Comparison of atomic solvation parametric sets: applicability and limitations in protein folding and binding.

Atomic solvation parameters (ASP) are widely used to estimate the solvation contribution to the thermodynamic stability of proteins as well as the free energy of association for protein-ligand complexes. They are also included in several molecular mechanics computer programs. In this work, a total of eight atomic solvation parametric sets has been employed to calculate the solvation contribution to the free energy of folding delta Gs for 17 proteins. A linear correlation between delta Gs and the number of residues in each protein was found for each ASP set. The calculations also revealed a great variety in the absolute value and in the sign of delta Gs values such that certain ASP sets predicted the unfolded state to be more stable than the folded, whereas others yield precisely the opposite. Further, the solvation contribution to the free energy of association of helix pairs and to the disassociation of loops (connection between secondary structural elements in proteins) from the protein tertiary structures were computed for each of the eight ASP sets and discrepancies were evident among them.     

Estimating protein-ligand binding free energy: atomic solvation parameters for partition coefficient and solvation free energy calculation

Solvation energy calculation is one of the main difficulties for the estimation of protein-ligand binding free energy and the correct scoring in docking studies. We have developed a new solvation energy estimation method for protein-ligand binding based on atomic solvation parameter (ASP), which has been shown to improve the power of protein-ligand binding free energy predictions. The ASP set, designed to handle both proteins and organic compounds and derived from experimental n-octanol/water partition coefficient (log P) data, contains 100 atom types (united model that treats hydrogen atoms implicitly) or 119 atom types (all-atom model that treats hydrogen atoms explicitly). By using this unified ASP set, an algorithm was developed for solvation energy calculation and was further integrated into a score function for predicting protein-ligand binding affinity. The score function reproduced the absolute binding free energies of a test set of 50 protein-ligand complexes with a standard error of 8.31 kJ/mol. As a byproduct, a conformation-dependent log P calculation algorithm named ASPLOGP was also implemented. The predictive results of ASPLOGP for a test set of 138 compounds were r = 0.968, s = 0.344 for the all-atom model and r = 0.962, s = 0.367 for the united model, which were better than previous conformation-dependent approaches and comparable to fragmental and atom-based methods. ASPLOGP also gave good predictive results for small peptides. The score function based on the ASP model can be applied widely in protein-ligand interaction studies and structure-based drug design.     

Atomic solvation parameters in the analysis of protein-protein docking results.

Several sets of amino acid surface areas and transfer free energies were used to derive a total of nine sets of atomic solvation parameters (ASPs). We tested the accuracy of each of these sets of parameters in predicting the experimentally determined transfer free energies of the amino acid derivatives from which the parameters were derived. In all cases, the calculated and experimental values correlated well. We then chose three parameter sets and examined the effect of adding an energetic correction for desolvation based on these three parameter sets to the simple potential function used in our multiple start Monte Carlo docking method. A variety of protein-protein interactions and docking results were examined. In the docking simulations studied, the desolvation correction was only applied during the final energy calculation of each simulation. For most of the docking results we analyzed, the use of an octanol-water-based ASP set marginally improved the energetic ranking of the low-energy dockings, whereas the other ASP sets we tested disturbed the ranking of the low-energy dockings in many of the same systems. We also examined the correlation between the experimental free energies of association and our calculated interaction energies for a series of proteinase-inhibitor complexes. Again, the octanol-water-based ASP set was compatible with our standard potential function, whereas ASP sets derived from other solvent systems were not.     

Discrimination of the native from misfolded protein models with an energy function including implicit solvation.

An essential requirement for theoretical protein structure prediction is an energy function that can discriminate the native from non-native protein conformations. To date most of the energy functions used for this purpose have been extracted from a statistical analysis of the protein structure database, without explicit reference to the physical interactions responsible for protein stability. The use of the statistical functions has been supported by the widespread belief that they are superior for such discrimination to physics-based energy functions. An effective energy function which combined the CHARMM vacuum potential with a Gaussian model for the solvation free energy is tested for its ability to discriminate the native structure of a protein from misfolded conformations; the results are compared with those obtained with the vacuum CHARMM potential. The test is performed on several sets of misfolded structures prepared by others, including sets of about 650 good decoys for six proteins, as well as on misfolded structures of chymotrypsin inhibitor 2. The vacuum CHARMM potential is successful in most cases when energy minimized conformations are considered, but fails when applied to structures relaxed by molecular dynamics. With the effective energy function the native state is always more stable than grossly misfolded conformations both in energy minimized and molecular dynamics-relaxed structures. The present results suggest that molecular mechanics (physics-based) energy functions, complemented by a simple model for the solvation free energy, should be tested for use in the inverse folding problem, and supports their use in studies of the effective energy surface of proteins in solution. Moreover, the study suggests that the belief in the superiority of statistical functions for these purposes may be ill founded.     

蛋白质-蛋白质对接中打分函数的研究

通过分析蛋白质－蛋白质间的静电、疏水作用和熵效应与相对于晶体结构的蛋白质主链原子的均方根偏差（RMSD）的相关性,定量地考查了它们在蛋白质－蛋白质对接中作为打分函数评价近天然构象的能力。对7个蛋白质复合物体系的分析表明,就水化能而言,原子接触势模型（ACE）优于原子水化参数模型（ASP）,且修正的ACE模型具有更好的评价近天然构象的能力;水化能与静电能结合对评价能力有进一步的提高。最后,我们将静电和修正的ACE水化能结合作为打分函数用于36个蛋白质复合物体系的对接研究,进一步证实了这两种能量项的组合能有效地将近天然结构从分子对接模式中区分出来。     

Polar and nonpolar atomic environments in the protein core: Implications for folding and binding

Hydrophobic interactions are believed to play an important role in protein folding and stability. Semi-empirical attempts to estimate these interactions are usually based on a model of solvation, whose contribution to the stability of proteins is assumed to be proportional to the surface area buried upon folding. Here we propose an extension of this idea by defining an environment free energy that characterizes the environment of each atom of the protein, including solvent, polar or nonpolar atoms of the same protein or of another molecule that interacts with the protein. In our model, the difference of this environment free energy between the folded state and the unfolded (extended) state of a protein is shown to be proportional to the area buried by nonpolar atoms upon folding. General properties of this environment free energy are derived from statistical studies on a database of 82 well-refined protein structures. This free energy is shown to be able to discriminate misfolded from correct structural models, to provide an estimate of the stabilization due to oligomerization, and to predict the stability of mutants in which hydrophobic residues have been substituted by site-directed mutagenesis, provided that no large structural modifications occur. © 1994 Wiley-Liss, Inc.     

Stability scale and atomic solvation parameters extracted from 1023 mutation experiments

The stability scale of 20 amino acid residues is derived from a database of 1023 mutation experiments on 35 proteins. The resulting scale of hydrophobic residues has an excellent correlation with the octanol-to-water transfer free energy corrected with an additional Flory-Huggins molar-volume term (correlation coefficient r = 0.95, slope = 1.05, and a near zero intercept). Thus, hydrophobic contribution to folding stability is characterized remarkably well by transfer experiments. However, no corresponding correlation is found for hydrophilic residues. Both the hydrophilic portion and the entire scale, however, correlate strongly with average burial accessible surface (r = 0.76 and 0.97, respectively). Such a strong correlation leads to a near uniform value of the atomic solvation parameters for atoms C, S, O/N, O(-0.5), and N(+0.5,1). All are in the range of 12-28 cal x mol(-1) A(-2), close to the original estimate of hydrophobic contribution of 25-30 cal x mol(-1) A(-2) to folding stability. Without any adjustable parameters, the new stability scale and new atomic solvation parameters yielded an accurate prediction of protein-protein binding free energy for a separate database of 21 protein-protein complexes (r = 0.80 and slope = 1.06, and r = 0.83 and slope = 0.93, respectively).     

Thermodynamics of protein folding: a microscopic view

Statistical thermodynamics provides a powerful theoretical framework for analyzing, understanding and predicting the conformational properties of biomolecules. The central quantity is the potential of mean force or effective energy as a function of conformation, which consists of the intramolecular energy and the solvation free energy. The intramolecular energy can be reasonably described by molecular mechanics-type functions. While the solvation free energy is more difficult to model, useful results can be obtained with simple approximations. Such functions have been used to estimate the intramolecular energy contribution to protein stability and obtain insights into the origin of thermodynamic functions of protein folding, such as the heat capacity. With reasonable decompositions of the various energy terms, one can obtain meaningful values for the contribution of one type of interaction or one chemical group to stability. Future developments will allow the thermodynamic characterization of ever more complex biological processes.     

A combined steepest descent and genetic algorithm (SD/GA) approach for the optimization of solvation parameters

An accurate solvation model is essential for computer modeling of protein folding and other biomolecular self-assembly processes. Compared to explicit solvent models, implicit solvent models, such as the Poisson-Boltzmann (PB) with solvent accessible surface area model (PB/SA), offer a much faster speed—the most compelling reason for the popularity of these implicit solvent models. Since these implicit solvent models typically use empirical parameters, such as atomic radii and the surface tensions, an optimal fit of these parameters is crucial for the final accuracy of properties such as solvation free energy and folding free energy. In this paper, we proposed a combined approach, namely SD/GA, which takes the advantage of both local optimization with the steepest descent (SD), and global optimization with the genetic algorithm (GA), for parameters optimization in multi-dimensional space. The SD/GA method is then applied to the optimization of solvation parameters in the non-polar cavity term of the PB/SA model. The results show that the newly optimized parameters from SD/GA not only increase the accuracy in the solvation free energies for ～200 organic molecules, but also significantly improve the free energy landscape of a β-hairpin folding. The current SD/GA method can be readily applied to other multi-dimensional parameter space optimization as well.     

Energetics of protein folding

The energetics of protein folding determine the 3D structure of a folded protein. Knowledge of the energetics is needed to predict the 3D structure from the amino acid sequence or to modify the structure by protein engineering. Recent developments are discussed: major factors are reviewed and auxiliary factors are discussed briefly. Major factors include the hydrophobic factor (burial of non-polar surface area) and van der Waals interactions together with peptide hydrogen bonds and peptide solvation. The long-standing model for the hydrophobic factor (free energy change proportional to buried non-polar surface area) is contrasted with the packing-desolvation model and the approximate nature of the proportionality between free energy and apolar surface area is discussed. Recent energetic studies of forming peptide hydrogen bonds (gas phase) are reviewed together with studies of peptide solvation in solution. Closer agreement is achieved between the 1995 values for protein unfolding enthalpies in vacuum given by Lazaridis-Archontis-Karplus and Makhatadze-Privalov when the solvation enthalpy of the peptide group is taken from electrostatic calculations. Auxiliary factors in folding energetics include salt bridges and side-chain hydrogen bonds, disulfide bridges, and propensities to form alpha-helices and beta-structure. Backbone conformational entropy is a major energetic factor which is discussed only briefly for lack of knowledge.     

H-bonding in protein hydration revisited

H-bonding between protein surface polar/charged groups and water is one of the key factors of protein hydration. Here, we introduce an Accessible Surface Area (ASA) model for computationally efficient estimation of a free energy of water-protein H-bonding at any given protein conformation. The free energy of water-protein H-bonds is estimated using empirical formulas describing probabilities of hydrogen bond formation that were derived from molecular dynamics simulations of water molecules at the surface of a small protein, Crambin, from the Abyssinian cabbage (Crambe abyssinica) seed. The results suggest that atomic solvation parameters (ASP) widely used in continuum hydration models might be dependent on ASA for polar/charged atoms under consideration. The predictions of the model are found to be in qualitative agreement with the available experimental data on model compounds. This model combines the computational speed of ASA potential, with the high resolution of more sophisticated solvation methods.     

Contribution of Thr29 to the thermodynamic stability of goat alpha-lactalbumin as determined by experimental and theoretical approaches

The Thr29 residue in the hydrophobic core of goat alpha-lactalbumin (alpha-LA) was substituted with Val (Thr29Val) and Ile (Thr29Ile) to investigate the contribution of Thr29 to the thermodynamic stability of the protein. We carried out protein stability measurements, X-ray crystallographic analyses, and free energy calculations based on molecular dynamics simulation. The equilibrium unfolding transitions induced by guanidine hydrochloride demonstrated that the Thr29Val and Thr29Ile mutants were, respectively, 1.9 and 3.2 kcal/mol more stable than the wild-type protein (WT). The overall structures of the mutants were almost identical to that of WT, in spite of the disruption of the hydrogen bonding between the side-chain O-H group of Thr29 and the main-chain C=O group of Glu25. To analyze the stabilization mechanism of the mutants, we performed free energy calculations. The calculated free energy differences were in good agreement with the experimental values. The stabilization of the mutants was mainly caused by solvation loss in the denatured state. Furthermore, the O-H group of Thr29 favorably interacts with the C=O group of Glu25 to form hydrogen bonds and, simultaneously, unfavorably interacts electrostatically with the main-chain C=O group of Thr29. The difference in the free energy profile of the unfolding path between WT and the Thr29Ile mutant is discussed in light of our experimental and theoretical results.     

Exhaustive mutagenesis in silico: multicoordinate free energy calculations on proteins and peptides

We have extended and applied a multicoordinate free energy method, chemical Monte Carlo/Molecular Dynamics (CMC/MD), to calculate the relative free energies of different amino acid side-chains. CMC/MD allows the calculation of the relative free energies for many chemical species from a single free energy calculation. We have previously shown its utility in host:guest chemistry (Pitera and Kollman, J Am Chem Soc 1998;120:7557-7567)1 and ligand design (Eriksson et al., J Med Chem 1999;42:868-881)2, and here demonstrate its utility in calculations of amino acid properties and protein stability. We first study the relative solvation free energies of N-methylated and acetylated alanine, valine, and serine amino acids. With careful inclusion of rotameric states, internal energies, and both the solution and vacuum states of the calculation, we calculate relative solvation free energies in good agreement with thermodynamic integration (TI) calculations. Interestingly, we find that a significant amount of the unfavorable solvation of valine seen in prior work (Sun et al., J Am Chem Soc 1992;114:6798-6801)3 is caused by restraining the backbone in an extended conformation. In contrast, the solvation free energy of serine is calculated to be less favorable than expected from experiment, due to the formation of a favorable intramolecular hydrogen bond in the vacuum state. These monomer calculations emphasize the need to accurately consider all significant conformations of flexible molecules in free energy calculations. This development of the CMC/MD method paves the way for computations of protein stability analogous to the biochemical technique of "exhaustive mutagenesis." We have carried out just such a calculation at position 133 of T4 lysozyme, where we use CMC/MD to calculate the relative stability of eight different side-chain mutants in a single free energy calculation. Our T4 calculations show good agreement with the prior free energy calculations of Veenstra et al. (Prot Eng 1997;10:789-807)4 and excellent agreement with the experiments of Mendel et al. (Science 1992;256:1798-1802).     

Contributions of a highly conserved VH/VL hydrogen bonding interaction to scFv folding stability and refolding efficiency.

The assembly of single-chain Fv (scFv) antibody fragments, consisting of an interconnected variable heavy chain (VH) and variable light chain (VL), is a cooperative process that requires coupled folding and domain association. We report here an initial investigation of VH/VL domain-domain assembly with a site-directed mutagenesis study that probes a highly conserved VH/VL hydrogen bonding interaction. Gln168 of the S5 scFv (Kabat VH 39) is absolutely conserved in 95% of all VH, and Gln44 (Kabat VL 38) is found in 94% of all kappa VL (Glx in 95% of all lambda VL). These side chains form two hydrogen bonds in head-to-tail alignment across the VH/VL interface. Double mutant cycles at Gln168 and Gln44 were constructed to first investigate their contribution to thermodynamic folding stability, second to investigate whether stability can be improved, and third to determine whether refolding efficiencies are affected by mutations at these positions. The results demonstrate that the Gln168-Gln44 interaction is not a key determinant of S5 scFv folding stability, as sequential modification to alanine has no significant effect on the free energy of folding. Several mutations that alter the glutamines to methionine or charged amino acids significantly increase the thermodynamic stability by increasing the m(g) associated with the unfolding isotherm. These effects are hypothesized to arise largely from an increase in the VH/VL association free energy that leads to tighter coupling between domain-domain association and folding. All of the mutants also display a reduced antigen binding affinity. Single and double methionine mutants also displayed significant increases in refolding efficiency of 2.4- to 3-fold over the native scFv, whereas the double alanine/methionine mutants displayed moderate 1.9- to 2.4-fold enhancement. The results suggest that reengineering the VH/VL interface could be useful in improving the stability of single-chain antibodies, as Ala/Met mutations at these conserved positions increase the free energy of folding by 46% while minimally perturbing binding affinity. They also could be useful in improving scFv recovery from inclusion bodies as the mutations increase the refolding efficiency by more than twofold.     

A computational protocol to probe the role of solvation effects on the reduction potential of azurin mutants

Semiquantitative relationships between thermodynamic parameters of Cu2+ reduction experimentally measured for a series of azurin mutants and the solvation free energy of the oxidized state of the proteins were derived. Solvation free energy calculations were carried out within an ONIOM/PCM scheme specifically adapted to this protein series. The method proved to be able to capture the main determinants of the measured reduction parameters, providing satisfactory predictions of the E degrees '.     

Toward Correct Protein Folding Potentials

Empirical protein folding potentialfunctions should have a global minimum nearthe native conformationof globular proteins that fold stably, andthey should give the correct free energy offolding. We demonstrate that otherwise verysuccessful potentials fail to have even alocal minimumanywhere near the native conformation, anda seemingly well validated method ofestimatingthe thermodynamic stability of the nativestate is extremely sensitive to smallperturbations inatomic coordinates. These are bothindicative of fitting a great deal ofirrelevant detail. Here weshow how to devise a robust potentialfunction that succeeds very well at bothtasks, at least for alimited set of proteins, and this involvesdeveloping a novel representation of thedenatured state.Predicted free energies of unfolding for 25mutants of barnase are in close agreementwith theexperimental values, while for 17 mutantsthere are substantial discrepancies.     

Evaluation of a fast implicit solvent model for molecular dynamics simulations.

A solvation term based on the solvent accessible surface area (SASA) is combined with the CHARMM polar hydrogen force field for the efficient simulation of peptides and small proteins in aqueous solution. Only two atomic solvation parameters are used: one is negative for favoring the direct solvation of polar groups and the other positive for taking into account the hydrophobic effect on apolar groups. To approximate the water screening effects on the intrasolute electrostatic interactions, a distance-dependent dielectric function is used and ionic side chains are neutralized. The use of an analytical approximation of the SASA renders the model extremely efficient (i.e., only about 50% slower than in vacuo simulations). The limitations and range of applicability of the SASA model are assessed by simulations of proteins and structured peptides. For the latter, the present study and results reported elsewhere show that with the SASA model it is possible to sample a significant amount of folding/unfolding transitions, which permit the study of the thermodynamics and kinetics of folding at an atomic level of detail.     

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).     

An Effective Solvation Term Based on Atomic Occupancies for Use in Protein Simulations

Abstract

Several approaches to the treatment of solvent effects based on continuum models are reviewed and a new method based on occupied atomic volumes (occupancies) is proposed and tested. The new method describes protein-water interactions in terms of atomic solvation parameters, which represent the solvation free energy per unit of volume. These parameters were determined for six different atoms types, using experimental free energies of solvation. The method was implemented in the GROMOS and PRESTO molecular simulation program suites. Simulations with the solvation term require 20-50% more CPU time than the corresponding vacuum simulations and are approximately 20 times faster than explicit water simulations. The method and parameters were tested by carrying out 200 ps simulations of BPTI in water, in vacuo, and with the solvation term. The performance of the solvation term was assessed by comparing the structures and energies from the solvation simulations with the equivalent quantities derived from several BPTI crystal structures and from the explicit water and vacuum simulations. The model structures were evaluated in terms of exposed total surface, buried and exposed polar surfaces, secondary structure preservation, number of hydrogen bonds, energy contributions, and positional deviations from BPTI crystal structures. Vacuum simulations produced unrealistic structures with respect to all criteria applied. The structures resulting from the simulations with explicit water were closer to the 5PTI crystal structure, although part of the secondary structure dissolved. The simulations with the effective solvation term produce structures that are normal according to all evaluations and in most respects are remarkably similar to the 5PTI crystal structure despite considerable positional fluctuations during the simulations. The segments where the model and crystal structures differ are known to be flexible and the observed difference may be physically realistic. The effective solvation term based on occupancies is not only very efficient in terms of computer time but also results in meaningful structural properties for BPTI. It may therefore be generally useful in molecular dynamics of macromolecules.     

Coupling between conformation and proton binding in proteins

Interest centers here on whether the use of a fixed charge distribution of a protein solute, or a treatment that considers proton-binding equilibria by solving the Poisson equation, is a better approach to discriminate native from non-native conformations of proteins. In this analysis of the charge distribution of 7 proteins, we estimate the solvation free energy contribution to the total free energy by exploring the 2(zeta) possible ionization states of the whole molecule, with zeta being the number of ionizable groups in the amino acid sequence, for every conformation in the ensembles of 7 proteins. As an additional consideration of the role of electrostatic interactions in determining the charge distribution of native folds, we carried out a comparison of alternative charge assignment models for the ionizable residues in a set of 21 native-like proteins. The results of this work indicate that (1) for 6 out of 7 proteins, estimation of solvent polarization based on the Generalized Born model with a fixed charge distribution provides the optimal trade-off between accuracy, with respect to the Poisson equation, and speed when compared to the accessible surface area model; for the seventh protein, consideration of all possible ionization states of the whole molecule appears to be crucial to discriminate the native from non-native conformations; (2) significant differences in the degree of ionization and hence the charge distribution for native folds are found between the different charge models examined; (3) the stability of the native state is determined by a delicate balance of all the energy components, and (4) conformational entropy, and hence the dynamics of folding, may play a crucial role for a successful ab initio protein folding prediction.