Influence of the solvent structure on the electrostatic interactions in proteins

The proper estimation of the influence of the many-body dynamic solvent microstructure on a pairwise electrostatic interaction (PEI) at the protein-solvent interface is very important for solving many biophysical problems. In this work, the PEI energy was calculated for a system that models the interface between a protein and an aqueous solvent. The concept of nonlocal electrostatics for interfacial electrochemical systems was used to evaluate the contribution of a solvent orientational polarization, correlated by the network of hydrogen bonds, into the PEI energy in proteins. The analytical expression for this energy was obtained in the form of Coulomb's law with an effective distance-dependent dielectric function. The asymptotic and numerical analysis carried out for this function revealed several features of dielectric heterogeneity at the protein-solvent interface. For charges located in close proximity to this interface, the values of the dielectric function for the short-distance electrostatic interactions were found to be remarkably smaller than those determined by the classical model, in which the solvent was considered as the uniform dielectric medium of high dielectric constant. Our results have shown that taking into consideration the dynamic solvent microstructure remarkably increases the value of the PEI energy at the protein-solvent interface.     

On the truncation of long-range electrostatic interactions in DNA

Long-range interactions are known to play an important role in highly polar biomolecules like DNA. In molecular dynamics simulations of nucleic acids and proteins, an accurate treatment of the long-range interactions are crucial for achieving stable nanosecond trajectories. In this report, we evaluate the structural and dynamic effects on a highly charged oligonucleotide in aqueous solution from different long-range truncation methods. Two group-based truncation methods, one with a switching function and one with a force-switching function were found to fail to give accurate stable trajectories close to the crystal structure. For these group-based truncation methods, large root mean square (rms) deviations from the initial structure were obtained and severe distortions of the oligonucleotide were observed. Another group-based truncation scheme, which used an abrupt truncation at 8. 0 A or at 12.0 A was also investigated. For the short cutoff distance, the conformations deviated far away from the initial structure and were significantly distorted. However, for the longer cutoff, where all necessary electrostatic interactions were included, the trajectory was quite stable. For the particle mesh Ewald (PME) truncation method, a stable DNA simulation with a heavy atom rms deviation of 1.5 A was obtained. The atom-based truncation methods also resulted in stable trajectories, according to the rms deviation from the initial B-DNA structure, of between 1.5 and 1.7 A for the heavy atoms. In these stable simulations, the heavy atom rms deviations were approximately 0.6-1.0 A lower for the bases than for the backbone. An increase of the cutoff radius from 8 to 12 A decreased the rms deviation by approximately 0.2 A for the atom-based truncation method with a force-shifting function, but increased the computational time by a factor of 2. Increasing the cutoff from 12 to 18 A for the atom-based truncation method with a force-shifting function requires 2-3 times more computational time, but did not significantly change the rms deviation. Similar rms deviations from the initial structure were found for the atom-based method with a force-shifting function and for the PME method. The computational cost was longer for the PME method with a cutoff of 12. 0 A for the direct space nonbonded calculations than for the atom-based truncation method with a force-shifting function and a cutoff of 12.0 A. If a nonperiodic boundary, e.g., a spherical boundary, was used, a considerable speedup could be achieved. From the rms fluctuations, the terminal nucleotides and especially the cytidines were found to be more flexible than the nonterminal nucleotides. The B-DNA form of the oligonucleotide was maintained throughout the simulations and is judged to depend on the parameters of the energy function and not on the truncation method used to handle the long-range electrostatic interactions. To perform accurate and stable simulations of highly charged biological macromolecules, we recommend that the atom-based force-shift method or the PME method should be used for the long-range electrostatics interactions.     

Spatial optimization of electrostatic interactions between the ionized groups in globular proteins

A model approach is suggested to estimate the degree of spatial optimization of the electrostatic interactions in protein molecules. The method is tested on a set of 44 globular proteins, representative of the available crystallographic data. The theoretical model is based on macroscopic computation of the contribution of charge–charge interactions to the electrostatic term of the free energy for the native proteins and for a big number of virtual structures with randomly distributed on protein surface charge consetellations (generated by a Monte-Carlo technique). The statistical probability of occurrence of random structures with electrostatic energies lower than the energy of the native protein is suggested as a criterion for spatial optimization of the electrostatic interactions. The results support the hypothesis that the folding process optimizes the stabilizing effect of electrostatic interactions, but to very different degree for different proteins. A parallel analysis of ion pairs shows that the optimization of the electrostatic term in globular proteins has increasingly gone in the direction of rejecting the repulsive short contacts between charges of equal sign than of creating of more salt bridges (in comparison with the statistically expected number of shortrange ion pairs in the simulated random structures). It is observed that the decrease in the spatial optimization of the electrostatic interactions is usually compensated for by an appearance of disulfide bridges in the covalent structure of the examined proteins. © 1994 Wiley-Liss, Inc.     

Ionic interactions and anion binding in the gramicidin channel. An electrostatic calculation

An electrostatic calculation is performed in order to examine basic features of interactions between ions (including anions) within the gramicidin channel. The calculation focuses on the effect of image forces. The substitute charge method is used for the calculation of image-force energies. Good arrangements of fictitious charges and contour points are described. Errors of calculated image-force energies are estimated not to greatly exceed 0.1%. The cases assumed are (i) the effective radius r of the channel is between 2.5 and 3.5 A, (ii) the binding site with the highest affinity is between 1 and 3.5 A from the channel end (outer site), and (iii) the dimple at the channel mouth is 0-5 A in depth. The induced energy of an ion placed at the outer site increases (and hence the affinity of the outer site decreases) with the increase in the depth of dimples, whereas the barrier height for translocation between the outer sites decreases in the presence of deeper dimples. The interactional energy between two monovalent cations placed at the outer sites is relatively small in the absence of dimples. It is large, however, in the presence of deeper dimples if the outer sites are 2.5 or 3.5 A from the ends; but, it is still relatively small even in the presence of dimples if the sites are 1 A from the ends. The interactional energy is very unfavorable for simultaneous occupancy by three cations. It is suggested that an ion pair may be formed at the channel mouth. Deeper positions of the outer site, smaller values of r, and deeper dimples favor the formation of the ion pair. In the presence of 5 A dimples, the binding constant of an anion (Cl-) for a cation (Na+) which has already been bound at an outer site (with no second cation at the opposite mouth) is estimated to be 0.4-8 molal-1 if local interactions between the bound anion and the channel wall is negligibly small. The anion binding constant increases in the presence of a cation (or an ion pair) at the opposite mouth. It decreases markedly in the absence of dimples. The interactional energy is considerably unfavorable for the binding of a third cation even if the presence of an ion pair is postulated. It is still large in the presence of an ion pair at each of the mouths.     

Electrostatic interactions in proteins: Calculations of the electrostatic term of free energy and the electrostatic potential field

The pH-dependence of the electrostatic energy of interactions between titratable groups is calculated for some well studied globular proteins: basic pancreatic trypsin inhibitor, sperm whale myoglobin and tuna cytochrome c. The calculations are carried out using a semi-empirical appraach in terms of the macroscopic model based on the Kirkwood-Tanford theory. The results are discussed in the light of their physicochemical and biological properties. It was found that the pH-dependence of the electrostatic energy correlates with the III–IV transition of cytochrome c. The electrostatic field of the cysteine proteinase inhibitor, cystatin, was calculated in two ways. In the first one, the electrostatic field created by the pH dependent charges of the ionizable groups and peptide dipoles was calculated using the approach proposed. In the second one, the finite-difference method was used. The results obtained by the two methods are in overall agreement. The calculated field was discussed in terms of the binding of cystatin to papain.     

On the calculation of pKas in proteins

This paper describes a general method to calculate the pK_as of ionizable groups in proteins. Electrostatic calculations are carried out using the finite difference Poisson–Boltzmann (FDPB) method. A formal treatment of the calculation of pK_as within the framework of the FDPB method is presented. The major change with respect to previous work is the specific incorporation of the complete charge distribution of both the neutral and charged forms of each ionizable group into the formalism. This is extremely important for the treatment of salt bridges. A hybrid statistical mechanical/Tanford–Roxby method, which is found to be significantly faster than previous treatments, is also introduced. This simplifies the problem of summing over the large number of possible ionization states for a complex polyion. Applications to BPTI and serine proteases suggest that the calculations can be quite reliable. However, the necessity of including bound waters in the treatment of the Asp-70…His-31 salt bridge in T4 lysozyme and experience with other proteins suggest that additional factors ultimately need to be considered in a comprehensive treatment of pK_as in proteins. © 1993 Wiley-Liss, Inc.     

Dendrimers destabilize proteins in a generation-dependent manner involving electrostatic interactions

Dendrimers are well-defined chemical polymers with a characteristic branching pattern that gives rise to attractive features such as antibacterial and antitumor activities as well as drug delivery properties. In addition, dendrimers can solubilize prion protein aggregates at very low concentrations, but their mode of action is unclear. We show that poly(propylene imine) dendrimers based on di-aminobutane (DAB) and modified with guanidinium surface groups reduce insulin thermostability and solubility considerably at microgram per microliter concentrations, while urea-modified groups have hardly any effect. Destabilization is markedly generation-dependent and is most pronounced for generation 3, which is also the most efficient at precipitating insulin. This suggests that proteins can interact with both dendrimer surface and interior. The pH-dependence reveals that interactions are mainly mediated by electrostatics, confirmed by studies on four other proteins. Ability to precipitate and destabilize are positively correlated, in contrast to conventional small-molecule denaturants and stabilizers, indicating that surface immobilization of denaturing groups profoundly affects its interactions with proteins.     

Optimization of the electrostatic interactions in proteins of different functional and folding type

The 3-dimensional optimization of the electrostatic interactions between the charged amino acid residues was studied by Monte Carlo simulations on an extended representative set of 141 protein structures with known atomic coordinates. The proteins were classified by different functional and structural criteria, and the optimization of the electrostatic interactions was analyzed. The optimization parameters were obtained by comparison of the contribution of charge-charge interactions to the free energy of the native protein structures and for a large number of randomly distributed charge constellations obtained by the Monte Carlo technique. On the basis of the results obtained, one can conclude that the charge-charge interactions are better optimized in the enzymes than in the proteins without enzymatic functions. Proteins that belong to the mixed αβ folding type are electrostatically better optimized than pure α-helical or β-strand structures. Proteins that are stabilized by disulfide bonds show a lower degree of electrostatic optimization. The electrostatic interactions in a native protein are effectively optimized by rejection of the conformers that lead to repulsive charge-charge interactions. Particularly, the rejection of the repulsive contacts seems to be a major goal in the protein folding process. The dependence of the optimization parameters on the choice of the potential function was tested. The majority of the potential functions gave practically identical results.     

Molecular dynamics simulation of highly charged proteins: comparison of the particle-particle particle-mesh and reaction field methods for the calculation of electrostatic interactions

Molecular dynamics (MD) simulations of the activation domain of porcine procarboxypeptidase B (ADBp) were performed to examine the effect of using the particle-particle particle-mesh (P3M) or the reaction field (RF) method for calculating electrostatic interactions in simulations of highly charged proteins. Several structural, thermodynamic, and dynamic observables were derived from the MD trajectories, including estimated entropies and solvation free energies and essential dynamics (ED). The P3M method leads to slightly higher atomic positional fluctuations and deviations from the crystallographic structure, along with somewhat lower values of the total energy and solvation free energy. However, the ED analysis of the system leads to nearly identical results for both simulations. Because of the strong similarity between the results, both methods appear well suited for the simulation of highly charged globular proteins in explicit solvent. However, the lower computational demand of the RF method in the present implementation represents a clear advantage over the P3M method.     

On the role of electrostatic interactions in the design of protein-protein interfaces

Here, the methods of continuum electrostatics are used to investigate the contribution of electrostatic interactions to the binding of four protein-protein complexes; barnase-barstar, human growth hormone and its receptor, subtype N9 influenza virus neuraminidase and the NC41 antibody, the Ras binding domain (RBD) of kinase cRaf and a Ras homologue Rap1A. In two of the four complexes electrostatics are found to strongly oppose binding (hormone-receptor and neuraminidase-antibody complexes), in one case the net effect is close to zero (barnase-barstar) and in one case electrostatics provides a significant driving force favoring binding (RBD-Rap1A). In order to help understand the wide range of electrostatic contributions that were calculated, the electrostatic free energy was partitioned into contributions of individual charged and polar residues, salt bridges and networks involving salt bridges and hydrogen bonds. Although there is no one structural feature that accounts for the differences between the four interfaces, the extent to which the desolvation of buried charges is compensated by the formation of hydrogen bonds and ion pairs appears to be an important factor. Structural features that are correlated with contribution of an individual residue to stability are also discussed. These include partial burial of a charged group in the free monomer, the formation of networks involving charged and polar amino acids, and the formation of partially exposed ion-pairs. The total electrostatic contribution to binding is found to be inversely correlated with buried total and non-polar surface area. This suggests that different interfaces can be designed to exploit electrostatic and hydrophobic forces in very different ways.     

On the methods of calculation of the electrostatic potential in a protein channel

The profiles of the electrostatic potential along the axis of a gramicidin channel were calculated using two quantum chemistry methods (EHT and CNDO/2) and three methods of force fields (AMBER, CHARMM, and OPLS). The calculations were performed without taking into account the contribution of water. A comparative analysis of the calculated profiles indicated that the electrostatic field of point charges of the CHARMM force field is close to that obtained by the quantum chemistry methods. It was concluded that there is no need to calculate the electric field using laborious quantum-mechanical methods since the less laborious method of the CHARMM force field gives approximately the same results.     

Optimization of the electrostatic interactions between ionized groups and peptide dipoles in proteins.

The three-dimensional optimization of the electrostatic interactions between the charged amino acid residues and the peptide partial charges was studied by Monte-Carlo simulations on a set of 127 nonhomologous protein structures with known atomic coordinates. It was shown that this type of interaction is very well optimized for all proteins in the data set, which suggests that they are a valuable driving force, at least for the native side-chain conformations. Similar to the optimization of the charge-charge interactions (Spassov VZ, Karshikoff AD, Ladenstein R, 1995, Protein Sci 4:1516-1527), the optimization effect was found more pronounced for enzymes than for proteins without enzymatic function. The asymmetry in the interactions of acidic and basic groups with the peptide dipoles was analyzed and a hypothesis was proposed that the properties of peptide dipoles are a factor contributing to the natural selection of the basic amino acids in the chemical composition of proteins.     

Ca2+ induces clustering of membrane proteins in the plasma membrane via electrostatic interactions

Membrane proteins and membrane lipids are frequently organized in submicron-sized domains within cellular membranes. Factors thought to be responsible for domain formation include lipid-lipid interactions, lipid-protein interactions and protein-protein interactions. However, it is unclear whether the domain structure is regulated by other factors such as divalent cations. Here, we have examined in native plasma membranes and intact cells the role of the second messenger Ca(2+) in membrane protein organization. We find that Ca(2+) at low micromolar concentrations directly redistributes a structurally diverse array of membrane proteins via electrostatic effects. Redistribution results in a more clustered pattern, can be rapid and triggered by Ca(2+) influx through voltage-gated calcium channels and is reversible. In summary, the data demonstrate that the second messenger Ca(2+) strongly influences the organization of membrane proteins, thus adding a novel and unexpected factor that may control the domain structure of biological membranes.     

The influence of electrostatic interactions between buried charges on the properties of membrane proteins

The importance of electrostatic interactions between buried charges in determining the properties of membrane proteins is considered. It is demonstrated that in some cases altered properties may result from the extraction of a membrane protein into an aqueous medium even when the protein conformation is unperturbed.     

Single molecule force spectroscopy reveals that electrostatic interactions affect the mechanical stability of proteins

It is well known that electrostatic interactions play important roles in determining the thermodynamic stability of proteins. However, the investigation into the role of electrostatic interactions in mechanical unfolding of proteins has just begun. Here we used single molecule atomic force microscopy techniques to directly evaluate the effect of electrostatic interactions on the mechanical stability of a small protein GB1. We engineered a bi-histidine motif into the force-bearing region of GB1. By varying the pH, histidine residues can switch between protonated and deprotonated states, leading to the change of the electrostatic interactions between the two histidine residues. We found that the mechanical unfolding force of the engineered protein decreased by ∼34% (from 115 pN to 76 pN) on changing the pH from 8.5 to 3, due to the increased electrostatic repulsion between the two positively charged histidines at acidic pH. Our results demonstrated that electrostatic interactions can significantly affect the mechanical stability of elastomeric proteins, and modulating the electrostatic interactions of key charged residues can become a promising method for regulating the mechanical stability of elastomeric proteins.     

An empirical model for electrostatic interactions in proteins incorporating multiple geometry-dependent dielectric constants

Here we introduce an electrostatic model that treats the complexity of electrostatic interactions in a heterogeneous protein environment by using multiple parameters that take into account variations in protein geometry, local structure, and the type of interacting residues. The optimal values for these parameters were obtained by fitting the model to a large dataset of 260 experimentally determined pK(a) values distributed over 41 proteins. We obtain fits between the calculated and observed values that are significantly better than the null model. The model performs well on the groups that exhibit large pK(a) shifts from solution values in response to the protein environment and compares favorably with other, successful continuum models. The empirically determined values of the parameters correlate well with experimentally observed contributions of hydrogen bonds and ion pairs as well as theoretically predicted magnitudes of charge-charge and charge-polar interactions. The magnitudes of the dielectric constants assigned to different regions of the protein rank according to the strength of the relaxation effects expected for the core, boundary, and surface. The electrostatic interactions in this model are pairwise decomposable and can be calculated rapidly. This model is therefore well suited for the large computations required for simulating protein properties and especially for prediction of mutations for protein design.     

The effect of electrostatic intermolecular interactions on Brownian rotation of proteins in solution]

A qualitative model that takes into account the influence of electrostatic interactions on the form of correlation function of Brownian rotation of a protein as a whole is given. It is supposed that these interactions give rise to anisotropy of Brownian rotation and this leads to the nonexponentiality of the correlation function. To define experimentally the form of the correlation function nonselective measurements of relaxation times T1 and T2 of protein protons at different resonance frequencies in lysozyme solution were carried out. Literature data on frequency dependencies of relaxation time T1 of water in protein solutions were analysed. Analysis of experiments confirms the proposed model. Correlation times, activation energies and parameters of anisotropy were found.     

Helix-coil transition theory including long-range electrostatic interactions: application to globular proteins

An extension of the Zimm–Bragg two-state theory for the helix–coil transition in polypeptides, which takes into account the effect of peptide charge–dipole interactions on helix stability, is presented. This new theory incorporates these interactions in an expression that is parameterized on recently obtained experimental data on polypeptides for which electrostatic effects are known to influence helix content. Unlike previous two-state or multistate models, which are parameterized on protein x-ray data, the present theoretical treatment in independent of such protein data. The theoretical model is applied to a series of peptides derived from the C-peptide of ribonuclease A, which have been the object of recent spectroscopic studies. The new theoretical approach can account for most of the structural information derived from studies of these C-peptides, and for overall average helix probabilities that are close in magnitude to those observed for these polypeptides in solution. An application of this new formulation for the prediction of the locations of α-helices in globular proteins from their amino acid sequence is also presented.