Figure 1.
Structure of Calmodulin (CaM).
(A) A 1.7 angstrom ribbon structure of free CaM (blue) with four bound Ca2+ ions (yellow). PDB 1CLL [56] (B) A 2.4 angstrom ribbon structure of CaM bound to a peptide (green) corresponding to the CaM binding domain of CaMKII. (Residues 74–83 of the CaM linker region are not resolved in this structure.) PDB 1CLL [15].
Figure 2.
Model 1: binding among Ca2+, CaM, and mCaMKII.
The top layer (A) represents binding of Ca2+ to CaM. Red arrows correspond to Ca2+ binding to the C-terminus, and blue arrows binding to the N-terminus. The bottom layer (B) represents Ca2+ binding to CaM while CaM is bound to CaMKII. The CaM species are denoted as CaMnNcC with n, c , such that n is the number of Ca2+ bound to the amino (N) terminus and c is the number of Ca2+ bound to the carboxyl (C) terminus. The species of CaM bound to mCaMKII are denoted K•CaMnNcC. For convenience, we use CaM4 and K•CaM4 to denote species with n = c = 2, and CaM0 and K•CaM0 to denote those with n = c = 0. (C) The full model is represented as a cube, with yellow arrows indicating binding between CaMnNcC and mCaMKII.
Figure 3.
Energy loop diagram for derivation of cooperativity coefficients.
The thermodynamic free energy around a reaction loop must sum to zero. This principle (microscopic reversibility) constrains the relationship between the equilibrium constants in the loop. We define cooperativity coefficients s (for the N-terminus of CaM) and r (for the C-terminus of CaM) to quantify the relationship between the affinity of Ca2+ for free CaM and of Ca2+ for CaM when bound to CaMKII. The principle of microscopic reversibility indicates that these coefficients also quantify the relationship between the affinity of CaMKII for CaM with three bound Ca2+ ions, and the affinity of CaMKII for CaM4, as shown in the figure for the N-terminal coefficient s.
Figure 4.
Constraining of s and r cooperativity coefficients for on and off rates by fitting to experimental data.
Three independent sets of experimental data were used to constrain the values of the cooperativity coefficients s and r, that represent the ratios between the on and off binding constants for Ca2+ to the N- and C-termini of free CaM (respectively) and the corresponding binding constants for Ca2+ to the same termini in the K•CaM complex. The simplex method for gradient descent was used to fit the parameters to each set of data. A) Fits to data for dissociation of CaM from CaMKII in 50 µM Ca2+ (data from Figure 2B in [30]); B) Fits to data for dissociation of CaM from CaMKII in 200 nM Ca2+ (data from Figure 2B in [30]); and C) Fits to data for dissociation of Ca2+ from Ca2+/CaM/CaMKII (data renormalized from Figure 4A in [57]). Black, real data; Blue, best fit when all the cooperativity was assumed to reflect a change in on rates; Green, best fit when all the cooperativity was assumed to reflect a change in off rates; Red, best fit when cooperativity in on and off rates were allowed to vary simultaneously. (See Text S1 for details.)
Figure 5.
Model 2: coarse-grained model of binding among Ca2+, CaM and CaMKII.
The reaction network includes only pairs of Ca2+ ions, assuming highly cooperative binding at each CaM terminus. Rate constants were derived from those for Model 1 as described in Text S1.
Figure 6.
Model of autophosphorylation of one mCaMKII by another.
Autophosphorylation requires that CaM be bound to both the subunit acting as “enzyme” and the subunit acting as “substrate”. A range of association rate constants for the subunit complex (Table S1) were calculated based upon estimated affinity constants from experimental studies as described in Text S1. Phosphorylated K•CaMnNcC species are denoted pK•CaMnNcC.
Figure 7.
Time courses of species of CaM, K•CaM, and pK•CaM with varying numbers of bound Ca2+ ions, simulated with Model 1.
The initial conditions for the simulation were [CaM] = 30 µM, [mCaMKII] = 80 µM, and [Ca2+] = 10 µM. A) Time course of formation of species of free CaM. B) Time course of formation of species of CaM bound to CaMKII (K•CaM). C) Time course of formation of species of CaM bound to phosphorylated CaMKII (pK•CaM). The color code for Ca2+ occupation of sites on CaM is indicated on the lower left. *color code applies to all forms of CaM with the indicated bound Ca2+. Note differences in scale for panels A), B) and C).
Figure 8.
Time courses of species of CaM, K•CaM, and pK•CaM with varying numbers of bound Ca2+ ions, simulated with Model 1 altered to allow binding of only CaM4 to CaMKII, and autophosphorylation of only K•CaM4.
The initial conditions were as in Figure 7. A) Time course of formation of species of free CaM. B) Time course of formation of species of CaM bound to CaMKII (K•CaM). C) Time course of formation of species of CaM bound to phosphorylated CaMKII (pK•CaM). The level of pK•CaM4 after 1 sec is 3 times lower than in the simulation with the complete Model 1 (Figure 7C). This demonstrates that the dominant pathway to pK•CaM4 at short times under these conditions is via Ca2+ binding to K•CaM species with fewer than 4 bound Ca2+ ions. The color code for Ca2+ occupation of sites on CaM is indicated on the lower left. *color code applies to all forms of CaM with the indicated bound Ca2+. Note differences in scale for panels A), B) and C).
Figure 9.
Differences in predicted autophosphorylation between Model 1, Model 2, and an Empirical Model, at varying concentrations of Ca2+ and reaction times.
A) Surface plot of ratio of autophosphorylation predicted by the Empirical model and by Model 1. B) Surface plot of ratio of autophosphorylation predicted by Model 2 and by Model 1. In A and B Contour lines for 1, 5, and 60 sec reaction times are shown in light gray. C) Ca2+-dependence of the ratio of autophosphorylation predicted by the Empirical model and Model 1 at 1, 5, and 60 sec reaction times. D) Same as C for ratio of autophosphorylation predicted by Model 2 and Model 1.
Figure 10.
Frequency dependence of autophosphorylation produced by Ca2+ binding dynamics.
Simulations were performed with [CaM] = 30 µM and [mCaMKII] = 80 µM. Each line plots summed autophosphorylation of all kinase complexes in response to a series of 30 Ca2+ spikes at varying frequencies simulated with Model 1 as described in Methods. A) The half width of each spike (σ ) is set to 10 ms (width = 20 ms, FWHM = 16 ms) and the peak height () is 10 µM. B) The half width of each spike (σ ) is set to 50 ms (width = 100 ms, FWHM = 83 ms) and the peak height (
) is 10 µM. C) The half width of each spike (σ ) is set to 50 ms (width = 100 ms, FWHM = 83 ms) and the peak height (
) is 2 µM. Blue, simulations with all parameters set to default (midpoint of ranges in Table S1). Gold, same as blue except that the default
is multiplied by 10 to produce faster decay of K•CaM2C. Magenta, same as blue except that the default
is divided by 10 to produce slower decay of K•CaM2C.
Figure 11.
Interaction of time evolution of K•CaM2C and K•CaM4 with frequency of Ca2+ pulses.
Simulations were performed with [CaM] = 30 µM and [mCaMKII] = 80 µM. Time courses of Ca2+ (blue), K•CaM2C (magenta), K•CaM4 (gold) and summed autophosphorylated CaMKII (green) are plotted. A) Pulses with half width (σ) set to 10 ms (width = 20 ms, FWHM = 16 ms) and peak height () set to 10 µM were simulated at 0.5 Hz for 10 sec. B) Same as A) but frequency of 7 Hz was simulated for 1 sec. All parameters were set to default as in Figure 10, blue lines.
Table 1.
The sensitivity of phosphorylation of CaMKII to variations in input parameters as measured by partial rank correlation coefficient (PRCC) at different Ca2+ concentration ranges.
Figure 12.
Variation in PRCC of selected parameters as a function of Ca2+ concentration.
PRCC values for a 1 sec reaction are plotted as a function of initial free Ca2+ concentration. A) PRCC values were calculated using the range of experimental uncertainty in parameter values from Table S1. B) PRCC values were calculated as in panel A, except that more restricted ranges of parameter values were used (2.5-fold around the mean values in Table S1). C) PRCC values for the autophosphorylation rates of K•CaM complexes with odd numbers of bound Ca2+ were calculated as in panel A. D) PRCC values for the autophosphorylation rates of K•CaM complexes with odd numbers of bound Ca2+ were calculated as in panel B.
Figure 13.
Hypothetical kinetic pathways leading to autophosphorylation of CaMKII.
Paths shown in yellow are significant at Ca2+ concentrations below ∼30 µM and at times up to 1 sec after an increase in Ca2+ concentration. Paths shown in red predominate at Ca2+ concentrations above ∼30 µM.