The kinetics of Ca²⁺-dependent switching in a calmodulin-IQ domain complex

Abstract

We have performed a kinetic analysis of Ca²⁺-dependent switching in the complex between calmodulin (CaM) and the IQ domain from neuromodulin, and have developed detailed kinetic models for this process. Our results indicate that the affinity of the C-ter Ca²⁺-binding sites in bound CaM is reduced due to a ~10-fold decrease in the Ca²⁺ association rate, while the affinity of the N-ter Ca²⁺-binding sites is increased due to a ~3-fold decrease in the Ca²⁺ dissociation rate. Although the Ca²⁺-free and Ca²⁺-saturated forms of the CaM-IQ domain complex have identical affinities, CaM dissociates ~100 times faster in the presence of Ca²⁺. Furthermore, under these conditions CaM can be transferred to the CaM-binding domain from CaM kinase II via a ternary complex. These properties are consistent with the hypothesis that CaM bound to neuromodulin comprises a localized store that can be efficiently delivered to neuronal proteins in its Ca²⁺-bound form in response to a Ca²⁺ signal.

At some level, all physiological responses involve coordinated biochemical changes triggered by intracellular Ca²⁺ signals. The Ca²⁺-binding protein calmodulin (CaM¹), which engages in modulatory interactions with more than 100 known target proteins, is the primary mediator of Ca²⁺-dependent biochemical changes. Although many CaM targets, such as phosphodiesterase, myosin light chain kinase and the constitutive nitric oxide synthases do not interact significantly with the Ca²⁺-free protein (1–4), a large class bind Ca²⁺-free CaM at least as well as the Ca²⁺-bound 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] (5–8). These regions bind apoCaM and/or Ca²⁺-bound CaM with dissociation constants ranging from subnanomolar to micromolar, depending upon their precise sequence and context (6). Complexes between CaM and IQ domains have been demonstrated to participate in a variety of regulatory processes, including positive and negative modulation of ion channels and unconventional myosin based motility (6). Some IQ domain proteins have been proposed to provide localized intracellular stores of CaM (9). The potential significance of such stores has been highlighted by recent investigations demonstrating that the intracellular CaM concentration can be limiting (10–12). Neuromodulin, a neuronal IQ domain protein found in axons and terminals, is perhaps the best studied example of such a protein (9). Neurogranin, a smaller protein with an essentially identical IQ domain, is thought to perform a similar function in dendritic spines (13, 14).

The results presented in this paper indicate that the properties of the neuromodulin CaM-IQ domain complex promote dissociation of CaM in its Ca²⁺-bound form, and allow it to be transferred to target proteins via a ternary complex. These features are conducive to the efficient delivery of Ca²⁺-bound CaM to target proteins. Our results also demonstrate that the association rate constant for the C-ter EF pair of Ca²⁺-binding sites in CaM is reduced by a factor of ~10 in the IQ domain complex. This somewhat novel finding is consistent with the accompanying reduction in the affinity of the complex (15). The detailed kinetic models that we present for Ca²⁺-dependent switching in this complex may be applicable to CaM-IQ domain complexes in proteins where Ca²⁺-dependent switching appears to directly modulate function, such as ion channels and unconventional myosins (5–8).

Materials and Methods

Proteins

The composition, expression and purification of the fluorescent reporter, BSCaM_IQ, have been described in detail elsewhere (15), as have the methods used to express and purify native and mutant CaMs (16, 17). The two mutant CaMs used in these studies are N_xCCaM, in which glutamic acid residues at positions 31 and 67 in the N-ter EF-hands have been replaced by alanines, and NC_xCaM, in which the homologous glutamic acid residues at positions 104 and 140 have been replaced. As designated by the “x” subscript, these mutations eliminate Ca²⁺ binding to the N-ter or C-ter EF hand pair. Two synthetic peptides were used in these studies. One, termed ckPEP, is based on the CaM-binding domain in CaM-dependent protein kinase II and has the sequence: MHRQETVDCLKKFNARRKLKGAILTTMLA (Calbiochem, San Diego, CA). The other, termed ngPEP, is based on the IQ domain in neurogranin and has the sequence: AAKIQASFRGHMARKK (Promega , Madison, WI).

Stopped-flow fluorescence measurements

All dynamic fluorescence measurements were performed using an SX18-MV Stopped-Flow Reaction Analyzer with a nominal ~1.4 ms dead time (Applied Photophysics, Leatherhead, UK). Excitation light from a 75 watt xenon arc lamp is supplied via a fiber optic-coupled monochromator (5 nm slit widths). Fluorescence emission is monitored using a high voltage PMT fitted with an appropriate absorbance filter. To monitor changes in FRET between ECFP and EYFP_C in BSCaM_IQ, ECFP fluorescence was excited at 430 nm and EYFP_C emission was monitored using an LG535 long-pass absorbance filter (Corion, Franklin, MA). Ca²⁺-dependent changes in quin-2 fluorescence excited at 330 nm were monitored using an LG505 long pass emission filter. In experiments where quin-2 or CaM-binding peptides were used to trap Ca²⁺ or CaM, a range of quin-2 or peptide concentrations were examined to ensure the absence of rebinding. All progress curves presented are the average of at least 6 individual determinations. Reactions were initiated by rapidly mixing equal volumes of reactant solutions to produce the stated final reactant concentrations. The base experimental buffer contained 25 mM Tris; pH 7.5, 0.1 M KCl and100 µg/ml BSA, with other components as specified in the text or captions. Where indicated, proteins and buffers were decalcified by successive treatments with Chelex™ and a BAPTA-polystyrene column (Molecular Probes, Inc.). Contaminating amounts of Ca²⁺ in decalcified protein solutions were 50 nM or less, based on the absence of any detectible effect on the A₂₆₃ of BAPTA. Stopped-flow experiments were performed at 22 °C.

Analysis and modeling of kinetic data

Rate constants were derived from fits of individual fluorescence time courses to mono or double exponentials or from global fits of multiple time courses to explicit kinetic models performed using the Dynafit program (18). Standard errors given for the fitted parameters are the square roots of the diagonal elements in the variance-covariance matrices calculated for the non-linear least squares fits. In order to perform global fitting to explicit models it was necessary to assign relative molar fluorescence amplitudes to all kinetic species so as to account for their contributions to observed fluorescence. Values of 1.0 and 0.68 were assigned to free BSCaM_IQ and the Ca²⁺-free CaM-BSCaM_IQ complex, and values of 0.83 and 0.85 were assigned to the Ca²⁺-saturated complex and the intermediate complexes in which one CaM EF hand pair or the other is Ca²⁺-saturated. These values were previously determined under equilibrium conditions, and were validated in the stopped-flow fluorometer (15). Occupancy of an EF hand pair by only a single Ca²⁺ ion was assumed to have no effect on fluorescence, because fluorescence changes observed under equilibrium conditions appear to require occupancy of both Ca²⁺-binding sites (15).

Ca²⁺ association and dissociation

We have modeled Ca²⁺ binding to each EF hand pair in CaM according to a sequential model, as illustrated by Scheme 1. By convention, the two Ca²⁺-binding steps corresponding with occupancy of the C-ter EF hand pair are numbered 1 and 2 (as in Scheme 1), while the two N-ter Ca²⁺-binding steps are numbered 3 and 4. A sequential Ca²⁺ binding model is the simplest one that accounts for the fact that dissociation of both Ca²⁺ ions from an EF hand pair is always observed to occur with a single apparent rate (19, 20). The trivial explanation that Ca²⁺ dissociates independently from both sites at the same rate is inconsistent with the high degree of binding cooperativity (19). It is also inconsistent with ¹⁵N spin relaxation experiments, which indicate that the second Ca²⁺ release step is at least 100 times faster than the first (21). Since the second Ca²⁺ ion is released much faster than the first, we also treat the first Ca²⁺ binding step as rapidly equilibrating. This assumption becomes invalid at free Ca²⁺ concentrations where k₂[Ca²⁺] ≈ k₋₁ or k₄[Ca²⁺] ≈k₋₃, but it appears to be applicable over the range of Ca²⁺ concentrations used in these investigations (see Fig. 5).

SCHEME 1.

Fig. 5. Dissociation of the initially Ca²⁺-free complex between BSCaM_IQ and native CaM or N_xCCaM after addition of Ca²⁺ and ckPEP.

Fluorescence data were measured after adding a solution containing 200 µM ckPEP, along with CaCl₂ in amounts producing the specified final concentrations, to an equal volume of a decalcified solution containing 20 µM BSCaM_IQ and either 4 µM native CaM or N_xCCaM. (A) Dissociation of the N_xCCaM-BSCaM_IQ complex in the presence of ckPEP with Ca²⁺ at concentrations of 30, 45, 67.5, 125 or 250 µM (lowermost to uppermost trace). These data were globally fit according to an abbreviated version of the model presented in Scheme 3 containing only the steps associated with formation and dissociation of NC₂-B. The fit shown was produced by iteratively varying the values for K₁ and k₂ using the DynaFit program (18). Relative molar fluorescence amplitudes were assigned to the various kinetic species as detailed under “Materials and Methods”. The dissociation rate constants assigned to the NC₂-B species is given in Table 1. The NC-B species is effectively non-dissociating on this time scale. No attempt was made to include the standard errors associated with the fixed parameter value. The K₁ and k₂ values derived from the global fit shown are 4.6±0.9 µM and 3.1±0.1×10⁶ M⁻¹-s⁻¹. (B) Dissociation of the native CaM-BSCaM_IQ complex in the presence of ckPEP with Ca²⁺ at a concentrations of 30, 45, 67.5, 125 or 250 µM (lowermost to uppermost trace). Fluorescence time courses were globally fit according to the model presented in Scheme 3 by iteratively varying the values for K′₁ and k′₂ using the DynaFit program (18). Previously determined values of 122 and 9.4 µM were assigned to K′₃ and K′₄ (15). The dissociation rate constants assigned to the NC-B, N₂C-B, NC₂-B and N₂C₂-B species are given in Table 1. The values used for the N₂C-B and NC₂-B species were determined using N_xCCaM and NC_xCaM. Values of 4.6±0.9 µM and 3.1±0.1×10⁶ M⁻¹-s⁻¹, which were determined using N_xCCaM, were assigned to K₁ and k₂ (Table 2). Relative molar fluorescence amplitudes were assigned to the various kinetic species as detailed under “Materials and Methods”. The K′₁ and k′₂ values derived from the global fit shown are 4.1±0.6 µM and 3.2±0.1×10⁶ M⁻¹-s⁻¹.

The transition from Ca²⁺-saturated to Ca²⁺-free complex

The data presented in Fig. 4 were globally fit to the kinetic model given in scheme 2. In this scheme, B corresponds with BSCaM_IQ, NC corresponds with Ca²⁺-free CaM, and N₂C₂ corresponds with CaM in which both the N-ter (N) and C-ter (C) EF hand pairs are replete with Ca²⁺. Intermediate Ca²⁺- bound states are designated appropriately. Since Ca²⁺ dissociates much more rapidly from the N-ter EF hand pair than it does from the C-ter pair, dissociation of Ca²⁺ is treated as a sequential process, with the N-ter pair of sites going first. The vertical dashed arrows denote steps that were omitted from fitting calculations because dissociation of the second Ca²⁺ ion from an EF hand pair is assumed to be much faster than dissociates of BSCaM_IQ. “Fast” rate constants were arbitrarily assigned values 10-fold larger than the rate constants preceding them.

Fig. 4. The transition from Ca²⁺-saturated to Ca²⁺-free CaM-BSCaM_IQ complex.

(A, B) Buffer containing 48 µM CaM and 4 µM BSCaM_IQ in 500 µM CaCl₂ was rapidly mixed with an equal volume of buffer containing 10 mM BAPTA. Data measured over 20, 50 and 200 ms time intervals are presented in panels A and B. Data measured over a 500 ms time interval are included in panel B. The individual data sets are offset on the y axis for presentation purposes. These data were globally fit to the model presented in Scheme 2 by iteratively varying the values for k′₋₂ and k′₋₄, the Ca²⁺ dissociation rate constants for bound CaM, using the DynaFit program (18). Relative molar fluorescence amplitudes were assigned to the various kinetic species as detailed under “Materials and Methods”. Association and dissociation rate constants applied to the various Ca²⁺-bound forms of the CaM-BSCaM_IQ complex are given in Table 1. Ca²⁺ dissociation rate constants applied to free CaM are given in Table 2. Parameters assigned to the NC₂-B species were determined using N_xCCaM. No attempt was made to include the standard errors associated with fixed parameter values. Steps marked as fast were arbitrarily assigned rates 10-fold faster than the steps preceding them. The fitted values obtained for k′₋₄ and k′₋₂ are 528.3±3.3 and 13.5±0.1 s⁻¹.

SCHEME 2.

Release of BSCaM_IQ after addition of Ca²⁺and ckPEP

The data presented in Fig. 5 were globally fit according to the model given in Scheme 3. In this scheme, P corresponds with a peptide (ckPEP) based on the CaM-binding domain in CaM kinase II. Since the peptide prevents reassociation of CaM, rate constants for reversal of the second C-ter Ca²⁺-binding step (k₋₂ and k′₋₂) can be omitted because the rate constants for dissociation of the CaM complex $(k-N{C}_{\mathrm{2}}\text{and}{k}_{N_{\mathrm{2}}{C}_{\mathrm{2}}}^T)$are much larger (see Table 1 and Table 2). Dissociation of the Ca²⁺-free complex can also be ignored, as it occurs at a rate of ~1 s⁻¹, which is far slower than the Ca²⁺ binding steps. Dissociation of CaM from other intermediates is effectively irreversible due the presence of a large molar excess of ckPEP. Since the dissociation rate constant for the N₂C-B complex (kN₂C) is much smaller than k′₋₄ (see Table 1 and Table 2), we can treat both N-ter Ca²⁺-binding steps on the lower pathway in the scheme as rapidly equilibrating, with dissociation constants of K′₃, K′₄. This approach is not applicable to the N-ter Ca²⁺-binding steps on the upper pathway because the apparent Ca²⁺ dissociation rate constant for the N-ter sites (k₋₄) is similar to the rate for dissociation of a presumptive peptide ternary complex ($k_{N_{\mathrm{2}}{C}_{\mathrm{2}}}^T;$ see Table 1 and Table 2). However, this is not a significant issue because the bracketed steps can be omitted from fitting calculations without significantly affecting the fit or the derived parameter values. The probable basis for this is explained under “Results”.

SCHEME 3.

Table 1. Association and dissociation rate constants for native and mutant CaM-BSCaM_IQ complexes.

The first two columns contain k_on and k_off values derived from linear least-squares fits to replots of k_obs vs [CaM] (see Fig. 1). K_d values calculated using these rate constants are consistent with previously determined equilibrium K_d values (15). The last column contains k_off values derived from dissociation time courses measured in the presence of larger molar excesses of ngPEP or ckPEP (see Fig. 2).

	kobsvs [CaM] plot		koff/kon	Equil	Peptide trap
CaM	kon (M−1s−1)	koff (s−1)	Kd (µM)	Kd (µM)	koff (s−1)
NC	3.6±0.2×105	0.9±0.2	2.5±0.6	2.3±0.1	0.8±0.2
NxC	3.9±0.6×105	1.1±0.3	2.8±0.7	2.1±0.2	0.9±0.2
NCx	2.9±0.5×105	0.9±0.2	3.1±0.9	2.5±0.3	0.7±0.3
NxC2	4.1±0.2×107	558.8±10.1	13.6±1.1	14.4±1.3	630.7±16.4
N2Cx	1.1±0.2×106	30.9±1.6	28.1±5.3	36.7±3.9	30.2±4.2
N2C2	3.1±0.2×107	69.4±9.6	2.2±0.3	2.5±0.1	565.1±13.1

Table 2. Ca²⁺association and dissociation rate constants for native and mutant CaMs free in solution or bound to BSCaM_IQ.

Ca²⁺ binding was modeled according to a sequential mechanism with a rapidly equilibrating first step (Scheme 1), so these rate constants correspond with the second Ca²⁺-binding step. Values indicated by an “NA” are not applicable; those indicated by an “ND” are too fast to measure in the stopped-flow fluorometer, which has a dead-time of ~1.4 ms. Association rate constants (k_on) designated by a superscript “A” were calculated using the dissociation rate constants (k_off ) given in this table and previously determined equilibrium constants for the second Ca²⁺ binding step (15). Association rate constants for the C-ter EF hand pair in the CaM-BSCaM_IQ complex were derived from a global analysis of the fluorescence time courses presented in Fig. 5. k_off values designated by a superscript “B” were determined using a 5 µl observation cell, which reduces the stopped-flow dead time to below 1 ms, but unfortunately cannot be used with solutions containing BSCaM_IQ due to their higher viscosity. k_off values for the CaM-BSCaM_IQ complex given in parenthesis were derived from a global analysis the fluorescence time courses presented in Fig. 4. All other k_off values were derived from quin-2 fluorescence data (Fig. 3).

	N-ter EF hand pair		C-ter EF hand pair
CaM	kon (M−1s−1)	koff (s−1)	kon (M−1s−1)	koff (s−1)
NC	3.1±1.2×108 A	1152±117B	3.4±2.4×107 A	10.3±0.7
NxC	NA	NA	5.8±3.2×107 A	10.8±0.6
NCx	3.4±1.5×108 A	1298±135B	NA	NA
CaM-BSCaMIQ	kon (M−1s−1)	koff (s−1)	kon (M−1s−1)	koff(s−1)
NC	3.0±1.2×108 A	473.4±37.9 (528.3±3.3)	3.2±0.1×106	11.7±0.5 (13.5±0.1)
NxC	NA	NA	3.1±0.1×106	11.8±0.5
NCx	ND	ND	NA	NA

Results

Association of CaM and BSCaM_IQ

The first step in these investigations was to derive apparent association and dissociation rate constants (k_on and k_off ) for the various complexes between native or mutant CaM and BSCaM_IQ, a fluorescent reporter containing the IQ domain from neuromodulin (15). This was accomplished by determining observed association rates (k_obs) under pseudo-first order conditions at a series of different CaM concentrations. Values for k_on and k_off were then derived from linear least-squares fits to replots of k_obs vs [CaM]. Values for k_on and k_off of 3.6±0.2×10⁵ M⁻¹s⁻¹ and 0.9±0.2 s⁻¹ were derived for the Ca²⁺-free native CaM complex from the replot presented in Fig. 1A. The k_off /k_on ratio of 2.5±0.6 µM calculated for this complex is essentially identical to the equilibrium K_d value of 2.3±0.1 µM (Table 1). Similar rate constants were derived for the Ca²⁺-free N_xCCaM and NC_xCaM complexes (Table 1; data not shown). Values for k_on and k_off of 1.1±0.2×10⁶ M⁻¹-s⁻¹ and 30.9±1.6 s⁻¹ were derived for the Ca²⁺-saturated NC_xCaM complex from the replot in Fig. 1B, and the k_off /k_on ratio of 28.1±5.3 µM calculated for this complex agrees well with the equilibrium K_d value of 36.7±3.9 µM (Table 1). Values for k_on and k_off of 3.1±0.2×10⁷ M⁻¹-s⁻¹ and 69.4±9.6 s⁻¹ were derived for the Ca²⁺-saturated complex with native CaM from the replot in Fig. 1C; and respective values of 4.1±0.2×10⁷ M⁻¹-s⁻¹ and 558.8±10.1 s⁻¹ were derived for the Ca²⁺-saturated N_xCCaM complex from the replot in Fig. 1D. The k_off /k_on ratios of 2.2±0.3 and 13.6±1.1 µM calculated for these complexes are essentially identical to their equilibrium K_d values of 2.5±0.1 and 14.4±1.3 µM (Table 1). The overall agreement between k_off /k_on ratios and equilibrium K_d values confirms that CaM binding to the neuromodulin IQ domain is a simple bimolecular process. Occupancy of one or both EF hand pairs in CaM significantly accelerates binding kinetics, although the greatest effect is seen when the C-ter EF hand pair is occupied. The accelerated rates observed in the presence of Ca²⁺ may serve to mobilize neuromodulin-bound CaM in response to a Ca²⁺ signal. The association rate constants for the CaM-IQ domain complexes in which the C-ter EF hand pair is Ca²⁺ bound are similar to those for the complexes between CaM and canonical target proteins, such as myosin light chain kinase or nitric oxide synthase (22, 23). In contrast, the association rates derived for complexes in which the C-ter EF hand pair is Ca²⁺-free are 30–100 times slower.

Fig. 1. Association of native and mutant CaMs with BSCaM_IQ.

Values for k_obs were derived from mono-exponential fits to time courses for BSCaM_IQ fluorescence measured after addition of CaM. The lowest final CaM concentration produced was in all cases at least 5-fold greater than final BSCaM_IQ concentration. Pseudo-first order conditions were thus maintained so that k_obs = k_on[CaM] + k_off. (A) Replot of k_obs values determined in the absence of Ca²⁺ vs the concentration of CaM. Nominally Ca²⁺-free conditions were produced by including 3 mM BAPTA in all experimental buffers. The k_on and k_off values derived from the linear fit shown are 3.6±0.2×10⁵ M⁻¹-s⁻¹ and 0.9±0.2 s⁻¹. k_on and k_off values derived for Ca²⁺-free N_xCCaM are 3.2±0.1×10⁵ M⁻¹-s⁻¹ and 1.1±0.1 s⁻¹, and values of 2.9±0.1×10⁵ M⁻¹-s⁻¹ and 0.7±0.1 s⁻¹ were derived for Ca²⁺-free NC_xCaM (data not shown). (B) Replot of k_obs values determined in the presence of 250 µM CaCl₂ vs the concentration of NC_xCaM. The k_on and k_off values derived from the linear fit shown are 1.1±0.2×10⁶ M⁻¹-s⁻¹ and 30.9±1.6 s⁻¹. (C) Replot of k_obs values determined in the presence of 250 µM CaCl₂ vs the concentration of native CaM. The k_on and k_off values derived from the linear fit shown are 3.1±0.2×10⁷ M⁻¹-s⁻¹ and 69.4±9.6 s⁻¹. (D) Replot of k_obs values determined in the presence of 250 µM CaCl₂ vs the N_xCCaM concentration. k_on and k_off values of 4.1±0.2×10⁷ M⁻¹-s⁻¹ and 558.8±10.1 s⁻¹ were derived from linear fit shown.

Dissociation of CaM in the presence of CaM-binding peptides

We extended our analysis of the kinetics of native and mutant CaM-BSCaM_IQ complexes by examining dissociation in the presence of a large molar excess of peptides based on the IQ domain in neurogranin (ngPEP) and the CaM-binding domain in CaM kinase II (ckPEP), which does not bind CaM with significant affinity in the absence of Ca²⁺. In the presence of ngPEP, Ca²⁺-free native CaM dissociates with an apparent rate constant of 0.8±0.2 s⁻¹ (Fig. 2A), and essentially identical rate constants were derived for the Ca²⁺-free complexes with the two mutant CaMs (data not shown). In the presence of ckPEP, Ca²⁺-saturated NC_xCaM and N_xCCaM dissociate with rate constants of 30.2±4.2 and 630.7±16.4 s⁻¹ (Figs. 2B and D). These values agree with those derived from replots of k_obs vs [CaM] (Table 1). In contrast, Ca²⁺-saturated native CaM dissociates with an apparent rate constant of 565.1±13.1 s⁻¹ in the presence of ckPEP (Fig. 2C), which is ~10-fold faster than the rate derived from a replot of k_obs vs [CaM] (Table 1). The accelerated dissociation rate observed in the presence of ckPEP indicates that dissociation occurs via a ternary complex between ckPEP, CaM and BSCaM_IQ. Since the measured fluorescence time course is monophasic and has an amplitude consistent with formation of free BSCaM_IQ, formation of the ternary complex itself does not appear to be associated with a significant change in fluorescence. However, it is conceivable that the fluorescence time course corresponds with formation of the ternary complex itself, rather than dissociation of BSCaM_IQ. This is unlikely because the apparent dissociation rate does not exhibit a second-order dependence on the ckPEP concentration (data not shown).

Fig. 2. Dissociation of complexes between native and mutant CaMs and BSCaM_IQ in the presence of CaM-binding peptides.

In all cases a range of peptide concentrations was investigated to ensure that a concentration sufficient to prevent rebinding of CaM was used. (A) Dissociation of the Ca²⁺-free CaM-BSCaM_IQ complex after addition of a peptide (ngPEP) based on the CaM-binding domain in neurogranin. Nominally Ca²⁺-free conditions were produced by including 3 mM BAPTA in all experimental buffers. The final BSCaM_IQ and CaM concentrations were 10 and 1 µM; the final peptide concentration was 100 µM. The k_off value derived from mono-exponential fits to these and similar data is 0.8±0.2 s ⁻¹. (B) Dissociation of the NC_xCaM-BSCaM_IQ complex in the presence of 250 µM CaCl₂ after addition of a peptide (ckPEP) based on the CaM-binding domain in CaM kinase II. The final BSCaM_IQ and N_xCCaM concentrations were 50 and 10 µM; the final ckPEP concentration was 100 µM. The dissociation rate constant derived from fits of these and similar data to single exponentials is 30.2±4.2 s⁻¹. (C) Dissociation of CaM-BSCaM_IQ complex in the presence of 250 µM CaCl₂ after addition of ckPEP at a final concentration of 100 µM. The final BSCaM_IQ and CaM concentrations were 12.5 and 2.5 µM. The apparent dissociation rate constant derived from fits to these and similar data to single exponentials is 565.1±13.1 s⁻¹. (D) Dissociation of the Ca²⁺-saturated N_xCCaM-BSCaM_IQ complex in the presence of 250 µM CaCl₂ after addition of ckPEP at a final concentration of 100 µM. The final BSCaM_IQ and N_xCCaM concentrations were 25 and 5 µM. The apparent dissociation rate constant derived from fits of these and similar data to single exponentials is 630.7±16.4 s⁻¹.

Dissociation of Ca²⁺

We have previously reported that under equilibrium conditions Ca²⁺ binding to the C-ter EF hand pair in the CaM-BSCaM_IQ complex reduces the affinity of the complex, and subsequent binding to the N-ter EF hand pair raises it (15). The Ca²⁺-binding affinity of the C-ter EF hand pair is thus reduced due to negative energy coupling, while the affinity of the N-ter pair is increased due to positive energy coupling (15). To investigate the mechanistic basis for these changes in Ca²⁺-binding affinity, we determined Ca²⁺ dissociation rates for free and bound native and mutant CaMs. In general agreement with others (19, 24–27), Ca²⁺ was found to dissociate from the C-ter and N-ter EF hand pairs in free CaM with rate constants of 10.3±0.7 and 1152±117 s⁻¹. It is important to note that dissociation rate constants were determined for free CaM using a 5 µl observation cell, rather than the standard 20 µl cell. This reduces the dead time of the stopped-flow fluorometer to below 1 ms, allowing this fast rate to be measured. Unfortunately, efficient rapid mixing was not obtained when we attempted to use the smaller cell with solutions containing BSCaM_IQ, presumably due to their higher viscosities. Dissociation rate constants of 11.7±0.5 s⁻¹ and 473.4±37.9 s⁻¹ were derived when CaM is bound to BSCaM_IQ (Fig. 3A). To confirm that the slower rate constant corresponds with the C-ter EF hand pair, dissociation rate constants were derived for N_xCCaM in the presence and absence of BSCaM_IQ (Fig. 3B), and respective values of 11.8±0.5 and 10.8±0.6 s⁻¹ were obtained. The dissociation rate constant of 473.4±37.9 s⁻¹ derived for the native CaM complex therefore corresponds with the N-ter EF hand pair and the slower rate corresponds with the C-ter pair. The increased Ca²⁺-binding affinity of the N-ter sites in the CaM-BSCaM_IQ complex is thus correlated with a decrease in the dissociation rate for Ca²⁺. The reduced affinity of the C-ter pair of sites does not appear to involve a change in the Ca²⁺ dissociation rate. Determination of a Ca²⁺ dissociation rate for the NC_xCaM-BSCaM_IQ complex, which exhibits negative energy coupling (15), was not possible because maintenance of the complex requires BSCaM_IQ solutions with viscosities that preclude efficient mixing.

Fig. 3. Dissociation of Ca²⁺ from the complex between BSCaM_IQ and CaM or N_xCCaM.

The fluorescent Ca²⁺ chelator quin-2 was used as a Ca²⁺ trap. Dissociation of Ca²⁺ from native or mutant CaM therefore corresponds directly with a Ca²⁺-dependent increase in quin-2 fluorescence. A range of quin-2 concentrations was investigated to ensure that a concentration sufficient to prevent rebinding of Ca²⁺ was used. (A) Dissociation of Ca²⁺ from free CaM (lower trace) and from the CaM-BSCaM_IQ complex (upper trace). The quin-2 fluorescence time course for Ca²⁺ dissociation from free CaM was generated by mixing a solution containing 4 µM CaM and 50 µM CaCl₂ with an equal volume of 400 µM quin-2. These data are fit by a single exponential with a rate constant of 10.3±0.7 s⁻¹ and an amplitude corresponding with dissociation of ~2 Ca²⁺ ions. Dissociation of two additional Ca²⁺ ions occurred within the instrument dead time. The quin-2 fluorescence time course for Ca²⁺ dissociation from the CaM-BSCaM_IQ complex was generated by mixing a solution containing 25 µM BSCaM_IQ, 4 µM CaM and 50 µM CaCl₂ with an equal volume of 400 µM quin-2. The data presented are fit by a double exponential. The slower process has an apparent rate constant of 14.7±0.5 s⁻¹ and an amplitude corresponding with dissociation of ~2 Ca²⁺ ions. The faster rate was derived from data measured over a shorter time interval (inset). These data are fit by a double exponential with rate constants of 427.4±35 and 11.7±0.5 s⁻¹, and respective amplitudes corresponding with dissociation of ~1.5 and ~2 Ca²⁺ ions. If the faster process is forced to have an amplitude corresponding with dissociation of 2 Ca²⁺ ions, then apparent rate constants of 473.4±37.9 s⁻¹ and 12.9±0.7 s⁻¹ are derived for the faster and slower rates. (B) Dissociation of Ca²⁺ from the N_xCCaM-BSCaM_IQ complex (●) and from free N_xCCaM (○). For these experiments a solution containing 4 µM N_xCCaM and 50 µM CaCl₂ in the presence or absence of 25 µM BSCaM_IQ was mixed with an equal volume of 400 µM quin-2. The two resulting quin-2 fluorescence time courses are essentially superimposable. Ca²⁺-dissociation rate constants of 10.8±0.6 s⁻¹ and 11.8±0.5 s⁻¹ were derived for free and bound N_xCCaM from fits of these data to single exponentials with amplitudes corresponding to dissociation of ~2 Ca²⁺ ions.

The transition from Ca²⁺-saturated to Ca²⁺-free complex

Having determined binding kinetics and Ca²⁺ dissociation rates for mutant and native CaM-BSCaM_IQ complexes, we next analyzed the fluorescence changes associated with the transition from the Ca²⁺-saturated to the Ca²⁺-free complex. Fluorescence time courses were measured after addition of a large molar excess of BAPTA to the Ca²⁺-saturated CaM-BSCaM_IQ complex (Fig. 4A and B). Individual time courses measured on different time scales are offset in the figure for presentation purposes. These data were globally fit to the kinetic model presented in Scheme 2. In this model Ca²⁺-dissociates sequentially from the N-ter and C-ter EF hand pairs because the N-ter sites have much faster kinetics. Relative molar fluorescence amplitudes were assigned to all kinetic species as detailed under “Materials and Methods”. The fitted curves presented in the figure were generated by varying only k′₋₂ and k′₋₄, the Ca²⁺ dissociation rate constants for N-ter and C-ter EF hand pairs in bound CaM. All other necessary parameters were fixed to the values given in Table 1 & Table 2. Parameter values derived for N_xCCaM were applied to the intermediate species in which Ca²⁺ remains bound to the C-ter EF hand pair (NC₂-B). Rate constants for “fast” steps were arbitrarily assigned values 10-fold higher than the rate constants for the steps preceding them. The rising phase in fluorescence corresponds largely with formation and dissociation of the NC₂-B intermediate, although dissociation of the initial Ca²⁺-saturated complex due to dilution also contributes. The falling phase corresponds with formation of the final Ca²⁺-free complex, which is not as fluorescent as the initial complex. The slight discrepancy between the fitted curves and the data measured during the first few milliseconds is probably due to the simplifying assumption that short-lived intermediates with Ca²⁺ bound to only a single site in an EF hand pair are effectively non-dissociating (dashed arrows in Scheme 2). The overall quality of the fit suggests that this scheme nevertheless represents a reasonable minimal model. The validity of the model is lent further support by the fact that fitted values of 13.5±0.1 and 528.3±3.3 s⁻¹ were derived for k′₋₂ and k′₋₄, which are essentially identical to the Ca²⁺-dissociation rate constants derived from Ca²⁺ trapping experiments (Table 2).

Ca²⁺-dependent release of CaM in the presence of a CaM-binding peptide

Given the hypothesis that neuromodulin participates in CaM storage and delivery (9, 28, 29), we were particularly interested in investigating release of CaM from the neuromodulin IQ domain in the presence of Ca²⁺ and a peptide (ckPEP) based on the CaM-binding domain in CaM kinase II, an abundant enzyme in neurons (30). From an experimental standpoint, analysis of this process is complicated by the fact that two pathways for sequential occupancy of the N-ter and C-ter EF hand pairs must be considered (see Scheme 3). We therefore initially analyzed the behavior of the N_xCCaM-BSCaM_IQ complex to eliminate the contribution of the N-ter pair of Ca²⁺ binding sites.

Fluorescence time courses measured after adding excess ckPEP and different amounts of Ca²⁺ to the Ca²⁺-free mutant complex are presented in Fig. 5A. These data were globally fit according the steps in Scheme 3 that correspond with formation and dissociation of the intermediate NC₂-B complex. The second Ca²⁺-binding step is effectively irreversible because Ca²⁺ dissociates from the NC₂-B complex at a rate of ~10 s⁻¹, while the complex itself dissociates at a rate of ~500 s⁻¹ (Table 1 & Table 2). The fit presented in Panel A was produced by varying the dissociation constant (K₁) for the first C-ter Ca²⁺-binding step and the association rate constant (k₂) for the second Ca²⁺-binding step. The other necessary parameter was the dissociation rate constant for the NC₂-B intermediate (k−NC₂), which was fixed to the value given in Table 2. Dissociation of this intermediate is effectively irreversible, as there is a large molar excess of ckPEP. Relative molar fluorescence amplitudes were assigned to all kinetic species as detailed under “Materials and Methods”. The observed increases in fluorescence reflect the increase that occurs when the NC₂-B intermediate forms, and the further increase that occurs when it dissociates. The quality of the fit suggests that a three step kinetic model we have used is a reasonable minimal description of this process. The fitted values obtained for K₁ and k₂ are 4.8±0.9 µM and 3.1±0.1×10⁶ M⁻¹-s⁻¹. The latter value is ~10-fold less than the Ca²⁺ association rate constant estimated for free CaM (Table 2).

We next measured a series of fluorescence time courses for the native CaM-BSCaM_IQ complex using the same experimental approach (Fig. 5B). These data were globally fit according to the model depicted in Scheme 3. The rate constant for dissociation of the Ca²⁺ saturated CaM-BSCaM_IQ complex in the presence of ckPEP is designated as $k_{N_{\mathrm{2}}{C}_{\mathrm{2}}}^T,$ since this step appears to involve formation of a ternary complex with the peptide. The bracketed portion of the scheme can be omitted from fitting calculation without significant effect, apparently because in the presence of ckPEP the NC₂-B and N₂C₂-B intermediates dissociate at essentially the same rate (Table 2), and there is also little difference in their fluorescence (15). Binding of Ca²⁺ to the N-ter EF hand pair prior to the C-ter pair is modeled as rapidly equilibrating because the rates at which N₂C-B dissociates or is converted to the N₂C₂-B intermediate are relatively slow (see Table 1 and Table 2). The fit shown in Fig. 5B was produced by varying only K′₁ and k′₂. Previously-determined dissociation constants of 122 and 9.4 µM were assigned to K′₃ and K′₄ (15). Other required kinetic parameters, including K₁ and k₂, were fixed to the values given in Table 1 & Table 2. The parameters for reactions involving NC₂-B and N₂C-B were derived using N_xCCaM and NC_xCaM. Relative molar fluorescence amplitudes were assigned to all kinetic species as detailed under “Materials and Methods”. The observed fluorescence time courses reflect increases due to formation of the NC₂-B and N₂C-B intermediates, and to release of BSCaM_IQ (B). Formation of the N₂C-B intermediate produces a fluorescence increase that occurs within the ~1.4 ms dead time of the stopped-flow (Fig. 5B). This increase thus corresponds with rapidly-equilibrating binding of Ca²⁺ to the N-ter EF hand pair, and its amplitude increases as a function of the free Ca²⁺ concentration in accordance with the values used for K′₃ and K′₄ . The amplitude of this phase is also linked to the amount of BSCaM_IQ dissociation occurring via the lower pathway in Scheme 3. Thus, at a free Ca²⁺ concentration of ~10 µM, dissociation via this pathway is negligible, while at a free Ca²⁺ concentration of ~70 µM dissociation via the upper and lower pathways is equivalent (data not shown). At a free Ca²⁺ concentration of 250 µM the proportion of dissociation via the lower pathway saturates at a value of ~65%. This occurs in spite of the much faster Ca²⁺-binding kinetics of the N-ter EF hand pair because the N₂C-B intermediate dissociates relatively slowly. The overall quality of the fit indicates that Scheme 3 represents an acceptable minimal kinetic model. Fitted values of 4.1±0.6 µM and 3.2±0.1×10⁶ M⁻¹-s⁻¹ were derived for K′₁ and k′₂, which are not significantly different from the values derived for K₁ and k₂. The association rate constant for the C-ter Ca²⁺-binding sites in CaM therefore appears to be reduced to the same extent, regardless of whether Ca²⁺ is bound to the N-ter pair of sites.

Discussion

In this paper we present the results of a kinetic analysis of the complex between CaM and BSCaM_IQ, a fluorescent reporter containing the IQ domain from neuromodulin (15). Association and dissociation rate constants for various Ca²⁺-bound forms of the complex were determined, as well as many of the rate constants governing Ca²⁺ binding to the complex. Kinetic models incorporating these rate constants were developed that account for the BSCaM_IQ fluorescence responses observed when Ca²⁺ is removed from the Ca²⁺-saturated complex or when Ca²⁺ is added to the Ca²⁺-free complex in the presence of a peptide based on the CaM-binding domain in CaM kinase II. Three key points are evident: (1) Association and dissociation of the complex is accelerated in the presence of Ca²⁺. (2) When CaM is bound to the IQ domain, the Ca²⁺-association rate constant for the C-ter EF hand pair is reduced ~10-fold and the Ca²⁺-dissociation rate constant for the N-ter EF hand pair is reduced ~3-fold. (3) Ca²⁺-saturated CaM can be transferred from the neuromodulin IQ domain to canonical CaM-binding domains, such as the one in CaM kinase II, via an intermediate ternary complex.

CaM-binding kinetics

As seen in Table 1, there is complete agreement between the association and dissociation rate constants for various native and mutant CaM-BSCaM_IQ complexes derived from replots of k_obs vs [CaM] and the corresponding equilibrium K_d values. The association and dissociation rates for the Ca²⁺-saturated CaM-IQ domain complex and the C-ter Ca²⁺-bound intermediate are 30 to 100-fold faster than for the Ca²⁺-free complex (Table 1). The association rate constants derived for the Ca²⁺-saturated complex and the C-ter Ca²⁺-bound intermediate are similar to those derived for the Ca²⁺-saturated complexes between CaM and other types of CaM-binding sequences (22, 23, 31). The kinetics of the N-ter Ca²⁺-bound intermediate are comparatively slow, as its association rate constant is only 3-fold faster than the rate constant for the Ca²⁺-free complex (Table 1). This indicates that slow binding kinetics are a feature of interactions between the Ca²⁺-free C-ter CaM lobe and the IQ domain.

Dissociation rate constants were also determined for native and mutant CaM-BSCaM_IQ complexes by using ckPEP or ngPEP to trap CaM. With only one exception, these values agree with those derived from replots of k_obs vs [CaM] (Table 1). The exception is the Ca²⁺-saturated native CaM-BSCaM_IQ complex, which dissociates at a rate of 565.1±13.1 in the presence of ckPEP, compared with a rate of 69.4±9.6 derived from an analysis of binding kinetics (Table 1). Dissociation is accelerated in the presence of the peptide, since the slower rate is consistent with the K_d value for this complex (Table 1). The only reasonable explanation for this behavior is that in the presence of ckPEP dissociation occurs via a ternary complex between the peptide, CaM and BSCaM_IQ. The absence of an effect of ckPEP on the dissociation rates for the intermediate CaM-BSCaM_IQ complexes in which Ca²⁺ is bound only to the N-ter or C-ter EF hand pair suggests that neither can participate in a ternary complex, or that they do so with no apparent effect on their kinetic properties. Gaertner and co-workers have previously presented evidence consistent with formation of a ternary complex between intact CaM kinase II, CaM and the IQ domain in neurogranin (32). A ternary complex intermediate provides a route for efficient delivery of CaM from neuromodulin to other CaM-binding proteins, consistent with its proposed role in CaM storage and delivery.

Ca²⁺-binding kinetics

Ca²⁺ dissociation rates for the N-ter and C-ter EF hand pairs in bound native and mutant CaMs were directly evaluated in Ca²⁺ trapping experiments (Table 2). These rates agree with those derived from a global analysis BSCaM_IQ fluorescence data measured during the transition from the Ca²⁺-saturated to the Ca²⁺-free complex (Fig. 4A and B; Table 2). The dissociation rate derived for the N-ter EF hand pair in bound CaM (k′₋₄) is 473.4±37.9 s⁻¹, while the corresponding value for free CaM (k₋₄) is 1298±135 s⁻¹. In principle, the k₋₄/k′₋₄ ratio of 2.7±0.4 should be comparable to the K₄/K′₄ ratio, but in practice the individual dissociation constants for an EF hand pair are not as well determined as the product of the constants (15). It is therefore preferable to compare the K₃K₄/K′₃K′₄ ratio with the square of the k₋₄/k′₋₄ ratio. The latter ratio is squared because k₋₄ and k′₋₄ both correspond with dissociation of two Ca²⁺ ions (see Scheme 2). The value of 10.2±1.8 derived for K₃K₄/K′₃K′₄ from data published previously is in reasonable agreement with the square of k₋₄/k′₋₄, which is 7.3±1.1 (15). This suggests that the increased Ca²⁺-binding affinity of the N-ter EF hand pair in the CaM-IQ domain complex is due to a decreased Ca²⁺ dissociation rate. The Ca²⁺ dissociation rates determined for the C-ter EF hand pair in bound and free CaM are essentially identical (Table 2), so the reduced affinity of these sites in the CaM-IQ domain complex is not due to an accelerated dissociation rate.

Association rates for Ca²⁺ were derived for the C-ter EF hand pair in bound CaM from a global analysis of fluorescence data measured after addition of Ca²⁺ and ckPEP to the Ca²⁺-free native or N_xCCaM complex with BSCaM_IQ (Fig. 5A and B; Table 2). Association rates could not be determined for the N-ter EF hand pair. Since essentially the same kinetic parameters were derived for the C-ter EF hand pairs in the native and N_xCCaM complexes with BSCaM_IQ, we shall only discuss our analysis of the latter in detail. We have modeled Ca²⁺ binding to an EF hand pair as a sequential process, with a rapidly equilibrating first step and a slower second step. Fitted values of 4.6±0.9 µM and 3.1±0.1×10⁶ M⁻¹-s⁻¹ were derived for K₁, the dissociation constant for the first step and k₂, the association rate constant for the second step. In the presence of ckPEP, we can ignore k₋₂, the rate constant for reversal of the second step, because Ca²⁺ dissociates ~50-fold slower from the complex than does Ca²⁺-saturated N_xCCaM, which is then trapped by ckPEP (Table 1). The value derived for k₂ is ~10-fold less than the corresponding value for free N_xCCaM (Table 2). By combining the values we have derived for K₁ and k₂ with a k₋₂ value of 11.8±0.5 (Table 2), we can calculate a value of 18.2±5.1 µM² for the product of the two Ca²⁺ dissociation constants for the N_xCCaM-BSCaM_IQ complex. This is in reasonable agreement with the value of 24.6±2.7 µM² derived from equilibrium Ca²⁺-binding data (15). Thus, the reduced affinity of the C-ter EF hand pair in bound CaM appears to be due to a reduced Ca²⁺ association rate, as expected given the absence of any effect on the dissociation rate.

A surprising aspect of our results is that the same association rate constant is derived for Ca²⁺ binding to the C-ter EF hand pair, regardless of whether the N-ter EF hand pair is occupied by Ca²⁺. Since the affinity of C-ter EF hand pair for Ca²⁺ is higher when the N-ter sites are occupied, it appears that the dissociation rate constant must be reduced to account for this (15). This is difficult to prove because Ca²⁺ dissociates from the C-ter sites much more slowly than it does from the N-ter sites. Thus, dissociation from the C-ter sites while the N-ter sites remain occupied cannot be observed in Ca²⁺ trapping experiments.

Implications for neuromodulin function

We have shown previously that under equilibrium conditions the apparent dissociation constant for the neuromodulin CaM-IQ domain complex has a bell-shaped dependence on the free Ca²⁺ concentration, peaking at a concentration of ~ 6 µM (15). Thus, release of CaM is promoted over a relatively narrow range of free Ca²⁺ concentrations. During a Ca²⁺ transient in a neuron the free Ca²⁺ concentration is likely to pass rapidly through this range, so we have proposed that release of CaM is only promoted briefly (15). Although the bell-shaped response curve has important implications with regard to regulation via CaM-IQ domain switches under equilibrium or quasi-equilibrium conditions, the analysis presented in this paper suggests some modifications to our understanding of what occurs during a rapid Ca²⁺ transient. The overall picture that emerges is one in which neuromodulin continuously maintains a local store of CaM that is efficiently delivered to target proteins in its Ca²⁺-bound form during a Ca²⁺ transient.

The principal difference between the equilibrium and transient behaviors of the CaM-IQ domain complex is that the N-ter Ca²⁺-bound intermediate plays a significant role when Ca²⁺ is rapidly increased to levels above 10 µM, as can occur locally during a neuronal Ca²⁺ transient (33–38). This intermediate does not form to a significant extent under equilibrium conditions, primarily because the C-ter Ca²⁺-binding sites, although slower kinetically, have an EC50(Ca²⁺) of ~5 µM, while the value for the N-ter sites is ~ 35 µM (15). The N-ter Ca²⁺ bound intermediate dissociates at a relatively slow rate of ~30 s⁻¹, compared with a rate of ~500 s⁻¹ for the C-ter intermediate. The kinetic properties of the CaM-IQ domain complex therefore appear to inhibit release of CaM in its Ca²⁺ free and N-ter Ca²⁺ bound intermediate forms (Table 1). When the C-ter Ca²⁺-bound CaM intermediate dissociates it is presumably captured by target proteins and rapidly converted to Ca²⁺-saturated CaM, given the essentially diffusion-limited Ca²⁺ association rate constants for the N-ter EF hand pair (Table 2). If the N-ter Ca²⁺-bound intermediate were to dissociate to a significant extent it could have negative consequences. First, since at least some targets appear to capture CaM via its C-ter lobe, the N-ter Ca²⁺-bound intermediate may simply not be bound in some cases (39). Second, if a target were to capture this intermediate, the relatively slow Ca²⁺ association rate constants for the C-ter EF hand pair could impose a significant delay on target activation (Table 2). An implication of the latter point is that an abundant localized store accelerates production of CaM in its Ca²⁺-saturated and C-ter Ca²⁺-bound intermediate forms sufficiently to meet the speed requirements of neuronal signaling. Given a high enough local CaM concentration, this could be effected through simple mass action. The similar affinities of neuromodulin for Ca²⁺-free and Ca²⁺-saturated CaM may serve not only to minimize diffusional losses of CaM, as we have proposed previously, but also to continuously replenish the CaM store through diffusional recruitment from adjacent regions in the cell. The degree to which ternary complexes play a role in CaM delivery in neurons remains to be established, although they clearly have the potential to facilitate this process.

We are currently extending these investigations by determining how the CaM-IQ domain complex responds to synthetic Ca²⁺ transients. In conjunction with extensive modeling, this approach should allow us to develop a more quantitative understanding of Ca²⁺ switching among various states. The kinetic aspects of the CaM-IQ domain complex that we have described are likely to have counterparts in systems that are functionally modulated by CaM-IQ domain switches, such as ion channels and unconventional myosins. A particular intriguing possibility is that ratio of the N-ter and C-ter Ca²⁺-bound intermediates that is produced during a Ca²⁺ transient provides a mechanism for producing functional responses that depend upon the amplitude and speed of the transient.