Calcium Binding to Calmodulin by Molecular Dynamics with Effective

Nov 3, 2014 - The present study thus opens way to accurate calculations of interactions of calcium and other computationally difficult high-charge-den...
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Calcium Binding to Calmodulin by Molecular Dynamics with Effective Polarization Miriam Kohagen, Martin Lepšík, and Pavel Jungwirth* Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo nam. 2, 16610 Prague 6, Czech Republic S Supporting Information *

ABSTRACT: Calcium represents a key biological signaling ion with the EF-hand loops being its most prevalent binding motif in proteins. We show using molecular dynamics simulations with umbrella sampling that including electronic polarization effects via ionic charge rescaling dramatically improves agreements with experiment in terms of the strength of calcium binding and structures of the calmodulin binding sites. The present study thus opens way to accurate calculations of interactions of calcium and other computationally difficult high-charge-density ions in biological contexts.

SECTION: Biophysical Chemistry and Biomolecules

C

it is less clear how to properly rescale charged amino acid side chains.13 We have shown recently that when combined with a slight readjustment of ionic radii such an approach, which we denote as electronic continuum correction with rescaling (ECCR), quantitatively reproduces the experimental structure of aqueous calcium chloride solution obtained from neutron scattering.10 Here we apply an analogous approach to explore calcium binding to each of the four EF-hand loops of calmodulin with the aim of establishing a computational procedure, which compares favorably to the experiment for Ca2+ binding to the protein. We employ two charge-scaling schemes for the calmodulin EF-hand loops to keep the whole system neutral, either applying a very small scaling just to compensate for the reduced charge on calcium (ECCR) or also rescaling the partial charges on the relevant functional groups of the protein, as suggested in the literature13 (denoted as ECCRP here). Force-field details of these two schemes as well as of standard full-charges simulations performed for comparison14,15 (denoted as “full” below) are given in the Methods section. In addition, Table S3 in the SI provides partial charges on calcium and the coordinating oxygen atoms from electronic structure calculations employing either fitting to the electrostatic potential (RESP) or natural population analysis.8 We see a reasonable agreement among all approaches for the charges on the surrounding oxygen atoms, while for the calcium charge the

alcium dication is a key signaling species in living organisms that is involved in important processes such as muscle contraction, neuronal signal transmission, and others.1 The most abundant calcium binding motif in proteins is a helix−loop−helix structure denoted as the EF-hand.2,3 Within the large family possessing this motif, calmodulin represents the most prevalent calcium-binding messenger protein.4 Calmodulin is able to bind four calcium ions attaching a single Ca2+ to each of its four EF-hand binding sites.5,6 Despite considerable efforts and existing experimental benchmarks on calcium binding to calmodulin EF-hand loops grafted to a CD2 carrier protein,7 the strengths of calcium bindings in calmodulin and structures of the related binding sites are hard to establish computationally.8 This is a demonstration of general problems with the description of interactions between proteins and divalent ions,9 where strong polarization and charge-transfer effects, missing in standard MD force fields, come into play.10,11 Recently, a computationally simple and physically welljustified scheme for including electronic polarization effects for ions in aqueous solutions and in interaction with proteins has been suggested.12,13 The basic idea is to include electronic polarization in a mean-field way via rescaling the ionic charges by the inverse of the electronic part of water dielectric constant, that is, by a factor of 0.75. As a mean-field method, such an approach is applicable to homogeneous media in terms of electronic polarization. Because most organic materials have the electronic part of the dielectric constant around 2, that is, close to the value of 1.78 for water, the method is directly applicable to aqueous solutions of peptides and proteins.13 While the recipe for charge scaling is straightforward for atomic salt ions, © 2014 American Chemical Society

Received: October 2, 2014 Accepted: October 29, 2014 Published: November 3, 2014 3964

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Figure 1. Structure of calcium-containing calmodulin represented by its backbone (middle) taken from the crystal structure (PDB code 1CLL).17 Structure of loops (loop I, upper left-hand side; loop II, upper right-hand side; loop III, lower left-hand side; loop IV, lower right-hand side) are representative snapshots from equilibrium simulations. Calcium ions are colored in orange, carbon atoms in turquoise, oxygen atoms in red, nitrogen atoms in dark blue, and hydrogen atoms in white.

energies from −3.6 to −8.1 kcal/mol, which is even closer to the experiment. The biggest change from ECCR values can be observed for loop I in the absolute values, which has the largest number of charged amino acids (six in total). The ECCR-P value for loop I is thus in a nearly quantitative agreement with the experiment, but the ranking of loops based on calcium affinity is reversed compared with experiment. For both ECCR and ECCR-P, the best agreement with experiment was found for loop III, reproducing the experimental value within the error bars. In Table 1, the results from two other computational studies are presented, too. The results of a force-field MD-based study16 give close to correct results for loops I and III. Loops II and IV are, however, problematic within this approach, which employs a rather unusual combination of a standard nonpolarizable force field and continuum treatment of the solvent.16 Namely, the free-energy values are not negative, which, in principle, means that there would be no calcium binding in these loops. On top of the force-field problems, this could also be partially due to the fact that the authors took the loop geometries from the NMR structure of the whole calmodulin, not allowing for a subsequent structural relaxation of the loops.16 A direct experimental comparison of calcium binding is difficult for an earlier QM-based calculation8 due to limitations of the implicit solvent model for ion solvation and missing entropy effects. Therefore, only relative values with respect to loop I are given in Table 1 for that study.8 Comparing the relative values, loop I binds the strongest, while loops III and IV bind weaker, roughly in line with experiment. A significant difference can be seen for loop II, where the QM-based approach predicts by far the weakest binding, which is, however, not supported by experiment. The aim of the additional equilibrium simulations of the EFhand loops was to investigate the structural influence of the

two electronic structure approaches bracket out the ECCR value. Figure 1 shows the structure of calmodulin with four calcium ions and its four calcium-binding EF-hand loops. The protein has a dumbbell-shaped structure consisting of the N-lobe (loops I and II), the C-lobe (loops III and IV), and the central helix. The amino acid sequences and the corresponding residues are displayed in Table S1 in the SI. The main purpose of this study was to establish computationally reliable values of the free energies of calcium binding to calmodulin EF-hand loops using the charge-scaling approach. Such free energy differences are particularly interesting for force-field validation because they can also be determined experimentally. In Figure 2 the free energy profiles for calcium binding to the four EFhand loops of calmodulin are shown. The comparison of the binding free energy values with experimental data7 and previous calculations8,16 can be found in Table 1. The experimental values were determined for the individually grafted loops into the protein CD2.7 It can be clearly seen that scaling the charges of calcium leads to a much better agreement with experiment compared with the full-charge system, which were, for the sake of comparison, determined only for loops I and IV (Table 1 and Figure 2). The free energies of calcium binding for the full-charge system of loop I and loop IV are −15 and −19 kcal mol−1, respectively (inset of Figure 2). Not only are these values too large, but they also show a reverse relative binding trend compared with experiment. For ECCR, calcium binding is reduced to values ranging from −5.6 to −10.1 kcal mol−1, which are now closer to the experiment and, moreover, correctly predict loop I as the strongest binder. Furthermore, the binding preferences concerning N-lobe versus C-lobe determined from experiment can be reproduced; loops I and II (N-lobe) bind stronger than loops III and IV (C-lobe). Also, scaling the charged groups in the loops (ECCR-P) leads to a span of calcium binding free 3965

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amino acid in position nine (Asn 137, see Table S1 in the SI) and the calcium atom, showing that this oxygen atom temporarily coordinates to the calcium. The other fluctuations in the RMDSs, namely, in loop I for ECCR, in loop II for ECCR-P, and in loop IV for ECCR-P, result from conformational changes of the terminal glutamic acid residue. The higher flexibility also leads to more pronounced switching of the oxygen atoms of the monodentately coordinating carboxyl groups in the coordination shell of calcium. Even a temporary departure of the amino acids on positions three and five of loop I (Asp 22 and Asp 24) from the coordination sphere of calcium can be seen for ECCR and of the amino acid in position three of loop III (Asp 95) for ECCR-P. In addition, the coordination numbers of calcium were calculated. The upper part of Table 2 shows the coordination Table 2. Calcium Coordination Numbers for the Individual Loops Calculated from the Integral of the Radial Distribution Function loop I ECCR ECCR-P full

5.94 6.20 6.69

ECCR ECCR-P full

7.0 7.23 7.83

loop II excluding water 7.03 6.64 7.37 including water 7.04 7.27 7.95

loop III

loop IV

6.10 6.29 6.20

6.18 6.27 6.40

7.16 7.48 7.99

6.97 7.24 7.44

number of calcium considering only the oxygen atoms of the amino acids of the loops. Here the coordination number should be around six compared with the crystal structure,17 which is significantly better reproduced by the scaled than by the fullcharge approach. Bidentate binding of certain aspartic acid side chains, although these ligands normally coordinate only monodentately, can be found in simulations with full charges of loop I (position three; Asp 22), loop II (position one; Asp 56), and loop III (positions three and five; Asp 93 and 95). It is exemplified in a coordination number larger than six (see upper part of Table 2). It was suggested that this instability is due to the limitation of the nonpolarizable force field in describing calcium-containing systems.18 The reason for bidentate binding in the full-charge system may indeed be the too strong electrostatic interactions between the calcium and the oxygen atoms. Our approach based on scaling the calcium charge and thus taking electronic polarization effectively into account in nonpolarizable molecular dynamic simulations circumvents this problem. As a result, coordination numbers for ECCR in Table

Figure 2. Free energy profiles for ECCR (continuous lines) and ECCR-P (dashed lines) of the N-lobe (upper panel) and of the C-lobe (lower panel). Insets show free energy profiles for full charges for loop I (inset upper panel) and loop IV (inset lower panel).

charge scaling. The root-mean-square displacement (RMSD) for the backbone of the loops with respect to the crystal structure can be found in the SI (Figure S1). All setups led to stable loops on the simulation time scale. In general, the fluctuations in the ECCR and ECCR-P setups were slightly larger than those for the full charge system. The increased rigidity of the full-charge system correlates with stronger binding of calcium as compared with the charge-scaling approaches (see Table 1). The largest fluctuations in the RMSD can be seen for loop IV. For ECCR, these fluctuations correlate with the distance between the carbonyl oxygen of the

Table 1. Free Energies of Calcium Binding (in kcal/mol) from the Present Simulations, ECCR, ECCR-P, and Full (Loops I and IV), from Experiment and from Two Previous Calculationsa ECCR ECCR-P full ref 16 (theor.) ref 8 (theor.) ref 7 (exp.)

loop I

loop II

loop III

loop IV

−10.1 ± 1 −3.6 ± 1 −15 ± 1 −5.4 ± 2.9 0.0 −5.32 ± 0.07

−9.3 ± 1 −8.1 ± 1 n.d. 0.0 ± 1.9 22.9 −4.63 ± 0.03

−5.6 ± 1 −5.7 ± 1 n.d. −2.3 ± 1.5 2.5 −4.58 ± 0.04

−6.7 ± 1 −7.2 ± 1 −19 ± 1 4.2 ± 0.8 5.9 −4.05 ± 0.12

a

Results from ref 16 are MD-based, while results from ref 8 are based on quantum chemical (QM) calculations. Data from Ref 8 are given as relative values with respect to loop I. 3966

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coordination numbers for the full-charge system are slightly lower than the corresponding values for the isolated loops but are still too high. There is less bidentate binding present, indicating that the geometries of the loops are more stable in the complete protein than in isolated loops. As for the individual loop II, also in the case of the simulations of the whole calmodulin, in the full-charge system the additional coordination of the amino acid in position nine of loop II (Asp 64) can also be observed; see the upper part of Table 3. In contrast, this additional coordination was not observed for the ECCR or ECCR-P systems, indicating that it may by an artifact of the full charges, which is essentially preserved upon moving from individual loops to the whole protein. In summary, we have shown here that interactions of calcium with the EF-hand motifs of calcium-binding protein calmodulin can be accurately described using a computationally efficient approach based on accounting for polarization effects via ionic charge rescaling. As a matter of fact, this simple but physically well-justified correction brings the binding energies of calcium to a practically quantitative agreement with experiment, particularly keeping in mind that the measured system of EFhand loops grafted on a carrier protein may differ slightly in calcium binding properties from the original calmodulin molecule. On top of calcium binding, charge scaling also reproduces better experimental structural characteristics of the individual EF-hand loops and the whole calmodulin molecule than standard nonpolarizable force fields. An open question remains how to scale best also the charged groups on the protein. The present calculations employing either scaling or practically not scaling the charges on the protein show that the results are quantitatively sensitive but qualitatively robust with respect to details of the scaling procedure. The present approach thus opens way to quantitative evaluations of the strengths and structural aspects of calcium binding in various biologically relevant protein contexts involving this key signaling ion.

2 (upper part) are well around six. Only loop II is an exception showing a coordination number of 7. This is due to the amino acid in position nine (Asp 64), which can also interact with the calcium ion. The lower part of Table 2 includes the coordination numbers, which also take the oxygen atoms of the water into account. One water molecule should coordinate, resulting in a total coordination number of around seven for scaled charges. For the full-charge approach, the corresponding coordination numbers are closer to eight, which can be explained by the bidentate binding of certain Asp residues or by temporary binding of two water molecules, both of which actually occur. In addition to the calculations of the isolated EF-hand loops, we also performed simulations of the whole calmodulin to see how the calcium charge scaling influences the structure of the protein. There have been several computational studies done on calmodulin in water with different concentrations of ions in the surrounding electrolyte.18−23 These nonpolarizable (full charge) simulations focus mainly on the general structure of the calmodulin, whereas a closer look at the coordination of the calcium ions in the loops was not presented. We evaluated the root-mean-square displacement (RMSD) for the backbones of the N-lobe (loops I and II), C-lobe (loops III and IV), and the connecting helix with reference to the crystal structure (Figure S2 in the SI). Whereas for ECCR calmodulin is stable and does not undergo structural changes, for ECCR-P, loop IV tends to lose its calcium. This can be seen in the increase in the RMSD of the C-lobe at ∼10 ns. A reason for this may be that with the additional scaling of the charged groups of the amino acids the balance between the favorable electrostatic interactions of the ligands with the calcium ion and the repulsion of the carboxylic groups toward each other has been disrupted. This only shows up in the simulation of the whole protein because the cooperativity between sites comes into play24 and the effect cannot be counterbalanced by a rearrangement of the loop amino acids, which are constrained by the rest of the protein. The other three loops are stable and do not show signs of rearrangements. The RMSD of the central helix is also presented (see Figure S2 in the SI). The peaks of the full-charge system and ECCR result from bending and temporary slight unwinding. This has been observed before in simulations18,20,23 as well as experiments, namely, NMR25 and single-molecule resonance energy transfer26 studies. For the whole calmodulin, the calcium coordination numbers for ECCR fit very well those deduced from the crystal structure, that is, six excluding water (Table 3, upper part) and seven with water (Table 3, lower part). The only exception is the higher coordination number of loop II, which is due to wiggling of the carboxyl group of the amino acid in position 1 (Asp 56). The

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METHODS Classical molecular dynamics (MD) simulations in this study were carried out using the Gromacs (version 4.6.5) program package.27 Starting geometries of calmodulin and its loops (all calcium-containing structures) were taken from the protein database (PDB code 1CLL17), known as the extended or dumbbell structure. Two different setups were prepared: (i) the whole calmodulin molecule and (ii) the four individual EFhand loops. The loops and the whole protein were solvated in SPC/E water28 containing 150 mM of KCl. The parameters for the ions, namely, potassium, chloride, and calcium, can be found in Table 4. The C-termini of the loop ends were capped Table 4. Parameters for the Ions

Table 3. Calcium Coordination Numbers for the Whole Calmodulin Calculated from the Integral of the Radial Distribution Function loop I ECCR full

6.00 6.18

ECCR full

7.01 7.46

loop II excluding water 6.54 7.01 including water 7.62 7.40

σ (Å)

ϵ (kJ/mol)

charge (e)

0.5072 0.5072

+1.5 +2.0

0.4184 0.4184

−0.75 −1.0

0.41868 0.41868

+0.75 +1.0

Ca

loop III

loop IV

ECCR10 full14

2.5376 2.8196

6.04 6.40

5.94 6.28

ECCR10 full14

3.7824 4.4499

7.10 7.91

6.95 7.30

ECCR40 full15

3.154 3.154

Cl

K

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by N-methyl amide (NME) groups and the N-termini by Nacetyl (ACE) groups. The parameters for the amino acids were taken from the ff03 force field.29 The mixed Lennard−Jones parameters were derived from self-parameters using Lorentz− Berthelot mixing rules. Bonds containing hydrogen atoms were constrained via the Lincs algorithm,30 which allowed for a time step of 2 fs. In all cases, 3D periodic boundary conditions were employed. The electrostatic and van der Waals interactions were truncated at 12 Å, and the long-range electrostatic interactions were accounted for by the particle mesh Ewald method.31 For the equilibrium calculations of the isolated loops and the whole protein, two minimizations steps, one with the solute and only water and the second one also containing potassium and chloride ions, were performed. These were followed by a 10 ns equilibration applying Berendsen barostat32 (coupling constant of 0.5 ps) fixed to a pressure of 1 bar and the velocity rescaling thermostat33 (coupling constant of 0.5 ps) fixed to a temperature of 310 K. For the 60 ns long production run the Parrinello−Rahman barostat34 with a coupling time of 0.5 ps was used. For all free-energy calculations, preceding the initial pull simulations from which the input structures for the umbrella windows were taken, equilibrium calculations with a duration of 10 ns and with translational and rotational constraints on the loop were performed. The pull rate for the initial pulling was 0.000196 Å/ps, and the force constant for the pulling was 10 kJ mol−1 Å−2. The reaction coordinate was the distance between the center of mass of the oxygen atoms coordinating the calcium plus the noncoordinating oxygen atoms of the corresponding carboxyl groups (e. g., atoms one to nine of loop I in Figure 3) and the calcium ion. This was done to take

chosen if the histograms did not overlap sufficiently. The simulations in each umbrella window were between 25 and 40 ns long. The free-energy profiles, calculated using the weighted histogram analysis method (WHAM), as well as the error estimates, determined from a bootstrap analysis based on generating bootstrapped trajectories from the umbrella histograms, were done according to ref 35. The free energy profiles were corrected for volume entropy by the factor of 2kBT ln(r),36 where kB is the Boltzmann constant, T is the temperature, and r is the reaction coordinate. Effectively, the calculated free energies thus assume analogous standard state as the experiment,37 which enables direct comparison (Table 1). We tested three different charge distributions on the loop. For the systems denoted as “full” all partial charges were taken from the ff03 force field without any changes. For systems abbreviated as “ECCR”, the charges on the ions were scaled by 0.75, which results in a charge of +1.5 e for the calcium ions.10 To restore neutrality, the charges on the coordinating oxygen atoms and the non-coordinating oxygen atoms of the corresponding carboxyl-groups were increased slightly (the largest increase being by 0.0625 e). The corresponding partial charges can be found in Table S2 in the SI. In the third setup, denoted as ECCR-P, not only were the ionic charges scaled by 0.75 but also the atoms of the carboxyl and amino groups of the loops and, in the case of the simulations of the whole protein, of all carboxyl and amino groups, were scaled by the same factor following refs 12, 38, and 39. By not scaling other partial charges on the protein we avoid compromising the integrity and internal consistency of the employed force field in any significant way. The corresponding partial charges on the amino acids in the loops can be found again in Table S2 in the SI.

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ASSOCIATED CONTENT

* Supporting Information S

Amino acid sequences and the corresponding residues and a detailed list of the employed partial charges on the amino acids. Root-mean-square displacements of the backbones of the individual loops and of the whole protein. Results of a natural bond orbital (NBO) analysis and a restrained electrostatic potential (RESP) fit for the calcium ions and the coordination oxygen atoms of loop I. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

Figure 3. Structure of loop I with only calcium (in orange) and coordinating residues shown (carbon atoms in turquoise, oxygen atoms in red, nitrogen atoms in dark blue, and hydrogen atoms in white). Numbering indicates atoms used for the definition of the reaction coordinate.

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ACKNOWLEDGMENTS This work was supported by the Czech Science Foundation (grant number P208/12/G016) and the Czech Ministry of Education (grant number LH12001). P.J. acknowledges the Academy of Sciences for the Praemium Academiae award. M.K. acknowledges funding within the framework of the IOCB Postdoctoral Project program. Allocation of computer time from the National supercomputing center IT4Innovations in Ostrava is highly appreciated.

into account switching of the coordination of the two oxygen atoms of a given carboxyl group to calcium. For the full-charge system 19 initial structures from the initial pull run were chosen, the first five with a distance of 1 Å, which was increased to 1.5 Å for the remaining structures. For the scaled charges, 13 initial structures from the initial pull simulation were taken, the first six with a difference of 1 Å, which was again increased to 1.5 Å for the remainder. Additional umbrella windows were

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REFERENCES

(1) Clapham, D. E. Calcium Signaling. Cell 2007, 131, 1047−1058.

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Mechanism in Calmodulin-Mediated Signal Transduction. Structure 2008, 16, 736−746. (26) Slaughter, B. D.; Allen, M. W.; Unruh, J. R.; Bieber Urbauer, R. J.; Johnson, C. K. Single-Molecule Resonance Energy Transfer and Fluorescence Correlation Spectroscopy of Calmodulin in Solution. J. Phys. Chem. B 2004, 108, 10388−10397. (27) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435−447. (28) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987, 91, 6269−6271. (29) Duan, Y.; Wu, C.; Chowdhury, S.; Lee, M. C.; Xiong, G.; Zhang, W.; Yang, R.; Cieplak, P.; Luo, R.; Lee, T.; et al. A Point-Charge Force Field for Molecular Mechanics Simulations of Proteins Based on Condensed-Phase Quantum Mechanical Calculations. J. Comput. Chem. 2003, 24, 1999−2012. (30) Hess, B.; Bekker, H.; Berendsen, H. J. C.; Fraaije, J. G. E. M. LINCS: A Linear Constraint Solver for Molecular Simulations. J. Comput. Chem. 1997, 18, 1463−1472. (31) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A Smooth Particle Mesh Ewald Method. J. Chem. Phys. 1995, 103, 8577−8593. (32) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. Molecular Dynamics with Coupling to an External Bath. J. Chem. Phys. 1984, 81, 3684−3690. (33) Bussi, G.; Donadio, D.; Parrinello, M. Canonical Sampling through Velocity Rescaling. J. Chem. Phys. 2007, 126, 014101. (34) Parrinello, M.; Rahman, A. Polymorphic Transitions in SingleCrystals − a New Molecular-Dynamics Method. J. Appl. Phys. 1981, 52, 7182−7190. (35) Hub, J. S.; de Groot, B. L.; van der Spoel, D. g_wham - A Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation Estimates. J. Chem. Theory Comput. 2010, 6, 3713−3720. (36) Timko, J.; De Castro, A.; Kuyucak, S. Ab Initio Calculation of the Potential of Mean Force for Dissociation of Aqueous Ca−Cl. J. Chem. Phys. 2011, 134, 204510. (37) Zhou, H.-X.; Gilson, M. K. Theory of Free Energy and Entropy in Noncovalent Binding. Chem. Rev. 2009, 109, 4092−4107. (38) Leontyev, I. V.; Stuchebrukhov, A. A. Electronic Continuum Model for Molecular Dynamics Simulations of Biological Molecules. J. Chem. Theory Comput. 2010, 6, 1498−1508. (39) Leontyev, I. V.; Stuchebrukhov, A. A. Polarizable Molecular Interactions in Condensed Phase and Their Equivalent Nonpolarizable Models. J. Chem. Phys. 2014, 141, 014103. (40) Mason, P. E.; Wernersson, E.; Jungwirth, P. Accurate Description of Aqueous Carbonate Ions: an Effective Polarization Model Verified by Neutron Scattering. J. Phys. Chem. B 2012, 116, 8145−8153.

(2) Gifford, J. L.; Walsh, M. P.; Vogel, H. J. Structures and Metal-IonBinding Properties of the Ca2+-Binding Helix-Loop-Helix EF-Hand Motifs. Biochem. J. 2007, 405, 199−221. (3) Chazin, W. J. Relating Form and Function of EF-Hand Calcium Binding Proteins. Acc. Chem. Res. 2011, 44, 171−179. (4) Sorensen, A. B.; Sondergaard, M. T.; Overgaard, M. T. Calmodulin in a Heartbeat. FEBS J. 2013, 280, 5511−5532. (5) Lewit−Bentley, A.; Rety, S. EF-Hand Calcium-Binding Proteins. Curr. Opin. Struct. Biol. 2000, 10, 637−643. (6) Tidow, H.; Nissen, P. Structural Diversity of Calmodulin Binding to Its Targets Sites. FEBS J. 2013, 280, 5551−5565. (7) Ye, Y.; Lee, H.-W.; Yang, W.; Shealy, S.; Yang, J. J. Probing SiteSpecific Calmodulin Calcium and Lanthanide Affinity by Grafting. J. Am. Chem. Soc. 2005, 127, 3743−3750. (8) Lepsik, M.; Field, M. J. Binding of Calcium and Other Metal Ions to the EF-Hand Loops of Calmodulin Studied by Quantum Chemical Calculations and Molecular Dynamics Simulations. J. Phys. Chem. B 2007, 111, 10012−10022. (9) Dudev, T.; Lim, C. Principles Governing Mg, Ca, and Zn Binding and Selectivity in Proteins. Chem. Rev. 2003, 103, 773−787. (10) Kohagen, M.; Mason, P. E.; Jungwirth, P. Accurate Description of Calcium Solvation in Concentrated Aqueous Solutions. J. Phys. Chem. B 2014, 118, 7902−7909. (11) Mamatkulov, S.; Fyta, M.; Netz, R. R. Force Fields for Divalent Cations Based on Single-Ion and Ion-Pair Properties. J. Chem. Phys. 2013, 138, 024505. (12) Leontyev, I.; Stuchebrukhov, A. Accounting for Electronic Polarization in Non-Polarizable Force Fields. Phys. Chem. Chem. Phys. 2011, 13, 2613−2626. (13) Leontyev, I. V.; Stuchebrukhov, A. A. Polarizable Mean-Field Model of Water for Biological Simulations with AMBER and CHARMM Force Fields. J. Chem. Theory Comput. 2012, 8, 3207− 3216. (14) Dang, L. X.; Smith, D. E. Comment on Mean Force Potential for the Calcium−Chloride Ion Pair in Water. J. Chem. Phys. 1993, 99, 4229; J. Chem. Phys. 1995, 102, 3483−3484. (15) Chang, T.-M.; Dang, L. X. Detailed Study of Potassium Solvation Using Molecular Dynamics Techniques. J. Phys. Chem. B 1999, 103, 4714−4720. (16) Chen, C.; Huang, Y.; Jiang, X.; Xiao, Y. Binding Free-Energy Calculation of an Ion-Peptide Complex by Constrained Dynamics. Phys. Rev. E 2013, 87, 062705. (17) Chattopadhyaya, R.; Meador, W. E.; Means, A. R.; Quiocho, F. A. Calmodulin Structure Refined at 1.7 Å Resolution. J. Mol. Biol. 1992, 228, 1177−1192. (18) Fiorin, G.; Biekofsky, R. R.; Pastore, A.; Carloni, P. Unwinding the Helical Linker of Calcium-Loaded Calmodulin: a Molecular Dynamics Study. Proteins 2005, 61, 829−839. (19) Project, E.; Friedman, R.; Nachliel, E.; Gutman, M. A Molecular Dynamics Study of the Effect of Ca2+ Removal on Calmodulin Structure. Biophys. J. 2005, 90, 3842−3850. (20) Shepherd, C. M.; Vogel, H. J. A Molecular Dynamics Study of Ca2+-Calmodulin: Evidence of Interdomain Coupling and Structural Collapse on the Nanosecond Timescale. Biophys. J. 2004, 87, 780− 791. (21) Komeiji, Y.; Ueno, Y.; Uebayasi, M. Molecular Dynamics Simulations Revealed Ca2+-Dependent Conformational Change of Calmodulin. FEBS Lett. 2002, 521, 133−139. (22) Yang, C.; Jas, G. S.; Kuczera, K. Structure and Dynamics of Calcium-Activated Calmodulin in Solution. J. Biomol. Struct. Dyn. 2001, 19, 247−271. (23) Aykut, A. O.; Atilgan, A. R.; Atilgan, C. Designing Molecular Dynamics Simulations to Shift Populations of the Conformational States of Calmodulin. PLOS Comput. Biol. 2013, 9, e1003366. (24) Linse, S.; Helmersson, A.; Forsen, S. Calcium Binding to Calmodulin and Its Globular Domains. J. Biol. Chem. 1991, 266, 8050−8054. (25) Gsponer, J.; Christodoulou, J.; Cavalli, A.; Bui, J. M.; Richter, B.; Dobson, C. M.; Vendruscolo, M. A Coupled Equilibrium Shift 3969

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