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.     

Electrostatic Potential of B-DNA: Effect of Interionic Correlations

Modified Poisson-Boltzmann (MPB) equations have been numerically solved to study ionic distributions and mean electrostatic potentials around a macromolecule of arbitrarily complex shape and charge distribution. Results for DNA are compared with those obtained by classical Poisson-Boltzmann (PB) calculations. The comparisons were made for 1:1 and 2:1 electrolytes at ionic strengths up to 1 M. It is found that ion-image charge interactions and interionic correlations, which are neglected by the PB equation, have relatively weak effects on the electrostatic potential at charged groups of the DNA. The PB equation predicts errors in the long-range electrostatic part of the free energy that are only ∼1.5 kJ/mol per nucleotide even in the case of an asymmetrical electrolyte. In contrast, the spatial correlations between ions drastically affect the electrostatic potential at significant separations from the macromolecule leading to a clearly predicted effect of charge overneutralization.     

Optimization of electrostatic interactions in protein-protein complexes

In this article, we present a statistical analysis of the electrostatic properties of 298 protein-protein complexes and 356 domain-domain structures extracted from the previously developed database of protein complexes (ProtCom, http://www.ces.clemson.edu/compbio/protcom). For each structure in the dataset we calculated the total electrostatic energy of the binding and its two components, Coulombic and reaction field energy. It was found that in a vast majority of the cases (>90%), the total electrostatic component of the binding energy was unfavorable. At the same time, the Coulombic component of the binding energy was found to favor the complex formation while the reaction field component of the binding energy opposed the binding. It was also demonstrated that the components in a wild-type (WT) structure are optimized/anti-optimized with respect to the corresponding distributions, arising from random shuffling of the charged side chains. The degree of this optimization was assessed through the Z-score of WT energy in respect to the random distribution. It was found that the Z-scores of Coulombic interactions peak at a considerably negative value for all 654 cases considered while the Z-score of the reaction field energy varied among different types of complexes. All these findings indicate that the Coulombic interactions within WT protein-protein complexes are optimized to favor the complex formation while the total electrostatic energy predominantly opposes the binding. This observation was used to discriminate WT structures among sets of structural decoys and showed that the electrostatic component of the binding energy is not a good discriminator of the WT; while, Coulombic or reaction field energies perform better depending upon the decoy set used.     

Do salt bridges stabilize proteins? A continuum electrostatic analysis

The electrostatic contribution to the free energy of folding was calculated for 21 salt bridges in 9 protein X-ray crystal structures using a continuum electrostatic approach with the DELPHI computer-program package. The majority (17) were found to be electrostatically destabilizing; the average free energy change, which is analogous to mutation of salt bridging side chains to hydrophobic isosteres, was calculated to be 3.5 kcal/mol. This is fundamentally different from stability measurements using pKa shifts, which effectively measure the strength of a salt bridge relative to 1 or more charged hydrogen bonds. The calculated effect was due to a large, unfavorable desolvation contribution that was not fully compensated by favorable interactions within the salt bridge and between salt-bridge partners and other polar and charged groups in the folded protein. Some of the salt bridges were studied in further detail to determine the effect of the choice of values for atomic radii, internal protein dielectric constant, and ionic strength used in the calculations. Increased ionic strength resulted in little or no change in calculated stability for 3 of 4 salt bridges over a range of 0.1-0.9 M. The results suggest that mutation of salt bridges, particularly those that are buried, to "hydrophobic bridges" (that pack at least as well as wild type) can result in proteins with increased stability. Due to the large penalty for burying uncompensated ionizable groups, salt bridges could help to limit the number of low free energy conformations of a molecule or complex and thus play a role in determining specificity (i.e., the uniqueness of a protein fold or protein-ligand binding geometry).     

Electrostatic interactions in sperm whale myoglobin. Site specificity, roles in structural elements, and external electrostatic potential distributions

The electrostatic free energy contribution to the stability of sperm whale ferrimyoglobin was evaluated according to the static accessibility modified Tanford-Kirkwood model. The electrostatic free energy contribution of each distinct structural element was divided into one term arising from interactions between it and other elements (interelemental) and another from interactions within the particular element itself (intraelemental). At pH 7 the majority of the terms were found to be stabilizing. The interelemental terms are the dominant ones for most structural elements. The small interelemental terms of the C and D helices are compensated by large intraelemental interactions which stabilize these short helices. Perturbations in pH can be accommodated by the structural elements through a redistribution of stabilizing and destabilizing interactions. The electrostatic potentials calculated at the surface of the protein indicate that the internal compensation of local potentials achieved during folding results in a generally neutral protein-solvent interface save for two distinct areas of nonzero potential. The accessibility of each charged atom to solvent was analyzed in terms of the surface area lost to charged, polar and nonpolar atoms separately. The net solvent accessibility lost parallels closely that lost to nonpolar atoms alone, indicating a specific role for nonpolar atoms in defining dielectric shielding of charged atoms, aside from their participation in the well-known hydrophobic interactions.     

Optimization of binding electrostatics: charge complementarity in the barnase-barstar protein complex

Theoretical and experimental studies have shown that the large desolvation penalty required for polar and charged groups frequently precludes their involvement in electrostatic interactions that contribute strongly to net stability in the folding or binding of proteins in aqueous solution near room temperature. We have previously developed a theoretical framework for computing optimized electrostatic interactions and illustrated use of the algorithm with simplified geometries. Given a receptor and model assumptions, the method computes the ligand-charge distribution that provides the most favorable balance of desolvation and interaction effects on binding. In this paper the method has been extended to treat complexes using actual molecular shapes. The barnase-barstar protein complex was investigated with barnase treated as a target receptor. The atomic point charges of barstar were varied to optimize the electrostatic binding free energy. Barnase and natural barstar form a tight complex (K(d) approximately 10(-14) M) with many charged and polar groups near the interface that make this a particularly relevant system for investigating the role of electrostatic effects on binding. The results show that sets of barstar charges (resulting from optimization with different constraints) can be found that give rise to relatively large predicted improvements in electrostatic binding free energy. Principles for enhancing the effect of electrostatic interactions in molecular binding in aqueous environments are discussed in light of the optima. Our findings suggest that, in general, the enhancements in electrostatic binding free energy resulting from modification of polar and charged groups can be substantial. Moreover, a recently proposed definition of electrostatic complementarity is shown to be a useful tool for examining binding interfaces. Finally, calculational results suggest that wild-type barstar is closer to being affinity optimized than is barnase for their mutual binding, consistent with the known roles of these proteins.     

Lipid demixing and protein-protein interactions in the adsorption of charged proteins on mixed membranes

The adsorption free energy of charged proteins on mixed membranes, containing varying amounts of (oppositely) charged lipids, is calculated based on a mean-field free energy expression that accounts explicitly for the ability of the lipids to demix locally, and for lateral interactions between the adsorbed proteins. Minimization of this free energy functional yields the familiar nonlinear Poisson-Boltzmann equation and the boundary condition at the membrane surface that allows for lipid charge rearrangement. These two self-consistent equations are solved simultaneously. The proteins are modeled as uniformly charged spheres and the (bare) membrane as an ideal two-dimensional binary mixture of charged and neutral lipids. Substantial variations in the lipid charge density profiles are found when highly charged proteins adsorb on weakly charged membranes; the lipids, at a certain demixing entropy penalty, adjust their concentration in the vicinity of the adsorbed protein to achieve optimal charge matching. Lateral repulsive interactions between the adsorbed proteins affect the lipid modulation profile and, at high densities, result in substantial lowering of the binding energy. Adsorption isotherms demonstrating the importance of lipid mobility and protein-protein interactions are calculated using an adsorption equation with a coverage-dependent binding constant. Typically, at bulk-surface equilibrium (i.e., when the membrane surface is "saturated" by adsorbed proteins), the membrane charges are "overcompensated" by the protein charges, because only about half of the protein charges (those on the hemispheres facing the membrane) are involved in charge neutralization. Finally, it is argued that the formation of lipid-protein domains may be enhanced by electrostatic adsorption of proteins, but its origin (e.g., elastic deformations associated with lipid demixing) is not purely electrostatic.     

Electrostatic calculations of amino acid titration and electron transfer, Q-AQB-->QAQ-B, in the reaction center.

The titration of amino acids and the energetics of electron transfer from the primary electron acceptor (QA) to the secondary electron acceptor (QB) in the photosynthetic reaction center of Rhodobacter sphaeroides are calculated using a continuum electrostatic model. Strong electrostatic interactions between titrating sites give rise to complex titration curves. Glu L212 is calculated to have an anomalously broad titration curve, which explains the seemingly contradictory experimental results concerning its pKa. The electrostatic field following electron transfer shifts the average protonation of amino acids near the quinones. The pH dependence of the free energy between Q-AQB and QAQ-B calculated from these shifts is in good agreement with experiment. However, the calculated absolute free energy difference is in severe disagreement (by approximately 230 meV) with the observed experimental value, i.e., electron transfer from Q-A to QB is calculated to be unfavorable. The large stabilization energy of the Q-A state arises from the predominantly positively charged residues in the vicinity of QA in contrast to the predominantly negatively charged residues near QB. The discrepancy between calculated and experimental values for delta G(Q-AQB-->QAQ-B) points to limitations of the continuum electrostatic model. Inclusion of other contributions to the energetics (e.g., protein motion following quinone reduction) that may improve the agreement between theory and experiment are discussed.     

Kerr effect of charged dipolar macromolecules without condensed counterions in conducting solution.

The theoretical treatment of the Kerr constant of rigid, dipolar, conducting ellipsoidal macromolecules of O'Konski and Krause (1970. J. Phys. Chem. 74:3243) has been extended to very low ionic strength solutions for charged macromolecules. The O'Konski and Krause theoretical treatment postulated a surface conductivity directly on the surface of each macromolecule. For charged macromolecules, this surface conductivity was generally assumed to be caused by movement of condensed counterions on the macromolecules. In the present work, it has been assumed that, at very low ionic strength, the average counterion is at the Debye characteristic distance from the surface of each charged macromolecule and contributes to surface conductivity at that distance, with no additional surface conductivity on the true surface of the macromolecule. Essentially, these considerations change the calculated interaction energy of the macromolecule with an externally applied electric field via a change in both the internal field components and in the reaction field of the macromolecular dipole. The new interaction energy is used to calculate the orientation distribution function of the macromolecules in solution and this distribution function can, in principle, be used to calculate the steady state electric linear or circular dichroism, electric light scattering, anisotropy of conductivity, etc., using the appropriate theoretical treatment for each of these quantities.     

Electrostatic potentials and electrostatic interaction energies of rat cytochrome b5 and a simulated anion-exchange adsorbent surface.

Electrostatic potentials were determined for the soluble tryptic core of rat cytochrome b5 (using a structure derived from homology modeling) and a simulated anion-exchange surface through application of the linearized finite-difference Poisson-Boltzmann equation with the simulation code UHBD. Objectives of this work included determination of the contributions of the various charged groups on the protein surface to electrostatic interactions with a simulated anion-exchange surface as a function of orientation, separation distance, and ionic strength, as well as examining the potential existence of a preferred contact orientation. Electrostatic interaction free energies for the complex of the model protein and the simulated surface were computed using the electrostatics section of UHBD employing a 110(3) grid. An initial coarse grid spacing of 2.0 A was required to obtain correct boundary conditions. The boundary conditions of the coarse grid were used in subsequent focusing steps until the electrostatic interaction free energies were relatively independent of grid spacing (at approximately 0.5 A). Explicit error analyses were performed to determine the effects of grid spacing and other model assumptions on the electrostatic interaction free energies. The computational results reveal the presence of a preferred interaction orientation; the interaction energy between these two entities, of opposite net charge, is repulsive over a range of orientations. The electrostatic interaction free energies appear to be the summation of multiple fractional interactions between the protein and the anion-exchange surface. The simulation results are compared with those of ion-exchange adsorption experiments with site-directed mutants of the recombinant protein. Comparisons of the results from the computational and experimental studies should lead to a better understanding of electrostatic interactions of proteins and charged surfaces.     

Structural determinants of trypsin affinity and specificity for cationic inhibitors

The binding free energies of four inhibitors to bovine beta-trypsin are calculated. The inhibitors use either ornithine, lysine, or arginine to bind to the S1 specificity site. The electrostatic contribution to binding free energy is calculated by solving the finite difference Poisson-Boltzmann equation, the contribution of nonpolar interactions is calculated using a free energy-surface area relationship and the loss of conformational entropy is estimated both for trypsin and ligand side chains. Binding free energy values are of a reasonable magnitude and the relative affinity of the four inhibitors for trypsin is correctly predicted. Electrostatic interactions are found to oppose binding in all cases. However, in the case of ornithine- and lysine-based inhibitors, the salt bridge formed between their charged group and the partially buried carboxylate of Asp189 is found to stabilize the complex. Our analysis reveals how the molecular architecture of the trypsin binding site results in highly specific recognition of substrates and inhibitors. Specifically, partially burying Asp189 in the inhibitor-free enzyme decreases the penalty for desolvation of this group upon complexation. Water molecules trapped in the binding interface further stabilize the buried ion pair, resulting in a favorable electrostatic contribution of the ion pair formed with ornithine and lysine side chains. Moreover, all side chains that form the trypsin specificity site are partially buried, and hence, relatively immobile in the inhibitor-free state, thus reducing the entropic cost of complexation. The implications of the results for the general problem of recognition and binding are considered. A novel finding in this regard is that like charged molecules can have electrostatic contributions to binding that are more favorable than oppositely charged molecules due to enhanced interactions with the solvent in the highly charged complex that is formed.     

Prediction of charge-induced molecular alignment of biomolecules dissolved in dilute liquid-crystalline phases

Alignment of macromolecules in nearly neutral aqueous lyotropic liquid-crystalline media such as bicelles, commonly used in macromolecular NMR studies, can be predicted accurately by a steric obstruction model (Zweckstetter and Bax, 2000). A simple extension of this model is described that results in improved predictions for both the alignment orientation and magnitude of protein and DNA solutes in charged nematic media, such as the widely used medium of filamentous phage Pf1. The extended model approximates the electrostatic interaction between a solute and an ordered phage particle as that between the solute's surface charges and the electric field of the phage. The model is evaluated for four different proteins and a DNA oligomer. Results indicate that alignment in charged nematic media is a function not only of the solute's shape, but also of its electric multipole moments of net charge, dipole, and quadrupole. The relative importance of these terms varies greatly from one macromolecule to another, and evaluation of the experimental data indicates that these terms scale differently with ionic strength. For several of the proteins, the calculated alignment is sensitive to the precise position of the charged groups on the protein surface. This suggests that NMR alignment measurements can potentially be used to probe protein electrostatics. Inclusion of electrostatic interactions in addition to steric effects makes the extended model applicable to all liquid crystals used in biological NMR to date.     

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.     

Charge-charge interactions influence the denatured state ensemble and contribute to protein stability

Several recent studies have shown that it is possible to increase protein stability by improving electrostatic interactions among charged groups on the surface of the folded protein. However, the stability increases are considerably smaller than predicted by a simple Coulomb's law calculation, and in some cases, a charge reversal on the surface leads to a decrease in stability when an increase was predicted. These results suggest that favorable charge-charge interactions are important in determining the denatured state ensemble, and that the free energy of the denatured state may be decreased more than that of the native state by reversing the charge of a side chain. We suggest that when the hydrophobic and hydrogen bonding interactions that stabilize the folded state are disrupted, the unfolded polypeptide chain rearranges to compact conformations with favorable long-range electrostatic interactions. These charge-charge interactions in the denatured state will reduce the net contribution of electrostatic interactions to protein stability and will help determine the denatured state ensemble. To support this idea, we show that the denatured state ensemble of ribonuclease Sa is considerably more compact at pH 7 where favorable charge-charge interactions are possible than at pH 3, where unfavorable electrostatic repulsion among the positive charges causes an expansion of the denatured state ensemble. Further support is provided by studies of the ionic strength dependence of the stability of charge-reversal mutants of ribonuclease Sa. These results may have important implications for the mechanism of protein folding.     

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.     

A precise analytical method for calculating the electrostatic energy of macromolecules in aqueous solution

A new method for calculating the total electrostatic free energy of a macromolecule in solution is presented. It is applicable to molecules of arbitrary shape and size, including membranes or macromolecular assemblies with substrate molecules and ions. The method is derived from integrating the energy density of the electrostatic field and is termed the field energy method. It is based on the dielectric model, in which the solute and the surrounding water are regarded as different continuous dielectrics. The field energy method yields both the interaction energy between all charge pairs and the self energy of single charges, effectively accounting for the interaction with water. First, the dielectric boundary and mirror charges are determined for all charges of the solute. The energy is then given as a simple function of the interatomic distances, and the standard atomic partial charges and volumes. The interaction and self energy are shown to result from three-body and pairwise interactions. Both energy terms explicitly involve apolar atoms, revealing that apolar groups are also subject to electrostatic forces. We applied the field energy method to a spherical model protein. Comparison with the Kirkwood solution shows that errors are within a small percentage. As a further test, the field energy method was used to calculate the electrostatic potential of the protein superoxide dismutase. We obtained good agreement with the result from a program that implements the numerical finite difference algorithm. The field energy method provides a basis for energy minimization and dynamics programs that account for the solvent and screening effect of water at little computational expense.     

Allowance for spatial dispersion of dielectric permittivity in polyelectrolyte model of DNA.

In order to allow for real dielectric properties of a solvent in calculating of electrostatic characteristics of strongly charged polyions such as DNA in salt solution we consider a simple model of linear dielectric response of a medium. The interactions between charged particles are treated in the framework of self-consistent-field approximation. The basic characteristic of the problem, electrostatic potential, can be found from the solution of non-linear integro-differential equation. Specifically we consider so-called quasimacroscopic model where dielectric response of a medium depends only on the distance from the polyion. Application of the approach for calculating of the B-to-Z free energy qualitatively retains the main conclusion obtained previously within the model with fixed dielectric constant: non-monotonous behavior of the free energy differences as a function of ionic strength. At the same time, essential sensitivity of the results to specific values of dielectric parameters is observed.     

Allowance for Spatial Dispersion of Dielectric Permittivity in Polyelectrolyte Model of DNA

Abstract

In order to allow for real dielectric properties of a solvent in calculating of electrostatic characteristics of strongly charged polyions such as DNA in salt solution we consider a simple model of linear dielectric response of a medium. The interactions between charged particles are treated in the framework of self-consistent-field approximation. The basic characteristic of the problem, electrostatic potential, can be found from the solution of non-linear integro-differential equation. Specifically we consider so-called quasimacroscopic model where dielectric response of a medium depends only on the distance from the polyion. Application of the approach for calculating of the B-to-Z free energy qualitatively retains the main conclusion obtained previously within the model with fixed dielectric constant: non-monotonous behavior of the free energy difference as a function of ionic strength. At the same time, essential sensitivity of the results to specific values of dielectric parameters is observed.     

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.