Free Energies of Solvation with Surface, Volume, and Local Electrostatic Effects and Atomic Surface Tensions to Represent the First Solvation Shell.
ABSTRACT: Building on the SVPE (surface and volume polarization for electrostatics) model for electrostatic contributions to the free energy of solvation with explicit consideration of both surface and volume polarization effects, on the SMx approach to including first-solvation-shell contributions, and on the linear relationship between the electric field and short-range electrostatic contributions found by Chipman, we have developed a new method for computing absolute aqueous solvation free energies by combining the SVPE method with semiempirical terms that account for effects beyond bulk electrostatics. The new method is called SMVLE, and the elements it contains are denoted by SVPE-CDSL where SVPE denotes accounting for bulk electrostatic interactions between solute and solvent with both surface and volume contributions, CDS denotes the inclusion of solvent cavitation, changes in dispersion energy, and possible changes in local solvent structure by a semiempirical term utilizing geometry-dependent atomic surface tensions as implemented in SMx models, and L represents the local electrostatic effect derived from the outward-directed normal electric field on the cavity surface. The semiempirical CDS and L terms together represent the deviation of short-range contributions to the free energy of solvation from those accounted for by the SVPE term based on the bulk solvent dielectric constant. A solute training set containing a broad range of molecules used previously in the development of SM6 is used here for SMVLE model calibration. The aqueous solvation free energies predicted by the parameterized SMVLE model correlate exceedingly well with experimental values. The square of the correlation coefficient is 0.9949 and the slope is 1.0079. Comparison of the final SMVLE model against the earlier SMx solvation model shows that the parameterized SMVLE model not only yields good accuracy for neutrals but also significantly increases the accuracy for ions, making it the best implicit solvation model to date for aqueous solvation free energies of ions. The semiempirical terms associated with the outward-directed electric field account in a physical way for the improvement in the predictive accuracy for ions. The SMVLE method greatly decreases the need to include explicit water molecules for accurate modeling of solvation free energies of ions.
Project description:The division of thermodynamic solvation free energies of electrolytes into contributions from individual ionic constituents is conventionally accomplished by using the single-ion solvation free energy of one reference ion, conventionally the proton, to set the single-ion scales. Thus, the determination of the free energy of solvation of the proton in various solvents is a fundamental issue of central importance in solution chemistry. In the present article, relative solvation free energies of ions and ion-solvent clusters in methanol, acetonitrile, and dimethyl sulfoxide (DMSO) have been determined using a combination of experimental and theoretical gas-phase free energies of formation, solution-phase reduction potentials and acid dissociation constants, and gas-phase clustering free energies. Applying the cluster pair approximation to differences between these relative solvation free energies leads to values of -263.5, -260.2, and -273.3 kcal/mol for the absolute solvation free energy of the proton in methanol, acetonitrile, and DMSO, respectively. The final absolute proton solvation free energies are used to assign absolute values for the normal hydrogen electrode potential and the solvation free energies of other single ions in the solvents mentioned above.
Project description:A new implicit solvation model was developed for calculating free energies of transfer of molecules from water to any solvent with defined bulk properties. The transfer energy was calculated as a sum of the first solvation shell energy and the long-range electrostatic contribution. The first term was proportional to solvent accessible surface area and solvation parameters (?(i)) for different atom types. The electrostatic term was computed as a product of group dipole moments and dipolar solvation parameter (?) for neutral molecules or using a modified Born equation for ions. The regression coefficients in linear dependencies of solvation parameters ?(i) and ? on dielectric constant, solvatochromic polarizability parameter ?*, and hydrogen-bonding donor and acceptor capacities of solvents were optimized using 1269 experimental transfer energies from 19 organic solvents to water. The root-mean-square errors for neutral compounds and ions were 0.82 and 1.61 kcal/mol, respectively. Quantification of energy components demonstrates the dominant roles of hydrophobic effect for nonpolar atoms and of hydrogen-bonding for polar atoms. The estimated first solvation shell energy outweighs the long-range electrostatics for most compounds including ions. The simplicity and computational efficiency of the model allows its application for modeling of macromolecules in anisotropic environments, such as biological membranes.
Project description:Electrostatic forces enormously impact the structure, interactions, and function of biomolecules. We perform all-atom molecular dynamics simulations for 5 proteins and 5 RNAs to determine the dependence on ionic strength of the ion and water charge distributions surrounding the biomolecules, as well as the contributions of ions to the electrostatic free energy of interaction between the biomolecule and the surrounding salt solution (for a total of 40 different biomolecule/solvent combinations). Although water provides the dominant contribution to the charge density distribution and to the electrostatic potential even in 1M NaCl solutions, the contributions of water molecules and of ions to the total electrostatic interaction free energy with the solvated biomolecule are comparable. The electrostatic biomolecule/solvent interaction energies and the total charge distribution exhibit a remarkable insensitivity to salt concentrations over a huge range of salt concentrations (20 mM to 1M NaCl). The electrostatic potentials near the biomolecule's surface obtained from the MD simulations differ markedly, as expected, from the potentials predicted by continuum dielectric models, even though the total electrostatic interaction free energies are within 11% of each other.
Project description:Dielectric boundary based implicit-solvent models provide efficient descriptions of coarse-grained effects, particularly the electrostatic effect, of aqueous solvent. Recent years have seen the initial success of a new such model, variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett. 96, 087802 (2006) and J. Chem. Phys. 124, 084905 (2006)], in capturing multiple dry and wet hydration states, describing the subtle electrostatic effect in hydrophobic interactions, and providing qualitatively good estimates of solvation free energies. Here, we develop a phase-field VISM to the solvation of charged molecules in aqueous solvent to include more flexibility. In this approach, a stable equilibrium molecular system is described by a phase field that takes one constant value in the solute region and a different constant value in the solvent region, and smoothly changes its value on a thin transition layer representing a smeared solute-solvent interface or dielectric boundary. Such a phase field minimizes an effective solvation free-energy functional that consists of the solute-solvent interfacial energy, solute-solvent van der Waals interaction energy, and electrostatic free energy described by the Poisson-Boltzmann theory. We apply our model and methods to the solvation of single ions, two parallel plates, and protein complexes BphC and p53/MDM2 to demonstrate the capability and efficiency of our approach at different levels. With a diffuse dielectric boundary, our new approach can describe the dielectric asymmetry in the solute-solvent interfacial region. Our theory is developed based on rigorous mathematical studies and is also connected to the Lum-Chandler-Weeks theory (1999). We discuss these connections and possible extensions of our theory and methods.
Project description:Previous work describes a computational solvation model called semi-explicit assembly (SEA). The SEA water model computes the free energies of solvation of nonpolar and polar solutes in water with good efficiency and accuracy. However, SEA gives systematic errors in the solvation free energies of ions and charged solutes. Here, we describe field-SEA, an improved treatment that gives accurate solvation free energies of charged solutes, including monatomic and polyatomic ions and model dipeptides, as well as nonpolar and polar molecules. Field-SEA is computationally inexpensive for a given solute because explicit-solvent model simulations are relegated to a precomputation step and because it represents solvating waters in terms of a solute's free-energy field. In essence, field-SEA approximates the physics of explicit-model simulations within a computationally efficient framework. A key finding is that an atom's solvation shell inherits characteristics of a neighboring atom, especially strongly charged neighbors. Field-SEA may be useful where there is a need for solvation free-energy computations that are faster than explicit-solvent simulations and more accurate than traditional implicit-solvent simulations for a wide range of solutes.
Project description:Using precomputed near neighbor or proximal distribution functions (pDFs) that approximate solvent density about atoms in a chemically bonded context one can estimate the solvation structures around complex solutes and the corresponding solute-solvent energetics. In this contribution, we extend this technique to calculate the solvation free energies (?G) of a variety of solutes. In particular we use pDFs computed for small peptide molecules to estimate ?G for larger peptide systems. We separately compute the non polar (?GvdW) and electrostatic (?Gelec) components of the underlying potential model. Here we show how the former can be estimated by thermodynamic integration using pDF-reconstructed solute-solvent interaction energy. The electrostatic component can be approximated with Linear Response theory as half of the electrostatic solute-solvent interaction energy. We test the method by calculating the solvation free energies of butane, propanol, polyalanine, and polyglycine and by comparing with traditional free energy simulations. Results indicate that the pDF-reconstruction algorithm approximately reproduces ?GvdW calculated by benchmark free energy simulations to within ? kcal/mol accuracy. The use of transferable pDFs for each solute atom allows for a rapid estimation of ?G for arbitrary molecular systems.
Project description:Solvation is of fundamental importance to biomolecular systems. Implicit solvent models, particularly those based on the Poisson-Boltzmann equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces are commonly used in the implicit solvent theory. Recently, we have introduced differential geometry based solvation models which allow the solvent-solute interface to be determined by the variation of a total free energy functional. Atomic fixed partial charges (point charges) are used in our earlier models, which depends on existing molecular mechanical force field software packages for partial charge assignments. As most force field models are parameterized for a certain class of molecules or materials, the use of partial charges limits the accuracy and applicability of our earlier models. Moreover, fixed partial charges do not account for the charge rearrangement during the solvation process. The present work proposes a differential geometry based multiscale solvation model which makes use of the electron density computed directly from the quantum mechanical principle. To this end, we construct a new multiscale total energy functional which consists of not only polar and nonpolar solvation contributions, but also the electronic kinetic and potential energies. By using the Euler-Lagrange variation, we derive a system of three coupled governing equations, i.e., the generalized Poisson-Boltzmann equation for the electrostatic potential, the generalized Laplace-Beltrami equation for the solvent-solute boundary, and the Kohn-Sham equations for the electronic structure. We develop an iterative procedure to solve three coupled equations and to minimize the solvation free energy. The present multiscale model is numerically validated for its stability, consistency and accuracy, and is applied to a few sets of molecules, including a case which is difficult for existing solvation models. Comparison is made to many other classic and quantum models. By using experimental data, we show that the present quantum formulation of our differential geometry based multiscale solvation model improves the prediction of our earlier models, and outperforms some explicit solvation model.
Project description:Deciphering the structural determinants of protein-protein interactions (PPIs) is essential to gain a deep understanding of many important biological functions in the living cells. Computational approaches for the structural modeling of PPIs, such as protein-protein docking, are quite needed to complement existing experimental techniques. The reliability of a protein-protein docking method is dependent on the ability of the scoring function to accurately distinguish the near-native binding structures from a huge number of decoys. In this study, we developed HawkRank, a novel scoring function designed for the sampling stage of protein-protein docking by summing the contributions from several energy terms, including van der Waals potentials, electrostatic potentials and desolvation potentials. First, based on the solvation free energies predicted by the Generalized Born model for ~ 800 proteins, a SASA (solvent accessible surface area)-based solvation model was developed, which can give the aqueous solvation free energies for proteins by summing the contributions of 21 atom types. Then, the van der Waals potentials and electrostatic potentials based on the Amber ff14SB force field were computed. Finally, the HawkRank scoring function was derived by determining the most optimal weights for five energy terms based on the training set. Here, MSR (modified success rate), a novel protein-protein scoring quality index, was used to assess the performance of HawkRank and three other popular protein-protein scoring functions, including ZRANK, FireDock and dDFIRE. The results show that HawkRank outperformed the other three scoring functions according to the total number of hits and MSR. HawkRank is available at http://cadd.zju.edu.cn/programs/hawkrank .
Project description:We investigated the relative free energies of hapten binding to the germ line and mature forms of the 48G7 antibody Fab fragments by applying a continuum model to structures sampled from molecular dynamics simulations in explicit solvent. Reasonable absolute and very good relative free energies were obtained. As a result of nine somatic mutations that do not contact the hapten, the affinity-matured antibody binds the hapten >10(4) tighter than the germ line antibody. Energetic analysis reveals that van der Waals interactions and nonpolar contributions to solvation are similar and drive the formations of both the germ line and mature antibody-hapten complexes. Affinity maturation of the 48G7 antibody therefore appears to occur through reorganization of the combining site geometry in a manner that optimizes the balance of gaining favorable electrostatic interactions with the hapten and losing those with solvent during the binding process. As reflected by lower rms fluctuations in the antibody-hapten complex, the mature complex undergoes more restricted fluctuations than the germ line complex. The dramatically increased affinity of the 48G7 antibody over its germ line precursor is thus made possible by electrostatic optimization.