal convoluted tubule (DCT), but here CB-D28k is the major player. Indeed, the appearance of CB in urine has been proposed as a biomarker for damage to the distal nephron (542). PV is also expressed in the cells of the DCT (543). Knockout of PV resulted in diuresis. PV also appeared to act as a Ca²⁺ buffer and thereby reduced the amplitude of intracellular Ca²⁺ signals, suggesting that the effects of PV are as an intracellular Ca²⁺ buffer modulating Ca²⁺ signaling as opposed to transport (544). It has also been shown that most of the PV in the kidney is located in the early DCT, a region where there is little Ca²⁺ transport (543, 545). In other sections we have discussed the importance of the kinetics of PV in shaping Ca²⁺ signals. Given the slow kinetics of changes of [Ca²⁺]_i in the DCT (544), it is unclear whether these kinetics are relevant. It is, of course, possible that fast changes of [Ca²⁺]_i in a subcompartment of the cytoplasm are affected by PV.

Work showing that CB-D9k is localized to the basolateral membrane in the rat distal nephron has also led to the suggestion that it may regulate Ca²⁺ transport as well as buffering (543). The entry of Ca²⁺ along its electrochemical gradient from lumen into cell occurs in many epithelia through TRPV5 channels, with the Ca²⁺ subsequently binding to CB and being transported across the cell. It has been shown that the expressions of CB and TRPV5 are coordinated (546). As well as being present in the cytoplasm, a fraction of the CB is localized on the apical membrane, and this apical fraction is decreased in TRPV5 knockout mice. It has been suggested that Ca²⁺ buffering by CB in the vicinity of the TRPV5 channel increases influx through this channel.

Mg²⁺ is also reabsorbed by the DCT, and it has been suggested that it enters the cell from the lumen via a TRPM6/7 channel (547). That work showed that the TRPM channel was located close to either PV or CB-D28k, and it was suggested that binding of Mg²⁺ to buffers may be important in transepithelial Mg²⁺ transport (548). As pointed out in sect. 2.2, many Ca²⁺ buffers can also bind Mg²⁺. The major Mg²⁺ buffer is probably ATP. The relative molecular weights (atomic mass of Mg²⁺ is 24 and MW of ATP is 500) mean that the bound form diffuses at (24/500)^0.33 = 0.37 of the free. Given a free Mg²⁺ of 1 mM, a total ATP concentration of 5 mM and K_d of 100 µM for Mg²⁺ binding to ATP, we obtain from Eq. 27 that the flux of bound will be only 12% of that at the free. The contribution to Mg²⁺ diffusion of protein buffers, with higher molecular weights and lower concentrations than ATP, will be even smaller. Consistent with this, knockout of CB-D28k does not affect Mg²⁺ balance (549).

11. IMMUNE CELLS

Early studies using the Ca²⁺ indicator quin-2 found that the intrinsic buffering in human neutrophils could be represented by ∼0.76 mM of a buffer with K_d of 0.55 µM (550), equivalent to a buffer power of ∼1,000 at low [Ca²⁺]_i. Neutrophils and monocytes were then shown to contain CBPs of the S100 family (551). The major components are migration inhibitory factor-related proteins 8 and 14 (MRP8 and MRP14), more commonly known, respectively, as S100A8 and S100A9, which form a dimer known as calprotectin. Two such dimers can form a tetramer, particularly at elevated [Ca²⁺], and this tetramerization is essential for biological function (552). Calprotectin can also bind Mn²⁺ and Zn²⁺, and it has been shown that release of calprotectin into the extracellular fluid has an antibacterial action by chelating these ions (553–555). Mn²⁺ is required for the function of bacterial superoxide dismutase as well as a variety of other bacterial enzymes, and Zn²⁺ is required for several bacterial enzymes (556). It appears that Ca²⁺ binding to the EF hands on calprotectin increases the affinity for Zn²⁺. Consequently, the affinity for Zn²⁺ and Mn²⁺ will be much greater outside, where Ca²⁺ is higher, than inside the cell, thereby allowing calprotectin to avidly bind Mn²⁺ or Zn²⁺ once it is released into the extracellular fluid where the bacteria are present (557, 558). The sequestration of extracellular Mn²⁺ and Zn²⁺ will therefore deprive bacteria of these essential metal ions, thereby preventing their growth (556).

Activated macrophages have been shown to release β-PV (oncomodulin), and this stimulates the outgrowth of axons from retinal ganglion cells (559). This effect could not be mimicked by other CBPs, suggesting that it results from an action of oncomodulin other than Ca²⁺ binding. Subsequent studies have also shown that oncomodulin released from neutrophils has similar effects (560).

A very different role of Ca²⁺ buffers has been suggested as a defense against West Nile virus. Infection of a cell by this virus has been shown to increase [Ca²⁺]_i (561). Subsequent work found that CB-D28k decreased viral replication in cultured cells (562). A study with another virus (Borna disease virus) found that infection increased expression of CB-D28k in submucous and myenteric neurons (563). Although the effects of CB on viral invasion may be due to effects on [Ca²⁺]_i, direct measurements are required to confirm this.

12. CONCLUSIONS

The physiological properties of Ca²⁺ buffers have been studied in a variety of tissues. Their biochemical parameters such as ion specificity, binding kinetics, affinity, and cooperativity of binding generate a range of properties required for optimal cell function. Endogenous and exogenous Ca²⁺ buffers shape local and global [Ca²⁺]_i transients in predictable ways in different cell compartments. Together with Ca²⁺ influx and extrusion, the specific properties of Ca²⁺-binding molecules enable cells to encode activity using the universal second messenger Ca²⁺ and relay signals to specific intracellular pathways. By shaping and confining local [Ca²⁺]_i domains, Ca²⁺ buffering allows local signaling at spatially separate sites to coexist with global Ca²⁺ actions.

Some Ca²⁺-binding proteins serve a dual role as detectors of Ca²⁺ signals and Ca²⁺ buffers, whereas others act mainly as buffers shaping the spatiotemporal properties of intracellular Ca²⁺ signals. Ca²⁺ buffers can sculpt intracellular Ca²⁺ signaling in many ways. They can accelerate or retard the diffusion of Ca²⁺ in the cell, sharpen the spatial profile of local Ca²⁺ domains that build up during transmembrane Ca²⁺ flux, and thereby contribute to isolating local from global Ca²⁺ signaling pathways.

Each Ca²⁺ buffer can be used in several cell types. For example, the calbindins facilitate both epithelial Ca²⁺ transport and neuronal signaling, and the slow kinetics of parvalbumin are used to selectively accelerate the decay of Ca²⁺ signals in both neurons and skeletal muscle without interfering with their rise and amplitude. There are, however, tissue-dependent differences in buffering. Cardiac muscle is at one extreme, with most of the buffering provided by the nondiffusible buffers TnC and SERCA, essential for excitation-contraction coupling, with only a small contribution from molecules whose major function is to buffer. Skeletal muscle is broadly similar but also makes use of the diffusible buffer parvalbumin. In contrast, in neurons a high cytosolic Ca²⁺ buffering power is often achieved by expressing high amounts of one or two species of mobile Ca²⁺ buffer proteins. In general, neurons with low Ca²⁺ buffering power exhibit relatively fast decays of global [Ca²⁺]_i transients, whereas those with high buffer power, as a consequence of expression of high amounts of Ca²⁺ binding proteins, exhibit slower or biphasic global [Ca²⁺]_i transients. In neurons, this type of multiphasic kinetics of [Ca²⁺]_i transients allows cells to shape responses to action potentials in cell-specific ways and thereby produce a variety of short-term plasticity patterns. Slow tails of [Ca²⁺]_i transients build up during repetitive activity and may support asynchronous transmitter release and enable various forms of synaptic plasticity at intermediate timescales. Understanding of the quantitative effects of buffering has advanced less for many other tissues than is the case in nerve and muscle, and more research is required. For now, we will have to be satisfied with knowing which buffers are present and applying the basic principles learned from work on excitable cells.

A major area for future work concerns the role of changes of Ca²⁺ buffering in disease. Although there is evidence for such a link in cardiac muscle, it remains to be seen what the situation is in other tissues.

GRANTS

D.E. was funded by a British Heart Foundation Chair (CH/2000004/12801) and Grant FS/CRTF/21/24140. E.N.’s and H.T.’s work is supported by the German Research Foundation (DFG), Collaborative Research Center 1286 “Quantitative Synaptology.” E.N. acknowledges funding by the DFG under Germany’s Excellence Strategy-EXC 2067/1-390729940. G.S. was funded by British Heart Foundation Grant PG/19/55/34545.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

D.E., E.N., H.T., and G.S. conceived and designed research; D.E., H.T., and G.S. prepared figures; D.E., E.N., H.T., and G.S. drafted manuscript; D.E., E.N., H.T., and G.S. edited and revised manuscript; D.E., E.N., H.T., and G.S. approved final version of manuscript.