Measuring the Kinetics of Calcium Binding Proteins with Flash Photolysis

Abstract

Background

Calcium-binding proteins (CBPs) are instrumental in the control of Ca²⁺ signaling. They are the fastest players within the Ca²⁺ toolkit responding within microseconds to [Ca²⁺] changes. The CBPs compete for Ca²⁺ which plays a direct role in modulating Ca²⁺ transients and the resulting biochemical message. The kinetic properties of the CBPs have to be known to have a good understanding of Ca²⁺ signaling.

Scope of review

Most techniques used to measure binding kinetics are too slow to accurately determine the fast kinetics of most CBP. Furthermore, many CBPs bind Ca²⁺ in a cooperative way, which should be incorporated in the kinetic modeling. Here we will review a new ultra-fast in vitro technique for measuring Ca²⁺ binding properties of CBPs following flash photolysis of caged Ca²⁺. Compartmental modeling is used to resolve the kinetics of fast cooperative Ca²⁺ binding to CBPs.

Major conclusions

Currently this technique has only been used to quantify the kinetics of three CBPs (calbindin, calretinin and calmodulin), but has already provided remarkable insights into the specific role that these kinetics in Ca²⁺ signaling.

General significance

The potential to gain novel insights into Ca²⁺ signaling by quantifying kinetics of other CBPs using this technique is very promising.

1 Introduction

1.1 The role of Calcium Binding Proteins in Ca²⁺ signaling

Calcium ions (Ca²⁺) are the signaling particles that function in the largest variety of biological signaling pathways. In all eukaryotic cells, Ca²⁺ signals play a crucial messenger role in the regulation of many processes including neurotransmission, muscle contraction, metabolism, cytoskeleton dynamics, gene transcription, cell cycle and cell death. Some of these Ca²⁺ signals are highly localized within a cell, while others are more global. Moreover, the regulation of Ca²⁺ practically covers the whole temporal spectrum over which biological processes are modulated, from (sub) milliseconds to years [1, 2]. Notably, some of the processes triggered by an increase in intracellular [Ca²⁺] in a given cell oppose one another. For example, neuronal growth cone outgrowth/exploration vs. growth cone retraction [3] and long-term potentiation (LTP) vs. long-term depression (LTD) [4, 5] are diametrically opposed processes. It is remarkable how a simple ion can regulate cellular functions in such a multitude of ways. How can changes in intracellular [Ca²⁺] modify cellular signaling over such a broad spectrum of processes with distinct temporal and spatial outcomes [6]? Since the serendipitous discovery of Ca²⁺ as an essential signaling ion in 1883 by Ringer [7] many strides have been made towards answering this question.

The structure of a Ca²⁺ signal can generally be described as follows: at resting conditions the intracellular [Ca²⁺] is kept low, around 100 nM. Upon an appropriate Ca²⁺ stimulus, so-called ON-mechanisms are activated [1, 2]. These ON-mechanisms (e.g., voltage- or ligand-gated ion channels in the plasma membrane or IP3 activated channels) let Ca²⁺ into the cytoplasm from the extracellular space or intracellular organelles (Ca²⁺ stores, i.e. sarco-endoplasmatic reticulum or mitochondria) causing a rapid increase in cytosolic [Ca²⁺]. If this “signal” is sufficiently large it will be “translated” into a biochemical message. When the [Ca²⁺] increases sufficiently, Ca²⁺ will bind to sensor Ca²⁺ binding proteins (CBPs), changing the physiological properties of these proteins. A hallmark for these sensor CBPs is a relatively large conformational change upon Ca²⁺ binding that is often accompanied by exposure to hydrophobic surfaces. Consequently, this allows interactions with specific ligands linked to subsequent biochemical regulation of downstream effectors [8]. Meanwhile, OFF-mechanisms work to lower the [Ca²⁺] in the cytoplasm to the resting concentrations [1, 2]. These OFF-mechanisms are the pumps and exchangers that transport the Ca²⁺ either back into the Ca²⁺ stores or to the extracellular space. Furthermore, there are buffering CBPs that rapidly bind free Ca²⁺, causing a seemingly immediate decrease in [Ca²⁺]. However, in later phases of the OFF-period, as the [Ca²⁺] decreases, these CBPs will release the bound Ca²⁺, causing a prolonged Ca²⁺ signal. Therefore, CBPs are not strictly OFF-mechanisms, but they are involved in shaping the amplitude and duration of the Ca²⁺ signal [1, 2, 9,10]. According to its specific function, each cell expresses a unique and specific set of Ca²⁺ signaling tools, i.e., ON and OFF components, to create the distinctive spatial and temporal Ca²⁺ signaling properties needed for the cells function [11]. Depending on their exact composition of their Ca²⁺ signaling toolkit, each Ca²⁺ signal system will produce Ca²⁺ transients varying from milliseconds to several hundreds of milliseconds. Various names are given to the Ca²⁺ transients, such as sparks, embers, quarks, puffs, blips or waves, depending on their exact spatial and temporal properties and the cell type in which they occur [2, 12]. Furthermore, the Ca²⁺ signals can be highly repetitive, forming Ca²⁺ oscillations [13]. In short, the spatiotemporal characteristics of short-lived and often highly localized changes in intracellular [Ca²⁺] result from a complex interplay between Ca²⁺ influx/extrusion systems, mobile/stationary CBPs, and intracellular sequestering mechanisms.

To understand the kinetics of cellular Ca²⁺ transients and their influence on the processes they regulate requires an in-depth knowledge of the Ca²⁺ sensitivities and binding properties of all the components involved. Upon an increase in [Ca²⁺], the CBPs are the first to respond as they immediately start binding Ca²⁺. Within each system, a Ca²⁺ signal will be interpreted and translated depending on the amplitude and temporal pattern of Ca²⁺ binding to the sensor CBPs. Both buffering and sensing CBPs are the fastest players within the Ca²⁺ toolkit and respond directly, working on a timescale of tens of microseconds to tens of milliseconds. The various CBPs are in an immediate competition to bind the freshly available Ca²⁺. On the other hand, the OFF components work on a somewhat slower timescale of tens of milliseconds to seconds and will not immediately reduce the [Ca²⁺] back to normal [14]. Hence, the competition for Ca²⁺ between the various CBPs within a system plays an essential and direct role in modulating the shape of Ca²⁺ transients and the outcome of the conveyed biochemical message [10]. Evidently, to have a good understanding of Ca²⁺ signaling, it is essential to know the properties of the CBPs that are involved in the studied process. A few key features of CBPs determine the spatiotemporal characteristics of Ca²⁺ signals and their transduction: the overall Ca²⁺ affinity of CBPs, their localization and concentration, their mobility inside cells, and their binding kinetics [15]. The latter of which are conceivably the most critical determinant of cellular Ca²⁺ signaling [16]. The lack of accurate data on the kinetic properties of CBPs gives rise to uncertainties in models studying intracellular Ca²⁺ signaling [10]. Two major obstacles make it challenging to accurately determine the kinetic properties of CBPs. First, the Ca²⁺ binding kinetics are very fast and, for accurate quantification, require the ability to measure changes in [Ca²⁺] (or any other parameter related to Ca²⁺ binding) with an accuracy of 10–100 μs. Conventional techniques used to measure binding kinetics to macromolecules, like stopped flow fluorimetry, have dead times >1ms [17], precluding accurate determination of the faster Ca²⁺ binding kinetics of CBPs. Secondly, many of the CBPs bind Ca²⁺ in a cooperative way, which is the ability to influence ligand binding at a site of a macromolecule by previous ligand binding to another site of the same macromolecule. There are four commonly used descriptions for cooperativity (for review see [18]): the Hill[19], the Adair-Klotz [20, 21], the Monod-Wyman-Changeux (MWC) [22], and the Koshland-Némethy-Filmer (KNF) [23] models. Yet all these models describe cooperativity only when the binding reactions are at equilibrium. Only under specific conditions [24–26] the MWC model was used to describe kinetics of cooperative binding. Such conditions do not hold for Ca²⁺ binding to CBPs. Furthermore, when using the MCW model with most CBPs the mathematical description becomes too complex for simple/practical interpretations [18, 27]. Over the last few years we have been working on overcoming these obstacles. We have developed an in vitro technique to measure the fast Ca²⁺-binding kinetics CBPs following flash photolysis of caged Ca²⁺ [28, 29]. In combination with compartmental kinetic modeling and a simple kinetic model for cooperative binding, we have begun to resolve the Ca²⁺ binding kinetics of some CBPs [28, 30, 31]. In this paper we will give a short overview some of the commonly used techniques that give insight into the Ca²⁺ binding kinetics of CBPs. We will then discuss our technique and describe various findings we have discovered while developing our technique that may be relevant to others using similar methods, such as measuring [Ca²⁺] with fluorescent dyes.

1.2 Ca²⁺ Buffering Capacity (κ) is a Description of Ca²⁺ binding Kinetics

One of the practical ways to quantify Ca²⁺ buffering in a cell is the buffering capacity (κ), which is the ratio of buffer-bound Ca²⁺ to free Ca²⁺ upon a change in total Ca²⁺[32, 33]:

$${\kappa }_S=\frac{d[\mathit{CaS}]}{d[{Ca}^{2+}]}$$

where S is the endogenous buffer. For example, if κ_s=23, then out of every 24 ions entering a compartment, 23 will be bound by S (i.e, ~4% of Ca²⁺ entering remains unbound). This number gives important insights into several aspects of Ca²⁺ signaling. For instance, the size of the Ca²⁺ influx required to reach a certain free [Ca²⁺] can be determined using κ. As it is defined in the equation above κ does not reveal anything about the dynamics of Ca²⁺ buffering. However, the κ that is generally used in literature does. It is not trivial to determine the theoretical κ in a (sub) cellular compartment because it requires a small known change in [Ca²⁺]_total and a measurement of the resulting Ca²⁺ signal. To evoke a change in intracellular [Ca²⁺], one can stimulate the cell to open Ca²⁺ permeable channels. In many structures, such as dendritic spines, it is impossible to use a technique (e.g., voltage clamping) to precisely determine the evoked Ca²⁺ influx (e.g., by measuring the Ca²⁺ current). Hence, it is impossible to exactly determine the amount of Ca²⁺ entering the structure. Estimates may be made based on the number of expected open channels and the driving force for Ca²⁺ over the whole time course of the Ca²⁺ influx. But unfortunately, often there are no exact data on the number of Ca²⁺ permeable channels open following stimulation, or the exact time-course of the membrane potential, hence the driving force for Ca²⁺. Another approach is to measure the Ca²⁺ signal following the Ca²⁺ influx by using Ca²⁺-indicators such as fura-2 or Oregon Green BAPTA (OGB). However, these dyes act as exogenous Ca²⁺ buffers, which will have a significant impact on the Ca²⁺ signal itself. Therefore, an approach has been developed that gives a quantification of the buffer capacity of endogenous buffers by extrapolating a series of indicator concentrations to zero [32, 34, 35]. It can be derived that changes in [Ca²⁺] at equilibrium:

$$\mathrm{\Delta }{\left[{Ca}^{2+}\right]}_{(t=\infty )}=\frac{\mathrm{\Delta }{\left[{Ca}^{2+}\right]}_{\mathit{total}(t=\infty )}}{1+{\kappa }_B+{\kappa }_S}$$

If Ca²⁺ binding to all the buffers (endogenous S, and exogenous B) is fast enough so that the binding reactions are always close to equilibrium, then by approximation:

$$\mathrm{\Delta }{\left[{Ca}^{2+}\right]}_{(t)}=\frac{\mathrm{\Delta }{\left[{Ca}^{2+}\right]}_{\mathit{total}(t)}}{1+{\kappa }_B+{\kappa }_S}$$

The assumption that the buffers are fast enough to always be in equilibrium (i.e., easily follow the [Ca²⁺] increase induced by the ON-systems) automatically implies that

$$\mathrm{\Delta }{\left[{Ca}^{2+}\right]}_{\mathit{peak}}=\frac{\mathrm{\Delta }{\left[{Ca}^{2+}\right]}_{\mathit{total}}}{1+{\kappa }_B+{\kappa }_S}$$

where κB can be approximated as [32, 34, 35]:

$${\kappa }_B=\frac{{[B]}_{\mathit{total}}{K}_B}{\left(K_B+{\left[{Ca}^{2+}\right]}_{\mathit{rest}}\right)\left(K_B+{\left[{Ca}^{2+}\right]}_{\mathit{peak}}\right)}$$

When 1/Δ[Ca²⁺]_peak is plotted as a function of κB (which can be varied by using different concentrations of Ca²⁺ buffer/indicator) the function will intercept with the y-axis at 1/Δ[Ca²⁺]_peak and with the x-axis at -(1+κ_S) (see figure 1A and B). The 1992 paper introducing this method has, thus far, been cited almost 500 times indicating that this method is widely used to determine κ. Generally, when buffering capacity is mentioned, it is the buffering capacity determined with this method. However, this method is based on the assumption that the system of which the capacity is determined buffers Ca²⁺ faster than the speed of the change in [Ca²⁺]_total. Anything slower is grouped in with the extrusion mechanisms (OFF-mechanisms) [32]. In practice, this means that only the buffering that is faster than the measured [Ca²⁺] change is considered part of the buffer capacity. Hence, it is often also termed the fast buffer capacity. Since the [Ca²⁺] is measured with the exogenous buffer (i.e. the Ca²⁺-indicator), κ most often indicates the buffer capacity that is faster than the dye which was used to measure κ. This does not necessarily mean that the on–rate of that portion of the buffer is faster than that of the dye, as the absolute forward rate is determined by the product of the on-rate and the concentration of the buffer.

Figure 1.

Simulation of an experiment to measure Ca²⁺ buffering capacity. With a computer model developed in Berkeley Madonna, we simulated a compartment with 200 μM buffer S (K_d,S=1 μM, k_on=1×10⁸ M⁻¹s⁻¹) at [Ca²⁺]_rest=100 nM. Buffer capacity is determined by measuring the change in [Ca²⁺] upon a 1 μM influx of Ca²⁺ (exponential step τ=0.5 ms) with OGB-1 (K_d,OGB=170 nM, k_on=10⁹). OGB-1 is often used to determine k. The experiment is performed with 100, 80, 60, 40, 20 and ~0 μM OGB-1. Zero OGB-1 is simulated by using 1 yM (10⁻²⁴ M), and indicates the theoretical limit of what one could directly measure in the experiment with OGB-1. A) The [Ca²⁺]_OGB traces, calculated from the measured OGB-1 signal, with the maxima ([Ca²⁺]_OGB,peak) indicated by round markers. Inset shows the [Ca²⁺]_OGB measured with ~0 μM OGB-1 curve in comparison to the actual [Ca²⁺] in red. OGB-1 cannot measure the actual [Ca²⁺] because it is limited by its k_on. The measured decrease in [Ca²⁺]_OGB, indicated with the yellow area, is caused by buffer S but is not considered part of κ when this method of determining κ is used. B) To determine κ, 1/[Ca²⁺]_OGB,peak is plotted as a function of κB (black circles). Extrapolation onto the x-axis gives -(1+κ_S) (indicated with green arrows). The measured κ for the black line is 79. The experiments were also simulated with a 10-times faster, hypothetical OGB-1* (k_on=10¹⁰ M⁻¹s⁻¹), which gives the blue squares, resulting in a κ of 18. This shows that the measurement of κ, with this method, is dependent on the speed of the used indicator. We also simulated a measurement with normal OGB-1 and with 96 μM buffer S* that has the same Kd as buffer S but is 3 times faster (k_on=3×10⁸ M⁻¹s⁻¹). These experiments give the red triangles and result in a κ of 79, just like the 200 μM buffer S. This shows that the measurement of κ with this method, is not a measure of the absolute buffer concentration/capacity, but only a measure of the fast buffer capacity.

$$\frac{d[\mathit{CaB}]}{dt}={\mathit{k}}_{\mathit{on}}[\mathit{B}][{Ca}^{2+}]-k_{\mathit{off}}[\mathit{CaB}]$$

It means that portion of the Ca²⁺ increase is buffered away before it can be detected by the dye and is therefore dependent on the on-rate of the dye and its concentration. A fast dye will give lower κ values than a slow dye (see figure 1B). Conversely, the value of κ, as it is generally used in the literature, is dependent on the concentration of the buffer, its Ca²⁺ affinity, and its speed (see figure 1B).

1.3 Measuring Ca²⁺ Binding Kinetics of CBPs in vitro

Thus far, we have established that κ is at least a quantification of the ‘fast’ buffer component. The buffer capacity is sometimes simplified as a portion of the Ca²⁺ signal that rapidly buffered before any message is conveyed (e.g. [36]). In that sense it would work like a simple attenuation factor. Maybe such simplifications are justified under certain conditions. However, it is unlikely that during periods of Δ[Ca²⁺] that are too fast for our detection methods, only buffering CBPs are active. For example, we have recently shown that the ubiquitous sensor CBP calmodulin (CaM) binds Ca²⁺ extremely fast and is likely to constitute a major part of the buffering capacities measured in cells. This confirms that at least some essential parts of Ca²⁺ signal transduction takes place during the initial fast phase of Δ[Ca²⁺], exactly during the period that is used to measure the amplitude of Ca²⁺ buffering and the quantification of κ.

The easiest and probably the most exact way to measure the binding kinetics of a CBP is to isolate the protein and study it in vitro under tightly controlled conditions. A great number of methods have been developed to study fast molecular interactions down to the picosecond range [17]. However, not every method is appropriate or practical to measure Ca²⁺ binding kinetics. Stopped flow and ⁴³Ca²⁺-NMR are commonly used to accurately quantify Ca²⁺ binding kinetics (for description of the techniques see [17, 37]). For example, these techniques have been utilized multiple times to determine the Ca²⁺ binding kinetics of free CaM that was not bound to another protein or peptide. These measurements of CaM are relatively consistent, and most differences can be explained by differences in experimental temperature. In summary the finding are that CaM has two slow binding sites on its C-terminus (k_off ~10 s⁻¹ at room temperature) and two fast binding sites on its N-terminus (k_off >1000 s⁻¹ at room temperature) [38–45]. However, no distinctions could ever be detected between the two binding sites on either terminus using these techniques due to limited temporal resolution. The 43Ca²⁺-NMR is limited to measuring dissociation rates in the window of 10–10⁵ s⁻¹ [37]. In addition, the ⁴³Ca²⁺-NMR works with the rare ⁴³Ca isotope (natural occurrence <0.14%), making it somewhat costly. The stopped flow technique has a dead time of 1–2 ms at the initiation of the binding reactions that are to be quantified, limiting the maximally measurable dissociation rates at 10³ s⁻¹.

One of the other techniques used to directly measure Ca²⁺ binding kinetics is the T-jump method. This method is capable of quantifying kinetics much faster than that allowed by stopped flow or ⁴³Ca²⁺-NMR, and was used to resolved the kinetics of EGTA, BAPTA, and several Ca²⁺-indicators (all have a k_on of 10⁸–10⁹ M⁻¹s⁻¹) [46]. So far, the T-jump method has only been used to resolve the kinetics of molecules that bind a single Ca²⁺ion. A probable reason for this is that the mathematics needed to resolve multiple bindings is too complex to resolve, especially if cooperativity is involved.

1.4 Measuring Ca²⁺ Binding Kinetics of CBPs in vitro

Another way to determine the kinetics of a CBP is to compare it to Ca²⁺ buffers with known properties. For instance, in cells of animals in which a certain buffering CBP has been genetically knocked out, other buffers can be introduced to examine whether they can rescue the knockout phenotype. For example, it has been shown in calretinin (CR) knockout animals that, in cells that normally contain CR, the wildtype firing behavior could be rescued by introducing intracellular BATPA [47]. Similarly, the altered paired pulse depression in the synaptic transmission from a presynaptic terminal that normally contained the CBP parvalbumin (PV) was rescued when EGTA was introduced in cells from PV knockout animals [48]. From this it can be concluded that the buffering speed of CR is comparable to that of BAPTA, which is fast (k_on=10⁸–10⁹ M⁻¹s⁻¹)[46], while the buffering speed of PV is comparable to that of EGTA, which is slow (k_on=3×10⁶–10⁷ M⁻¹s⁻¹) [28, 46]. This replacement method is used very often and thought to give great direct insights into the functioning of a CBP under the physiological conditions of the intracellular milieu. However, a quantitative comparison with the kinetics of the artificial buffers is not possible because the absolute amount of free binding sites should be the same for a one-to-one comparison. Since, BAPTA (K_d=160 nM) and EGTA (K_d=70 nM) have a much higher affinity than most CBPs and the exact resting [Ca²⁺] is not always known, it is impossible to know if the concentrations of the EGTA/BAPTA used are really comparable to the normal situation with the physiological CBP in place. A study with artificial buffers that have affinities comparable to those of the studied CBPs would be more conclusive (e.g., see [49]).

Furthermore, a replacement study may give information for the CBP under the specific studied condition but does not resolve the general property of the CBP. For instance, overexpression of the slow buffer PV in oocytes induces elementary Ca²⁺ release events of Ca²⁺ puffs via Ca²⁺-induced Ca²⁺ release at low concentrations of IP₃ [50]. This puff activity is comparable to the condition when EGTA is injected, but it is not seen in the presence of a fast buffer like BAPTA when these signals are more spatially uniform, or “globalized” [51]. The replacement experiment described above [46] and other replacement experiments performed in frog saccular hair cells [52] show that CR behaves like BAPTA. Therefore, one would expect that the introduction of CR in oocytes would lead to the “globalized” Ca²⁺ signaling observed in the presence of BAPTA. However, besides these “globalized” signals, CR can under certain conditions also produce puffs typical of the slow buffers that are never seen with BAPTA [53]. We measured with our new technique the exact Ca²⁺ binding kinetics of CR [30]. From these results we concluded that CR, due to its cooperative properties, it can function in a slow mode, comparable to EGTA and in a fast mode comparable to BAPTA. This probably explains CRs multiple calcium buffering behavior in oocytes [54].

All the techniques described above, and some more that we unfortunately don’t have space to discuss here, have given, and still give, invaluable new insights into the mechanisms of Ca²⁺ signaling. To further the quest of resolving the details of Ca²⁺ signaling we attempted to develop a technique to measure the Ca²⁺ binding kinetics of CBPs with a sufficiently high temporal resolution to give a clear insight into the “competition” for Ca²⁺ by the CBPs.

2 Measuring Ca²⁺ Kinetics With Flash-Photolysis

2.1 Uncaging Ca²⁺from DM-nitrophen

One of the fastest methods to measure reaction kinetics is flash-photolysis combined with spectroscopy [17]. The analysis of reaction kinetics using flash-photolysis is based on the activation of the reaction with a very short and intense light flash and observation of the initiated reaction. This means that at least one of the molecules within the system has to be photosensitive, and able to start the reaction by some form of photo conversion (e.g., radical formation or breaking up of the molecule forming new compounds). In 1988 Graham Ellis-Davies and Jack Kaplan developed DM-nitrophen (DMn, 1-(4,5-dimethoxy-2-nitrophenyl)-1,2-diaminoethane-N,N,N′,N′-tetraacetic acid) [55] which is a photo sensitive Ca²⁺ chealator. This so-called caged compound (or caged-Ca²⁺) made flash-photolysis a viable option for studying Ca²⁺ binding kinetics of CBPs. DMn (K_d ~5 nM) is an EDTA group, which strongly binds Ca²⁺, fused with a 2-nitophenyl group making the molecule light sensitive (see figure 2). When DMn captures a UV photon it breaks a covalent bond in the EDTA backbone, rapidly producing two photoproducts (PP) that have a ~6×10⁵ times lower affinity for Ca²⁺ (~3 mM) than the unbroken DMn (see figure 2). Under the right conditions, this photo transition causes virtually any Ca²⁺ that was bound to the irradiated DMn molecule to be ‘released’ from a ‘cage’. The fragmentation of DMn into it PPs was reported to be very fast (photolysis of 1.1×10⁴ – 8×10⁴s⁻¹ [56]). Therefore ‘ungaging’ of DMn should be able to step-like changes in [Ca²⁺] within tens of microseconds.

Figure 2.

Schematic view of DM-nitrophen. DMn is an EDTA molecule (green) with a photosensitive 2-nitophenyl group (blue) attached to it. When the 2-nitophenyl group absorbs a UV photon, the EDTA group breaks into two parts which have a much lower affinity for Ca²⁺, effectively causing the unbinding of Ca²⁺. Red dotted lines indicate coordination of the negative oxygen atoms with the chelated Ca²⁺.

2.2 Studying Ca²⁺ binding dynamics with DM-nitrophen

DMn (and molecules like it, see below) opened the possibility of studying the dynamics of fast Ca²⁺ binding, provided that the initiation of the studied reaction throughout the measurement space is instantaneous compared to the studied reaction kinetics. To achieve this requirement, Escobar et al., in the laboratory of Julio Vergara, used a pulsed laser that generated a 50 ns UV flash of sufficient power. In 1995 and 1997 they were the first ones that used flash photolysis of DMn to study Ca²⁺ binding kinetics of several Ca²⁺-indicators [57, 58]. We started collaboration with Julio Vergara to measure the kinetics of CBPs with this technique, and in 1999 we published our first success measuring the fast Ca²⁺ binding kinetics of calbindin D-28k (CB) [28]. CB is a buffering CBP with little or no cooperativity [31, 59] commonly found in neurons of all vertebrates and in the intestines, kidneys and pancreas of all mammals[60]. Since then we have been steadily improving this technique, making it more accurate, and including cooperative binding in the quantification of kinetics.

2.3 The basic setup

Since the first setup in 1995, we have made many changes; however, the basic principle stayed the same [28–31, 57, 58]. Figure 3 is a schematic layout of the current setup. It always consists of a small reaction chamber (currently 0.5–1 μL) in which epifluorescence is measured using an objective (currently 20×). The chamber is as small as possible so that the least amount of purified protein is used. There is a second optical path to deliver a short UV flash via a pulsed laser. In figure 3 the UV pathway is a direct one, but we have also successfully used flash delivery via an optic fiber. The laser should have enough power to initiate instantaneously (compared to the reaction kinetics, i.e., <1 μs) the uncaging of a sufficient amount of caged-Ca²⁺ molecules (DMn or other), so that change in [Ca²⁺] and the subsequent buffering is detectable with a fluorescent Ca²⁺-indicator. We currently use a frequency-tripled Nd:YAG laser (Surelite, Continuum, Santa Clara, CA) that can deliver enough energy in a single 5 ns UV flash (355 nm) to uncage at least 8% of the DMn. For most experiments, it should be sufficient to uncage up to ~2% per flash. It is important to have the ability to vary the output power of this UV laser (e.g., by using diffusion filters or by manipulating the timing of the pockels cell in the laser) to be able to repeat experiments with varying uncaging amplitudes. With 5mM DMn that is for 99% occupied with Ca²⁺ (at ~1μM [Ca²⁺]_rest), uncaging can be detected with OGB-5N already at ~0.05% (~2 μM release). However, for complete experiments a range of uncaging levels needs to be measured (see below). Furthermore, we have added a system that heats the reaction chamber to the desired experimental temperature.

Figure 3.

Schematic overview of the latest uncaging setup we use. In a small (<1 μL), temperature controlled (35°C) recording chamber Ca²⁺ is uncaged from DM-nitrophen (DMn) with a 5 ns UV flash. Epifluorescence is used to measure the fluorescence of the Ca²⁺-indicator OGB-5N in a small recording spot in the middle of the chamber.

For an experiment a solution is made that contains, a Ca²⁺-cage (e.g., DMn), Ca²⁺, a Ca²⁺-indicator (e.g., OGB-5N) and a CBP of interest. Furthermore, the solution contains KCl and a pH buffer to set the solution to a physiologicalionic strength and pH mimicking the intracellular milieu. The [Ca²⁺]_rest should be accurately titrated to a desired concentration so that enough Ca²⁺-cage is occupied with Ca²⁺ and the majority of the CBP’s binding sites is unoccupied. At the start of an experiment a sample of this solution is placed in the recording chamber. Then, while measuring the fluorescence of the Ca²⁺-indicator via the epifluorescence pathway, a UV flash is delivered starting the uncaging process. The resulting increase in [Ca²⁺] by release from the cage and ensuing decrease in [Ca²⁺] by Ca²⁺ binding to the CBP is reported by the fluorescence of the Ca²⁺-indicator (see figure 4). It is important in this process that the uncaging is homogeneous within the voxel where the [Ca²⁺] is recorded and a substantial volume around it, so that the recorded Ca²⁺ changes are only from the reactions occurring in that voxel. If uncaging is uneven, [Ca²⁺] gradients will occur and diffusion kinetics will contaminate the recording. To ensure that this will not happen, the recording spot should be relatively small compared to a large volume of UV illumination. To check if diffusion kinetics contaminate the recording, the recording spot should be moved to different locations within the uncaging area. The [Ca²⁺] transients should only change when the recording area is moved towards the outer edge of the uncaging area, were Ca²⁺ gradients are expected.

Figure 4.

Ca²⁺ uncaging in vitro. A) Examples of changes in free [Ca²⁺] after photolysis of DMn in the absence of protein (upper trace) and in the presence of 31 μM and 62 μM CR (middle red and lower orange traces, respectively). The UV flash energies used to uncage DMn were of similar magnitude, resulting in an equivalent amount of uncaged-Ca²⁺. B) Scheme of all equilibrium reactions occurring in the measurement chamber after photolysis of caged-Ca²⁺ (DMn). The rate constants for DMn, its photoproducts (PP) and uncaging time constants (τ_f and τ_s) of DMn are independently determined (blue parameters) for each experiment. The rate constants and the F_ratio for each batch of OGB-5N is also measured in an independent experiment (green parameters). The reaction parameters to be determined for describing the Ca²⁺ binding to a CBP are indicated by red question marks. The model/scheme for the buffering reaction is dependent on the used CBP, and is represented here by the simple equilibrium between [CBP] and [Ca_nCBP], but can become quite complex, see text and [30, 31]. Figures adapted from figure 1 in reference [30]

2.4 Electronics

A simple and cost-effective solution to measure the fluorescence of the Ca²⁺-indicator is to use a photodiode in the focal plane of the emission pathway of the epifluorescence. It is important to use a photodiode that has a low capacity and a very fast rise time so that it can follow fast changes in fluorescence. Photodiodes with a smaller surface area will have a lower capacity. In addition a small enough surface area can work as a quasi pinhole and minimize the measuring voxel in the Z-direction. For our measurements we use the PIN-HR008 (0.8 pF, 0.04 mm2, UDT Sensors, Hawthorne, CA).

Another significant problem is that the high-energy UV flashes are so powerful that it will excite most, if not all, Ca²⁺-indicators that have their peak excitation wavelength in the visual spectrum (UV dyes cannot be used because then dye excitation could inadvertently photolyse Ca²⁺-cage). In our experience, this flash of UV-induced fluorescence is so bright that it will saturate the amplifier circuit that is strong enough to detect the ‘normal’ Ca²⁺ signals. For most amplifiers it takes considerable time (tens of milliseconds) to recover from such an overload. Therefore, special operational amplifiers should be used that can rapidly recover from such an overload, or have some overload protection. We generally use OPA699 (Burr-Brown, Texas Instruments), which has a very fast recovery time, resulting in a overall recovery/dead time of our system of 50–60 μs. For lower noise, but somewhat slower systems OPA637 and OPA111 (Burr-Brown, Texas Instruments) should also be sufficiently fast. For more information on photodiode amplifier circuits Burr-Brown has a very informative bulletin: focus.ti.com/lit/an/sboa035/sboa035.pdf.

2.5 Reaction scheme

Figure 4A shows an example of uncaging data of 3 experiments under identical conditions (for [DMn]_total, [Ca²⁺]_rest, uncaging energy, etc.) 2 different concentrations of CBP present and with no CBP present. The most straightforward approach to determine the kinetics of a system is to fit the [Ca²⁺] decay with a set of exponential functions. However, the system underlying the kinetics is a bit more complex. Instead of just the binding of Ca²⁺ to the CBP, there are also equilibrium reactions with the Ca²⁺ indicator, the DMn that is not uncaged, and with the PPs (see figure 4B). For example, even when no CBP is present, a clear decay in the [Ca²⁺] is detected (Figure 1A, black trace), which is caused by some rebinding of uncaged Ca²⁺ to free DMn. Furthermore, upon flash delivery the uncaging process is initiated, but the uncaging process itself is not instantaneous compared to the Ca²⁺ binding by CBPs. Hence, to determine the kinetic parameters of the studied CBP from the fluorescence recordings we use a mathematical model built in an ordinary differential equation solver (Berkeley Madonna 8.0) that incorporates all of the reactions in the reaction chamber (figure 4B). Initially we used as kinetic parametes for DMn and the Ca²⁺ indicator values that were reported earlier [28]. For instance, for DMn a photolysis timeconstant of 20 μs was used. However, in a later study we found that DMn uncages with 2 time constants as depicted in figure 3B. Two thirds of the irradiated DMn indeed uncages with a τ of ~15 μs, but one third uncages much slower with a τ ~3 ms [29]. Furthermore, we found that variations in the properties Ca²⁺-indicators also occur (see below in 2.7 Choosing the right Ca²⁺-indicator). To assure correct modeling of the reactions in the reaction chamber, we determine the properties of the Ca²⁺ indicator and the DMn in separate experiments for each batch that we use.

2.6 Choosing the right Ca²⁺-cage

The fact that DMn uncages with two time constants, one of which is at least slow enough to interfere with the [Ca²⁺] decay, raises the question if DMn is the ideal Ca²⁺-cage to use for such experiments. Of the most commonly used and commercially available caged-Ca²⁺ compounds DMn seems to be the best choice to release caged-Ca²⁺ when rapid and large increases in [Ca²⁺] are desired. First of all, DMn has the highest affinity for Ca²⁺ (K_d=5 nM, the next best, NP-EGTA, has a K_d of 80 nM,), and its PPs have the lowest affinity for Ca²⁺ after photolysis [61, 62]. Consequently, about 95–99% of DMn is occupied with Ca²⁺ while the [Ca²⁺]_rest is at 0.1–1 μM, and most of the bound Ca²⁺ will be released from the PPs. Much higher [Ca²⁺]_rest than 1 μM would be useless, since most binding sites on CBPs will be occupied with Ca²⁺ at that concentration, making them unavailable to bind Ca²⁺ upon uncaging. Furthermore, DMn has a relatively high quantum efficiency of 0.18 [55, 61]. Moreover, choosing other Ca²⁺ cages might not solve the problem of two uncaging time constants at all. For example, the Ca²⁺-cage NP-EGTA also uncages with multiple and slower kinetics [29] [29]. Concerning Ca²⁺-cages in general, a few more facts need pointing out. First of all, we find that DMn is indeed very light sensitive, and special precautions need to be taken to prevent unwanted uncaging. All our experimentation rooms have special lighting that is >500nm (by using filters or LED lighting), and only in these rooms is DMn taken out of light-tight containers. Secondly, we found that the amount of DMn delivered by companies is generally inaccurate. We always make a stock solution directly in the vial delivered by the company and measure the accurate concentration via spectroscopy (ε_DMn=4330 M⁻¹cm⁻¹[55]) and find concentrations up to +/− 20% of the expected value. Most often it is lower than what would be expected from the amount indicated on the container. The accurate concentration of the total DMn is essential for a correct simulation of the experiment. Therefore, the [DMn] of every stock solution made should be verified individually.

2.7 Choosing the right Ca²⁺-indicator

To follow the [Ca²⁺] during the experiment, a Ca²⁺-indicator is used. This indicator has to be fast enough to follow the rapid [Ca²⁺] changes caused by Ca²⁺ binding to CBPs. Typically, the ion indicators have fast association constants that are always in the same range (k_on 10⁸–10⁹ M⁻¹s⁻¹[46, 57]). The indicators that can follow a fast drop in [Ca²⁺] are indicators with a faster dissociation rate, i.e., the indicators with lower affinities. We generally use OGB-5N (Kd ~35 μM), but indicators like Rhod-FF and Fluo-4FF might also work. We have to make an extremely important note of caution here: over the past eight years, we have determined the properties of each individual factory batch of OGB-5N we used, and found that their properties vary considerably (see Table 1). Although the properties within a batch are very stable, we found that between batches the K_d varied from 34 to 46 μM and the F_ratio (F_max/F_min) varied from from 10 to 40. Concurrently, we also found variations in the kinetics of the different batches of dye. We have no explanation for the variability between the batches other than the fact that specific contaminations might occur in different batches, as stated by the supplier (personal communication with Molecular Probes, Portland, OR). We found similar variations between the different batches of other Ca²⁺-indicators, like OGB-2 and Fluo-4. It is critical to have the correct properties of the dyes when quantifying data using such ion-indicators. Hence, we advise anyone using fluorescent probes for quantification purposes to measure the exact properties of each batch used. More details on how we measured those properties can be found in the text and supplements of these papers [29–31, 57].

Table 1.

Properties of different batches of OGB-5N

Date	Batch	Kd (μM)	Fratio
Jan-03	34b1-2	39	11
Aug-04	15c1-2	37	34
Jan-08	29020W	34	31
Aug-08	39391A	34	30
Mar-09	531987	42	40
Mar-11	25663W	46	38

2.8 Modeling CBPs

For each solution of DMn and batch of OGB-5N we determine the properties in individual experiments. With these properties known, we can start fitting data from uncaging experiments that had a CBP present (question marks figure 4B). In the simplest case, the binding of Ca²⁺ to the CBP is non-cooperative and can be added to the system as a simple equilibrium for each binding site (B):

$$\left[B_1\right]+\left[{Ca}^{2+}\right]\underset{k_{\mathit{off},B_1}}{\overset{k_{on,B_1}}{\rightleftarrows }}\left[{\mathit{CaB}}_1\right],\left[B_2\right]+\left[{Ca}^{2+}\right]\underset{k_{\mathit{off},B_2}}{\overset{k_{on,B_2}}{\rightleftarrows }}\left[{\mathit{CaB}}_1\right],\cdots ,\left[B_n\right]+\left[{Ca}^{2+}\right]\underset{k_{\mathit{off},B_n}}{\overset{k_{on,B_n}}{\rightleftarrows }}\left[{\mathit{CaB}}_n\right]$$

where B₁ through B_n represent individual binding sites with different properties. To minimize the number of parameters and the degrees of freedom of the fit, different binding sites on a CBP are often considered similar. For instance CB, which has 4 non cooperative binding sites, can be simplified by assuming only one or two different types of binding sites [28, 31].

The modeling of CBPs gets a little more complicated if cooperative binding needs to be included. In order for cooperativity to occur, the properties of the binding sites are not static but depend on the binding state of the individual binding sites of the CBP. Thus far, details about what exactly happens with the CBP molecules and their binding sites during cooperativite binding remain unclear. Therefore, it is impossible to have an exact mathematical model for quantifying the kinetics of cooperative binding. The most commonly used mathematical descriptions of chemical equilibria, the Hill[19] and the Adair-Klotz[20, 21] equations, describe equilibria on a macroscopic level. Only the more complex MWC[22] and KNF[23] models are appropriate for describing binding kinetics of individual binding sites. The MWC and KNF models use two conformational states in which each binding sites can occur. The state of each site determines whether it has a a low affinity (called the tense or T-state) or a high affinity (called the relaxed or R-state) [18]. To model kinetics using either the MWC or KNF model we would need to incorporate the association and dissociation rate constants for the R and T states, as well as the transition rate constants (k₊, k₋) between these states. For instance for the MWC the reaction scheme for two binding sites with cooperativity looks like this:

$$\begin{array}{ccccc}\left[B_T\right]+\left[{Ca}^{2+}\right]& \underset{k_{\mathit{off},T}}{\overset{2\times k_{on,T}}{\rightleftarrows }}& \left[{\mathit{CaB}}_T\right]+\left[{Ca}^{2+}\right]& \underset{2\times k_{\mathit{off},T}}{\overset{k_{on,T}}{\rightleftarrows }}& \left[C{a}_2{B}_T\right]\\ k_{+,1}\downarrow \uparrow k_{-,1}& & k_{+,2}\downarrow \uparrow k_{-,2}& & k_{+,3}\downarrow \uparrow k_{-,3}\\ \left[B_R\right]+\left[{Ca}^{2+}\right]& \underset{k_{\mathit{off},R}}{\overset{2\times k_{on,R}}{\rightleftarrows }}& \left[{\mathit{CaB}}_R\right]+\left[{Ca}^{2+}\right]& \underset{2\times k_{\mathit{off},R}}{\overset{k_{on,R}}{\rightleftarrows }}& \left[C{a}_2{B}_R\right]\end{array}$$

Assuming that k_+,1, k_+,2, k_+,3 and k_−,1, k_−,2, k_−,3 easily relate to one and other they can be reduced to one k₊ and one k₋ [30]. This means that for two identical sites that have cooperative binding the number of parameters to fit would at least be 6 (k_on,T, k_off,T, k_{on, R,} K_{off, R,} k₊, and k₋). Similarly, KNF models that incorporate kinetics would at least need 6 kinetic constants to describe cooperative binding between two cooperative identical sites. To decrease the number of parameters to fit, and to make the model more intuitively comprehensible, we developed a different model for cooperative binding that allows for the description of kinetics. In our model each cooperative binding site can also exist in either the T or R state. However, we assume a direct allosteric influence between bindings in a cooperative set. The binding of Ca²⁺ to one site always leads to a transition T→R in the other site, and an unbinding of Ca²⁺ from one site always leads to a transition R→T in the other site. These transitions are immediate and occur simultaneously with the binding of the Ca²⁺. In this case, Ca²⁺ binding by two identical cooperative binding sites is described by:

$$\left[B_T{B}_T\right]+\left[{Ca}^{2+}\right]\underset{k_{\mathit{off},T}}{\overset{2\times k_{on,T}}{\rightleftarrows }}\left[{\mathit{CaB}}_T{B}_R\right]+\left[{Ca}^{2+}\right]\underset{2\times k_{\mathit{off},R}}{\overset{k_{on,R}}{\rightleftarrows }}\left[{\mathit{CaB}}_R{\mathit{CaB}}_R\right]$$

So, with our model, only 4 transition rate constants are needed to describe the kinetics of two identical cooperative binding sites. For the fitting procedure it is important to minimize the number of variables to fit, so that degrees of freedom of the system are minimal, which increases the reliability of the fit. Furthermore, our model describes a simple two-step binding system that can easily translate to the macroscopic Adair-Klotz equation where the macroscopic binding constants K₁ and K₂ are:

$$K_1=\frac{k_{on,T}}{2\times k_{\mathit{off},T}}\text{and}{K}_2=\frac{2\times k_{on,R}}{k_{\mathit{off},R}}$$

We have used this model to fit data measured from the CBP calretinin (CR) which has four cooperative binding sites [63]. When comparing the fits with a MWC model describing CR, we found no differences and concluded that our new model was just as sufficient to describe the kinetics of CR[30].

2.9 Fitting the data

Though we have simplified the model with which the kinetics of cooperative binding can be quantified, most models that describe CBPs will still be fairly complex and will still have many variables to fit. For instance, CR has four cooperative sites and one independent site. In such a case, it is wise to explore how to simplify the model for the CBP. For instance, based on earlier findings on CR it is not unreasonable to assume that its cooperative binding sites function as two similar pairs of binding sites [30]. This compounds the number of parameters to fit for the cooperative sites of CR to 4, making a total of 6 when the independent site is also included. Although such simplifications are not always possible (e.g., for CaM [31]), it is a good first step to make the fitted parameters more reliable. Still 6 and sometimes more (e.g., 8 for CaM [31]) parameters result in too many degrees of freedom to accurately determine any of those parameters by fitting single curves as show in figure 4A. Therefore, we developed a procedure that significantly constrains the fit. In short, we obtain data under a variety of starting conditions for [Ca²⁺]_rest, [DMn]_total, [OGB-5N]_total and [CBP]_total. Furthermore, under each of these different conditions, we record many traces all initiated by different uncaging energies, i.e., different amounts of Ca²⁺ uncaging (figure 5, Step 1). This gives 100–200 different traces from which we compose random sets of 10–15 traces and fit them simultaneously (Figure 5, Step 2). This results in a parameter set (the fitted rate constants) that is constrained because the fit result has to describe all the different traces simultaneously with one single parameter set describing the CBP (Figure 5, Step 3, yellow markers). This procedure is then repeated 30–40 times with another random set of traces, every time resulting in a new value for each fitted parameter, creating a pool of 30–40 fit results for each parameter. Then, a distribution and average is determined for each parameter from this pool of fit results (Figure 5, Step 3). Combined with this procedure we use several other mechanisms to ensure that we probe whole physiologically feasible parameter domain and that we diminish the probability of assigning fit solutions to local error minima is. For more details please see [30, 31]

Figure 5.

Procedure that constrains the fits with a CBP model that has many degrees of freedom. In Step 1 many uncaging measurements are made with different uncaging energies at different starting conditions by varying [Ca²⁺]_rest, [DMn]_total, [OGB-5N]_total and [CBP]_total. These different conditions are represented as the colors in the traces under Step1. For instance for the yellow traces [Ca²⁺]_rest, [DMn]_total, [OGB-5N]_total and [CBP]_total are 1.9 μM, 5.6 mM, 50 μM and 123 μM, respectively while for the dark blue traces they are 0.4 μM, 3.6 mM, 100 μM and 47 μM, respectively. Of all the measured traces, a random group of traces is taken in Step 2 and fitted simultaneously. Each trace starts with it own set of starting conditions but they all have the same parameters that are fitted. In this case, the CBP is modeled with 2 types of binding sites that can occur in 2 states (R and T) making a total of 4 k_on’s and 4 k_off’s (a, b, c, d). The results of the binding sites and states (R or T) for this particular fit are plotted in the figure under Step 3 with yellow markers. Step 2 is repeated several times to create an average and a distribution for each fitted parameter as seen in Step 3.

3 The future of flash photolysis in biomolecular kinetics

3.1 Measurements beyond Ca²⁺ binding kinetics

There are few techniques that can replicate the speed of photolysis in which UV light is used to break a chemical bond that converts a biochemically inert molecule into one that is active, or simply releases a “caged” compound. In this special issue of Biochimica et Biophysica Acta on biochemical, biophysical and genetic approaches to intracellular Ca²⁺ signaling, we gave an overview on how we use photolysis to measure the fast Ca²⁺ binding properties of CBPs. However, we believe that the methods we applied here should also be applicable to measure reaction kinetics of a variety of biochemical processes. Ever since the first reported synthesis of a caged compound (ATP, [64]) the use of caged substances has been continuously developed, leading to the successful experimental use of more than 60 caged molecules of biological importance [65, 66], many of which are commercially available (e.g., Calbiochem, Invitrogen, Tocris, Probior, Enzo Life Sciences). Initially, only ions and small molecules could be caged such as nucleotides (and analogues), gasses (e.g., O₂, CO and NO), simple neurotransmitters (glutamate, GABA and 5-HT), and simple intracellular messengers (e.g., DAG and IP₃), as it is easier to shield their active domain. However, as new methods have been devised, it is now possible to specifically mask the active domain of much larger molecules, including proteins and oligonucleotides, with groups that can be removed with photolysis [65, 66]. The field of biochemical quantification/detection using fluorescent probes has also been developing steadily, resulting in many specific probes for ions (Invitrogen, Molecular Probes) and smaller molecules such as ATP [67], O₂ [68] and NO [69]. In addition, spectroscopical techniques such as fluorescence correlation spectroscopy and fluorescence polarization/anisotropy provide quantitative tools to measure the formation of macromolecular complexes by probing their size. We hope that our work will be an incentive for expanding this type of quantification to other molecular interactions where fast kinetics play a decisive role.

3.2 Future of CBP kinetics

Up until now we used our technique to quantify the Ca²⁺ binding kinetics of CB, CR and CaM, which gave immediately some remarkable insights. We found that CR is comparable to EGTA around a low [Ca²⁺]_rest (~100 nM), but shifts to a faster acting mode at higher [Ca²⁺]_rest (~1 μM) and acts more like BAPTA. This leads to the remarkable property that the overall buffering speed of CR seemingly does not change over a wide rage physiological of [Ca²⁺], even as less CR binding sites are available at higher [Ca²⁺][30, 54]. For CaM, we found that the pair of binding sites on the N-terminus are much faster than ever estimated (or expected). The binding sites on the N-terminus have a ~10× lower affinity than the pair of binding sites on the C-terminus or the binding sites on CB. Nevertheless, upon Ca²⁺ influx, the N-terminal binding sites will initially win the competition for the Ca²⁺ because the N-terminus is the fastest. It is later during the Ca²⁺-signal transduction that Ca²⁺ leaves the N-terminus and trickles down to the higher affinity, and slower binding sites [31]. Furthermore, two very different types of cooperativity (on the N-terminus primarily caused by increasing k_on in the T→R transition and on the C terminus primarily caused by decreasing k_off in the T→R transition) provide a ‘two-step’ mechanism, one within the bulk solution and one within the nanodomain[70], to fully activate CaM. Although we have just started to quantify the kinetic properties of a few CBPs with a higher accuracy then ever before, the results, thus far, suggest that quantifying the kinetics of more CBPs will give a whole new perspective to Ca²⁺ signaling. There are many more CBPs that could and should be studied this way. Furthermore, the (regulating) effects of molecular interactions between other proteins and CBPs (e.g., CaM and Neurogranin or IQ domains[42, 43]), or the effects of molecular crowding on CBPs could be studies using this technique. This technique could potentially give many new insights into the mechanisms of Ca²⁺ signaling. With the three CBPs we quantified thus far, we have barely scratched the.

Highlights.

• Kinetics of Ca²⁺ binding proteins (CBPs) are too fast to gauge with normal methods

• The fast kinetics of CBPs can be determined using flash photolysis

• Cooperativity should be included when quantifying binding kinetics of CBPs

• The binding kinetics of CBPs play a key role in calcium signaling