A CFF 91-based Continuum Solvation Model: Solvation Free Energies of Small Organic Molecules and Conformations of the Alanine Dipeptide in Solution

Abstract

For molecular mechanics simulations of solvated molecules, it is important to use a consistent approach for calculating both the force field energy and the solvation free energy. A continuum solvation model based upon the atomic charges provided with the CFF91 force field is derived. The electrostatic component of the solvation free energy is described by the Poisson-Bolzmann equation while the nonpolar comonent of the solvation energy is assumed to be proportional to the solvent accessible surface area of the solute. Solute atomic radii used to describe the interface between the solute and solvent are fitted to reproduce the energies of small organic molecules. Data for 140 compounds are presented and compared to experiment and to the results from the well-characterized quantum mechanical solvation model AM1-SM2. In particular, accurate results are obtained for amino acid neutral analogues (mean unsigned error of 0.3 kcal/mol). The conformational energetics of the solvated alanine dipeptide is discussed.     

Theoretical investigation of the triphosphate forms of azidothymidine and thymidine

In this paper we investigate (using AM1 semi-empirical as well as HF methods at the STO-3G, 3-21G, 6-31G, 6-31G* and 6-31+G** level) the conformations, geometrical parameters, Mulliken charges, and solvation effects of the triphosphate form of AZT (AZTTP), as well as the thymidine nucleotide (dTTP) structure. Our calculated geometrical parameters and Mulliken charges, with and without solvation effects, are correlated with recent experimental results.     

A model binding site for testing scoring functions in molecular docking

Prediction of interaction energies between ligands and their receptors remains a major challenge for structure-based inhibitor discovery. Much effort has been devoted to developing scoring schemes that can successfully rank the affinities of a diverse set of possible ligands to a binding site for which the structure is known. To test these scoring functions, well-characterized experimental systems can be very useful. Here, mutation-created binding sites in T4 lysozyme were used to investigate how the quality of atomic charges and solvation energies affects molecular docking. Atomic charges and solvation energies were calculated for 172,118 molecules in the Available Chemicals Directory using a semi-empirical quantum mechanical approach by the program AMSOL. The database was first screened against the apolar cavity site created by the mutation Leu99Ala (L99A). Compared to the electronegativity-based charges that are widely used, the new charges and desolvation energies improved ranking of known apolar ligands, and better distinguished them from more polar isosteres that are not observed to bind. To investigate whether the new charges had predictive value, the non-polar residue Met102, which forms part of the binding site, was changed to the polar residue glutamine. The structure of the resulting Leu99Ala and Met102Gln double mutant of T4 lysozyme (L99A/M102Q) was determined and the docking calculation was repeated for the new site. Seven representative polar molecules that preferentially docked to the polar versus the apolar binding site were tested experimentally. All seven bind to the polar cavity (L99A/M102Q) but do not detectably bind to the apolar cavity (L99A). Five ligand-bound structures of L99A/M102Q were determined by X-ray crystallography. Docking predictions corresponded to the crystallographic results to within 0.4A RMSD. Improved treatment of partial atomic charges and desolvation energies in database docking appears feasible and leads to better distinction of true ligands. Simple model binding sites, such as L99A and its more polar variants, may find broad use in the development and testing of docking algorithms.     

On contribution of known atomic partial charges of protein backbone in electrostatic potential density maps

Partial charges of atoms in a molecule and electrostatic potential (ESP) density for that molecule are known to bear a strong correlation. In order to generate a set of point‐field force field parameters for molecular dynamics, Kollman and coworkers have extracted atomic partial charges for each of all 20 amino acids using restrained partial charge‐fitting procedures from theoretical ESP density obtained from condensed‐state quantum mechanics. The magnitude of atomic partial charges for neutral peptide backbone they have obtained is similar to that of partial atomic charges for ionized carboxylate side chain atoms. In this study, the effect of these known atomic partial charges on ESP is examined using computer simulations and compared with the experimental ESP density recently obtained for proteins using electron microscopy. It is found that the observed ESP density maps are most consistent with the simulations that include atomic partial charges of protein backbone. Therefore, atomic partial charges are integral part of atomic properties in protein molecules and should be included in model refinement.     

Linkage isomerism of pentaammine(dimethylsulfoxide)ruthenium(II/III) complexes: A theoretical study

Density functional theory (DFT) calculations have been performed for understanding the linkage isomerism of [Ru^II/III(NH₃)₅(dmso)]^2+/3+ (dmso = dimethylsulfoxide) from a theoretical point of view. In particular, we focus on the interchange between O-bonded and S-bonded structures of the dmso ligand by oxidation/reduction. We have examined five different exchange-correlation functionals (SVWN, BP86, mPWPW91, B3PW91, and B3LYP) in our DFT calculations and found that the relative stabilities of the O-bonded and S-bonded structures are largely dependent on the functional employed. From detailed analyses of atomic charge distributions, it has been found that the calculated atomic charges on the central metal ions are strongly correlated with the relative energies. We also studied the effect of solvation on the linkage isomerism using continuum solvation models.     

Electrostatic calculations of the pKa values of ionizable groups in bacteriorhodopsin.

The effects of solvation and charge-charge interactions on the pKa of ionizable groups in bacteriorhodopsin have been studied using a macroscopic dielectric model with atom-level detail. The calculations are based on the atomic model for bacteriorhodopsin recently proposed by Henderson et al. Even if the structural data are not resolved at the atomic level, such calculations can indicate the quality of the model, outline some general aspects of electrostatic interactions in membrane proteins, and predict some features. The effects of structural uncertainties on the calculations have been investigated by conformational sampling. The results are in reasonable agreement with experimental measurements of several unusually large pKa shifts (e.g. the experimental findings that Asp96 and Asp115 are protonated in the ground state over a wide pH range). In general, we find that the large unfavorable desolvation energies of forming charges in the protein interior must be compensated by strong favorable charge-charge interactions, with the result that the titrations of many ionizable groups are strongly coupled to each other. We find several instances of complex titration behavior due to strong electrostatic interactions between titrating sites, and suggest that such behavior may be common in proton transfer systems. We also propose that they can help to resolve structural ambiguities in the currently available density map. In particular, we find better agreement between theory and experiment when a structural ambiguity in the position of the Arg82 side-chain is resolved in favor of a position near the Schiff base.     

Charge calculations in molecular mechanics 6: the calculation of partial atomic charges in nucleic acid bases and the electrostatic contribution to DNA base pairing.

A previously described scheme for the direct calculation of the partial atomic charges in molecules (CHARGE2) is applied to the nucleic acid bases. It is shown that inclusion of the omega-technique for the calculation of HMO derived pi charges is of particular importance for these highly polar systems. The molecular dipole moments obtained for the resulting charges are in very good agreement with the observed values for a variety of substituted purine and pyrimidine bases. The partial atomic charges for cytosine, thymine, guanine and adenine (as the 1-methyl and 9-methyl forms) are given and compared with values calculated by a variety of molecular orbital and empirical schemes. All the schemes reproduce the same general trends, with the possible exception of those calculated by the Del Re method, though the charges given by Kollman are in general somewhat larger than the others. The electrostatic contribution to the Watson-Crick base pair interaction energies are calculated using these partial atomic charges. The electrostatic contributions obtained from the M.O. derived atomic charges are less than half the observed values, as are those obtained by the Gasteiger method. The electrostatic contributions calculated from the CHARGE2 atomic charges and those of Kollman are in reasonable agreement with the observed values. The influence of a distant-dependent dielectric constant is examined, but no clear pattern emerges.     

Application of the Poisson-Nernst-Planck theory with space-dependent diffusion coefficients to KcsA

The Poisson-Nernst-Planck electrodiffusion theory serves to compute charge fluxes and is here applied to the ion current through a protein channel. KcsA was selected as an example because of the abundance of experimental and theoretical data. The potassium channels MthK and KvAP were used as templates to define two open channel models for KcsA. Channel boundary surfaces and protein charge distributions were defined according to atomic radii and partial atomic charges. To establish the sensitivity of the results to these parameters, two different sets were used. Assigning the potassium diffusion coefficients equal to the value for free-diffusion in water (1.96 x 10(-9) m(2)/s), the computed currents overestimated the experimental data. Ion distributions inside the channel suggest that the overestimate is not due to an excess of charge shielding. A good agreement with the experimental data was achieved by reducing the potassium diffusion coefficient inside the channel to 1.96 x 10(-10) m(2)/s, a value of substantial motility but nonetheless in accord with the intuitive notion that the channel has a high affinity for the ions and therefore slows them down. These results are independent of the open channel model and the parameterization adopted for atomic radii and partial atomic charges. The method offers a reliable estimate of the channel current with low computational effort.     

Interactions of macromolecules with salt ions: an electrostatic theory for the Hofmeister effect

Salting-out of proteins was discovered in the nineteenth century and is widely used for protein separation and crystallization. It is generally believed that salting-out occurs because at high concentrations salts and the protein compete for solvation water. Debye and Kirkwood suggested ideas for explaining salting-out (Debeye and MacAulay, Physik Z; 1925;131:22-29; Kirkwood, In: Proteins, amino acids and peptides as ions and dipolar ions. New York: Reinhold; 1943. p 586-622). However, a quantitative theory has not been developed, and such a theory is presented here. It is built on Kirkwood's idea that a salt ion has a repulsive interaction with an image charge inside a low dielectric cavity. Explicit treatment is given for the effect of other salt ions on the interaction between a salt ion and its image charge. When combined with the Debye-Hückel effect of salts on the solvation energy of protein charges (i.e., salting-in), the characteristic curve of protein solubility versus salt concentration is obtained. The theory yields a direct link between the salting-out effect and surface tension and is able to provide rationalizations for the effects of salt on the folding stability of several proteins.     

Parametric sensitivity analysis of avian pancreatic polypeptide (APP)

Computer simulations utilizing a classical force field have been widely used to study biomolecular properties. It is important to identify the key force field parameters or structural groups controlling the molecular properties. In the present paper the sensitivity analysis method is applied to study how various partial charges and solvation parameters affect the equilibrium structure and free energy of avian pancreatic polypeptide (APP). The general shape of APP is characterized by its three principal moments of inertia. A molecular dynamics simulation of APP was carried out with the OPLS/Amber force field and a continuum model of solvation energy. The analysis pinpoints the parameters which have the largest (or smallest) impact on the protein equilibrium structure (i.e., the moments of inertia) or free energy. A display of the protein with its atoms colored according to their sensitivities illustrates the patterns of the interactions responsible for the protein stability. The results suggest that the electrostatic interactions play a more dominant role in protein stability than the part of the solvation effect modeled by the atomic solvation parameters. © 1995 Wiley-Liss, Inc.     

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.     

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.     

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。     

Complementary DNA base interactions: application of recently refined electrostatic interaction theory

Electrostatic interactions between the DNA bases in the Watson-Crick hydrogen bonding configuration are examined in both the molecular and the atomic multipole representation using three different methods of calculation: (a) CNDO wave functions and definitions of moments, (b) IEHT wave functions and division of two-center densities and (c) IHET wave functions with equally divided overlap densities. It is shown that the inclusion in the interaction series of terms at least as high as the quadrupole-quadrupole is required to quantitatively characterize the interactions. Convergence is more rapid with the atomic multipole representation and is unaffected by the type of assignment of formal charges. A quantitative approach to the problem of the role of electrostatic interactions in hydrogen bonding in DNA is thus provided, with obvious impact on the investigation of molecular recognition processes.     

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.     

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.     

The sensitivity of conformational free energies of the alanine dipeptide to atomic site charges

Different atomic point charge sets are obtained for the α_R and C_7.eq conformations of the alanine dipeptide by fitting the charges of each conformation to the respective ab initio electrostatic potential surfaces both individually and simultaneously, in both the united atom and the all-atom representations. Using these charge sets, the sensitivity of the relative conformational aqueous free energies to the atomic site charges is investigated. For this particular system, we find that the solute-water contributions to the conformational free energy differences have a rather weak dependence on site charges; the calculated intramolecular contributions, however, show a rather strong dependence on the atomic site charges. It is suggested that the calculated results for the alanine dipeptide using a single, simultaneously fit set of charges for both conformations are in better agreement with experiments than the calculations carried out with charges determined individually for each conformation. © 1997 John Wiley & Sons, Inc.     

Implicit solvent models

Implicit solvent models for biomolecular simulations are reviewed and their underlying statistical mechanical basis is discussed. The fundamental quantity that implicit models seek to approximate is the solute potential of mean force, which determines the statistical weight of solute conformations, and which is obtained by averaging over the solvent degrees of freedom. It is possible to express the total free energy as the reversible work performed in two successive steps. First, the solute is inserted in the solvent with zero atomic partial charges; second, the atomic partial charges of the solute are switched from zero to their full values. Consequently, the total solvation free energy corresponds to a sum of non-polar and electrostatic contributions. These two contributions are often approximated by simple geometrical models (such as solvent exposed area models) and by macroscopic continuum electrostatics, respectively. One powerful route is to approximate the average solvent density distribution around the solute, i.e. the solute-solvent density correlation functions, as in statistical mechanical integral equations. Recent progress with semi-analytical approximations makes continuum electrostatics treatments very efficient. Still more efficient are fully empirical, knowledge-based models, whose relation to explicit solvent treatments is not fully resolved, however. Continuum models that treat both solute and solvent as dielectric continua are also discussed, and the relation between the solute fluctuations and its macroscopic dielectric constant(s) clarified.