Opposing Intermolecular Tuning of Ca²⁺ Affinity for Calmodulin by Neurogranin and CaMKII Peptides

Abstract

We investigated the impact of bound calmodulin (CaM)-target compound structure on the affinity of calcium (Ca²⁺) by integrating coarse-grained models and all-atomistic simulations with nonequilibrium physics. We focused on binding between CaM and two specific targets, Ca²⁺/CaM-dependent protein kinase II (CaMKII) and neurogranin (Ng), as they both regulate CaM-dependent Ca²⁺ signaling pathways in neurons. It was shown experimentally that Ca²⁺/CaM (holoCaM) binds to the CaMKII peptide with overwhelmingly higher affinity than Ca²⁺-free CaM (apoCaM); the binding of CaMKII peptide to CaM in return increases the Ca²⁺ affinity for CaM. However, this reciprocal relation was not observed in the Ng peptide (Ng_13–49), which binds to apoCaM or holoCaM with binding affinities of the same order of magnitude. Unlike the holoCaM-CaMKII peptide, whose structure can be determined by crystallography, the structural description of the apoCaM-Ng_13–49 is unknown due to low binding affinity, therefore we computationally generated an ensemble of apoCaM-Ng_13–49 structures by matching the changes in the chemical shifts of CaM upon Ng_13–49 binding from nuclear magnetic resonance experiments. Next, we computed the changes in Ca²⁺ affinity for CaM with and without binding targets in atomistic models using Jarzynski’s equality. We discovered the molecular underpinnings of lowered affinity of Ca²⁺ for CaM in the presence of Ng_13–49 by showing that the N-terminal acidic region of Ng peptide pries open the β-sheet structure between the Ca²⁺ binding loops particularly at C-domain of CaM, enabling Ca²⁺ release. In contrast, CaMKII peptide increases Ca²⁺ affinity for the C-domain of CaM by stabilizing the two Ca²⁺ binding loops. We speculate that the distinctive structural difference in the bound complexes of apoCaM-Ng_13–49 and holoCaM-CaMKII delineates the importance of CaM’s progressive mechanism of target binding on its Ca²⁺ binding affinities.

Introduction

Calcium (Ca²⁺) is exquisitely used by a cell for transducing external stimuli through its gradient of extracellular (∼1000 μM) and intracellular (∼0.1 μM) concentration (1). A broad spectrum of Ca²⁺ signals are encoded by protein calmodulin (CaM) (2) (the structure is shown in Fig. 1 a) through specific binding with various targets regulating CaM-dependent Ca²⁺ signaling pathways in neurons (3). The targets enhance CaM’s affinity for Ca²⁺ by up to 30 times or accelerate dissociation of Ca²⁺ from CaM (4). Therefore, this mechanism tunes CaM’s capacity of encoding global Ca²⁺ signals by its differential binding affinity for Ca²⁺. Among those targets, Ca²⁺/CaM-dependent protein kinase II (CaMKII) (5, 6, 7) (the structure and sequence of the CaM-binding domain are shown in Fig. 1 b) and neurogranin (Ng) (8) (the sequence of the Ng_13–49 peptide is shown in Fig. 1 c) play an essential role in synaptic plasticity (9), which is critical to learning and memory formation shown by early behavior experiments on Ng-mutated or Ng-knocked-out mice (10, 11). We summarized several experimental observations (3, 7) in Fig. S1 on how CaM sensitizes downstream CaM-binding enzymes to Ca²⁺ regulating synaptic plasticity in memory formation: CaM activates CaMKII at high Ca²⁺ levels (6) while the availability of CaM is controlled by a group of postsynaptic proteins including Ng at a lower Ca²⁺ level (8, 12).

Figure 1.

Illustration of structures of CaM and sequences of the target peptides. (a) Solution structure of Ca²⁺-free CaM (apoCaM) (PDB: 1CFD) and crystal structure of Ca²⁺/CaM (holoCaM) (PDB: 1CLL). CaM is colored as follows, red → nCaM (residue 1–76), gray → central linker (residue 77–82), blue → cCaM (residue 83–148), and the Ca²⁺ ions are colored in green; Ca²⁺ binding sites are labeled from I to IV. (b) Structure of Ca²⁺/CaM-dependent kinase II (CaMKII) peptide from the holoCaM-CaMKII crystal structure (PDB: 1CDM) and the sequence of the peptide. (c) X-ray structure of holoCaM-CaMKII (PDB: 1CDM). CaM and the Ca²⁺ ions are colored as in (a) and the CaMKII peptide is colored in green. (d) Sequence of the neurogranin peptide (Ng_13–49). The two minimum compositions of the Ng_13–49 peptide are marked as “acidic region” and “IQ motif.” To see this figure in color, go online.

Waxham et al. (13, 14) used fluorescence experiments to show that the CaMKII kinase increases the affinity of Ca²⁺ for CaM while Ng significantly decreases the affinity of Ca²⁺ for Ca²⁺-binding loop III and IV (Fig. 1 a) in C-domain of CaM (cCaM) by up to 60-fold. These experiments raised questions about the dependence of CaM’s affinity for Ca²⁺ ions on structural models of CaM (13, 15). Recent studies by Le Novère et al. (16, 17) demonstrated the alteration of Ca²⁺ affinity for CaM by plotting the binding affinity curves with elaborated allosteric models and fitted rates. They investigated the effect of competing targets on CaM by showing the enhancement of binding affinity in the presence of some targets (such as CaMKII), as well as the diminishment in the presence of other targets (such as Ng). Dieckmann et al. (18) used steady-state fluorescence and nuclear magnetic resonance (NMR) experiments and found that the binding of endothelial nitric oxide synthase (eNOS) to CaM enhances CaM’s affinity for Ca²⁺ while phosphorylated eNOS does not due to electrostatic repulsion. They speculated that the phosphorylation on eNOS diminished its helical propensity, possibly affecting CaM’s affinity for Ca²⁺. On the other hand, the structural basis of the regulation of Ca²⁺ affinity for CaM by Ng and CaMKII remains elusive.

CaM has two domains separated by a flexible central linker. Each domain consists of two helix-linker-helix motifs (marked as I–IV in Fig. 1 a), which can bind a Ca²⁺ ion. The flexible central linker allows adjustable CaM conformations, thus accommodates the binding of distinct CaM binding targets (CaMBTs) (19, 20, 21, 22, 23). In a canonical complex of Ca²⁺/CaM (holoCaM) and CaMKII peptide, the two domains of holoCaM wrap around the CaMKII peptide, which forms a helical structure (24). In our previous work, by using a combined approach of coarse-grained molecular simulations and experiments, we have established the binding mechanism of holoCaM and CaMKII peptide (25, 26) that follows “conformational and mutually induced fit” (27). Both holoCaM and CaMKII undergoes large conformational changes in the two-step binding mechanism.

Unlike the CaMKII peptide in complex with holoCaM, which was solved by X-ray crystallography decades ago (24), the weak binding between Ng and Ca²⁺-free CaM (apoCaM) makes the determination of its three-dimensional complex structure challenging (28). Ng belongs to the IQ motif family. In this family, the CaMBTs share a common motif (IQXXXRGXXXR), where X stands for any amino acid. Recently, Kumar et al. (29) determined the crystal structure of apoCaM and IQ motif of Ng (NgIQ), however, NgIQ was artificially covalently linked with cCaM in the bound structure. Furthermore, a previous experimental study (30) revealed that the IQ motif alone cannot represent the biophysical characteristics of the intact Ng protein. Inclusion of the acidic region in the N-terminal before the IQ motif (or Ng_13–49), which are largely composed of Asp or Glu residues, reproduced the Ng-mediated affinity of Ca²⁺ to apoCaM, as well as the intermolecular interactions between the intact Ng and apoCaM. However, the main obstacle to investigate apoCaM-Ng_13–49 binding is a lack of experimentally solved structures because of their weak binding affinity (approximately micromolar) (30). To determine the apoCaM-Ng_13–49 complex structures, we modeled the interaction between intrinsically disordered Ng_13–49 and apoCaM by introducing statistical dihedral angle potentials of Ng_13–49 (31). After obtaining the appropriate coarse-grained models of apoCaM-Ng_13–49, we reconstructed them into all-atomistic structures (32). We noted that in comparison to the canonical complex of CaM and CaMBT that includes the two domains of CaM wrapping around a helical CaMBT, the conformation of CaM in the complexes of apoCaM-Ng_13–49 remains extended instead. The conformations of Ng in the bound complexes are not entirely helical.

The reconstructed atomistic models of the holoCaM-Ng_13–49 complex and the crystal structure of holoCaM-CaMKII complex (Protein Data Bank (PDB): 1CDM) allow us to develop a hypothesis that the conformation of the Ca²⁺ binding loops from cCaM in a holoCaM-CaMBT complex dictates cCaM’s affinity for Ca²⁺. To validate this hypothesis, we computationally applied all-atomistic steered molecular dynamics (MD) simulations of holoCaM-CaMBT (33) and used Jarzynski’s equality (JE) (34) to calculate the change in Ca²⁺ binding free energy. As a reference, the same simulations were performed on a conformation of holoCaM without a CaMBT (PDB: 1CLL).

One of the challenges is the modeling of the bivalent Ca²⁺ ions. It has been shown that the charge on Ca²⁺ is < +2e due to charge transfer and polarization effects in the solution and especially in the Ca²⁺-bound state (35, 36, 37). Moreover, Jungwirth et al. (36, 38) suggested that both the size and the charge require adjustment to account for the polarization effects. Following our previous work (39), we computed the charges of calcium ions according to the protonation states of CaM by employing a semiempirical quantum chemistry program MOPAC (40). Thereby we revealed a mechanism that the presence of Ng peptide destabilizes the Ca²⁺ binding to cCaM, whereas the CaMKII peptide stabilizes the Ca²⁺ binding to cCaM. We speculate that CaM’s progressive mechanism of target binding, which yields distinctive complexes of apoCaM-Ng_13–49 and holoCaM-CaMKII, modulates Ca²⁺ affinities for CaM.

Materials and Methods

Coarse-grained protein or peptide models

We performed coarse-grained molecular simulations of the intact Ng protein as well as the binding between apoCaM and Ng_13–49 peptide. Sample preparation of the intact Ng or the Ng_13–49 peptide is provided in Section I of the Supporting Material. The Hamiltonian of the coarse-grained protein models including Ng protein and the apoCaM-Ng_13–49 complex is described in Section II of the Supporting Material. Ca²⁺ ions are absent from the coarse-grained models. The details about the coarse-grained molecular simulations are included in Section III of the Supporting Material.

Free energy calculation using JE

Preparation of the structures

The preparation of the coordinates as initial conditions for the JE calculation is highly nontrivial for the computation of Ca²⁺ binding free energy ΔG. For both systems, we determined the accurate protonation states by using H++ server (41) according to the protein conformation, pH, and the ionic strength of the solution. We then assigned the partial charges based on the geometry of the proteins by using a semiempirical quantum chemistry program MOPAC (40). We applied those protonated protein structures and partial charges for minimization and further procedures to carry out all-atomistic calculations of the Ca²⁺ binding free energy (find the details in Section IV of the Supporting Material). For holoCaM and holoCaM-CaMKII, which have experimentally determined structures, we fixed the heavy atoms during the preparation; for holoCaM-Ng, we constrained the atoms with harmonic potentials for the preparation of the structures (holoCaM: calcium-bound calmodulin).

holoCaM-CaMKII and holoCaM. We fixed the positions of Ca²⁺ atoms and backbone heavy atoms from holoCaM (PDB: 1CLL) or holoCaM-CaMKII (PDB: 1CDM) during the minimization, solvation, ionization, and the equilibration procedures (see Section IV of the Supporting Material for details).

holoCaM-Ng_13–49. Since there is no experimentally determined structure, we reconstructed the all-atomistic structures from the selected coarse-grained side-chain-C_α models of apoCaM-Ng_13–49 using SCAAL method (32) (see Section IV.1 of the Supporting Material for the criteria of selecting apoCaM-Ng_13–49 models). We estimated the position of each Ca²⁺ ion as the center of mass of the side chains of the corresponding Ca²⁺-coordinating residues from the four Ca²⁺ binding loops. We inserted the Ca²⁺ ions into these positions as an initial condition for the next minimization process with the all-atomistic AMBER99SB-ILDN force field to define their final positions. During the minimization, only the backbone heavy atoms (excluding Ca²⁺) of the holoCaM-Ng_13–49 were constrained. It was then followed by solvation of TIP3P water molecules and ionization of Na⁺/Cl⁻ ions, which required another round of energy minimization and equilibration. The backbone heavy atoms and the Ca²⁺ ions were constrained (but not fixed) for the holoCaM-Ng_13–49 complexes. After preparation, the positions of the Ca²⁺ ions were robust and did not drift away because 1) there were ∼5–7 oxygen atoms from the side chains in the loop within 4 Å of each Ca²⁺ ion; 2) our calculation showed that the average stability of the Ca²⁺ ions at binding site III and IV is ΔG = −16.0 and −12.8 kcal/mol, respectively.

Pulling simulations and computation of the free energy differences

We performed all-atomistic steered molecular dynamics (MD) simulations (see Sections IV.3 and IV.4 in the Supporting Material for the procedures and details of the steered MD simulations) to calculate the Ca²⁺ binding free energy (ΔG) using JE (34). JE relates ΔG and the irreversible work along an ensemble of non-equilibrium trajectories pulling the Ca²⁺ from the bound state to the unbound state (Eq.uation S10). The nonequilibrium trajectories (number M = 100∼150) were generated by steered MD simulations with all-atomistic models. The difference in the Ca²⁺ binding free energy ΔG between holoCaM-CaMBT (CaMBT: calmodulin binding targets) and CaM is defined as ΔΔG = ΔG^{holoCaM-CaMBT} − ΔG^holoCaM. ΔΔG allows us to evaluate the influence of different CaMBTs on Ca²⁺ binding to CaM, where ΔG^{holoCaM-CaMBT} and ΔG^holoCaM were estimated from independent simulations of pulling Ca²⁺ from the holoCaM-CaMBT and the holoCaM, respectively.

Analyses: calculation of “apparent chemical shifts”

In the NMR experimental work by Hoffman et al. (30), a semiquantitative comparison of amide chemical shifts were presented for residues in apoCaM (calmodulin without calcium ions) that are affected by binding of Ng_13–49. In the NMR spectroscopy, the chemical shift is the relative resonant frequency in the local induced magnetic field and is diagnostic of the molecular structure. A threshold was applied to generate a set of Boolean numbers, with “1” representing a significant change in the chemical shifts and “0” indicating no change. We refer to the Boolean series as “apparent chemical shifts” throughout this study. Berjanskii and Wishart (42) showed that the inverse absolute chemical shifts roughly correlates with root mean square fluctuations (RMSF), which reflects the flexibility of the structure. Therefore, to compare with the change of chemical shifts from unbound to bound apoCaM in the experiment, we approximated the amide chemical shifts by the inverse of RMSF of C_α beads and defined “apparent chemical shifts” as Δ = $\text{Θ}$ (RMSF^unbound/RMSF^bound − τ). τ = 50% was used. Δ measures the change of local flexibility of the apoCaM: larger values of Δ indicate stabilization of the corresponding residue upon binding with Ng_13–49.

Results

Building weakly bound apoCaM-Ng_13–49 complexes in coarse-grained models

Because of the lack of experimentally determined apoCaM-Ng_13–49 complex structures, we used low-resolution information on the bound complex of apoCaM-Ng_13–49 from NMR measurements (30) for building plausible models from coarse-grained molecular simulations. The NMR experiments showed the change in the backbone chemical shifts of apoCaM upon Ng_13–49 binding (Fig. 2 a). It revealed the residual information on the structural changes of apoCaM upon binding with Ng_13–49 (30), but did not guarantee a direct contact between apoCaM and Ng_13–49. The experiment showed that the major structural changes occur in cCaM as well as Helices B and C in nCaM, as in Fig. 2 a.

Figure 2.

Reweighted PMF of apoCaM-Ng_13–49 binding and changes in chemical shifts for apoCaM upon Ng_13–49 binding. (a and b) The residues that experienced significant changes in chemical shifts are projected on the apoCaM structure (PDB: 1CFD) as a ball-and-stick representation from experimental measurement in (a) (30) and from our calculations according to the coarse-grained molecular simulations in (b). (c) The PMF from the coarse-grained molecular simulations is plotted against the center of mass distance between apoCaM and Ng_13–49 (d_COM) and the number of intermolecular contacts (Z). The coarse-grained molecular simulations were performed at pH = 6.3 and ionic strength = 0.1 M according to the conditions of the nuclear magnetic resonance experiments (30). We used a reduced unit of length σ = 3.8Å. The color is scaled in k_BT, T = 1.1 ε/k_B, where ε is reduced unit of energy and k^B is Boltzmann constant. For visual guidance, we provided bars above the schematic representation of secondary structures in red and blue segments of apoCaM on the half circles in (a and b). To see this figure in color, go online.

One of the prominent reasons that we used coarse-grained simulations is to achieve efficient sampling of the conformational space (see Sections I–III in the Supporting Material for details about the coarse-grained simulations). We implemented the statistical potentials into the structural Hamiltonian of the Ng_13–49, as well as the intermolecular interaction between apoCaM and Ng_13–49. For the modeling of apoCaM, we kept limited structural information that favors an extended conformation and matches the structural description of the experimental measurements (25, 43). We found that apoCaM-Ng_13–49 complex samples an ensemble of varying conformations through nonspecific intermolecular interactions, indicated by the broad distribution of the bound complex in the potential of mean force (PMF) (see Fig. 2 c).

Once we generated the ensemble of bound complexes, we strategically selected the most probable complex structures of apoCaM-Ng_13–49 with the previously mentioned NMR measurement as a guide (Fig. 2 a) by following the procedures: 1) we reweighed the ensemble of apoCaM-Ng_13–49 structures from the umbrella sampling simulations (44) using Weighted Histogram Analysis Method (45, 46), and employed an importance sampling method (32) (see Section V.4 in the Supporting Material) to select a subset of 23,722 structures from five million independently sampled conformations. The surprisal value between the sample distribution P^sample(d_COM) and the original unbiased distribution P^ori(d_COM) = 0.14 to show that the sample distribution represents the original distribution well. 2) We performed a clustering analysis on the sampled structures (see Section V.5 in the Supporting Material for the clustering method); 3) we computed the “apparent chemical shifts” (see Analyses: calculation of “apparent chemical shifts” for the definition, Fig. 2 b) from the major clusters. The population of the major four clusters (comprising 86%, Table S2) and the correlation coefficients between computationally obtained “apparent chemical shifts” from the four clusters and the experimental NMR data are shown in Table S2. We identified the cluster (the dominant cluster) of complex structures, which best matched the experiment (30), with a correlation coefficient of 0.36. From the dominant cluster (i.e., cluster 1 in Table S2), cCaM is mostly stabilized by binding with Ng_13–49 and helices B and C are partially stabilized (Fig. 2 c).

We next analyzed the structures of the weakly bound apoCaM-Ng_13–49 by comparing the probability of contact formation from the unbound state (defined by d_COM ≈ 20 σ in Fig. 2 c) in Fig. S3. In the selected cluster (cluster 1) of the apoCaM-Ng_13–49 complexes, contacts within apoCaM (triangles in solid lines in Fig. S3 c) became less probable upon Ng_13–49 binding. In addition, the probability of interdomain contacts between Helix A from nCaM and inter-domain linker, helices G and H from cCaM (the solid rectangles in Fig. S3 c) decreased to allow interaction with Ng_13–49 (the solid rectangles in Fig. S3 a). In contrast, after binding with apoCaM, Ng_13–49 diminished interactions between IQ motif and the acidic region (Fig. S3 b, the rectangle in dotted lines); subsequently, probability of forming α-helix structure in the IQ motif increases (Fig. S3 b, the rectangle in solid line). Provided that there was no bias to the formation of α-helix structure in Ng_13–49, our model predicted formation of secondary structures in the IQ motif after binding with apoCaM.

For the intermolecular interaction of the weakly bound complex from the main cluster, IQ motif of Ng_13–49 interacted with Helix A, B/C Helix linker, and Helix D from nCaM, and interdomain linker, Helix E and Helix H, and the F/G Helix linker from cCaM (Fig. S3 a, ellipse in dotted lines). These regions from CaM (either apoCaM or holoCaM) also participate in canonical binding of holoCaM with CaMKI or CaMKII (25). Although the IQ motif of Ng_13–49 formed a helical structure and interacts with cCaM of high probability, the acidic region of Ng_13–49 remains unstructured (Fig. S3 b, no change in contact formation along diagonal for the acidic region). It is highly probable for the acidic region to interact with both nCaM and cCaM, especially with F/G helix linker and the central linker (Fig. S3 a, ellipse in solid lines). We further calculated the correlation among these pairwise contacts in Section V.6 of the Supporting Material, and found that the interaction between acidic region of Ng_13–49 and Ca²⁺ binding loops from apoCaM anticorrelated with those within cCaM (shown in magenta ellipse in Fig. S4).

Molecular mechanism of apoCaM-Ng_13–49 binding

We next investigated the conformational changes of apoCaM-Ng_13–49 during the association process along their center-of-mass separation (d_COM) for better understanding of the molecular mechanism of binding. The unbound structure was taken from d_COM = 20.0 σ, where the interaction between the two proteins is negligible; the encounter state structure (25) was taken from d_COM = 10.0 σ, where the two proteins began to make contact; the bound state structure was take from d_COM = 2.8 σ, where the PMF(d_COM) reached the minimum (see the magenta curve Fig. S2 for the PMF). Superposed structures of apoCaM-Ng_13–49 complex at d_COM = 20.0, 10.0, and 2.8 σ are shown, representing unbound, encounter, and bound states, respectively (Fig. 3). There was no apparent structural change in apoCaM from the unbound state (Fig. 3 a) to the encounter complex (Fig. 3 b) that the conformation of apoCaM remains extended. The onset of binding in Fig. 3 b shows that the IQ motif of the Ng_13–49 mainly interacted with cCaM, which was not involved in a global conformational change of apoCaM. From the encounter complex (Fig. 3 b) to the bound state (Fig. 3 c), Ng_13–49 remained partially structured and mainly gained interactions with nCaM and local conformational change of apoCaM was observed. In particular, the EF-hand β-scaffold (47), which stabilizes the two helix-loop-helix motifs (EF-hand) in cCaM (see Fig. S5 for illustration of the EF-hand β-scaffold), is broken by insertion of the acidic region of Ng_13–49.

Figure 3.

Illustration of the structural changes in unbound, encounter, and bound ensemble of CaM-Ng_13–49 complexes. Structures of CaM in (a) was taken from the unbound state when CaM and Ng_13–49 are well separated at d_COM = 20.0 σ. σ = 3.8 Å. (b) Structures from the encounter of binding when apoCaM and Ng is separated at d_COM = 10.0 σ. (c) Structures from the bound state at d_COM = 2.8 σ. For visual guidance, we superposed 20 sets of structures in each panel. The CaM is colored in black; the residues (residues 99∼101 in Ca²⁺ binding loop III and residues 135∼137 in Ca²⁺ binding loop IV), which form EF-hand β-scaffold in cCaM are colored in blue; the acidic region and IQ motif of Ng_13–49 are colored in pink and yellow, respectively. To see this figure in color, go online.

To understand their binding at the residual level, we plotted the probability of contact formation at d_COM = 20.0, 10.0, and 2.8 σ in Fig. S6. At d_COM = 20.0 σ, or the unbound state, there was no contact formed between apoCaM and Ng_13–49 (in Fig. S6 a). The contacts within Ng_13–49 were ubiquitous and of low probability, corresponding to the transient nature of conformations of an intrinsically disordered protein/peptide (IDP). Upon initial binding with apoCaM at d_COM = 10.0 σ, only IQ motif from the Ng_13–49 gained contacts with Helix F and Ca²⁺ binding loop IV from cCaM. This indicates a crucial role of the IQ motif in the recognition by apoCaM. Those contacts were kept when d_COM became 2.8 σ, which suggests that the IQ motif also facilitated the stabilization of the apoCaM-Ng_13–49 complex. At this stage, the contacts between the acidic region of Ng_13–49 and both of nCaM and cCaM formed broadly but with low probability. For apoCaM, from unbound to bound states, most of the contact formation within apoCaM remained the same (of high probability), except when d_COM = 2.8 σ, the side chain-side chain contacts between Helix E and Helix H, between Helix F and Ca²⁺ binding site IV, and the β-sheet contacts between Ca²⁺ binding sites III and IV (encircled in Fig. S6). In particular, the probability of the contacts that form the EF-hand β-scaffold (encircled) became less when the acidic region of Ng_13–49 formed contacts with cCaM. Ng became partially helical in the bound form. We will relate this finding to its importance of specific functions under Discussion.

Binding of the CaMBTs to CaM modulates the Ca²⁺ binding affinity validated by atomistic pulling simulations

We found that interactions between the acidic region of Ng_13–49 and the Ca²⁺ binding loops from cCaM-apoCaM competed with those within apoCaM. We hypothesized that, due to this competition, the EF-hand β-scaffold, which is shown to control the opening and closing of the EF-hands (47, 48), become less stable, thus facilitating the release of Ca²⁺ from CaM. To test this hypothesis, we strategically selected apoCaM-Ng_13–49 complex structures from the most dominant cluster (i.e., cluster 1 in Table S2) in the coarse-grained molecular simulations for the calculation of Ca²⁺ binding free energy. The selection was based on the characteristics of apoCaM binding with either Ng protein or Ng peptides according to the results from several experimental studies: 1) EF-hands in cCaM are open and EF-hands in nCaM are closed from X-ray crystallography and NMR experiments (29, 49); 2) Ng_13–49 has more interactions with cCaM as suggested from NMR studies, $\Delta Z=Z_n-Z_c<0$ (30). Z_n (Z_c) is the number of intermolecular contacts between Ng and nCaM (cCaM). (See Section V in the Supporting Material for the definition of Z.) This was further shown by the EF-hand angles in CaM in forms of Ca²⁺-absent, Ca²⁺-loaded, apoCaM-NgIQ, and holoCaM-CaMKII in Table S3. As a result, four coarse-grained structures were selected from the major cluster (cluster 1) for further reconstruction of all-atomistic protein models with four Ca²⁺ ions included (see (50) for the protocol of reconstructing the all-atomistic model from a side-chain-C_α model).

We evaluated the free energy difference between Ca²⁺-unbound and Ca²⁺-bound state (ΔG = G_B − G_U, see Fig. 4 for illustration) using JE (34, 51) by pulling the two Ca²⁺ ions independently from the Ca²⁺ binding sites III and IV of the cCaM (see simulations details in IV.5 from the Supporting Material). We further computed the free energy changes in the absence or the presence of a target (ΔΔG = ΔG^{holoCaM-CaMBT} − ΔG^holoCaM, see Fig. 4 for illustration). ΔΔG allows us to evaluate the influence of CaMBT on Ca²⁺ binding to CaM. If ΔΔG >0, it means that the CaMBT destabilizes the bound state and thus decreases the Ca²⁺ affinity, as illustrated in Fig. 4. If ΔΔG <0, CaMBT enhances Ca²⁺ affinity for CaM.

Figure 4.

Illustration of the definitions of the binding free energy ΔG and ΔΔG. ΔG = G_B − G_U. ΔΔG = ΔG^{holoCaM-CaMBT} − ΔG^holoCaM. B and U stand for bound and unbound states of the Ca²⁺, respectively. ΔΔG >0 means that the CaMBT destabilizes the bound state and thus decreases the Ca²⁺ affinity.

We found that the distribution of work values does not follow Gaussian distribution (Fig. S14). The estimation of free energy difference ΔG could be very inaccurate by directly applying JE or its second-order cumulants approximation (51) (we reported the direct estimation from JE in Table S6). As shown in Fig. S13, the binding free energy ΔG was estimated for Ca²⁺ at binding site III or site IV of holoCaM and holoCaM-CaMKII using a running JE estimate or a block-average method (BA, i.e., using subsets of all available work data using Jarzynski’s equality). ΔG converged to values, which deviate from experimental values (∼ −5 to −4 kcal/mol). To improve the efficiency of the free energy estimation, we implemented the cumulative integral (CI) extrapolation method developed by Ytreberg and Zuckerman (51). CI uses an integral for more accurate estimations than the linear extrapolation method by extrapolating to 1/n → 0, where n is total number of work values. It was shown that CI extrapolation could reduce the required data by 5- to 40-fold (51, 52). Therefore, we adopted the CI extrapolation method to estimate the free energy difference.

We summarized the binding free energies of Ca²⁺ estimated by the CI extrapolation in Table 1 for a total of six conformations: four holoCaM-Ng₁₃₋₄₉ (showing averaged values), one holoCaM and one holoCaM-CaMKII. For all of the four conformations of holoCaM-Ng₁₃₋₄₉, the binding of Ng₁₃₋₄₉ to CaM destabilized the Ca²⁺ in site III and site IV, respectively, by showing an averaged positive ΔΔG (Table 1). In comparison, we examined the importance of the canonical bound structure for the release of Ca²⁺ from the complex structure of holoCaM-CaMKII (PDB: 1CDM) where the CaM wraps around and binds with a well-formed helical structure of CaMKII peptide at an antiparallel position. From CI extrapolation, each site presented a negative ΔΔG, implying that the presence of CaMKII stabilizes the Ca²⁺ in both site III and site IV from CaM.

Table 1.

Difference in Binding Free Energy of Ca²⁺ Calculated from Nonequilibrium Molecular Simulations and from the Experiments at pH = 7.4.

		holoCaM-Ng13–49	holoCaM-CaMKII
ΔΔGCI (kcal/mol)	Site III	9.2 ± 2.2	−2.5
	Site IV	22.4 ± 0.9	−1.7
ΔΔGexp (kcal/mol)	Site III/IV	2.5	−3.3

The CI extrapolation was used in the calculation of binding free energy of Ca²⁺ ΔΔG^CI from the simulations. The averaged value of ΔΔG statistical errors from the four conformations of the holoCaM-Ng_13–49 complex are provided. The experimental binding free energy ΔΔG^exp for holoCaM-Ng_13–49 was from literature (30) and the experimental values of the holoCaM-CaMKII were from (14).

Conformation of bound CaM-CaMBT complex dictates Ca²⁺ release

HoloCaM-CaMKII forms a canonical bound complex, while apoCaM-Ng₁₃₋₄₉ does not. In the following, we unveiled the molecular mechanism that governs varying Ca²⁺ binding affinity for cCaM in complexes of CaM and distinct CaMBTs. We examined one holoCaM-Ng₁₃₋₄₉ model reconstructed from the coarse-grained structure that led to a maximal increase of Ca²⁺ binding free energy, as well as the crystal structure of holoCaM-CaMKII (PDB: 1CLL).

In Fig. 5 a, Ng_13–49 is bent from the middle between residues P24 and G25 from the acidic regions (in green and in gray on the amino acid sequence). On the one hand, the IQ motif interacts with Helix F, Helix G, and F/G helix linker from cCaM to stabilize the holoCaM-Ng₁₃₋₄₉ complex. On the other hand, the acidic N-term interacts with both nCaM and cCaM. Surprisingly, the four residues D22-D23-P24-G25 (DDPG) (in ball-and-stick representation) before the IQ motif on Ng₁₃₋₄₉ stick out and insert into the middle of the EF-hand β-scaffold (colored in blue segments) between Ca²⁺ binding loops III and IV from cCaM, disrupting the stability of EF-hand β-scaffold. As a result, the distance between the two β-strands becomes 7.9 ± 1.2 Å (average over the four conformations) comparing to ∼5.0 Å in the intact holoCaM (PDB: 1CLL). In contrast, the distance decreases slightly to 4.8 Å in holoCaM-CaMKII (PDB: 1CDM).

Figure 5.

Differential intermolecular interactions in holoCaM-Ng_13–49 and holoCaM-CaMKII complex structure tune Ca²⁺ binding affinity for cCaM. (a) The atomistic structure of holoCaM-Ng_13–49 complex was reconstructed from the coarse-grained simulations that led to the largest decrease in Ca²⁺ affinity for site III and site IV. (b) The structure of holoCaM-CaMKII complex, showing a wrap-around binding pattern, is from the X-ray crystallography (PDB: 1CDM). The complete structures of the complexes are on the left, CaM is in black, Ca²⁺ ions are represented by yellow beads, and the CaMBTs are in white. The sequences of the CaMBTs are provided above the figures. For visual guidance, the cCaM and the CaMBTs are enlarged and recolored on the right. The cCaM is in ribbon representation and colored in orange. The residues forming EF-hand β-scaffold in the crystal structure, i.e., residues Y99, I100 from site III, and residues Q135, V136 from site IV, are colored in blue. The invariant Glu residue in the 12th position of each Ca²⁺-binding loop contributes two oxygen atoms to the coordination of the Ca²⁺ ion and is shown in ball-and-stick representation. The dotted lines show the distance between Ca²⁺ and the two oxygen atoms from Glu12 and the distance between the two β-strands in cCaM. The four residues that stick out from Ng_13–49 are D22 (red) D23 (red) P24 (green) G25 (magenta) in (a).The residues from CaM, which form contacts with CaMKII peptides, are colored in light green in (b). To see this figure in color, go online.

Moreover, the average distance between the Ca²⁺ and the Ca²⁺ coordinating oxygen atoms from the 12th residue (Glu-12), or $\overline{d}$^Glu-Ca, in site III and IV from cCaM is 4.5 ± 0.7 and 3.7 ± 0.5 Å, respectively (Fig. 5 a). As a reference, for Ca²⁺ in site III and site IV of the crystal structure of holoCaM without a target (PDB: 1CLL), $\overline{d}$^Glu-Ca = 2.3 and 2.5 Å, respectively. The 12th residue in the Ca²⁺ binding loop, or Glu-12, plays a crucial role in stabilizing Ca²⁺ in the binding loop (1, 47). However, the presence of the acidic region from Ng₁₃₋₄₉ increases $\overline{d}$^Glu-Ca in the holoCaM-Ng_13–49 complex (Fig. 5 a), especially for site IV, which is slightly closer to the center of mass of the DDPG motif than site III. The motif DDPG from the acidic region of Ng₁₃₋₄₉ pries open the EF-hand β-scaffold and facilitates the release of the Ca²⁺ from cCaM. In comparison, we examined the importance of the canonical bound structure for the release of Ca²⁺ from the crystal structure of holoCaM-CaMKII (PDB: 1CDM) in Fig. 5 b. In contrast, $\overline{d}$^Glu-Ca for sites III and IV (Fig. 5 b) are similar to those in the crystal structure of holoCaM without a target (PDB: 1CLL).

To understand the evolutionary role of the acidic region of Ng₁₃₋₄₉ and its biological significance in modulating Ca²⁺ binding affinity of CaM, we performed sequence alignment of Ng from different species available in the protein knowledgebase (UniProtKB, http://www.uniprot.org/uniprot/) (Table S14). Sequence alignment results of Ng revealed that the amino acids in the acidic region are either conserved across the species or found as amino acids with similar physicochemical properties (see Fig. S15). In particular, we noted that the cluster of residues “DIPLDDP” from the acidic region of Ng that show anti-correlation with the binding loops III and IV of CaM based on the pairwise contacts (see Fig. S4; Table S8) are conserved across all the species (see Fig. S15). Moreover, the “DDPG” motif from the acidic region of Ng is conserved (see Fig. S15) across the higher vertebrate species (from rodent to human; see Table S14). Interestingly, in the lower vertebrate species the Gly (G) residue of this motif is found as Asp (D) (in reptiles and birds) or Glu (E) (in fish) or Ala (A) (in zebrafish), whereas the rest of the residues (DDP) are conserved across all the vertebrates (see Fig. S15). We also found that the DDPG motif, which maintains close proximity to the middle part of both the Ca²⁺ binding loops III and IV in the holoCaM-Ng_13–49 complex (see Fig. S16) plays an important role in disrupting the EF-hand β-scaffold in CaM as we mentioned before. We speculate that the acidic region of Ng and especially the DDPG motif is evolutionarily important for their biological role in suppressing and/or fine-tuning the Ca²⁺ binding affinity of CaM.

Discussion

The energy landscape of apoCaM-Ng_13–49 binding is rugged

The weakly bound complexes are commonly observed in protein-protein associations involving intrinsic disordered proteins (IDPs) in both experiments (53, 54) and computer simulations (55, 56, 57, 58, 59, 60). Long-range electrostatic interactions enhance the rate of association of several weakly bound complexes (61). Generally, the nonspecific interactions, including hydrophobic and electrostatic interactions, are known to be a major contributor to the weakly bound complexes involving IDPs. Sugase et al. (54) showed from NMR experiments that the weakly bound transient complexes of the phosphorylated kinase inducible domain (pKID) of transcription factor CREB and the kinase-induced domain of the CREB-binding protein were predominantly stabilized by nonspecific hydrophobic contacts instead of electrostatic interactions. The importance of nonspecific intermolecular interactions was further addressed by computer simulations on phosphorylated kinase inducible domain and kinase-induced domain by Turjanski et al. (55), as well as on nuclear-receptor coactivator binding domain of CREB-binding protein and the p160 steroid receptor coactivator ACTR by Chen et al. (57). In both cases structure- or topology- based models (62) were used for the intermolecular interactions that define a specific bound structure.

Determination of the structure of the apoCaM-Ng_13–49 complex experimentally is challenging due to its low stability (28). To overcome this problem, we incorporated statistical nonbonded interactions and electrostatic interactions, which do not rely on a specific complex structure, in our protein model. In addition, to model the disordered Ng_13–49, we implemented a sequence-based statistical dihedral angle potential (31) in the Hamiltonian. Our study reveals a rugged free energy landscape of apoCaM-Ng_13–49 binding (Fig. 2 c). The conformations of apoCaM-Ng_13–49 thermally fluctuate between shallow basins separated by 1∼2 k_BT (T = 1.1 ε/k_B, where ε is reduced unit of energy and k^B is Boltzmann constant.).

The weakly bound complexes comprises “fuzzy” structures, in which either one of the binding partners or both stay dynamic (63). According to our simulations of the apoCaM-Ng_13–49 complex, Ng_13–49 remains partially structured as shown in the low probability of contact formation within Ng_13–49 (Fig. S3 b and S6 c). Our model of the CaM model (25) samples a wide range of states by incorporating non-native interactions between residues. This idea of modeling beyond a simple structure-based model meets the experimental exploration of CaM with single-molecule experiments that its energy landscape is rather rugged and complex with plenty of intermediates (19). Our approach differs from the approaches adopted by those studies that the conformational changes of the target were ignored. For example, in the investigation of the interactions between the transcriptional activation domain of an oncoprotein and its target by Chan et al. (64), the target protein was modeled as a sphere of distributed charges on the surface.

To generalize, the structural flexibility and nonspecific interactions, corresponding to entropic and enthalpic effects, respectively, result in the rugged energy landscape of apoCaM-Ng_13–49 that presents multiple weakly bound complexes without a global minimum.

IQ motif of Ng_13–49 is crucial for the initial binding of apoCaM

It was postulated that the residual structure of an IDP is necessary for molecular recognition in CaM-CaMBT complex formation (65). We found that the residual structure in Ng is crucial for recognition and binding with CaM. We found that the IQ motif started to interact with cCaM at a distance of d_COM = 10 σ and remained during the binding process, indicating its key role in binding with apoCaM. Creamer et al. (66) using CaM-CaMBT systems as well as Clarke et al. (67) using the BH3 motif of the largely disordered protein p53 upregulated modulator of apoptosis (PUMA) and a folded protein induced myeloid leukemia cell differentiation protein (MCL-1), however, postulated that the residual structure of the IDP did not affect binding kinetics, but weakened the binding affinity upon helix-breaking mutation. It is important to note that in Creamer’s study, most of the CaMBTs bind CaM in a canonical form where CaM undergoes large global conformational changes. In such scenarios, the “conformational and mutually induced fit” mechanism (25) is needed for the recognition and binding (see The binding mechanism of CaM-CaMBT might be key to regulating Ca2+ binding affinity on the binding mechanism of CaM-CaMBT). However, Ng predominantly interacts with cCaM and does not form a full helical structure, therefore the binding does not require global conformational changes of CaM.

The acidic region is key to Ng_13–49 for tuning CaM’s affinity for Ca²⁺ comparing to other IQ-motif peptides

Our computation of the change in free energy of Ca²⁺ binding to cCaM from nonequilibrium atomistic pulling simulations reveals that the target peptides Ng_13–49 and CaMKII have opposing effects on Ca²⁺ binding affinity to cCaM. It is important to note that the CaMKII peptide binds to CaM in a canonical form in which the two domains of CaM wrap around a helical CaMKII peptide (24), whereas Ng_13–49 forms weakly bound complexes with a rather extended CaM. Such a difference results in distinct conformations of the EF-hand motifs and the Ca²⁺ binding loops in CaM.

The binding and dissociation of Ca²⁺ to/from cCaM essentially depend on the two EF-hand motifs, which are connected by the F/G helix linker and are rigid in holoCaM (Fig. S5). This construct of EF-hand motif pair is often referred as the “EF-hand β-scaffold” (47) proposed by Grabarek (47). The EF-hand β-scaffold immobilizes the Ca²⁺ ion during its initial binding to the Ca²⁺ binding site. Our findings with regard to target binding that modulate CaM’s calcium affinity is supported by experimental observations (1). An enhanced structural stability of an EF-hand β-scaffold through target binding in a canonical CaM-CaMBT form increases CaM’s calcium affinity, which is discussed in the detailed review by Gifford et al. (1). In those experiments, a severe disruption in the Ca²⁺ binding loops due to the repacking of cCaM causes the Ca²⁺ coordinating oxygen atoms from the Glu-12 of the Ca²⁺ binding loop to move away from their Ca²⁺ binding positions and the release of the Ca²⁺ (68). In addition, several experiments showed that when CaMBT peptides bind to CaM canonically, the Ca²⁺ affinity for cCaM increases (69): ΔΔG varies from −1.5 kcal/mol for phosphorylase kinase, −3.3 kcal/mol for CaMKII (70) to −4.8 kcal/mol for β-calcineurin (71).

We found from this work that during the binding process, on one hand, IQ motif of Ng_13–49 carries the function of recognition and stabilization. On the other hand, the role of the acidic region of Ng_13–49 might relate to the biological functions of the protein because of its influence on the stability of EF-hand β-scaffold (Fig. S6 c) regulating Ca²⁺ binding to CaM. Ng belongs to the IQ motif CaMBTs family. IQ-motif CaMBTs such as the sodium channel (Na_V1.2), the calcium channel (Ca_V1.1 and Ca_V1.2), PEP-19, and Ng present distinct effects on CaM’s affinity for Ca²⁺.

The presence of the acidic region rather than the IQ motif determines whether the interactions between CaM and the IQ-motif CaMBT are disruptive or constructive. For Na_V1.2 and PEP-19 (Purkinje cell protein 4; PCP 4) that contain an IQ motif and a previous acid region, both of them bind to cCaM. Binding of them lowers the Ca²⁺ binding affinity for cCaM: binding of the Na_V1.2 causes an increase in ΔΔG of about +2 kcal/mol (72) and PEP-19 an increase of about +0.2 kcal/mol (49). However, for Ca_V1.1 and Ca_V1.2, which contain an IQ motif but no such previous acidic region, they behave like a canonical binding motif, where the CaMBT forms a helical structure wrapped by the compact CaM, and stabilize the Ca²⁺ binding by ΔΔG = −1 and −2.6 kcal/mol, respectively (73). The results support the active role of the acidic region, but do not imply the molecular mechanism of how it regulates Ca²⁺ binding to CaM. By carrying out multiscale molecular simulations, we identified the key residues DDPG in the acidic region of Ng_13–49 that “pry” open the β-sheet structure between the two Ca²⁺ binding loops.

The binding mechanism of CaM-CaMBT might be key to regulating Ca²⁺ binding affinity

A number of recent advancements have been made in experimental and computational approaches to examine protein-protein interactions involving IDPs (74, 75, 76, 77, 78). A key emerging concept is the idea of “specificity on demand” where protein interactions are dictated by concerted interactions between both binding partners. From this view, the process of binding cannot be inferred even if the structures of the initial reactants and final complex are known. The importance of structural flexibility motivated the development of theories for binding mechanisms (79, 80, 81, 82, 83), such as fly casting (61, 84), folding upon binding (58, 85), “dock-and-coalesce” (74, 86), and conformational selection (87, 88). These multiple steps mechanisms underlie possible kinetic bottlenecks due to subsequent conformational changes in a post-collision event (74, 86). Despite differences in these theories, past efforts that focus on IDPs binding to known structures have not dealt with the complexities of the conformational variability inherent in the binding process that can ultimately lead to different final products involving potentially large changes in both partners. This view is highlighted by our efforts that revealed that CaM binding to its targets is mediated by a conformational and mutually induced fit model (25).

In our previous study (25), we discovered that the binding between CaM and CaMBTs that forms a canonical bound complex, such as the CaMKII peptide, require a “conformational and mutually induced fit” mechanism. In this mechanism, the binding of the CaMKII peptide and CaM presents a two-stage process: at the onset of binding (as in an early stage), the binding is driven by diffusion and electrostatic steering effect that both CaM and CaMKII do not undergo large conformational changes. At the late stage, both experience large conformational changes that the two domains of CaM wrap around the emerging rod-like CaMKII peptide. The latter event of binding dictates a small, but significant, difference in the association rates of CaM with various CaMBTs. However, this is not the case for apoCaM-Ng_13–49 binding. After the onset of binding where, the IQ motif of Ng_13–49 binds to cCaM, there is no subsequent large conformational change of CaM.

The difference in the bound complexes of CaMBT-CaM along its progressive binding mechanism delineates their effects on Ca²⁺ binding affinity. The Ca²⁺ affinity is increased by binding of CaMKII peptide. The EF-hand motifs of CaM wrap around the rod-like CaMKII peptide; hence, they enhances the stability of the “EF-hand β-scaffold” that retains Ca²⁺ in Ca²⁺ binding loops. In contrast, the Ca²⁺ affinity is decreased by binding of Ng peptide because of lack of such wrap-and-enhance pattern of CaM. In addition, insertion of the DDPG motif into the “EF-hand β-scaffold” further destabilizes the Ca²⁺ binding loops. Therefore, we speculate that the benefit of a progressive binding mechanism of CaM that can be modulated by CaMBTs underlies their distinct effects on CaM’s Ca²⁺ binding affinities.

Force fields affect the magnitude of free energy estimation

From Table 1, the signs of ΔΔG from our computed values agreed with the experimental measurements. For holoCaM-CaMKII, they were in the same order of magnitude, while for the holoCaM-Ng_13–49 complexes, the computed values were about one order of magnitude larger than the experimental measured ones. Majorly the force field contributed to the accuracy in the calculation of ΔΔG. We break the reasoning down into three categories relating to force fields:

Initial structures might matter

We found that the current all-atomistic force fields, including AMBER99SB-ILDN and CHARMM27, alter the initial structures after minimization and equilibration if the positions of the heavy atoms were not strictly fixed in space. This is true for coordinates from the crystal structures of holoCaM and holoCaM-CaMKII, as well as the all-atomistic structures of holoCaM-Ng_13–49 reconstructed from coarse-grained models. The shifts in the positions are especially prominent for the Ca²⁺ ions. According to the study by Shukla et al. (89) on the same structure of holoCaM (PDB: 1CLL) using the AMBER99SB-ILDN force field, the root mean-square deviation of the equilibrated structure from the crystal structure was around 1 Å. This is in agreement with our simulations using the same force field that after minimization and equilibration without fixing the heavy atoms, the displacement between the Ca²⁺ atom and the center of mass of the corresponding Ca²⁺ binding loop (d^Ca) changed by δd^Ca ∼0.5 Å for holoCaM, δd^Ca ∼1.0 Å for holoCaM-CaMKII, and δd^Ca ∼1.0–2.1 Å for holoCaM-Ng_13–49. This shift in d^Ca affected the free energy of any Ca²⁺ bound state. For a crude estimation of the free energy differences due to a shift in d^Ca, suppose the average force is 500 kJ/mol/nm, an underestimation of ΔG^holoCaM would be by 6 kcal/mol if δd^Ca = 0.5 Å. Likewise, an underestimate of ΔG^{holoCaM-CaMKII} would be by 12 kcal/mol if δd^Ca = 1 Å. Such deficiency would cause a net underestimation of ΔΔG^{holoCaM-CaMKII} by 6 kcal/mol.

Therefore, we adopted the following strategy in our estimation of ΔΔG: for a system that has experimentally determined structure, such as holoCaM or holoCaM-CaMKII, we fixed the positions of the Ca²⁺ atoms and the backbone heavy atoms during the energy minimization and equilibration simulations; otherwise, for holoCaM-Ng_13–49 which has no experimentally determined structure, we reconstructed the all-atomistic coordinates from coarse-grained models of apoCaM-Ng_13–49 and constrained the positions of the Ca²⁺ ions and the backbone heavy atoms.

We determined the initial positions of the Ca²⁺ ions carefully. We estimated the position of each Ca²⁺ ion as the center of mass of the side chains of the corresponding Ca²⁺ coordinating residues and minimized the potential energy with the all-atomistic AMBER99SB-ILDN force field for optimization. During the energy minimization, only the backbone heavy atoms (excluding Ca²⁺) of holoCaM-Ng_13–49 were constrained. Afterward, 1) there were ∼5–7 oxygen atoms in the loop within 4 Å of each Ca²⁺ ion; 2) later calculation showed that the Ca²⁺ ions at binding site III and IV had average ΔG = −16.0 and −12.8 kcal/mol, respectively. In summary, the final positions of the Ca²⁺ ions of holoCaM-Ng_13–49 in the initial structures were robustly determined. Our results with respect to the sign of the differences in the free energy calculation whether targets are present or not were not affected.

The protonation states of the proteins might matter

ApoCaM is a highly charged protein with a net charge of −24e, where e is the elementary charge. The IDP target peptide Ng_13–49 contains 12 charged residues. Therefore, accurate determination of the partial charges according to the protonation states particularly at the Ca²⁺-binding loops impacts the estimation of the binding free energy of Ca²⁺ for CaM. The standard procedure of assigning protonation states according to a neural pH and its pKa eludes the correct prediction of the actual protonation states for Glu and Asp amino-acids in the Ca²⁺-binding loops of CaM. Therefore, it requires a careful treatment on the protonation states. We employed the H++ program (41) to predict the protonation states based on pH and electrostatic energies that vary with the protein conformation and ionic strength of the solution.

After determining the protonation states of the proteins (complexes) at pH = 7.4 and ionic strength of = 0.15 M using H++ server (41), we found that there was a significant change in the net charges in comparison with the outcome from the standard protonation protocol of the MD package GROMACS (90). In the standard protocol, the Asp and the Glu amino acids in the Ca²⁺-binding are deprotonated at neutral pH and they carry negative charges. However, from the predictions by H++, they are protonated instead. For holoCaM, the newly protonated residues by H++ included D20, D56, E67, D93, and D129 from the Ca²⁺ binding loops I–IV. For holoCaM-CaMKII, the newly protonated residues by H++ included D20, D56, E67, D93, D133, and E140. For holoCaM-Ng_13–49, the results depended on the conformations: most of the protonated residues by H++ included D22, E67, and D93. Because the acetyl groups (-COO⁻) from the Ca²⁺ binding loops stabilize the Ca²⁺-bound state, the numerical estimate of free energies was way off from the experimental values. Once the side chains of these residues in the Ca²⁺ binding loop were adequately protonated, the order of magnitude in Ca²⁺ binding free energy from computer simulations became comparable to the experimentally measured ones (shown in Table 1).

As a comparative study, we explored the robustness of our results by changing the pH from 7.4 to 6.8. According to H++, the protonation states of holoCaM remained the same at the range of pH ∈ [6.9–7.8]. However, at pH ∈ [6.5–6.8], E104 at Ca²⁺ binding loop III was additionally protonated. This changed the net charge of the loop III as well as the charge of the corresponding Ca²⁺ ion. We found that the Ca²⁺ binding free energy of loop III (ΔG) at pH = 6.8 increased by 3.15 kcal/mol comparing to that at pH = 7.4. ΔG for holoCaM-CaMKII remains the same at pH = 6.8 as the protonation states did not change. Therefore, ΔΔG for holoCaM-CaMKII still kept the same negative sign at pH = 6.8 as at pH = 7.4. For holoCaM-Ng₁₃₋₄₉, depending on different structures, the gain of additional protonated residues at pH = 6.8 varied: residues D58, D11 (from Ng) for the first structure, H107 for the second structure, E84 for the third structure, and D95, H107 for the fourth structure. We found that ΔΔG for holoCaM-Ng₁₃₋₄₉ remained the same positive sign at pH = 6.8 as at pH = 7.4. Our results remain robust and can be further tested by experiments.

We provided the calculated ΔΔG values of Ca²⁺ binding site III for both holoCaM-CaMKII and holoCaM-Ng₁₃₋₄₉ in Table S7. When the pH was lowered to 6.8, the ΔΔG values decreased for holoCaM-CaMKII (favoring retaining of the Ca²⁺) and increased for holoCaM-Ng₁₃₋₄₉, (favoring release of Ca²⁺) as illustrated in Fig. S17. The range of pH we explored here is typical for CaM to carry its specific function in a cell. We concluded that our finding is consistently robust with regard to how CaM encodes calcium incidents by binding to distinctive targets.

The charges of the Ca²⁺ ions depend on the environment

It has been shown that the charge on Ca²⁺ can be < +2e due to charge transfer and polarization in the solution and especially in the Ca²⁺-bound state (35, 36, 37). We computed the charges of calcium ions according to the protonation states of CaM by employing a semiempirical quantum chemistry program MOPAC (40). Similar to our previous work (39), we found that the charges on Ca²⁺ ions in holoCaM were approximately in the range of +1.2e to +1.6e. However, we did not rescale the size of the calcium ions in this study, which can be critical to the development of proper effective polarizable force fields for Ca²⁺ according to Jungwirth et al. (36, 38).

Despite those issues, our calculated free energy successfully matched the signs of the experimental values, whereas they differed by an order of magnitude for the holoCaM-Ng₁₃₋₄₉ complexes. By using classical MD simulations, we were able to capture that Ng₁₃₋₄₉ greatly reduces affinity of Ca²⁺ for cCaM whereas CaMKII peptide increases the affinity. More importantly, we provided a molecular mechanism of how the CaMBTs tune CaM’s capacity of sensing Ca²⁺.

The systematic error from the parameters used in steered MD simulations was minimized for the estimation of free energy changes

Computationally, free energy difference can be estimated from equilibrium ensemble using methods including umbrella sampling (44), free energy perturbation (91), and thermodynamic integration (92), as well as from nonequilibrium ensemble by using JE based on nonequilibrium work (51). We employed the nonequilibrium work method by carrying out many steered MD simulations for its simplicity and a particular reaction coordinate is not required. The drawback of this method is that the accuracy is highly dependent on sufficient sampling of the small work (34). Although theoretically JE does not depend on the pathways of pulling when removing Ca²⁺ from its binding site, in practice, pulling along some relevant pathways leads to small work and small variance of the work distribution; while pulling along irrelevant pathways usually yields larger work and larger variance (51). In the latter case, significantly more trajectories are required for ample sampling. Therefore, in several studies, the pulling was only along one or more predetermined pathways repeatedly (52, 93, 94, 95). However, for complex systems, it becomes even more difficult to find the relevant pathways. To solve this problem, we first searched the pathways leading to small work by pulling the Ca²⁺ from each binding site for ∼100 times along randomly generated directions. Second, we increased the number of simulations by pulling along those specific pathways that generate smallest work until the differences in the free energy converges between the direct JE estimation and the CI extrapolation estimation. We minimized the systematic error from sampling by running the simulations until the extrapolation from CI as well as JE converges. The signs of ΔΔG for both systems we studied agreed with the experimental measured ones.

There are other computational studies on the mechanisms of Ca²⁺ releasing/binding in CaM (96, 97) arguing that the deformation of protein structures attributes the discrepancies in the free energy calculation by allowing backbones to sample wide conformations in the pulling simulations (97). Even though the protein conformation can deform during pulling, we argue that this part of the work associated with protein deformation from the course of pulling Ca²⁺ should be part of the free energy calculation according to the concept of the JE: only the initial state and the final state determine the free energy difference.

Conclusions

CaM coordinates the activation of a family of Ca²⁺-regulated proteins that are crucial for synaptic plasticity at the molecular and cellular level associated with learning and memory in neurons (3). Ng is a neural-specific postsynaptic IDP, for which Ca²⁺ decreases binding to CaM (12). Due to the low binding affinity of apoCaM-Ng₁₃₋₄₉ interactions, experimentally it is challenging to determine the bound structures. Our coarse-grained molecular simulations of apoCaM-Ng₁₃₋₄₉ binding guided by experimental measurements demonstrated the importance of conformational flexibility of both the binding partners in various states of the bound complex. Our study revealed that the acidic region of Ng₁₃₋₄₉ (the DDPG residues right before the IQ motif; refer to Fig. 1 for the sequence of Ng₁₃₋₄₉) sticks out into the middle and “pries open” the EF-hand β-scaffold of cCaM. We speculate that this feature of destabilizing Ca²⁺/CaM at low Ca²⁺ concentration could possibly explain CaM in apo-form in the resting cell. CaMKII on the other hand plays a pivotal role in learning and memory formation for both long-term potentiation and mechanisms for the modulation of synaptic efficacy (98). Our study demonstrated that in an apoCaM-Ng₁₃₋₄₉ complex, CaM dominantly remains in an extended conformation. This is in contrast to a canonical bound complex where the two domains of CaM wrap around a rod-like CaMKII peptide that essentially stabilizes the Ca²⁺ binding loops of CaM. The embedded CaMKII peptide by two domains increases the binding affinity of Ca²⁺ to CaM. This proposed mechanism leads to a broader understanding of the reciprocal relation between Ca²⁺/CaM binding and CaM/CaMBT binding (30) that involves major conformational changes in both partners. To the best of our knowledge, this is the first computational study providing a detailed description at atomistic level about how binding of CaM with two distinct targets (Ng and CaMKII) influences the release of Ca²⁺ from cCaM as a molecular underpinning of CaM-dependent Ca²⁺ signaling in neurons, which has been investigated for decades (27, 30, 99, 100). Molecular basis for learning and memory formation has aroused attention of the neuroscience community dating back to 1980s (101). We believe this study allows opportunities to connecting the molecular regulations in atomistic detail to the understanding of cellular process cascade of learning and memory formation.

Author Contributions

M.S.C. and P.Z. designed the research; P.Z., S.T., and H.T. performed the research; P.Z., S.T., and H.T. analyzed data; M.S.C., P.Z., and S.T. wrote the article.

Editor: Michael Feig.

Supporting Citations

References (102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124) appear in the Supporting Material.