Biphasic Ca²⁺-dependent switching in a calmodulin-IQ domain complex

Abstract

The relationship between the free Ca²⁺ concentration and the apparent dissociation constant for the complex between calmodulin (CaM) and the neuromodulin IQ domain consists of two phases. In the first phase Ca²⁺ bound to the C-ter EF hand pair in CaM increases the K_d for the complex from the Ca²⁺-free value of 2.3±0.1 μM to a value of 14.4±1.3 μM. In the second phase Ca²⁺ bound to the N-ter EF hand pair reduces the K_d for the complex to a value of 2.5±0.1 μM, reversing the effect of the first phase. Due to energy coupling effects associated with these phases the mean dissociation constant for Ca²⁺-binding to the C-ter EF hand pair is increased ~3-fold, from 1.8±0.1 to 5.1±0.7 μM, and the mean dissociation constant for Ca²⁺-binding to the N-ter EF hand pair is decreased by the same factor, from 11.2±1.0 to 3.5±0.6 μM. These characteristics produce a bell-shaped relationship between the apparent dissociation constant for the complex and the free Ca²⁺ concentration, with a distance of 5–6 μM between the midpoints of the rising and falling phases. Release of CaM from the neuromodulin IQ domain therefore appears to be promoted over a relatively narrow range of free Ca²⁺ concentrations. Our results demonstrate that CaM-IQ domain complexes can function as a biphasic Ca²⁺ switches through opposing effects of Ca²⁺ bound sequentially to the two EF hand pairs in CaM.

The Ca²⁺-binding protein calmodulin (CaM) plays a central role in transducing Ca²⁺ signals through its interactions with more than 30 different target proteins. Many of these, such as phosphodiesterase, myosin light chain kinase and the constitutive nitric oxide synthases do not interact significantly with Ca²⁺-free CaM (apoCaM) (1–4). However, a large class of targets bind apoCaM at least as well as the Ca²⁺-liganded forms of the protein. The majority of these, including neuromodulin, neurogranin, the unconventional myosins and some Ca²⁺, K⁺ and Na⁺ channels interact with CaM via IQ domains, which have the consensus sequence: [I,L,V]QxxxR[G,x]xxx[R,K] (5, 6). These regions bind apoCaM and/or Ca²⁺-liganded CaM with dissociation constants ranging from subnanomolar to micromolar, depending upon their precise sequence and context (6). CaM-IQ domain complexes have been implicated in a variety of regulatory processes, including positive and negative regulation of ion channels and unconventional myosin based motility (6). Some IQ domain proteins have been proposed to function as local intracellular stores of CaM (7).

The potential importance of such stores has been heightened by recent investigations indicating that the intracellular CaM concentration is limiting: We have found that a dephosphorylation-dependent increase in the amount of CaM bound to nitric oxide synthase in endothelial cells significantly reduces the available CaM concentration during a Ca²⁺ signal, and inhibits the activity of the plasma membrane Ca²⁺ pump and presumably other CaM targets (8). Rahkilin and coworkers have recently demonstrated that a limiting CaM concentration in neurons results in similar coupling among target activities (9). Finally, the work of Isotani and coworkers suggests that the CaM concentration is limiting in smooth muscle tissue (10). Thus, CaM and its targets can be considered to form what we have termed the CaM network (11). Although the available CaM concentration is a function of all its various interactions, proteins that function as CaM stores are of particular interest, as they are likely to contribute in important ways to the form and function of the CaM network. Neuromodulin, a neuronal IQ domain protein found in axons and terminals, is perhaps the best studied example of such a protein (7). Neurogranin, a smaller protein with an essentially identical IQ domain, is thought to perform a similar function in dendritic spines (12, 13).

In this paper we describe a steady-state mechanism for Ca²⁺-dependent switching in the neuromodulin CaM-IQ domain complex. A surprising aspect of this mechanism is its fundamentally biphasic nature: Ca²⁺ binding one EF hand pair in CaM decreases the affinity of the complex; binding to the other then completely reverses this effect. The result is a bell-shaped relationship between the apparent dissociation constant for the complex and the free Ca²⁺ concentration.

Materials and Methods

Proteins

The cDNA encoding BSCaM_IQ¹, a fluorescent reporter that binds CaM via an IQ domain sequence derived from neuromodulin, was assembled in a modified pET30a vector (Novagen, Inc.). The composition of BSCaM_IQ is similar to that of other CaM biosensors we have developed (14, 15), except that it contains a form of enhanced yellow fluorescent protein (EYFP_C) in which the pK_a for fluorescence quenching is shifted from a value of ~7 to a value of ~6, which increases EYFP fluorescence emission under the conditions used in these investigations (16). The CaM-binding sequence bridging the ECFP and EYFP_C variants in BSCaM_IQ: AAATKIQA[A]FRGHITRKKLKGEKKGAA, is based on the IQ domain region in neuromodulin (neuromodulin sequence underlined), differing only in the substitution of an Ala residue (in brackets) for a Ser. This corresponds with position 41 in the neuromodulin amino acid sequence (17). Phosphorylation at this position in full-length neuromodulin blocks CaM binding, but substitution of a Gly residue does not affect binding (17). We have also developed a bipartite fluorescent reporter system consisting of EYFP_C-neuromodulin and ECFP-CaM fusion proteins. In the neuromodulin fusion the fluorescent protein is joined to the N-terminus of full-length native neuromodulin via a Gly-Thr amino acid pair. In the CaM fusion the fluorescent protein is joined to the N-terminus of native CaM via a GASGSAAAG polypeptide linker. All fluorescent protein constructs were expressed with amino-terminal 6-His tags in BL21(DE3), and were purified using Ni⁺-chelate affinity chromatography as described previously (18). Both of these fluorescent reporter systems are represented schematically in Fig. 1.

Fig. 1. Fluorescent reporter systems used to monitor interactions between CaM and the neuromodulin IQ domain. (A).

BSCaM_IQ consists of ECFP and EYFP variants of GFP joined by an IQ domain. When CaM is bound to this domain changes in the orientation and/or distance between the two fluorescent proteins decrease fluorescence resonance energy transfer (FRET) between the ECFP and EYFP components. Thus, under 430 nm excitation ECFP donor fluorescence, measured at 480 nm, is increased and EYFP acceptor fluorescence, measured at 525 nm, is decreased. (B) Complete fluorescence emission spectra for BSCaM_IQ under 430 nm excitation. The solid line is the emission spectrum determined in the absence of CaM, the dashed line is the spectrum determined in the presence of a saturating apoCaM concentration. The remaining spectra were determined in the presence of saturating concentrations of Ca²⁺-free NC_xCaM or N_xCCaM (□), Ca²⁺-saturated native CaM (●), N_xC₂CaM (○) and N₂C_xCaM (△). (C) A bipartite reporter system consisting of ECFP-CaM and EYFP-neuromodulin fusion proteins. As illustrated in the figure, formation of the complex between CaM and neuromodulin allows FRET between the ECFP and EYFP labels to occur under 430 nm excitation.

Native and mutant CaMs were expressed and purified as described in detail elsewhere (19, 20). The two mutant CaMs used in these studies are N_xCCaM (N_xC), in which glutamic acid residues at positions 31 and 67 in the N-ter EF-hands have been replaced by alanines, and NC_xCaM (NC_x), in which the homologous glutamic acid residues at positions 104 and 140 have been replaced. These mutations eliminate Ca²⁺ binding to the N-ter or C-ter EF hand pair, as indicated by the “x” subscript.

Fluorescence measurements

A Photon Technologies International (Monmouth Junction, NJ) QM-1 fluorometer operated in photon-counting mode was used for all steady-state fluorescence measurements. Monochromator excitation and emission slit widths were set to produce bandwidths of ~2.5 nm. All experiments were performed at 23 °C. The standard experimental buffer contained 25 mM Tris (pH 7.5), 0.1 M KCl, 100 μg/ml BSA, and other components as specified in the text or captions. For analysis of the Ca²⁺-dependencies of native and mutant CaM complexes, buffered free Ca²⁺ concentrations were produced using 1.5 mM BAPTA, 1.5 mM dibromo-BAPTA and various amounts of added of CaCl₂. Stated free Ca²⁺ concentrations were measured using 250 nM indo-5F or mag indo-1 according to established procedures (Molecular Probes, Inc.). As we have demonstrated elsewhere, there is no significant spillover in the fluorescence emissions of these Ca²⁺ indicator dyes and the BSCaM_IQ reporter (8, 21).

When required, proteins and buffers were decalcified by successive treatments with Chelex^™ and a BAPTA-polystyrene column (Molecular Probes, Inc.). Contaminating amounts of Ca²⁺ in protein solutions at their stated working concentrations were 150 nM or less, based on the absence of any detectible effect on the A₂₆₃ of dibromo-BAPTA.

Analysis of fluorescence data

Fractional changes in fluorescence were analyzed to extract apparent K_d values for native or mutant CaMs using a standard hyperbolic binding equation, where FR is fractional response as defined in the relevant figure legends:

$$\text{FR}=[\mathit{CaM}]/([\mathit{CaM}]+K_d)$$ (1)

A sequential Ca²⁺ binding model was used to analyze fractional changes in fluorescence due to Ca²⁺-dependent dissociation of the N_xCCaM or NC_xCaM complexes with BSCaM_IQ:

$$\text{FR}=\frac{\left({[C{a}^{2+}]}^2/K_1{K}_2\right)}{\left(1+[C{a}^{2+}]/K_1+{[C{a}^{2+}]}^2/K_1{K}_2\right)}$$ (2)

where K₁ and K₂ in this case designate the apparent dissociation constants for the two sites in the functional EF hand pairs. A sequential mechanism for Ca²⁺ binding to the individual EF hands is assumed. This is supported by investigations in which Ca²⁺ binding to individual EF hands have been monitored spectrally (22–24). We have also assumed that dissociation requires occupancy of both sites in an EF hand pair. This may not be strictly correct, since NMR investigations indicate that occupancy of a single Ca²⁺-binding site can produce significant conformational changes in CaM (24). However, under steady-state conditions positive cooperativity between the sites in each EF hand pair restricts the amount of CaM with only one site occupied to negible levels (25).

Direct determinations of Ca²⁺ binding constants

Direct Ca²⁺-binding measurements were performed as described by Linse and coworkers (26, 27). In this approach Ca²⁺ binding to a BAPTA or dibromo-BAPTA chelator is measured based on its optical absorbance at 263 nm as known increments of Ca²⁺ are added to an initially decalcified solution containing the chelator and the Ca²⁺-binding protein of interest. The absolute amounts of free Ca²⁺ and Ca²⁺ bound to the chelator after each addition can thus be estimated, with the amount bound to the protein accounting for the remainder (28). We have found a 0.5 to 1 molar ratio of chelator to protein Ca²⁺-binding sites to yield the best determined Ca²⁺ dissociation constants. Apparent Ca²⁺ dissociation constants for proteins were derived from direct fits to observed chelator absorbance using the Caligator software package (28). A general four-site Adair equation was used to define Ca²⁺ binding to native CaM:

$$\theta =\frac{1}{4}\left(\frac{K_1[C{a}^{2+}]+2K_1{K}_2{[C{a}^{2+}]}^2+3K_1{K}_2{K}_3{[C{a}^{2+}]}^3+4K_1{K}_2{K}_3{K}_4{[C{a}^{2+}]}^4}{1+K_1[C{a}^{2+}]+K_1{K}_2{[C{a}^{2+}]}^2+K_1{K}_2{K}_3{[C{a}^{2+}]}^3+K_1{K}_2{K}_3{K}_4{[C{a}^{2+}]}^4}\right)$$ (3)

where θ is the fractional saturation of the four sites in this protein. An abbreviated form of this expression was used to describe binding to the two CaM mutants, NC_xCaM and N_xCCaM, which have only one functional EF hand pair:

$$\theta =\frac{1}{2}\left(\frac{K_1[C{a}^{2+}]+2K_1{K}_2{[C{a}^{2+}]}^2}{1+K_1[C{a}^{2+}]+K_1{K}_2{[C{a}^{2+}]}^2}\right)$$ (4)

Modeling

The theoretical curves presented in Figs 8 and 9 were calculated using the Berkeley Madonna software package (Macey and Oster, Inc). For this purpose an expanded version of the scheme presented in Fig. 7 was used in which Ca²⁺ binding to each EF hand pair is treated as a two-step sequential process. Since all simulations were allowed to reach a steady-state, only the ratios of the rate constants used for each step in the mechanism are important, and these are defined by the steady-state interaction parameters listed in Tables 1 and 2.

Fig. 8. The relationship between the free Ca²⁺-concentration and the dissociation constant for the complex between CaM and the neuromodulin IQ domain is bell shaped.

All free Ca²⁺ concentrations were verified using indo-5F or mag-indo-1. (A) The fractional fluorescence response of 250 nM BSCaM_IQ in the presence of 20 μM CaM (B) The fractional fluorescence response of 5 μM BSCaM_IQ in the presence of 1 μM CaM (■), and the fractional response of a solution of 1 μM ECFP-CaM and 5 μM EYFP-neuromodulin (△). Because FRET increases when this complex is formed, the fractional response in this case defined as (F−F_min)/(F_max−F_min). The curves in both panels were calculated as described under “Materials and Methods” according to the scheme depicted in Fig. 7. The F_min/F_max values used to generate for these curves were adjusted slightly to achieve the fits shown. All adjusted values were within 3% of the mean values given in Table 1.

Fig. 9. Various species produced in a solution of neuromodulin (NM) and CaM as a function of the free Ca²⁺ concentration.

Calculations were performed as described under “Materials and Methods” using CaM and NM concentrations of 10 μM based on the scheme depicted in Fig. 7. All calculated concentrations are expressed relative to the total CaM concentration. Curves correspond with the relative concentrations of bound NM (△), total free CaM (no symbol), free calci-CaM (○), NCCaM-NM complex (▲), NC₂CaM-NM complex (■), and N₂C₂CaM-NM complex (◆). Calci-CaM refers to the total of all free Ca²⁺-liganded CaM species, which primarily consist of NC₂CaM and N₂C₂-CaM. Otherwise, the nomenclature for the various Ca²⁺-liganded species of CaM is given in the legend to Table 1.

Fig. 7. Minimal scheme for Ca²⁺-dependent switching in the neuromodulin CaM-IQ domain complex.

Ca²⁺ binding via the N-ter→C-ter pathway depicted in the general scheme appears to be strongly disfavored, so it can be omitted from the minimal scheme describing the Ca²⁺-dependence of the CaM-neuromodulin complex under steady-state conditions.

Table 1. Apparent K_d values for the complexes between BSCaM_IQ and native or mutant CaMs.

B refers to bound BSCaM_IQ. N and C refer to the C-ter and N-ter EF hand pairs in CaM, with subscripts indicating the Ca²⁺-liganded state or the inability to bind Ca²⁺ due to mutagenesis (x). The absence of a subscript indicates a native Ca²⁺-free EF hand pair. The nominal affinity given for the NC₂-B complex was determined at a 10 μM free Ca²⁺ concentration. Standard errors were derived from the diagonal elements in the variance-covariance matrices for the fitted curves. F_min/F_max is the ratio of the 525 nm fluorescence emissions of the BSCaM_IQ complex with native or mutant CaM (F_min) and the emission of free BSCaM_IQ (F_max).

	NC-B	N2C2-B	NCx-B	N2Cx-B	NxC-B	NxC2-B	NC2-B
Kd (μM)	2.3±0.1	2.5±0.1	2.5±0.3	36.7±3.9	2.1±0.2	14.4±1.3	10.8±1.1
Fmin/Fmax	0.68±0.2	0.83±0.3	0.69±0.2	0.83±0.3	0.68±0.2	0.85±0.2	0.85±0.2

Table 2. Ca²⁺ binding constants for native and mutant CaMs in the presence and absence of BSCaM_IQ.

The nomenclature used here is defined in the legend to Table 1. The “F” superscript identifies dissociation constants derived from data for Ca²⁺-dependent dissociation of mutant CaM-BSCaM_IQ complexes. Otherwise, all dissociation constants were derived from direct Ca²⁺ binding measurements as described under “Materials and Methods.” Standard errors were derived from the diagonal elements in the variance-covariance matrices for fits to at least five pooled data sets. K_1,2 and K_3,4 are the geometric means of the Ca²⁺-binding constants for the C-ter or N-ter EF hand pair.

	μM						μM2
	K1	K2	K3	K4	K1,2	K3,4	K1K2	K3K4
NC	11.2±5.4	0.3±0.2	25.1±10.3	5.0±2.6	1.8±0.1	11.2±1.0	3.1±0.2	126±11.4
NxC	14.1±4.9	0.2±0.1	–	–	1.6±0.2	–	2.4±0.3	–
NCx	–	–	24.0±9.5	3.9±1.6	–	9.7±1.0	–	93.3±9.2
NC-B	10.7±3.8	2.4±0.8	7.8±3	1.6±0.7	5.1±0.7	3.5±0.6	25.7±3.5	12.3±1.9
NxC-B	22.4±11.3	1.1±0.6	–	–	4.9±0.5	–	24.6±2.7	–
NxC-BF	23.2±8.6	0.7±0.2	–	–	4.0±0.3	–	16.1±1.1	–
NCx-BF	–	–	122±68.0	9.4±4.0	–	33.8±4.0	–	1140±122.0

Results

Binding of native and mutant CaMs to BSCaM_IQ in the presence and absence of Ca²⁺

The initial step in these investigations was to determine K_d values for the complexes between the BSCaM_IQ fluorescent reporter containing the neuromodulin IQ domain and apoCaM or (Ca²⁺)₄-CaM. Respective values of 2.3±0.1 and 2.5±0.1 μM were derived from the data presented in Fig. 2 (Table 1). Purified neuromodulin has previously been reported to bind apoCaM and (Ca²⁺)₄-CaM with K_d values of 3.0 and 3.4 μM under similar experimental conditions (29, 30). As seen in Fig. 2, at a free Ca²⁺ concentration of 10 μM the apparent K_d value for the CaM-BSCaM_IQ complex increases to 10.8±1.1 μM, suggesting that the transition between the apoCaM and (Ca²⁺)₄-CaM complexes involves more weakly bound forms of CaM (Table 1).

Fig. 2. Binding of CaM to BSCaM_IQ in the presence of 10 (◆) and 250 (□) μM free Ca²⁺, or 3 mM BAPTA (■).

The fractional change in 525 nm fluorescence produced by the decrease in FRET associated with formation of the complex is defined as (F_max−F)/(F_max−F_min), where F corresponds with the emission measured after each addition, and F_max and F_min correspond with the emissions of CaM-free and CaM-saturated BSCaM_IQ. A 50 μM BSCaM_IQ concentration was used for these experiments. The apparent K_d values determined from fits of these data to a simple one-site hyperbolic binding equation (not shown) are listed in Table 1.

To further investigate the basis for this apparent reduction in affinity at an intermediate free Ca²⁺ concentration we employed N_xCCaM and NC_xCaM, mutants of CaM in which Ca²⁺ binding to the N-ter or C-ter EF hand pair has been abolished (19). These mutants provide a convenient way to isolate the effects of Ca²⁺ binding to each EF hand pair. Our results indicate that the properties of these mutant proteins are consistent with the properties of native CaM. Nevertheless, it should be borne in mind that the mutant EF hands in these proteins are likely to adopt conformations that differ from the corresponding native Ca²⁺-free conformations (31). As seen in Fig 3A, in the absence of Ca²⁺ both mutants bind the BSCaM_IQ reporter with a K_d value of ~2.3 μM, essentially identical to the value for native apoCaM (Table 1). In the presence of a saturating Ca²⁺ concentration the K_d values for the complexes with N_xCCaM and NC_xCaM are respectively increased to 14.4±1.3 and 36.7±3.9 μM (Fig. 3B, Table 1). Data for dissociation of the mutant CaM complexes as a function of the free Ca²⁺ concentration are presented in Fig. 4. Binding constants for the functional EF hand pair in each mutant complex can be estimated based on fits of these data to equation 2 (Table 2). The geometric means of the dissociation constants derived for the C-ter (K_1,2) and N-ter (K_3,4) EF hand pairs in bound N_xCCaM and NC_xCaM are 4.0±0.3 and 33.8±4.0 μM; the corresponding values for the free mutant proteins are 1.6±0.2 and 9.7±1.0 (Table 2). Thus, the mean Ca²⁺-binding affinities of the functional EF hand pairs in both mutant CaMs are reduced 3 to 4-fold when they are associated with BSCaM_IQ.

Fig. 3. Binding of N_xCCaM or NC_xCaM to BSCaM_IQ.

(A) Fractional changes in 525 nm fluorescence emission, defined as described in the legend to Fig. 2, associated with binding of N_xCCaM (□) or NC_xCaM (△) to 50 nM BSCaM_IQ under nominally Ca²⁺ free conditions (3 mM BAPTA). (B) Fractional changes in 525 nm fluorescence emission associated with binding of N_xCCaM (■) and NC_xCaM (▲) to 150 nM BSCaM_IQ at a free Ca²⁺ concentration of ~250 μM. Apparent K_d values derived from the data presented in panels A and B are listed in Table 1.

Fig. 4. Ca²⁺-dependent dissociation of the N_xCCaM or NC_xCaM complexes with BSCaM_IQ.

Fractional changes in 525 nm fluorescence emission associated with formation of the complexes between 12.5 μM BSCaM_IQ and 1 μM N_xCCaM (◆) or NC_xCaM (■). All free Ca²⁺ concentrations were verified using indo-5F or mag-indo-1. Fractional changes in fluorescence are defined using an F_max value measured at the end of the experiment, which accounts for residual CaM binding in the presence of Ca²⁺. Otherwise fractional changes are defined as described in the legend to Fig. 2. Apparent Ca²⁺-binding constants derived from fits of these data to equation 2 are listed in Table 2.

Measurements of Ca²⁺ binding to native and mutant CaMs in the presence and absence of BSCaM_IQ

Ca²⁺-binding data measured in the presence and absence of BSCaM_IQ are presented in Figs 5A and 5B. Significant dissociation of CaM from the IQ domain is prevented during the course of these experiments by using at total concentration of CaM and BSCaM_IQ that is ~10-fold or more above the K_d value for the lowest affinity form of the complex. Otherwise, one observes the Ca²⁺ binding characteristics of a mixture of free and bound CaM. Indeeed, this technique could not be applied to the complex between NC_xCaM-BSCaM_IQ because a total protein concentration of ~200 μM is required to prevent dissociation of this complex at elevated free Ca²⁺ concentrations, which was found to be above the usable limit due to solubility problems.

Fig. 5. Direct measurements of Ca²⁺ binding to native and mutant CaMs in the presence and absence of BSCaM_IQ.

(A) 263 nm absorbance data for 40 μM dibromo-BAPTA measured in the presence of 20 μM native CaM (■) or 20 μM native CaM and 100 μM BSCaM_IQ (□). (B) Absorbance data for 40 μM dibromo-BAPTA measured the presence of 20 μM N_xCCaM (●) or 20 μM N_xCCaM and 100 μM BSCaM_IQ (○). For presentation purposes these data have been normalized to the absorbance of Ca²⁺-free dibromo-BAPTA determimed at the completion of each titration experiment. Pooled data from 3 separate Ca²⁺ binding experiments are presented for each set of conditions examined. The dissociation constants derived from fits of these and similar data to equation 3 or 4 are listed in Table 2 (28).

The Ca²⁺-binding constants we have derived for native CaM are essentially identical to the literature values (27), and the correspondence between these values and those determined for the N_xCCaM and NC_xCaM mutants suggests that the presence of a non-functional EF hand pair in one CaM lobe does not significantly perturb Ca²⁺ binding to the other (Table 2). There is also reasonable agreement between the mean dissociation constants for the C-ter EF hand pair (K_1,2 ) derived for the N_xCCaM-BSCaM_IQ complex based on data for Ca²⁺-dependent dissociation (4.0±0.3) and from direct measurements of Ca²⁺ binding (4.9±0.5). Perhaps most importantly, our results demonstrate that in the native CaM-BSCaM_IQ complex the affinity of the C-ter EF hand pair in CaM is decreased and the affinity of the N-ter EF hand pair is increased. These opposing effects result in similar mean dissociation constants of 5.1±0.7 and 3.5±0.6 μM for the two EF hand pairs. The first of these values is assumed to be K_1,2, the mean dissociation constant for the C-ter EF hand pair, because it is closest to the value for the N_xCCaM-BSCaM_IQ complex (Table 2).

A general four-state mechanism for Ca²⁺-dependent switching in a CaM-target complex

A general steady-state mechanism for Ca²⁺-dependent switching in a CaM-IQ domain complex is presented in Fig. 6. It includes the four major Ca²⁺-liganded forms of CaM: apoCaM (NC), CaM with two Ca²⁺ ions bound to the C-ter (NC₂) or N-ter (N₂C) EF hand pair, and CaM with Ca²⁺ bound to both EF hand pairs (N₂C₂). In this model Ca²⁺ binding to the individual sites in an EF hand pair is treated as a single step governed by a K₁K₂ or K₃K₄ value.

Fig. 6. A general four-state scheme for Ca²⁺-dependent switching in a CaM-IQ domain complex.

B indicates the bound IQ domain protein; N and C indicate the N-ter and C-ter EF hand pairs in CaM, with subscripts denoting their Ca²⁺-liganded states; the absence of a subscript indicates a Ca²⁺-free EF hand pair.

Thermodynamic relationships

Thermodynamic linkage or energy coupling associated with formation of a CaM-target complex can be quantitively defined according to the relation:

$$\mathrm{\Delta }\mathrm{\Delta }{G}_C=\mathit{RT}ln\frac{K_{N_2{C}_2}}{K_{NC}}=\mathit{RT}ln\frac{{(K_1{K}_2{K}_3{K}_4)}_B}{{(K_1{K}_2{K}_3{K}_4)}_F}$$ (5)

where K₁ and K₂ are the Ca²⁺ binding constants for the C-ter EF hand pair and K₃ and K₄ are the constants for the N-ter pair. K_NC and K_N2C2 are the dissociation constants for the apoCaM (NC) and (Ca²⁺)₄-CaM (N₂C₂) complexes with a target. The F and B subscripts identify the Ca²⁺ binding constants for free CaM and CaM bound to a target. These mathematical relationships formalize the basic thermodynamic requirement that a Ca²⁺-dependent change in the affinity of a CaM-target complex must be coupled to a corresponding change in the Ca²⁺-binding affinity of CaM when bound to the target. A negative ΔΔG_C value is produced when Ca²⁺ binding increases the affinity of CaM for a target. This is termed favorable or “positive” energy coupling because it is linked to an increase in Ca²⁺-binding affinity. A positive ΔΔG_C value is produced when Ca²⁺ binding decreases the affinity of CaM for a target. This type of energy coupling is termed unfavorable or “negative” because it is linked to a decrease in Ca²⁺-binding affinity. We can also define energy coupling in terms of the the individual EF hand pairs:

$$\begin{array}{l}\mathrm{\Delta }\mathrm{\Delta }{G}_C^C=\mathit{RT}ln\alpha ,\\ \text{where}\alpha =\frac{K_{N{C}_2}}{K_{NC}}=\frac{{(K_1{K}_2)}_B}{{(K_1{K}_2)}_F}\end{array}$$ (6)

$$\begin{array}{l}\mathrm{\Delta }\mathrm{\Delta }{G}_C^N=\mathit{RT}ln\beta ,\\ \text{where}\beta =\frac{K_{N_2{C}_2}}{K_{N{C}_2}}=\frac{{(K_3{K}_4)}_B}{{(K_3{K}_4)}_F}\end{array}$$ (7)

The C and N superscripts designate the ΔΔG_C values for the C-ter and N-ter EF hand pairs. The proportionality constants α and β are coupling coefficients; values less than one correspond with positive coupling and values greater than one correspond with negative coupling. As seen in Fig. 6, Ca²⁺ can in principal bind first to either the N-ter or C-ter EF hand pair, so two sets of coupling coefficients and ΔΔG values must be considered. Unprimed symbols are used for the C-ter→N-ter pathway, and primed symbols for the alternative N-ter→C-ter pathway (see Fig. 6). Since the apoCaM and (Ca²⁺)₄-CaM complexes with BSCaM_IQ have essentially identical affinities, the complete transition from one type of complex to the other cannot produce significant net energy coupling (ΔΔG_C ≈ 0). In terms of the individual EF hand pairs this means that $\mathrm{\Delta }\mathrm{\Delta }{G}_C^C+\mathrm{\Delta }\mathrm{\Delta }{G}_C^N\approx \mathrm{\Delta }\mathrm{\Delta }{G}_C^{C^{\prime }}+\mathrm{\Delta }{\mathrm{\Delta }}_C^{N^{\prime }}\approx 0$ and αβ ≈ α′β′ ≈ 1. Thus, in spite of an overall lack of energy coupling, energetically opposing effects of Ca²⁺-binding to the two EF hand pairs are not precluded, and this is in fact what we have observed.

As seen in Table 3, α has a value of ~ 8.5, indicating negative coupling, while β has a value of ~ 0.14, indicating positive coupling. The product of these values is ~1.2, satisfying the requirement that αβ ≈ 1. Thus, along the C-ter→N-ter pathway negatively coupled Ca²⁺ binding to the C-ter EF hand pair, which necessarily reduces the affinity of the CaM-BSCaM_IQ complex, is followed by positively coupled binding to the N-ter EF hand, which in this case necessarily restores the affinity of the complex to its initial value. Based on the properties of the NC_xCaM-BSCaM_IQ complex, we have estimated a value of ~13.5 for β′, the coupling coefficient for the first step in the alternative N-ter→C-ter pathway (Table 3). This pathway thus appears to be strongly disfavored for at least three reasons: (1) The Ca²⁺-binding affinity of the N-ter EF hand pair in CaM is inherently ~6-fold lower than the affinity of the C-ter pair (Table 2), (2) The β′ value is ~2-fold larger than the α value, which widens this inherent difference by ~30%. (3) The affinity of the N₂CCaM complex with BSCaM_IQ is 2-fold lower than the affinity of the NC₂CaM complex (Table 1). Thus, we can simplify our steady-state scheme by omitting the N-ter→C-ter pathway (Fig. 7). This pathway is likely to be of greater importance under transient conditions because the N-ter EF hand pair binds Ca²⁺ more rapidly than the C-ter pair (32).

Table 3. Coupling coefficients and ΔΔG_C values for the CaM-BSCaM_IQ complex.

The K₃K₄ value indicated by an “F” superscript was derived from data for Ca²⁺-dependent dissociation of the of NC_x-B complex. All other K₁K₂ and K₃K₄ values were derived from direct measurements of Ca²⁺-binding. Dissociation constants for the various CaM-BSCaM_IQ complexes are designated by subscripts identifying the bound CaM species. The products of the dissociation constants for the EF hand pairs are designated by subscripts identifying the bound or free CaM species. The nomenclature used for these subscripts is defined in the legends to Tables 1 and 2. Values given for ΔΔG_C and coupling coefficients were calculated according to equations 6 and 7. As depicted in Fig. 6, unprimed values are those for the favored C-ter→N-ter order of Ca²⁺ binding, primed values are those for the alternative N-ter→C-ter order of binding.

	KNXC2/KNXC	$\frac{{({\text{K}}_1{\text{K}}_2)}_{{\text{N}}_{\text{X}}\text{C}-\text{B}}}{{({\text{K}}_1{\text{K}}_2)}_{{\text{N}}_{\text{X}}\text{C}}}$	$\frac{{({\text{K}}_1{\text{K}}_2)}_{\text{NC}-\text{B}}}{{({\text{K}}_1{\text{K}}_2)}_{\text{NC}}}$		KN2C2/KNXC2	–	$\frac{{({\text{K}}_3{\text{K}}_4)}_{{\text{NC}}_{\text{2}}-\text{B}}}{{({\text{K}}_3{\text{K}}_4)}_{{\text{NC}}_{\text{2}}}}$
α	6.9±0.9	10.3±1.7	8.3±1.2	β	0.17±0.02	–	0.1±0.02
$\mathrm{\Delta }\mathrm{\Delta }{G}_C^C$	1.14±0.08	1.4±0.1	1.25±0.1	$\mathrm{\Delta }\mathrm{\Delta }{G}_C^N$	−1.03±0.06	–	−1.4±0.1
	KN2C2/KN2CX	–	–		KN2CX/KNCX	$\frac{{{({\text{K}}_3{\text{K}}_4)}^{\text{F}}}_{{\text{NC}}_{\text{X}}-\text{B}}}{{({\text{K}}_3{\text{K}}_4)}_{{\text{NC}}_{\text{X}}}}$	–
α′	0.07±0.01	–	–	β′	14.7±2.4	12.2±1.8	–
$\mathrm{\Delta }\mathrm{\Delta }{G}_C^{C^{\prime }}$	−1.59±0.07	–	–	$\mathrm{\Delta }\mathrm{\Delta }{G}_C^{N^{\prime }}$	1.58±0.1	1.48±0.1	–

The transition between the apoCaM and (Ca²⁺)₄-CaM complexes with BSCaM_IQ and full-length neuromodulin

The results we have presented thus far are consistent with a minimal biphasic mechanism (Fig. 7) in which the apparent affinity of the CaM-BSCaM_IQ complex is decreased when Ca²⁺ is bound to the C-ter EF hand pair in CaM, and is restored to its initial value when Ca²⁺ is bound to the N-ter EF hand pair. This mechanism should produce a bell-shaped relationship between the apparent dissociation constant for the CaM-BSCaM_IQ complex and the free Ca²⁺ concentration.

The fractional fluorescence response of 250 nM BSCaM_IQ measured in the presence of 20 μM CaM is plotted versus the free Ca²⁺ concentration in Fig. 8A. The EC₅₀(Ca²⁺) value for the transition between the apoCaM and (Ca²⁺)₄-CaM forms of the CaM-BSCaM_IQ complex is 2.5 μM, and there appears to be little dissociation of the complex at any free Ca²⁺ concentration. In contrast, the response of 5 μM BSCaM_IQ measured in the presence of 1 μM CaM is bell-shaped, consistent with significant dissociation of the complex at intermediate free Ca²⁺ concentrations. The amount of dissociation appears to be maximal at a free Ca²⁺ concentration of ~6 μM, and the rising and falling phases of this relationship have EC₅₀(Ca²⁺) values of ~2 and ~11 μM. The agreement between the observed BSCaM_IQ fluorescence responses and the theoretical curves calculated based on our steady-state model is excellent under both sets of conditions (Fig. 8A, B).

To verify the applicability of our results to the complex between CaM and full-length neuromodulin, we employed fluorescently-labeled versions of CaM (ECFP-CaM) and full-length neuromodulin (EYFP_C-neuromodulin). As illustrated in Fig. 1C, under 430 nm illumination formation of the complex between these proteins results in an increase in fluorescence emission at 525 nm due to FRET between the CFP and EYFP_C moieties. The fractional fluorescence response of a mixture of 5 μM EYFP_C-neuromodulin and 1 μM ECFP-CaM is plotted as a function of the free Ca²⁺ concentration in Fig. 8B. This relationship has a more marked bell shape than the accompanying BSCaM_IQ response determined under essentially identical experimental conditions. This is because the complexes between labeled neuromodulin and labeled apoCaM or (Ca²⁺)₄-CaM have the same fluorescence emission, while the complexes between the two forms of CaM and BSCaM_IQ have different emissions (Table 1, Fig. 1B). These results clearly demonstrate that the apparent dissociation constants for the complexes between CaM and BSCaM_IQ or full-length neuromodulin have similar biphasic dependencies on the free Ca²⁺ concentration.

Discussion

The relationship between the apparent dissociation constant for the complex between calmodulin (CaM) and the neuromodulin IQ domain and the free Ca²⁺ concentration consists of two phases. In the first phase Ca²⁺ bound to the C-ter EF hand pair in CaM increases the K_d for the complex from the Ca²⁺-free value of 2.3±0.1 μM to a value of 14.4±1.3 μM. In the second phase Ca²⁺ bound to the N-ter EF hand pair reduces the K_d for the complex to a value of 2.5±0.1 μM, reversing the effect of the first phase. This behavior demonstrates that CaM-IQ domain complexes can function as a biphasic Ca²⁺ switches through opposing effects of Ca²⁺ bound sequentially to the two EF hand pairs in CaM. In the case of neuromodulin these opposing effects serve to promote dissociation of CaM over a relatively narrow range of free Ca²⁺ concentrations.

Gaertner and coworkers (33) recently published a study of the Ca²⁺-dependencies of the CaM-neurogranin complex. This protein has essentially the same IQ domain as neuromodulin, and it is thought to have a similar CaM-buffering function (34). These investigators report that Ca²⁺ is released from the CaM-neurogranin complex at an accelerated rate compared with the rate for free CaM, consistent with negative coupling, although they were unable to verify this with steady-state Ca²⁺ binding measurements (33).

During a Ca²⁺ signal in an excitable cell such as a neuron CaM must be rapidly provided to targets like CaM kinase II that have high local concentrations (35, 36). It has been proposed that CaM-binding proteins such as neuromodulin provide the required local stores of CaM (37–40). However, if neuromodulin were simply to release CaM above a threshold free Ca²⁺ concentration, any not taken up by targets would be free to diffuse away until the free Ca²⁺ concentration fell below this threshold. Our results suggest that release of CaM from neuromodulin is promoted only within a relatively narrow 5 to 6-fold range in the free Ca²⁺ concentration. Our current hypothesis is that during a Ca²⁺ transient in a neuron the local free Ca²⁺ concentration passes rapidly through this range, producing a transient burst of free CaM that rebinds neuromodulin if not taken up by targets. Maintenance of a defined distribution of CaM through this and similar mechanisms may be of particular importance in neurons and other cells whose specific responses to different types of Ca²⁺ signals suggest a high degree of spatial discrimination (41–43).

The concentrations of the major species produced in a solution of CaM and neuromodulin as a function of the free Ca²⁺ concentration can be calculated based the minimal mechanism presented in Fig. 7 and the parameters listed in Tables 1 and 2. Given physiologically reasonable total neuromodulin and CaM concentrations of 10 μM, these calculations indicate that essentially all of the CaM remains Ca²⁺-free at Ca²⁺ concentrations below 0.1 μM, with ~60% of the protein bound to the IQ domain. As the free Ca²⁺ concentration is increased the total concentration of free CaM rises by ~40% with an EC₅₀(Ca²⁺) of ~2 μM, peaks at a free Ca²⁺ concentration of ~5 μM, and declines back to the starting value with an EC₅₀(Ca²⁺) of ~10 μM. To place the range of free Ca²⁺ concentrations over which this occurs in a physiological context, it appears that local free Ca²⁺ concentrations as high as 50–100 μM are produced in a variety of cell types, including neurons (44–49). There is of course also an inverse bell-shaped relationship between the concentration of the CaM-IQ domain protein complex and the free Ca²⁺ concentration. This highlights the possibility that the switching mechanism we have identified produces biphasic responses in the activities of some IQ domain proteins.