Fluctuations between stabilizing and destabilizing electrostatic contributions of ion pairs in conformers of the c-Myc-Max leucine zipper

In solution proteins often exhibit backbone and side-chain flexibility. Yet electrostatic interactions in proteins are sensitive to motions. Hence, here we study the contribution of ion pairs toward protein stability in a range of conformers which sample the conformational space in solution. Specifically, we focus on the electrostatic contributions of ion pairs to the stability of each of the conformers in the NMR ensemble of the c-Myc-Max leucine zipper and to their average energy minimized structure. We compute the electrostatic contributions of inter- and intra-helical ion pairs and of an ion pair network. We find that the electrostatic contributions vary considerably among the 40 NMR conformers. Each ion pair, and the network, fluctuates between being stabilizing and being destabilizing. This fluctation reflects the variability in the location of the ion pairing residues and in the geometric orientation of these residues, both with respect to each other and with respect to other charged groups in the rest of the protein. Ion pair interactions in the c-Myc-Max leucine zipper in solution depend on the protein conformer which is analyzed. Hence, the overall stabilizing (or destabilizing) contribution of an ion pair is conformer population-dependent. This study indicates that free energy calculations performed using the continuum electrostatics methodology are sensitive to protein conformational details.     

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.     

Negatively charged residues and hydrogen bonds tune the ligand histidine pKa values of Rieske iron-sulfur proteins

Rieske proteins carry a redox-active iron-sulfur cluster, which is bound by two histidine and two cysteine side chains. The reduction potential of Rieske proteins depends on pH. This pH dependence can be described by two pK(a) values, which have been assigned to the two iron-coordinating histidines. Rieske proteins are commonly grouped into two major classes: Rieske proteins from quinol-oxidizing cytochrome bc complexes, in which the ligand histidines titrate in the physiological pH range, and bacterial ferredoxin Rieske proteins, in which the ligand histidines are protonated at physiological pH. In the study presented here, we have calculated pK(a) values of the cluster ligand histidines using a combined density functional theory/continuum electrostatics approach. Experimental pK(a) values for a bc-type and a ferredoxin Rieske protein could be reproduced. We could identify functionally important differences between the two proteins: hydrogen bonds toward the cluster, which are present in bc-type Rieske proteins, and negatively charged residues, which are present in ferredoxin Rieske proteins. We removed these differences by mutating the proteins in our calculations. The Rieske centers in the mutated proteins have very similar pK(a) values. We thus conclude that the studied structural differences are the main reason for the different pH-titration behavior of the proteins. Interestingly, the shift caused by neutralizing the negative charges in ferredoxin Rieske proteins is larger than the shift caused by removing the hydrogen bonds toward the cluster in bc-type Rieske proteins.     

A continuum method for determining membrane protein insertion energies and the problem of charged residues

Continuum electrostatic approaches have been extremely successful at describing the charged nature of soluble proteins and how they interact with binding partners. However, it is unclear whether continuum methods can be used to quantitatively understand the energetics of membrane protein insertion and stability. Recent translation experiments suggest that the energy required to insert charged peptides into membranes is much smaller than predicted by present continuum theories. Atomistic simulations have pointed to bilayer inhomogeneity and membrane deformation around buried charged groups as two critical features that are neglected in simpler models. Here, we develop a fully continuum method that circumvents both of these shortcomings by using elasticity theory to determine the shape of the deformed membrane and then subsequently uses this shape to carry out continuum electrostatics calculations. Our method does an excellent job of quantitatively matching results from detailed molecular dynamics simulations at a tiny fraction of the computational cost. We expect that this method will be ideal for studying large membrane protein complexes.     

Effect of mutations involving charged residues on the stability of staphylococcal nuclease: a continuum electrostatics study

A continuum electrostatics model is used to calculate the relative stabilities of 117 mutants of staphylococcal nuclease (SNase) involving the mutation of a charged residue to an uncharged residue. The calculations are based on the crystallographic structure of the wild-type protein and attempt to take implicitly into account the effect of the mutations in the denatured state by assuming a linear relationship between the free energy changes caused by the mutation in the native and denatured states. A good correlation (linear correlation coefficient of approximately 0.8) is found with published experimental relative stabilities of these mutants. The results suggest that in the case of SNase (i) charged residues contribute to the stability of the native state mainly through electrostatic interactions, and (ii) native-like electrostatic interactions may persist in the denatured state. The continuum electrostatics method is only moderately sensitive to model parameters and leads to quasi-predictive results for the relative mutant stabilities (error of 2-3 kJ mol(-1) or of the order of k(B)T), except for mutants in which a charged residue is mutated to glycine.     

Electrostatic aspects of protein-protein interactions

Structural and mutational analyses reveal a central role for electrostatic interactions in protein-protein association. Experiment and theory both demonstrate that clusters of charged and polar residues that are located on protein-protein interfaces may enhance complex stability, although the total effect of electrostatics is generally net destabilizing. The past year also witnessed significant progress in our understanding of the effect of electrostatics on protein association kinetics, specifically in the characterization of a partially desolvated encounter complex.     

MCCE analysis of the pKas of introduced buried acids and bases in staphylococcal nuclease

The pK(a)s of 96 acids and bases introduced into buried sites in the staphylococcal nuclease protein (SNase) were calculated using the multiconformation continuum electrostatics (MCCE) program and the results compared with experimental values. The pK(a)s are obtained by Monte Carlo sampling of coupled side chain protonation and position as a function of pH. The dependence of the results on the protein dielectric constant (ε(prot)) in the continuum electrostatics analysis and on the Lennard-Jones non-electrostatics parameters was evaluated. The pK(a)s of the introduced residues have a clear dependence on ε(prot,) whereas native ionizable residues do not. The native residues have electrostatic interactions with other residues in the protein favoring ionization, which are larger than the desolvation penalty favoring the neutral state. Increasing ε(prot) scales both terms, which for these residues leads to small changes in pK(a). The introduced residues have a larger desolvation penalty and negligible interactions with residues in the protein. For these residues, changing ε(prot) has a large influence on the calculated pK(a). An ε(prot) of 8-10 and a Lennard-Jones scaling of 0.25 is best here. The X-ray crystal structures of the mutated proteins are found to provide somewhat better results than calculations carried out on mutations made in silico. Initial relaxation of the in silico mutations by Gromacs and extensive side chain rotamer sampling within MCCE can significantly improve the match with experiment.     

Relationship between ion pair geometries and electrostatic strengths in proteins

The electrostatic free energy contribution of an ion pair in a protein depends on two factors, geometrical orientation of the side-chain charged groups with respect to each other and the structural context of the ion pair in the protein. Conformers in NMR ensembles enable studies of the relationship between geometry and electrostatic strengths of ion pairs, because the protein structural contexts are highly similar across different conformers. We have studied this relationship using a dataset of 22 unique ion pairs in 14 NMR conformer ensembles for 11 nonhomologous proteins. In different NMR conformers, the ion pairs are classified as salt bridges, nitrogen-oxygen (N-O) bridges and longer-range ion pairs on the basis of geometrical criteria. In salt bridges, centroids of the side-chain charged groups and at least a pair of side-chain nitrogen and oxygen atoms of the ion-pairing residues are within a 4 A distance. In N-O bridges, at least a pair of the side-chain nitrogen and oxygen atoms of the ion-pairing residues are within 4 A distance, but the distance between the side-chain charged group centroids is greater than 4 A. In the longer-range ion pairs, the side-chain charged group centroids as well as the side-chain nitrogen and oxygen atoms are more than 4 A apart. Continuum electrostatic calculations indicate that most of the ion pairs have stabilizing electrostatic contributions when their side-chain charged group centroids are within 5 A distance. Hence, most (approximately 92%) of the salt bridges and a majority (68%) of the N-O bridges are stabilizing. Most (approximately 89%) of the destabilizing ion pairs are the longer-range ion pairs. In the NMR conformer ensembles, the electrostatic interaction between side-chain charged groups of the ion-pairing residues is the strongest for salt bridges, considerably weaker for N-O bridges, and the weakest for longer-range ion pairs. These results suggest empirical rules for stabilizing electrostatic interactions in proteins.     

Developing hybrid approaches to predict pKa values of ionizable groups

Accurate predictions of pKa values of titratable groups require taking into account all relevant processes associated with the ionization/deionization. Frequently, however, the ionization does not involve significant structural changes and the dominating effects are purely electrostatic in origin allowing accurate predictions to be made based on the electrostatic energy difference between ionized and neutral forms alone using a static structure and the subtle structural changes be accounted by using dielectric constant larger than two. On another hand, if the change of the charge state is accompanied by a large structural reorganization of the target protein, then the relevant conformational changes have to be explicitly taken into account in the pKa calculations. Here we report a hybrid approach that first predicts the titratable groups whose ionization is expected to cause large conformational changes, termed "problematic" residues, and then applies a special protocol on them, while the rest of the pK(a)s are predicted with rigid backbone approach as implemented in multi-conformation continuum electrostatics (MCCE) method. The backbone representative conformations for "problematic" groups are generated with either molecular dynamics simulations with charged and uncharged amino acid or with ab-initio local segment modeling. The corresponding ensembles are then used to calculate the titration curves of the "problematic" residues and then the results are averaged to obtain the corresponding pKa.     

Energetics of sequence-specific protein-DNA association: computational analysis of integrase Tn916 binding to its target DNA

The N-terminal domain of the bacterial integrase Tn916 specifically recognizes the 11 bp DNA target site by positioning the face of a three-stranded beta-sheet into the major groove. Binding is linked to structural adaptation. We have characterized INT-DBD binding to DNA in detail by calorimetry [Milev, S., Gorfe, A., Karshikoff, A., Clubb, R. T., Bosshard, H. R., and Jelesarov, I. (2003) Biochemistry 42, 3481-3491]. Our thermodynamic analysis has indicated that the major driving force of association is the hydrophobic effect while polar interactions contribute less. To gain more comprehensive information about the binding process, we performed a computational analysis of the binding free energy and report here the results. A hybrid molecular mechanics/continuum approach was followed. The total binding free energy is predicted with reasonable accuracy. The calculations confirm that nonpolar effects stabilize the protein-DNA complex while electrostatics opposes binding. Structural changes optimizing surface complementarity are costly in terms of energy. The energetic consequences from the replacement of nine DNA-contacting residues by alanine were investigated. The calculations correctly predict the binding affinity decrease of eight mutations and the destabilizing effect of one wild-type residue. Bulky side chains stabilize the wild-type complex through packing interactions and favorable nonpolar dehydration, but the net nonpolar energy changes do not correlate with the relative affinity loss upon mutation. Discrete protein-DNA electrostatic interactions may be net stabilizing or net destabilizing depending on the local environment. In contrast to nonpolar energy changes, the magnitude of the electrostatic free energy ranks the mutations according to the experimentally measured DeltaDeltaG. Free energy decomposition analysis from a structural perspective leads to detailed information about the thermodynamic strategy used by INT-DBD for sequence-specific DNA binding.     

Native-state conformational dynamics of GART: a regulatory pH-dependent coil-helix transition examined by electrostatic calculations

Glycinamide ribonucleotide transformylase (GART) undergoes a pH-dependent coil-helix transition with pK(a) approximately 7. An alpha-helix is formed at high pH spanning 8 residues of a 21-residue-long loop, comprising the segment Thr120-His121-Arg122-Gln123-Ala124-Leu125-Glu126-Asn127. To understand the electrostatic nature of this loop-helix, called the activation loop-helix, which leads to the formation and stability of the alpha-helix, pK(a) values of all ionizable residues of GART have been calculated, using Poisson-Boltzmann electrostatic calculations and crystallographic data. Crystallographic structures of high and low pH E70A GART have been used in our analysis. Low pK(a) values of 5.3, 5.3, 3.9, 1.7, and 4.7 have been calculated for five functionally important histidines, His108, His119, His121, His132, and His137, respectively, using the high pH E70A GART structure. Ten theoretical single and double mutants of the high pH E70A structure have been constructed to identify pairwise interactions of ionizable residues, which have aided in elucidating the multiplicity of electrostatic interactions of the activation loop-helix, and the impact of the activation helix on the catalytic site. Based on our pK(a) calculations and structural data, we propose that: (1) His121 forms a molecular switch for the coil-helix transition of the activation helix, depending on its protonation state; (2) a strong electrostatic interaction between His132 and His121 is observed, which can be of stabilizing or destabilizing nature for the activation helix, depending on the relative orientation and protonation states of the rings of His121 and His132; (3) electrostatic interactions involving His119 and Arg122 play a role in the stability of the activation helix; and (4) the activation helix contains the helix-promoting sequence Arg122-Gln123-Ala124-Leu125-Glu126, but its alignment relative to the N and C termini of the helix is not optimal, and is possibly of a destabilizing nature. Finally, we provide electrostatic evidence that the formation and closure of the activation helix create a hydrophobic environment for catalytic-site residue His108, to facilitate catalysis.     

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 fields near the active site of human aldose reductase: 1. New inhibitors and vibrational stark effect measurements

Vibrational Stark effect spectroscopy was used to measure electrostatic fields in the hydrophobic region of the active site of human aldose reductase (hALR2). A new hALR2 inhibitor was designed and synthesized that contains a nitrile probe with a Stark tuning rate of 0.77 cm-1/(MV/cm). Mutations to amino acid residues in the vicinity of the nitrile functional group were selected based on electrostatics calculations, possible complications from hydrogen bonds near the nitrile, and comparison with the active site of human aldehyde reductase, whose structure is very similar. Changes in the absorption energy of the nitrile probe when bound to those mutated proteins were then used to quantify perturbations to the protein's electrostatic field. Electrostatic field changes as large as -10 MV/cm were observed. Measured electrostatic fields were compared to predictions based on continuum electrostatics calculations, revealing that substantial modifications to the calculation strategy are necessary. The effects of hydrogen bonding of amino acid side chains to the nitrile probe are considered, and applications of vibrational Stark effect spectroscopy to investigations of ligand binding and biological function are discussed.     

High-performance prediction of functional residues in proteins with machine learning and computed input features

One of the major challenges in genomics is to understand the function of gene products from their 3D structures. Computational methods are needed for the high-throughput prediction of the function of proteins from their 3D structure. Methods that identify active sites are important for understanding and annotating the function of proteins. Traditional methods exploiting either sequence similarity or structural similarity can be unreliable and cannot be applied to proteins with novel folds or low homology with other proteins. Here, we present a machine-learning application that combines computed electrostatic, evolutionary, and pocket geometric information for high-performance prediction of catalytic residues. Input features consist of our structure-based theoretical microscopic anomalous titration curve shapes (THEMATICS) electrostatics data, enhanced with sequence-based phylogenetic information from INTREPID and topological pocket information from ConCavity. Our THEMATICS-based input features are augmented with an additional metric, the theoretical buffer range. With the integration of the three different types of input, each of which performs admirably on its own, significantly better performance is achieved than that of any of these methods by itself. This combined method achieves 86.7%, 92.5%, and 93.8% recall of annotated functional residues at 5, 8, and 10% false-positive rates, respectively.     

An electrostatic basis for the stability of thermophilic proteins

Two factors provide key contributions to the stability of thermophilic proteins relative to their mesophilic homologues: electrostatic interactions of charged residues in the folded state and the dielectric response of the folded protein. The dielectric response for proteins in a "thermophilic series" globally modulates the thermal stability of its members, with the calculated dielectric constant for the protein increasing from mesophiles to hyperthermophiles. This variability results from differences in the distribution of charged residues on the surface of the protein, in agreement with structural and genetic observations. Furthermore, the contribution of electrostatic interactions to the stability of the folded state is more favorable for thermophilic proteins than for their mesophilic homologues. This leads to the conclusion that electrostatic interactions play an important role in determining the stability of proteins at high temperatures. The interplay between electrostatic interactions and dielectric response also provides further rationalization for the enhanced stability of thermophilic proteins with respect to cold-denaturation. Taken together, the distribution of charged residues and their fluctuations have been shown to be factors in modulating protein stability over the entire range of biologically relevant temperatures.     

Explicit solvent models in protein pKa calculations.

Continuum methods for calculation of protein electrostatics treat buried and ordered water molecules by one of two approximations; either the dielectric constant of regions containing ordered water molecules is equal to the bulk solvent dielectric constant, or it is equal to the protein dielectric constant though no fixed atoms are used to represent water molecules. A method for calculating the titration behavior of individual residues in proteins has been tested on models of hen egg white lysozyme containing various numbers of explicit water molecules. Water molecules were included based on hydrogen bonding, solvent accessibility, and/or proximity to titrating groups in the protein. Inclusion of water molecules significantly alters the calculated titration behavior of individual titrating sites, shifting calculated pKa values by up to 0.5 pH unit. Our results suggest that approximately one water molecule within hydrogen-bonding distance of each charged group should be included in protein electrostatics calculations.     

High apparent dielectric constant inside a protein reflects structural reorganization coupled to the ionization of an internal Asp

The dielectric properties of proteins are poorly understood and difficult to describe quantitatively. This limits the accuracy of methods for structure-based calculation of electrostatic energies and pK(a) values. The pK(a) values of many internal groups report apparent protein dielectric constants of 10 or higher. These values are substantially higher than the dielectric constants of 2-4 measured experimentally with dry proteins. The structural origins of these high apparent dielectric constants are not well understood. Here we report on structural and equilibrium thermodynamic studies of the effects of pH on the V66D variant of staphylococcal nuclease. In a crystal structure of this protein the neutral side chain of Asp-66 is buried in the hydrophobic core of the protein and hydrated by internal water molecules. Asp-66 titrates with a pK(a) value near 9. A decrease in the far UV-CD signal was observed, concomitant with ionization of this aspartic acid, and consistent with the loss of 1.5 turns of alpha-helix. These data suggest that the protein dielectric constant needed to reproduce the pK(a) value of Asp-66 with continuum electrostatics calculations is high because the dielectric constant has to capture, implicitly, the energetic consequences of the structural reorganization that are not treated explicitly in continuum calculations with static structures.     

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.     

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).