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.     

Theoretical studies on solvation contribution to the thermodynamic stability of mutants of lysozyme T4

Atomic solvation parameters (ASPs) 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. In view of discrepancies in the results of free energies of solvation of folding for various proteins obtained using different atomic solvation parameter sets, systematic studies have been carried out for the calculation of accessible surface area and the changes in free energy of solvation of folding (deltaG(s,f)) for mutants of lysozyme T4 where threonine 157 is replaced by amino acids: cysteine, aspartate, glutamate, phenylalanine, glycine, histidine, isoleucine, leucine, asparagine, arginine, serine and valine. The deviations of the calculated results from the experimental results are discussed to highlight the discrepancies in the atomic solvation parameter sets and possible reasons for them. The results are also discussed to throw light on the effect of chain free energy and hydrogen bonding on the stability of mutants. The octanol to water-based ASP sets 'Sch1' and 'EM' perform better than the vacuum to water-based ASP sets. The vacuum to water-based ASP sets 'Sch3' and 'WE' can be used to predict the stability of mutants if a proper method to calculate the hydrogen bond contribution to overall stability is in place.     

Free energy surfaces of miniproteins with a betabetaalpha motif: replica exchange molecular dynamics simulation with an implicit solvation model

Designed miniproteins with a betabetaalpha motif, such as BBA5, 1FSD, and 1PSV can serve as a benchmark set to test the validity of all-atom force fields with computer simulation, because they contain all the basic structural elements in protein folding. Unfortunately, it was found that the standard all-atom force fields with the generalized Born (GB) implicit solvation model tend to produce distorted free energy surfaces for the betabetaalpha proteins, not only because energetically those proteins need to be described by more balanced weights of the alpha- and beta-strands, but also because the GB implicit solvation model suffers from overestimated salt bridge effects. In an attempt to resolve these problems, we have modified one of the standard all-atom force fields in conjunction with the GB model, such that each native state of the betabetaalpha proteins is in its free energy minimum state with reasonable energy barriers separating local minima. With this modified energy model, the free energy contour map in each protein was constructed from the replica exchange molecular dynamics REMD simulation. The resulting free energy surfaces are significantly improved in comparison with previous simulation results and consistent with general views on small protein folding behaviors with realistic topology and energetics of all three proteins.     

CIRSE: a solvation energy estimator compatible with flexible protein docking and design applications

We present the Coordinate Internal Representation of Solvation Energy (CIRSE) for computing the solvation energy of protein configurations in terms of pairwise interactions between their atoms with analytic derivatives. Currently, CIRSE is trained to a Poisson/surface-area benchmark, but CIRSE is not meant to fit this benchmark exclusively. CIRSE predicts the overall solvation energy of protein structures from 331 NMR ensembles with 0.951+/-0.047 correlation and predicts relative solvation energy changes between members of individual ensembles with an accuracy of 15.8+/-9.6 kcal/mol. The energy of individual atoms in any of CIRSE's 17 types is predicted with at least 0.98 correlation. We apply the model in energy minimization, rotamer optimization, protein design, and protein docking applications. The CIRSE model shows some propensity to accumulate errors in energy minimization as well as rotamer optimization, but these errors are consistent enough that CIRSE correctly identifies the relative solvation energies of designed sequences as well as putative docked complexes. We analyze the errors accumulated by the CIRSE model during each type of simulation and suggest means of improving the model to be generally useful for all-atom simulations.     

Conformational analysis of endothelin-1: Effects of solvation free energy

In order to investigate conformational preferences of the 21-residue peptide hormone endothelin-1 (ET-1), an extensive conformational search was carried out in vacuo using a combination of high temperature molecular dynamics / annealing and a Monte Carlo / minimization search in torsion angle space. Fully minimized conformations from the search were grouped into families using a clustering technique based on rms fitting over the Cartesian coordinates of the atoms of the peptide backbone of the ring region. A wide range of local energy minima were identified even though two disulfide bridges (Cys¹-Cys¹⁵ and Cys³-Cys¹¹) constrain the structure of the peptide. Low energy conformers of ET-1 as a nonionized species in vacuo arestabilized by intramolecular interaction of the ring region (residues 1-15) with the tail (residues 16–21). Strained conformations for individual residues are observed. Conformational similarity to protein loops is established by matching to protein crystal structures In order to assess the influence of aqueous environment on conformational preference, the electrostatic contribution to the solvation energy was calculated for ET-1 as a fully ionized species (Asp⁸, Lys⁹, Glu¹⁰, Asp¹⁸, N- and C-terminus) using a continuum electrostatics model (DelPhi) for each of the conformed generated in vacuo, and the total solvation free energy was estimated by adding a hydrophobic contribution proportional to solvent accessible surface area. Solvation dramatically alters the relative energetics of ET-1 conformers from that calculated in vacuo. Conformers of ET-1 favored by the electrostatic salvation energy in water include conformers with helical secondary structure in the region of residues 9–15. Perhaps of most importance, it was demonstrated that the contribution tosolvation by an individual charge depends not only on its solvent accessibility but on the proximity of other charges, i.e., it is a cooperative effect. This was shown by the calculation of electrostatic solvation energy as afunction of conformation with individual charges systematically turned “on” and “off”. The cooperative effect of multiple charges on solvation demonstrated in this manner calls into question models that relate solvation energysimply to solvent accessibility by atom or residue alone. © 1995 John Wiley & Sons, Inc.     

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。     

Development, validation, and application of adapted PEOE charges to estimate pKa values of functional groups in protein-ligand complexes

For routine pK(a) calculations of protein-ligand complexes in drug design, the PEOE method to compute partial charges was modified. The new method is applicable to a large scope of proteins and ligands. The adapted charges were parameterized using experimental free energies of solvation of amino acids and small organic ligands. For a data set of 80 small organic molecules, a correlation coefficient of r(2) = 0.78 between calculated and experimental solvation free energies was obtained. Continuum electrostatics pK(a) calculations based on the Poisson-Boltzmann equation were carried out on a validation set of nine proteins for which 132 experimental pK(a) values are known. In total, an overall RMSD of 0.88 log units between calculated and experimentally determined data is achieved. In particular, the predictions of significantly shifted pK(a) values are satisfactory, and reasonable estimates of protonation states in the active sites of lysozyme and xylanase could be obtained. Application of the charge-assignment and pK(a)-calculation procedure to protein-ligand complexes provides clear structural interpretations of experimentally observed changes of protonation states of functional groups upon complex formation. This information is essential for the interpretation of thermodynamic data of protein-ligand complex formation and provides the basis for the reliable factorization of the free energy of binding in enthalpic and entropic contributions. The modified charge-assignment procedure forms the basis for future automated pK(a) calculations of protein-ligand complexes.     

Optimized atomic radii for protein continuum electrostatics solvation forces

Recently, we presented a Green's function approach for the calculation of analytic continuum electrostatic solvation forces based on numerical solutions of the finite-difference Poisson-Botzmann (FDPB) equation [Im et al., Comp. Phys. Comm. 111 (1998) 59]. In this treatment the analytic forces were explicitly defined as the first derivative of the FDPB continuum electrostatic free energy with respect to the coordinates of the solute atoms. A smooth intermediate region for the solute-solvent dielectric boundary needed to be introduced to avoid abrupt discontinuous variations in the solvation free energy and forces as a function of the atomic positions. In the present paper we extend the set of optimized radii, which was previously parametrized from molecular dynamics free energy simulations of the 20 standard amino acids with explicit solvent molecules [Nina et al., J. Phys. Chem. 101 (1997) 5239], to yield accurate solvation free energy by taking the influence of the smoothed dielectric region into account.     

Molecular docking study and development of an empirical binding free energy model for phosphodiesterase 4 inhibitors

In the present work, several computational methodologies were combined to develop a model for the prediction of PDE4B inhibitors' activity. The adequacy of applying the ligand docking approach, keeping the enzyme rigid, to the study of a series of PDE4 inhibitors was confirmed by a previous molecular dynamics analysis of the complete enzyme. An exhaustive docking procedure was performed to identify the most probable binding modes of the ligands to the enzyme, including the active site metal ions and the surrounding structural water molecules. The enzyme-inhibitor interaction enthalpies, refined by using the semiempirical molecular orbital approach, were combined with calculated solvation free energies and entropy considerations in an empirical free energy model that enabled the calculation of binding free energies that correlated very well with experimentally derived binding free energies. Our results indicate that both the inclusion of the structural water molecules close to the ions in the binding site and the use of a free energy model with a quadratic dependency on the ligand free energy of solvation are important aspects to be considered for molecular docking investigations involving the PDE4 enzyme family.     

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.     

ParDOCK: an all atom energy based Monte Carlo docking protocol for protein-ligand complexes

We report here an all-atom energy based Monte Carlo docking procedure tested on a dataset of 226 protein-ligand complexes. Average root mean square deviation (RMSD) from crystal conformation was observed to be approximately 0.53 A. The correlation coefficient (r(2)) for the predicted binding free energies calculated using the docked structures against experimental binding affinities was 0.72. The docking protocol is web-enabled as a free software at www.scfbio-iitd.res.in/dock.     

Empirical free energy calculation: comparison to calorimetric data.

An effective free energy potential, developed originally for binding free energy calculation, is compared to calorimetric data on protein unfolding, described by a linear combination of changes in polar and nonpolar surface areas. The potential consists of a molecular mechanics energy term calculated for a reference medium (vapor or nonpolar liquid), and empirical terms representing solvation and entropic effects. It is shown that, under suitable conditions, the free energy function agrees well with the calorimetric expression. An additional result of the comparison is an independent estimate of the side-chain entropy loss, which is shown to agree with a structure-based entropy scale. These findings confirm that simple functions can be used to estimate the free energy change in complex systems, and that a binding free energy evaluation model can describe the thermodynamics of protein unfolding correctly. Furthermore, it is shown that folding and binding leave the sum of solute-solute and solute-solvent van der Waals interactions nearly invariant and, due to this invariance, it may be advantageous to use a nonpolar liquid rather than vacuum as the reference medium.     

An extended aqueous solvation model based on atom-weighted solvent accessible surface areas: SAWSA v2.0 model

A new method is proposed for calculating aqueous solvation free energy based on atom-weighted solvent accessible surface areas. The method, SAWSA v2.0, gives the aqueous solvation free energy by summing the contributions of component atoms and a correction factor. We applied two different sets of atom typing rules and fitting processes for small organic molecules and proteins, respectively. For small organic molecules, the model classified the atoms in organic molecules into 65 basic types and additionally. For small organic molecules we proposed a correction factor of hydrophobic carbon to account for the aggregation of hydrocarbons and compounds with long hydrophobic aliphatic chains. The contributions for each atom type and correction factor were derived by multivariate regression analysis of 379 neutral molecules and 39 ions with known experimental aqueous solvation free energies. Based on the new atom typing rules, the correlation coefficient (r) for fitting the whole neutral organic molecules is 0.984, and the absolute mean error is 0.40 kcal mol^–1, which is much better than those of the model proposed by Wang et al. and the SAWSA model previously proposed by us. Furthermore, the SAWSA v2.0 model was compared with the simple atom-additive model based on the number of atom types (NA). The calculated results show that for small organic molecules, the predictions from the SAWSA v2.0 model are slightly better than those from the atom-additive model based on NA. However, for macromolecules such as proteins, due to the connection between their molecular conformation and their molecular surface area, the atom-additive model based on the number of atom types has little predictive power. In order to investigate the predictive power of our model, a systematic comparison was performed on seven solvation models including SAWSA v2.0, GB/SA_1, GB/SA_2, PB/SA_1, PB/SA_2, AM1/SM5.2R and SM5.0R. The results showed that for organic molecules the SAWSA v2.0 model is better than the other six solvation models. For proteins, the model classified the atoms into 20 basic types and the predicted aqueous free energies of solvation by PB/SA were used for fitting. The solvation model based on the new parameters was employed to predict the solvation free energies of 38 proteins. The predicted values from our model were in good agreement with those from the PB/SA model and were much better than those given by the other four models developed for proteins.Figure The definition of hydrophobic carbons. Here CA, CB and CD are three carbon atoms; X represents a heteroatom. According to our definition, CB is a hydrophobic carbon, CA is not a hydrophobic carbon because a heteroatom is within four atoms and CD is not a hydrophobic carbon because CD is sp²- hydridized and in a six-member ring.Electronic Supplementary Material Supplementary material is available for this article at     

Calculation of ligand-nucleic acid binding free energies with the generalized-born model in DOCK

The calculation of ligand-nucleic acid binding free energies is investigated by including solvation effects computed with the generalized-Born model. Modifications of the solvation module in DOCK, including introduction of all-atom parameters and revision of coefficients in front of different terms, are shown to improve calculations involving nucleic acids. This computing scheme is capable of calculating binding energies, with reasonable accuracy, for a wide variety of DNA-ligand complexes, RNA-ligand complexes, and even for the formation of double-stranded DNA. This implementation of GB/SA is also shown to be capable of discriminating strong ligands from poor ligands for a series of RNA aptamers without sacrificing the high efficiency of the previous implementation. These results validate this approach to screening large databases against nucleic acid targets.     

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.     

Effect of partial atomic charges on the calculated free energy of solvation of poly(vinyl alcohol) in selected solvents

It is well-known that properties of poly(vinyl alcohol) (PVA) in the pure and solution states depend largely on the hydrogen bonding networks formed. In the context of molecular simulation, such networks are handled through the Coulombic interactions. Therefore, a good set of partial atom charges (PACs) for simulations involving PVA is highly desirable. In this work, we calculated the PACs for PVA using a few commonly used population analysis schemes with a hope to identify an accurate set of PACs for PVA monomers. To evaluate the quality of the calculated parameters, we have benchmarked their predictions for free energy of solvation (FES) in selected solvents by molecular dynamics simulations against the ab initio calculated values. Selected solvents were water, ethanol and benzene as they covered a range of size and polarity. Also, PVA with different tacticities were used to capture their effect on the calculated FESs. Based on our results, neither PACs nor FESs are affected by the chain tacticity. While PACs predicted by the Merz-Singh-Kollman scheme were close to original values in the OPLS-AA force field in way that no significant difference in properties of pure PVA was observed, free energy of solvation calculated using such PACs showed greater agreement with ab initio calculated values than those calculated by OPLS-AA (and all other schemes used in this work) in all three solvents considered.     

Amino acid conformational preferences and solvation of polar backbone atoms in peptides and proteins

Amino acids in peptides and proteins display distinct preferences for alpha-helical, beta-strand, and other conformational states. Various physicochemical reasons for these preferences have been suggested: conformational entropy, steric factors, hydrophobic effect, and backbone electrostatics; however, the issue remains controversial. It has been proposed recently that the side-chain-dependent solvent screening of the local and non-local backbone electrostatic interactions primarily determines the preferences not only for the alpha-helical but also for all other main-chain conformational states. Side-chains modulate the electrostatic screening of backbone interactions by excluding the solvent from the vicinity of main-chain polar atoms. The deficiency of this electrostatic screening model of amino acid preferences is that the relationships between the main-chain electrostatics and the amino acid preferences have been demonstrated for a limited set of six non-polar amino acid types in proteins only. Here, these relationships are determined for all amino acid types in tripeptides, dekapeptides, and proteins. The solvation free energies of polar backbone atoms are approximated by the electrostatic contributions calculated by the finite difference Poisson-Boltzmann and the Langevin dipoles methods. The results show that the average solvation free energy of main-chain polar atoms depends strongly on backbone conformation, shape of side-chains, and exposure to solvent. The equilibrium between the low-energy beta-strand conformation of an amino acid (anti-parallel alignment of backbone dipole moments) and the high-energy alpha conformation (parallel alignment of backbone dipole moments) is strongly influenced by the solvation of backbone polar atoms. The free energy cost of reaching the alpha conformation is by approximately 1.5 kcal/mol smaller for residues with short side-chains than it is for the large beta-branched amino acid residues. This free energy difference is comparable to those obtained experimentally by mutation studies and is thus large enough to account for the distinct preferences of amino acid residues. The screening coefficients gamma(local)(r) and gamma(non-local)(r) correlate with the solvation effects for 19 amino acid types with the coefficients between 0.698 to 0.851, depending on the type of calculation and on the set of point atomic charges used. The screening coefficients gamma(local)(r) increase with the level of burial of amino acids in proteins, converging to 1.0 for the completely buried amino acid residues. The backbone solvation free energies of amino acid residues involved in strong hydrogen bonding (for example: in the middle of an alpha-helix) are small. The hydrogen bonded backbone is thus more hydrophobic than the peptide groups in random coil. The alpha-helix forming preference of alanine is attributed to the relatively small free energy cost of reaching the high-energy alpha-helix conformation. These results confirm that the side-chain-dependent solvent screening of the backbone electrostatic interactions is the dominant factor in determining amino acid conformational preferences.     

Position-resolved free energy of solvation for amino acids in lipid membranes from molecular dynamics simulations

Studies of insertion and interactions of amino acids in lipid membranes are pivotal to our understanding of membrane protein structure and function. Calculating the insertion cost as a function of transmembrane helix sequence is thus an important step towards improved membrane protein prediction and eventually drug design. Here, we present position-dependent free energies of solvation for all amino acid analogs along the membrane normal. The profiles cover the entire region from bulk water to hydrophobic core, and were produced from all-atom molecular dynamics simulations. Experimental differences corresponding to mutations and costs for entire segments match experimental data well, and in addition the profiles provide the spatial resolution currently not available from experiments. Polar side-chains largely maintain their hydration and assume quite ordered conformations, which indicates the solvation cost is mainly entropic. The cost of solvating charged side-chains is not only significantly lower than for implicit solvation models, but also close to experiments, meaning these could well maintain their protonation states inside the membrane. The single notable exception to the experimental agreement is proline, which is quite expensive to introduce in vivo despite its hydrophobicity--a difference possibly explained by kinks making it harder to insert helices in the translocon.     

Calculation of the relative binding free energy of 2'GMP and 2'AMP to ribonuclease T1 using molecular dynamics/free energy perturbation approaches

We present a calculation of the relative changes in binding free energy between the complex of ribonuclease T1 (RNase Tr) with its inhibitor 2'-guanosine monophosphate (2'GMP) and that of RNase T1-2'-adenosine monophosphate (2'AMP) by means of a thermodynamic perturbation method implemented with molecular dynamics. Using the available crystal structure of the RNase T1-2'GMP complex, the structure of the RNase T1-2'AMP complex was obtained as a final structure of the perturbation calculation. The calculated difference in the free energy of binding (delta delta Gbind) was 2.76 kcal/mol. This compares well with the experimental value of 3.07 kcal/mol. The encouraging agreement in delta delta Gbind suggests that the interactions of inhibitors with the enzyme are reasonably represented. Energy component analyses of the two complexes reveal that the active site of RNase T1 electrostatically stabilizes the binding of 2'GMP more than that of 2'AMP by 44 kcal/mol, while the van der Waals' interactions are similar in the two complexes. The analyses suggest that the mutation from Glu46 to Gln may lead to a preference of RNase T1 for adenine in contrast to the guanine preference of the wild-type enzyme. Although the molecular dynamics equilibration moves the atoms of the RNase T1-2'GMP system about 0.9 A from their X-ray positions and the mutation of the G to A in the active site increases the deviation from the X-ray structure, the mutation of the A back to G reduces the deviation. This and the agreement found for delta delta Gbind suggest that the molecular dynamics/free energy perturbation method will be useful for both energetic and structural analysis of protein-ligand interactions.     

An all atom energy based computational protocol for predicting binding affinities of protein-ligand complexes

We report here a computationally fast protocol for predicting binding affinities of non-metallo protein-ligand complexes. The protocol builds in an all atom energy based empirical scoring function comprising electrostatics, van der Waals, hydrophobicity and loss of conformational entropy of protein side chains upon ligand binding. The method is designed to ensure transferability across diverse systems and has been validated on a heterogenous dataset of 161 complexes consisting of 55 unique protein targets. The scoring function trained on a dataset of 61 complexes yielded a correlation of r=0.92 for the predicted binding free energies against the experimental binding affinities. Model validation and parameter analysis studies ensure the predictive ability of the scoring function. When tested on the remaining 100 protein-ligand complexes a correlation of r=0.92 was recovered. The high correlation obtained underscores the potential applicability of the methodology in drug design endeavors. The scoring function has been web enabled at as binding affinity prediction of protein-ligand (BAPPL) server.