Partition of protein solvation into group contributions from molecular dynamics simulations

Linear response theory coupled to molecular dynamics simulations with an explicit solvent representation is used to derive fractional contributions of amino acid residues to the solvation of proteins. The new fractional methods developed here are compared with standard approaches based on empirical 1D and 3D statistical potentials, as well as with estimates obtained from the analysis of classical molecular interaction potentials. The new fractional methods, which have a clear physical basis and explicitly account for the effects due to protein structure and flexibility, provide an accurate picture of the contribution to solvation of different regions of the protein.     

On the origin of the electrostatic barrier for proton transport in aquaporin

The nature of the electrostatic barrier for proton transport in aquaporins is analyzed by semimacroscopic and microscopic models. It is found that the barrier is associated with the loss of the generalized solvation energy upon moving from the bulk solvent to the center of the channel. It is clarified that our solvation concept includes the effect of the protein polar groups and ionized residues. The nature of the contributions to the solvation barrier is examined by using the linear response approximation. It is found that the residues in the NPA region contribute much less than what would be deduced from calculations that do not consider the protein reorganization. It is clarified that the contributions of different structural or electrostatic elements to the solvation barrier can be established by removing these elements and examining the corresponding effect on the barrier height. Using this definition and “mutating” the NPA residues to their non-polar analogues establishes that these residues do not provide the major contribution to the solvation barrier.     

Amino acid side-chain partition energies and distribution of residues in soluble proteins

Energies required to transfer amino acid side chains from water to less polar environments were calculated from results of several studies and compared with several statistical analyses of residue distributions in soluble proteins. An analysis that divides proteins into layers parallel with their surfaces is more informative than those that simply classify residues as exposed or buried. Most residues appear to be distributed as a function of the distance from the protein-water interface in a manner consistent with partition energies calculated from partitioning of amino acids between water and octanol phases and from solubilities of amino acids in water, ethanol, and methanol. Lys, Arg, Tyr, and Trp residues tend to concentrate near the water-protein interface where their apolar side-chain components are more buried than their polar side-chain components. Residue distributions calculated in this manner do not correlate well with side-chain solvation energies calculated from vapor pressures of side-chain analogs over a water phase. Results of statistical studies that classify residues as exposed to solvent or buried inside the protein interior appear to depend on the method used to classify residues. Data from some of these studies correlate better with solvation energies, but other data correlate better with partition energies. Most other statistical methods that have been used to evaluate effects of water on residue distributions yield results that correlate better with partition energies than with solvation energies.     

Evaluation of the conformational free energies of loops in proteins

In this paper we discuss the problem of including solvation free energies in evaluating the relative stabilities of loops in proteins. A conformational search based on a gas-phase potential function is used to generate a large number of trial conformations. As has been found previously, the energy minimization step in this process tends to pack charged and polar side chains against the protein surface, resulting in conformations which are unstable in the aqueous phase. Various solvation models can easily identify such structures. In order to provide a more severe test of solvation models, gas phase conformations were generated in which side chains were kept extended so as to maximize their interaction with the solvent. The free energies of these conformations were compared to that calculated for the crystal structure in three loops of the protein E. coli RNase H, with lengths of 7, 8, and 9 residues. Free energies were evaluated with a finite difference Poisson-Boltzmann (FDPB) calculation for electrostatics and a surface area-based term for nonpolar contributions. These were added to a gas-phase potential function. A free energy function based on atomic solvation parameters was also tested. Both functions were quite successful in selecting, based on a free energy criterion, conformations quite close to the crystal structure for two of the three loops. For one loop, which is involved in crystal contacts, conformations that are quite different from the crystal structure were also selected. A method to avoid precision problems associated with using the FDPB method to evaluate conformational free energies in proteins is described. © 1994 John Wiley & Sons, Inc.     

Structural Determinants of Yeast Protein-Protein Interaction Interface Evolution at the Residue Level

Interfaces of contact between proteins play important roles in determining the proper structure and function of protein–protein interactions (PPIs). Therefore, to fully understand PPIs, we need to better understand the evolutionary design principles of PPI interfaces. Previous studies have uncovered that interfacial sites are more evolutionarily conserved than other surface protein sites. Yet, little is known about the nature and relative importance of evolutionary constraints in PPI interfaces. Here, we explore constraints imposed by the structure of the microenvironment surrounding interfacial residues on residue evolutionary rate using a large dataset of over 700 structural models of baker’s yeast PPIs. We find that interfacial residues are, on average, systematically more conserved than all other residues with a similar degree of total burial as measured by relative solvent accessibility (RSA). Besides, we find that RSA of the residue when the PPI is formed is a better predictor of interfacial residue evolutionary rate than RSA in the monomer state. Furthermore, we investigate four structure-based measures of residue interfacial involvement, including change in RSA upon binding (ΔRSA), number of residue-residue contacts across the interface, and distance from the center or the periphery of the interface. Integrated modeling for evolutionary rate prediction in interfaces shows that ΔRSA plays a dominant role among the four measures of interfacial involvement, with minor, but independent contributions from other measures. These results yield insight into the evolutionary design of interfaces, improving our understanding of the role that structure plays in the molecular evolution of PPIs at the residue level.     

Quantitative Characterization of Local Protein Solvation To Predict Solvent Effects on Protein Structure

Characterization of solvent preferences of proteins is essential to the understanding of solvent effects on protein structure and stability. Although it is generally believed that solvent preferences at distinct loci of a protein surface may differ, quantitative characterization of local protein solvation has remained elusive. In this study, we show that local solvation preferences can be quantified over the entire protein surface from extended molecular dynamics simulations. By subjecting microsecond trajectories of two proteins (lysozyme and antibody fragment D1.3) in 4 M glycerol to rigorous statistical analyses, solvent preferences of individual protein residues are quantified by local preferential interaction coefficients. Local solvent preferences for glycerol vary widely from residue to residue and may change as a result of protein side-chain motions that are slower than the longest intrinsic solvation timescale of ～10 ns. Differences of local solvent preferences between distinct protein side-chain conformations predict solvent effects on local protein structure in good agreement with experiment. This study extends the application scope of preferential interaction theory and enables molecular understanding of solvent effects on protein structure through comprehensive characterization of local protein solvation.     

Prediction of homologous protein structures based on conformational searches and energetics

A "knowledge-based" method of predicting the unknown structure of a protein from a homologous known structure using energetics to determine a sidechain conformation is proposed. The method consists of exchanging the residues in the known structure for the sequence of the unknown protein. Then a conformational search with molecular mechanics energy minimization is done on the exchanged residues. The lowest energy conformer is the one picked to be the predicted structure. In the structure of bovine trypsin, the importance of including a solvation energy term in the search is demonstrated for solvent accessible residues, while molecular mechanics alone is enough to correctly predict the conformation of internal residues. The correctness of the model is assessed by a volume error overlap of the predicted structure compared to the crystal structure. Finally, the structure of rat trypsin is predicted from the crystal structure of bovine trypsin. The sequences of these two proteins are 74% identical and all of the significant changes between them are on external residues. Thus, the inclusion of solvation energy in the conformational search is necessary to accurately predict the structure of the exchanged residues.     

Simple solvation potential for coarse-grained models of proteins

We formulate a simple solvation potential based on a coarsed-grained representation of amino acids with two spheres modeling the C(alpha) atom and an effective side-chain centroid. The potential relies on a new method for estimating the buried area of residues, based on counting the effective number of burying neighbors in a suitable way. This latter quantity shows a good correlation with the buried area of residues computed from all atom crystallographic structures. We check the discriminatory power of the solvation potential alone to identify the native fold of a protein from a set of decoys and show the potential to be considerably selective.     

Amino acid substitutions at protein–protein interfaces that modulate the oligomeric state

Despite similarities in their sequence and structure, there are a number of homologous proteins that adopt various oligomeric states. Comparisons of these homologous protein pairs, in terms of residue substitutions at the protein–protein interfaces, have provided fundamental characteristics that describe how proteins interact with each other. We have prepared a dataset composed of pairs of related proteins with different homo‐oligomeric states. Using the protein complexes, the interface residues were identified, and using structural alignments, the shadow‐interface residues have been defined as the surface residues that align with the interface residues. Subsequently, we investigated residue substitutions between the interfaces and the shadow interfaces. Based on the degree of the contributions to the interactions, the aligned sites of the interfaces and shadow interfaces were divided into primary and secondary sites; the primary sites are the focus of this work. The primary sites were further classified into two groups (i.e. exposed and buried) based on the degree to which the residue is buried within the shadow interfaces. Using these classifications, two simple mechanisms that mediate the oligomeric states were identified. In the primary‐exposed sites, the residues on the shadow interfaces are replaced by more hydrophobic or aromatic residues, which are physicochemically favored at protein–protein interfaces. In the primary‐buried sites, the residues on the shadow interfaces are replaced by larger residues that protrude into other proteins. These simple rules are satisfied in 23 out of 25 Structural Classification of Proteins (SCOP) families with a different‐oligomeric‐state pair, and thus represent a basic strategy for modulating protein associations and dissociations. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Dissecting the energetics of protein alpha-helix C-cap termination through chemical protein synthesis

The alpha-helix is a fundamental protein structural motif and is frequently terminated by a glycine residue. Explanations for the predominance of glycine at the C-cap terminal portions of alpha-helices have invoked uniquely favorable energetics of this residue in a left-handed conformation or enhanced solvation of the peptide backbone because of the absence of a side chain. Attempts to quantify the contributions of these two effects have been made previously, but the issue remains unresolved. Here we have used chemical protein synthesis to dissect the energetic basis of alpha-helix termination by comparing a series of ubiquitin variants containing an L-amino acid or the corresponding D-amino acid at the C-cap Gly35 position. D-Amino acids can adopt a left-handed conformation without energetic penalty, so the contributions of conformational strain and backbone solvation can thus be separated. Analysis of the thermodynamic data revealed that the preference for glycine at the C' position of a helix is predominantly a conformational effect.     

Long loop prediction using the protein local optimization program

We have developed an improved sampling algorithm and energy model for protein loop prediction, the combination of which has yielded the first methodology capable of achieving good results for the prediction of loop backbone conformations of 11 residue length or greater. Applied to our newly constructed test suite of 104 loops ranging from 11 to 13 residues, our method obtains average/median global backbone root-mean-square deviations (RMSDs) to the native structure (superimposing the body of the protein, not the loop itself) of 1.00/0.62 A for 11 residue loops, 1.15/0.60 A for 12 residue loops, and 1.25/0.76 A for 13 residue loops. Sampling errors are virtually eliminated, while energy errors leading to large backbone RMSDs are very infrequent compared to any previously reported efforts, including our own previous study. We attribute this success to both an improved sampling algorithm and, more critically, the inclusion of a hydrophobic term, which appears to approximately fix a major flaw in SGB solvation model that we have been employing. A discussion of these results in the context of the general question of the accuracy of continuum solvation models is presented.     

A model peptide with enhanced helicity

The sequence of a model monomeric peptide, acetylA(EAAAK)3Aamide was altered to expedite measurement of peptide concentration and to enhance its fractional helical content. Replacement of the N-terminal alanine residue with a tryptophan residue provides a convenient chromophore for measurement of peptide concentration without diminishing the helical content. Replacement of the three lysine residues with arginine residues enhances the helical content without loss of their electrostatic contributions. Increasing the number of EAAAR sequence units in the peptide acetylW(EAAAR)nAamide from three to five indicates that the spectral features anticipated for a completely helical peptide are closely approached.     

Identifying stabilizing key residues in proteins using interresidue interaction energy matrix

We are proposing an interresidue interaction energy map (IEM)--a new tool for protein structure analysis and protein bioinformatics. This approach employs the sum of pair-wise interaction energies of a particular residue as a measure of its structural importance. We will show that the IEM can serve as a means for identifying key residues responsible for the stability of a protein. Our method can be compared with the interresidue contact map but has the advantage of weighting the contacts by the stabilization energy content which they bring to the protein structure. For the theoretical adjustment of the proposed method, we chose the Trp-cage mini protein as a model system to compare a spectrum of computational methods ranging from the ab initio MP2 level through the DFT method to empirical force-field methods. The IEM method correctly identifies Tryptophane 6 as the key residue in the Trp-cage. The other residues with the highest stabilizing contributions correspond to the structurally important positions in the protein. We have further tested our method on the Trp2Cage miniprotein--a P12W mutant of the Trp-cage and on two proteins from the rubredoxin family that differ in their thermostability. Our method correctly identified the thermodynamically more stable variants in both cases and therefore can also be used as a tool for the relative measurement of protein stability. Finally, we will point out the important role played by dispersion energy, which contributes significantly to the total stabilization energy and whose role in aromatic pairs is clearly dominant. Surprisingly, the dispersion energy plays an even more important role in the interaction of prolines with aromatic systems.     

Use of a potential of mean force to analyze free energy contributions in protein folding.

A method for calculation of the free energy of residues as a function of residue burial is proposed. The method is based on the potential of mean force, with a reaction coordinate expressed by residue burial. Residue burials are calculated from high-resolution protein structures. The largest individual contributions to the free energy of a residue are found to be due to the hydrophobic interactions of the nonpolar atoms, interactions of the main chain polar atoms, and interactions of the charged groups of residues Arg and Lys. The contribution to the free energy of folding due to the uncharged side chain polar atoms is small. The contribution to the free energy of folding due to the main chain polar atoms is favorable for partially buried residues and less favorable or unfavorable for fully buried residues. Comparison of the accessible surface areas of proteins and model spheres shows that proteins deviate considerably from a spherical shape and that the deviations increase with the size of a protein. The implications of these results for protein folding are also discussed.     

Fast accurate evaluation of protein solvent exposure

Protein solvation energies are often taken to be proportional to solvent-accessible surface areas. Computation of these areas is numerically demanding and may become a bottleneck for folding and design applications. Fast graph-based methods, such as dead-end elimination (DEE), become possible if all energies, including solvation energies, are expressed as single-residue and pair-residue terms. To this end, Street and Mayo originated a pair-residue approximation for solvent-accessible surface areas (Street AG, Mayo SL. Pairwise calculation of protein solvent accessible surface areas. Fold Des 1998;3:253-258). The dominant source of error in this method is the overlapping burial of side-chain surfaces in the protein core. Here we report a new pair-residue approximation, which greatly reduces this overlap error by the use of optimized generic side-chains. We have tested the generic-side-chain method for the ten proteins studied by Street and Mayo and for 377 single-domain proteins from the CATH database (Orengo CA, Michie AD, Jones S, Jones DT, Swindells MB, Thornton JM. CATH-A hierarchic classification of protein domain structures. Structure 1997;5:1093-1108). With little additional cost in computation, the new method consistently reduces error for total areas and residue-by-residue areas by more than a factor of two. For example, the residue-by-residue error (for buried area) is reduced from 7.42 A(2) to 3.70 A(2). This difference translates into a solvation energy difference of approximately 0.2 kcal/mol per residue, amounting to a reduction in root-mean-square energy error of 2 kcal/mol for a 100 residue chain, a potentially critical difference for both protein folding and design applications.     

Folding of the villin headpiece subdomain from random structures. Analysis of the charge distribution as a function of pH

The structure of the 36 residue villin headpiece subdomain is investigated with the electrostatically driven Monte Carlo method. The ECEPP/3 (Empirical Conformational Energy Program for Peptides) force field, plus two different continuum solvation models, were used to describe the conformational energy of the chain with both blocked and unblocked N and C termini. A statistical analysis of an ensemble of ab initio generated conformations was carried out, based on a comparison with a set of ten native-like structures derived from published experimental data, by using rigid geometry and NMR-derived constraints obtained at pH 3.7. The ten native-like structures satisfy the NMR-derived constraints. The whole ensemble of conformations of the terminally unblocked villin headpiece sub-domain, generated by using ECEPP/3 with a continuum solvation model, were subsequently evaluated at pH 3.7 with a potential function that includes ECEPP/3 combined with a fast multigrid boundary element method. At pH 3.7, the lowest-energy conformation found during the conformational search satisfies approximately 70% of both the distance and the dihedral-angle constraints, and possesses the characteristic packing of three phenylalanine residues that constitute the main part of the hydrophobic core of the molecule. On the other hand, computations at pH 3.7 and pH 7.0 for the ten native-like structures satisfying the NMR-derived constraints indicate a substantial change in the charge distribution for each type of amino acid residue with the change in pH. The results of this study provide a basis to understand the effect of the interactions, such as hydrophobicity, charge-charge interaction and solvent polarization, on the stability of this small alpha-helical protein.     

15N backbone dynamics of the S-peptide from ribonuclease A in its free and S-protein bound forms: toward a site-specific analysis of entropy changes upon folding.

Backbone 15N relaxation parameters (R1, R2, 1H-15N NOE) have been measured for a 22-residue recombinant variant of the S-peptide in its free and S-protein bound forms. NMR relaxation data were analyzed using the "model-free" approach (Lipari & Szabo, 1982). Order parameters obtained from "model-free" simulations were used to calculate 1H-15N bond vector entropies using a recently described method (Yang & Kay, 1996), in which the form of the probability density function for bond vector fluctuations is derived from a diffusion-in-a-cone motional model. The average change in 1H-15N bond vector entropies for residues T3-S15, which become ordered upon binding of the S-peptide to the S-protein, is -12.6+/-1.4 J/mol.residue.K. 15N relaxation data suggest a gradient of decreasing entropy values moving from the termini toward the center of the free peptide. The difference between the entropies of the terminal and central residues is about -12 J/mol residue K, a value comparable to that of the average entropy change per residue upon complex formation. Similar entropy gradients are evident in NMR relaxation studies of other denatured proteins. Taken together, these observations suggest denatured proteins may contain entropic contributions from non-local interactions. Consequently, calculations that model the entropy of a residue in a denatured protein as that of a residue in a di- or tri-peptide, might over-estimate the magnitude of entropy changes upon folding.     

Packing-based difference of structural features between thermophilic and mesophilic proteins

Twenty pairs of thermophilic and mesophilic proteins were compared in terms of residue packing distribution to obtain structural features related to protein thermostability. Based on residue packing concept, structural features of residues such as residue packing distribution, inner/outer position, secondary structure and water solvation were investigated. The statistical tests revealed that higher frequency in well-packed state of residues, lower frequency in exposed state and higher frequency in well-packed state of inner positioned residues, and higher frequency in well-packed state of 3/10 helix residues could be general structural features thermophilic proteins have.     

Simulating the folding of small proteins by use of the local minimum energy and the free solvation energy yields native-like structures

Assuming that the protein primary sequence contains all information required to fold a protein into its native tertiary structure, we propose a new computational approach to protein folding by distributing the total energy of the macromolecular system along the torsional axes.We further derive a new semiempirical equation to calculate the total energy of a macromolecular system including its free energy of solvation. The energy of solvation makes an important contribution to the stability of biological structures. The segregation of hydrophilic and hydrophobic domains is essential for the formation of micelles, lipid bilayers, and biological membranes, and it is also important for protein folding. The free energy of solvation consists of two components: one derived from interactions between the atoms of the protein, and the second resulting from interactions between the protein and the solvent. The latter component is expressed as a function of the fractional area of protein atoms accessible to the solvent.The protein-folding procedure described in this article consists of two successive steps: a theoretical transition from an ideal α helix to an ideal β sheet is first imposed on the protein conformation, in order to calculate an initial secondary structure. The most stable secondary structure is built from a combination of the lowest energy structures calculated for each amino acid during this transition. An angular molecular dynamics step is then applied to this secondary structure. In this computational step, the total energy of the system consisting of the sum of the torsional energy, the van der Waals energy, the electrostatic energy, and the solvation energy is minimized. This process yields 3-D structures of minimal total energy that are considered to be the most probable native-like structures for the protein.This method therefore requires no prior hypothesis about either the secondary or the tertiary structure of the protein and restricts the input of data to its sequence. The validity of the results is tested by comparing the crystalline and computed structures of four proteins, i.e., the avian and bovine pancreatic polypeptide (36 residues each), uteroglobin (70 residues), and the calcium-binding protein (75 residues); the C_α-C_α maps show significant homologies and the position of secondary structure domains; that of the α helices is particularly close.