Molecular dynamics simulations of a calmodulin-peptide complex in solution

We have performed an 4-ns MD simulation of calmodulin complexed with a target peptide in explicit water, under realistic conditions of constant temperature and pressure, in the presence of a physiological concentration of counterions and using Ewald summation to avoid truncation of long-range electrostatic forces. During the simulation the system tended to perform small fluctuations around a structure similar to, but somewhat looser than the starting crystal structure. The calmodulin-peptide complex was quite rigid and did not exhibit any large amplitude domain motions such as previously seen in apo- and calcium-bound calmodulin. We analyzed the calmodulin-peptide interactions by calculating buried surface areas, CHARMM interaction energies and continuum model interaction free energies. In the trajectory, the protein surface area buried by contact with the peptide is 1373 A(2) approximately evenly divided between the calmodulin N-terminal, C-terminal and central linker regions. A majority of this buried surface, 803 A(2), comes from nonpolar residues, in contrast to the protein as a whole, for which the surface is made up of mostly polar and charged groups. Our continuum calculations indicate that the largest favorable contribution to peptide binding comes from burial of molecular surface upon complex formation. Electrostatic contributions are favorable but smaller in the trajectory structures, and actually unfavorable for binding in the crystal structure. Since nonpolar groups make up most of buried surface of the protein, our calculations suggest that the hydrophobic effect is the main driving force for binding the helical peptide to calmodulin, consistent with thermodynamic analysis of experimental data. Besides the burial of nonpolar surface area, secondary contributions to peptide binding come from burial of polar surface and electrostatic interactions. In the nonpolar interactions a crucial role is played by the nine methionines of calmodulin. In the electrostatic interactions the negatively charged protein residues and positively charged peptide residues play a dominant role.     

Molecular Dynamics Simulations of a Calmodulin-peptide Complex in Solution

Abstract

We have performed an 4-ns MD simulation of calmodulin complexed with a target peptide in explicit water, under realistic conditions of constant temperature and pressure, in the presence of a physiological concentration of counterions and using Ewald summation to avoid truncation of long-range electrostatic forces. During the simulation the system tended to perform small fluctuations around a structure similar to, but somewhat looser than the starting crystal structure. The calmodulin-peptide complex was quite rigid and did not exhibit any large amplitude domain motions such as previously seen in apo- and calcium-bound calmodulin. We analyzed the calmodulin-peptide interactions by calculating buried surface areas, CHARMM interaction energies and continuum model interaction free energies. In the trajectory, the protein surface area buried by contact with the peptide is 1373 Ų, approximately evenly divided between the calmodulin N-terminal, C-terminal and central linker regions. A majority of this buried surface, 803 ·A², comes from nonpolar residues, in contrast to the protein as a whole, for which the surface is made up of mostly polar and charged groups. Our continuum calculations indicate that the largest favorable contribution to pep- tide binding comes from burial of molecular surface upon complex formation. Electrostatic contributions are favorable but smaller in the trajectory structures, and actually unfavorable for binding in the crystal structure. Since nonpolar groups make up most of buried surface of the protein, our calculations suggest that the hydrophobic effect is the main driving force for binding the helical peptide to calmodulin, consistent with thermodynamic analysis of experimental data. Besides the burial of nonpolar surface area, secondary contributions to peptide binding come from burial of polar surface and electrostatic interactions. In the nonpolar interactions a crucial role is played by the nine methionines of calmodulin. In the electrostatic interactions the negatively charged protein residues and positively charged peptide residues play a dominant role.     

Electrostatic contribution of surface charge residues to the stability of a thermophilic protein: benchmarking experimental and predicted pKa values

Optimization of the surface charges is a promising strategy for increasing thermostability of proteins. Electrostatic contribution of ionizable groups to the protein stability can be estimated from the differences between the pKa values in the folded and unfolded states of a protein. Using this pKa-shift approach, we experimentally measured the electrostatic contribution of all aspartate and glutamate residues to the stability of a thermophilic ribosomal protein L30e from Thermococcus celer. The pKa values in the unfolded state were found to be similar to model compound pKas. The pKa values in both the folded and unfolded states obtained at 298 and 333 K were similar, suggesting that electrostatic contribution of ionizable groups to the protein stability were insensitive to temperature changes. The experimental pKa values for the L30e protein in the folded state were used as a benchmark to test the robustness of pKa prediction by various computational methods such as H++, MCCE, MEAD, pKD, PropKa, and UHBD. Although the predicted pKa values were affected by crystal contacts that may alter the side-chain conformation of surface charged residues, most computational methods performed well, with correlation coefficients between experimental and calculated pKa values ranging from 0.49 to 0.91 (p<0.01). The changes in protein stability derived from the experimental pKa-shift approach correlate well (r = 0.81) with those obtained from stability measurements of charge-to-alanine substituted variants of the L30e protein. Our results demonstrate that the knowledge of the pKa values in the folded state provides sufficient rationale for the redesign of protein surface charges leading to improved protein stability.     

Protein stability and electrostatic interactions between solvent exposed charged side chains

To investigate the contribution to protein stability of electrostatic interactions between charged surface residues, we have studied the effect of substituting three negatively charged solvent exposed residues with their side-chain amide analogs in bovine calbindin D9k--a small (Mr 8,500) globular protein of the calmodulin superfamily. The free energy of urea-induced unfolding for the wild-type and seven mutant proteins has been measured. The mutant proteins have increased stability towards unfolding relative to the wild-type. The experimental results correlate reasonably well with theoretically calculated relative free energies of unfolding and show that electrostatic interactions between charges on the surface of a protein can have significant effects on protein stability.     

Predicting the rate enhancement of protein complex formation from the electrostatic energy of interaction

The rate of association of proteins is dictated by diffusion, but can be enhanced by favorable electrostatic forces. Here the relationship between the electrostatic energy of interaction, and the kinetics of protein-complex formation was analyzed for the protein pairs of: hirudin-thrombin, acetylcholinesterase-fasciculin and barnase-barstar, and for a panel of point mutants of these proteins. Electrostatic energies of interaction were calculated as the difference between the electrostatic energy of the complex and the sum of the energies of the two individual proteins, using the computer simulation package DelPhi. Calculated electrostatic energies of interaction were compared to experimentally determined rates of association. One kcal/mol of Coulombic interaction energy increased the rate of association by a factor of 2.8, independent of the protein-complex or mutant analyzed. Electrostatic energies of interaction were also determined from the salt dependence of the association rate constant, using the same basic equation as for the theoretical calculation. A Br?nsted analysis of the electrostatic energies of interactions plotted versus experimentally determined ln(rate)s of association shows a linear relation between the two, with a beta value close to 1. This is interpreted as the energy of the transition state varies according to the electrostatic interaction energy, fitting a two state model for the association reaction. Calculating electrostatic rate enhancement from the electrostatic interaction energy can be used as a powerful tool to design protein complexes with altered rates of association and affinities.     

Protein stabilization by salt bridges: concepts, experimental approaches and clarification of some misunderstandings

Salt bridges in proteins are bonds between oppositely charged residues that are sufficiently close to each other to experience electrostatic attraction. They contribute to protein structure and to the specificity of interaction of proteins with other biomolecules, but in doing so they need not necessarily increase a protein's free energy of unfolding. The net electrostatic free energy of a salt bridge can be partitioned into three components: charge-charge interactions, interactions of charges with permanent dipoles, and desolvation of charges. Energetically favorable Coulombic charge-charge interaction is opposed by often unfavorable desolvation of interacting charges. As a consequence, salt bridges may destabilize the structure of the folded protein. There are two ways to estimate the free energy contribution of salt bridges by experiment: the pK(a) approach and the mutation approach. In the pK(a) approach, the contribution of charges to the free energy of unfolding of a protein is obtained from the change of pK(a) of ionizable groups caused by altered electrostatic interactions upon folding of the protein. The pK(a) approach provides the relative free energy gained or lost when ionizable groups are being charged. In the mutation approach, the coupling free energy between interacting charges is obtained from a double mutant cycle. The coupling free energy is an indirect and approximate measure of the free energy of charge-charge interaction. Neither the pK(a) approach nor the mutation approach can provide the net free energy of a salt bridge. Currently, this is obtained only by computational methods which, however, are often prone to large uncertainties due to simplifying assumptions and insufficient structural information on which calculations are based. This state of affairs makes the precise thermodynamic quantification of salt bridge energies very difficult. This review is focused on concepts and on the assessment of experimental methods and does not cover the vast literature.     

The role of electrostatic interactions in the process of diffusional encounter and docking of electron transport proteins

Electrostatic interaction of plastocyanin and cytochrome f in the process of protein–protein complex formation was investigated by computer simulation methods. It was shown that long-range electrostatic interaction promotes energetically favorable mutual orientation of protein molecules at distances between their cofactors shorter than 5 nm. At distances shorter than 3 nm, these electrostatic interactions lead to a significantly detectable increase in the rate of convergence of the cofactors.     

Electrostatic contributions to the stability of hyperthermophilic proteins.

Electrostatic contributions to the folding free energy of several hyperthermophilic proteins and their mesophilic homologs are calculated. In all the cases studied, electrostatic interactions are more favorable in the hyperthermophilic proteins. The electrostatic free energy is found not to be correlated with the number of ionizable amino acid residues, ion pairs or ion pair networks in a protein, but rather depends on the location of these groups within the protein structure. Moreover, due to the large free energy cost associated with burying charged groups, buried ion pairs are found to be destabilizing unless they undergo favorable interactions with additional polar groups, including other ion pairs. The latter case involves the formation of stabilizing ion pair networks as is observed in a number of proteins. Ion pairs located on the protein surface also provide stabilizing interactions in a number of cases. Taken together, our results suggest that many hyperthermophilic proteins enhance electrostatic interactions through the optimum placement of charged amino acid residues within the protein structure, although different design strategies are used in different cases. Other physical mechanisms are also likely to contribute, however optimizing electrostatic interactions offers a simple means of enhancing stability without disrupting the core residues characteristic of different protein families.     

Automated computational framework for the analysis of electrostatic similarities of proteins

Charge plays an important role in protein-protein interactions. In the case of excessively charged proteins, their electrostatic potentials contribute to the processes of recognition and binding with other proteins or ligands. We present an automated computational framework for determining the contribution of each charged amino acid to the electrostatic properties of proteins, at atomic resolution level. This framework involves computational alanine scans, calculation of Poisson-Boltzmann electrostatic potentials, calculation of electrostatic similarity distances (ESDs), hierarchical clustering analysis of ESDs, calculation of solvation free energies of association, and visualization of the spatial distributions of electrostatic potentials. The framework is useful to classify families of mutants with similar electrostatic properties and to compare them with the parent proteins in the complex. The alanine scan mutants introduce perturbations in the local electrostatic properties of the proteins and aim in delineating the contribution of each mutated amino acid in the spatial distribution of electrostatic potential, and in biological function when electrostatics is a dominant contributing factor in protein-protein interactions. The framework can be used to design new proteins with tailored electrostatic properties, such as immune system regulators, inhibitors, and vaccines, and in guiding experimental studies. We present an example for the interaction of the immune system protein C3d (the d-fragment of complement protein C3) with its receptor CR2, and we discuss our data in view of a binding site controversy.     

Modelling of lysozyme binding to a cation exchange surface at atomic detail: the role of flexibility

Different approaches were made to predict the adsorbed orientation based on rigid, flexible, or a mixture of both models. To determine the role of flexibility during adsorption, the orientation of lysozyme adsorbed to a negatively charged ligand surface was predicted by a rigid and a flexible model based on two differing protein structures at atomic resolution. For the rigid model, the protein structures were placed at different distances from the ligand surface and the electrostatic interaction energy was calculated for all possible orientations. The results were compared to a flexible model where the binding to the ligand surface was modeled by multiple molecular dynamics simulations starting with 14 initial orientations. Different aspects of the adsorption process were not covered by the rigid model and only detectable by the flexible model. Whereas the results of the rigid model depended sensitively on the protein-surface distance and the protein structure, the preferred orientation obtained by the flexible model was closer to a previous experimental determined orientation, robust toward the initial orientation and independent of the initial protein structure. Additionally, it was possible to obtain insights into the preferred binding process of lysozyme on a negatively charged surface by the flexible model.     

Do electrostatic interactions destabilize protein–nucleic acid binding?

The negatively charged phosphates of nucleic acids are often paired with positively charged residues upon binding proteins. It was thus counter-intuitive when previous Poisson-Boltzmann (PB) calculations gave positive energies from electrostatic interactions, meaning that they destabilize protein-nucleic acid binding. Our own PB calculations on protein-protein binding have shown that the sign and the magnitude of the electrostatic component are sensitive to the specification of the dielectric boundary in PB calculations. A popular choice for the boundary between the solute low dielectric and the solvent high dielectric is the molecular surface; an alternative is the van der Waals (vdW) surface. In line with results for protein-protein binding, in this article, we found that PB calculations with the molecular surface gave positive electrostatic interaction energies for two protein-RNA complexes, but the signs are reversed when the vdW surface was used. Therefore, whether destabilizing or stabilizing effects are predicted depends on the choice of the dielectric boundary. The two calculation protocols, however, yielded similar salt effects on the binding affinity. Effects of charge mutations differentiated the two calculation protocols; PB calculations with the vdW surface had smaller deviations overall from experimental data.     

Dynamic arrangement of ion pairs and individual contributions to the thermal stability of the cofactor-binding domain of glutamate dehydrogenase from Thermotoga maritima

The dynamics of a hyperthermophilic protein fragment in a water environment, as studied by performing molecular dynamics (MD) simulations at various temperatures, is compared to the dynamical behavior of a homologous mesophilic protein simulated under identical conditions. The effects on the stability of the spatial arrangement and mobility of the charged residues in solution were quantified by calculating free energy changes upon salt bridge formation in these proteins. Electrostatic free energy terms derived from a thermodynamic cycle were obtained by solving the linearized Poisson-Boltzmann equation for a series of protein conformations generated by MD simulations and placed subsequently in a continuum solvent medium. Our results show that the ion pairs are electrostatically stabilizing in most of the cases, but their individual contributions vary significantly. The greater contribution of the charged residues to the stability of the hyperthermophilic protein as compared with the mesophilic counterpart was evidenced only by the calculations that included conformations sampled at 343 and 373 K. The "dynamic" structure of the hyperthermophilic protein fragment simulated at elevated temperatures reveals an optimum placement of the ionizable residues within the protein structure as well as the role of their cooperative interactions in promoting thermal stability. The thermodynamic properties such as electrostatic free energy differences, configurational entropies, and specific heat capacities calculated in the dynamic context of the protein structure provided new insight into the mechanism of protein thermostabilization.     

Prediction of Protein-Protein Interaction Sites Using Electrostatic Desolvation Profiles

Protein-protein complex formation involves removal of water from the interface region. Surface regions with a small free energy penalty for water removal or desolvation may correspond to preferred interaction sites. A method to calculate the electrostatic free energy of placing a neutral low-dielectric probe at various protein surface positions has been designed and applied to characterize putative interaction sites. Based on solutions of the finite-difference Poisson equation, this method also includes long-range electrostatic contributions and the protein solvent boundary shape in contrast to accessible-surface-area-based solvation energies. Calculations on a large set of proteins indicate that in many cases (>90%), the known binding site overlaps with one of the six regions of lowest electrostatic desolvation penalty (overlap with the lowest desolvation region for 48% of proteins). Since the onset of electrostatic desolvation occurs even before direct protein-protein contact formation, it may help guide proteins toward the binding region in the final stage of complex formation. It is interesting that the probe desolvation properties associated with residue types were found to depend to some degree on whether the residue was outside of or part of a binding site. The probe desolvation penalty was on average smaller if the residue was part of a binding site compared to other surface locations. Applications to several antigen-antibody complexes demonstrated that the approach might be useful not only to predict protein interaction sites in general but to map potential antigenic epitopes on protein surfaces.     

Interactions of calmodulin with death-associated protein kinase peptides: experimental and modeling studies

We have studied the interactions between calmodulin (CaM) and three target peptides from the death-associated protein kinase (DAPK) protein family using both experimental and modeling methods, aimed at determining the details of the underlying biological regulation mechanisms. Experimentally, calorimetric binding free energies were determined for the complexes of CaM with peptides representing the DAPK2 wild-type and S308D mutant, as well as DAPK1. The observed affinity of CaM was very similar for all three studied peptides. The DAPK2 and DAPK1 peptides differ significantly in sequence and total charge, while the DAPK2 S308D mutant is designed to model the effects of DAPK2 Ser308 phosphorylation. The crystal structure of the CaM-DAPK2 S308D mutant peptide is also reported. The structures of CaM-DAPK peptide complexes present a mode of CaM-kinase interaction, in which bulky hydrophobic residues at positions 10 and 14 are both bound to the same hydrophobic cleft. To explain the microscopic effects underlying these interactions, we performed free energy calculations based on the approximate MM-PBSA approach. For these highly charged systems, standard MM-PBSA calculations did not yield satisfactory results. We proposed a rational modification of the approach which led to reasonable predictions of binding free energies. All three complexes are strongly stabilized by two effects: electrostatic interactions and buried surface area. The strong favorable interactions are to a large part compensated by unfavorable entropic terms, in which vibrational entropy is the largest contributor. The electrostatic component of the binding free energy followed the trend of the overall peptide charge, with strongest interactions for DAPK1 and weakest for the DAPK2 mutant. The electrostatics was dominated by interactions of the positively charged residues of the peptide with the negatively charged residues of CaM. The nonpolar binding free energy was comparable for all three peptides, the largest contribution coming from the Trp305. About two-thirds of the buried surface area corresponds to nonpolar residues, showing that hydrophobic interactions play an important role in these CaM-peptide complexes. The simulation results agree with the experimental data in predicting a small effect of the S308D mutation on CaM interactions with DAPK2, suggesting that this mutation is not a good model for the S308 phosphorylation.     

Electrostatic interactions during electron transfer reactions between c-type cytochromes and flavodoxin

The interaction of three different c-type cytochromes with flavodoxin has been studied by computer graphics modelling and computational methods. Flavodoxin and each cytochrome can make similar hypothetical electron transfer complexes that are characterized by nearly coplanar arrangement of the prosthetic groups, close intermolecular contacts at the protein-protein interface, and complementary intermolecular salt linkages. Computation of the electrostatic free energy of each complex showed that all were electrostatically stable. However, both the magnitude and behavior of the electrostatic stabilization as a function of solution ionic strength differed for the three cytochrome c-flavodoxin complexes. Variation in the computed electrostatic stabilization appears to reflect differences in the surface distribution of all charged groups in the complex, rather than differences localized at the site of intermolecular contact. The computed electrostatic association constants for the complexes and the measured kinetic rates of electron transfer in solution show a remarkable similarity in their ionic strength dependence. This correlation suggests electrostatic interactions influence electron transfer rates between protein molecules at the intermolecular association step. Comparative calculations for the three cytochrome c-flavodoxin complexes show that these ionic strength effects also involve all charged groups in both redox partners.     

Immunophysical exploration of C3d-CR2(CCP1-2) interaction using molecular dynamics and electrostatics

The formation of the complex between the d-fragment of the complement component C3 (C3d) and the modular complement receptor-2 (CR2) is important for cross-linking foreign antigens with surface-bound antibodies and C3d on the surface of B cells. The first two modules of CR2, complement control protein modules (CCPs), participate in non-bonded interactions with C3d. We have used computational methods to analyze the dynamic and electrostatic properties of the C3d-CR2(CCP1-2) complex. The interaction between C3d and CR2 is known to depend on pH and ionic strength. Also, the intermodular mobility of the CR2 modules has been questioned before. We performed a 10 ns molecular dynamics simulation to generate a relaxed structure from crystal packing effects for the C3d-CR2(CCP1-2) complex and to study the energetics of the C3d-CR2(CCP1-2) association. The MD simulation suggests a tendency for intermodular twisting in CR2(CCP1-2). We propose a two-step model for recognition and binding of C3d with CR2(CCP1-2), driven by long and short/medium-range electrostatic interactions. We have calculated the matrix of specific short/medium-range pairwise electrostatic free energies of interaction involved in binding and in intermodular communications. Electrostatic interactions may mediate allosteric effects important for C3d-CR2(CCP1-2) association. We present calculations for the pH and ionic strength-dependence of C3d-CR2(CCP1-2) ionization free energies, which are in overall agreement with experimental binding data. We show how comparison of the calculated and experimental data allows for the decomposition of the contributions of electrostatic from other effects in association. We critically compare predicted stabilities for several mutants of the C3d-CR2(CCP1-2) complex with the available experimental data for binding ability. Finally, we propose that CR2(CCP1-2) is capable of assuming a large array of intermodular topologies, ranging from closed V-shaped to open linear states, with similar recognition properties for C3d, but we cannot exclude an additional contact site with C3d.     

Electrostatic recognition between enzyme and inhibitor: interaction between papain and leupeptin

Electrostatic forces are involved in a wide variety of molecular interactions that are of biological interest, including, among others, DNA-Protein interactions, protein folding, and the interactions between enzymes and their substrates and inhibitors. In this work, the interaction between papain and an inhibitor, leupeptin, is analyzed from the point of view of their electrostatic interaction. The computations enable one to suggest that negatively charged amino acids located in the region of the active site are responsible for creating an environment that enables efficient binding of the inhibitor. This binding occurs despite the fact that the net global charge of both molecules is positive; an explanation for this apparent contradiction is proposed.     

Electrostatic Interactions in Aminoglycoside-RNA Complexes

Electrostatic interactions often play key roles in the recognition of small molecules by nucleic acids. An example is aminoglycoside antibiotics, which by binding to ribosomal RNA (rRNA) affect bacterial protein synthesis. These antibiotics remain one of the few valid treatments against hospital-acquired infections by Gram-negative bacteria. It is necessary to understand the amplitude of electrostatic interactions between aminoglycosides and their rRNA targets to introduce aminoglycoside modifications that would enhance their binding or to design new scaffolds. Here, we calculated the electrostatic energy of interactions and its per-ring contributions between aminoglycosides and their primary rRNA binding site. We applied either the methodology based on the exact potential multipole moment (EPMM) or classical molecular mechanics force field single-point partial charges with Coulomb formula. For EPMM, we first reconstructed the aspherical electron density of 12 aminoglycoside-RNA complexes from the atomic parameters deposited in the University at Buffalo Databank. The University at Buffalo Databank concept assumes transferability of electron density between atoms in chemically equivalent vicinities and allows reconstruction of the electron densities from experimental structural data. From the electron density, we then calculated the electrostatic energy of interaction using EPMM. Finally, we compared the two approaches. The calculated electrostatic interaction energies between various aminoglycosides and their binding sites correlate with experimentally obtained binding free energies. Based on the calculated energetic contributions of water molecules mediating the interactions between the antibiotic and rRNA, we suggest possible modifications that could enhance aminoglycoside binding affinity.     

Parametrization of halogen bonds in the CHARMM general force field: Improved treatment of ligand–protein interactions

A halogen bond is a highly directional, non-covalent interaction between a halogen atom and another electronegative atom. It arises due to the formation of a small region of positive electrostatic potential opposite the covalent bond to the halogen, called the ‘sigma hole.’ Empirical force fields in which the electrostatic interactions are represented by atom-centered point charges cannot capture this effect because halogen atoms usually carry a negative charge and therefore interact unfavorably with other electronegative atoms. A strategy to overcome this problem is to attach a positively charged virtual particle to the halogen. In this work, we extend the additive CHARMM General Force Field (CGenFF) to include such interactions in model systems of phenyl-X, with X being Cl, Br or I including di- and trihalogenated species. The charges, Lennard-Jones parameters, and halogen-virtual particle distances were optimized to reproduce the orientation dependence of quantum mechanical interaction energies with water, acetone, and N-methylacetamide as well as experimental pure liquid properties and relative hydration free energies with respect to benzene. The resulting parameters were validated in molecular dynamics simulations on small-molecule crystals and on solvated protein–ligand complexes containing halogenated compounds. The inclusion of positive virtual sites leads to better agreement across experimental observables, including preservation of ligand binding poses as a direct result of the improved representation of halogen bonding.