The Poisson-Boltzmann model for implicit solvation of electrolyte solutions: Quantum chemical implementation and assessment via Sechenov coefficients.

We present the theory and implementation of a Poisson-Boltzmann implicit solvation model for electrolyte solutions. This model can be combined with arbitrary electronic structure methods that provide an accurate charge density of the solute. A hierarchy of approximations for this model includes a linear approximation for weak electrostatic potentials, finite size of the mobile electrolyte ions, and a Stern-layer correction. Recasting the Poisson-Boltzmann equations into Euler-Lagrange equations then significantly simplifies the derivation of the free energy of solvation for these approximate models. The parameters of the model are either fit directly to experimental observables-e.g., the finite ion size-or optimized for agreement with experimental results. Experimental data for this optimization are available in the form of Sechenov coefficients that describe the linear dependence of the salting-out effect of solutes with respect to the electrolyte concentration. In the final part, we rationalize the qualitative disagreement of the finite ion size modification to the Poisson-Boltzmann model with experimental observations by taking into account the electrolyte concentration dependence of the Stern layer. A route toward a revised model that captures the experimental observations while including the finite ion size effects is then outlined. This implementation paves the way for the study of electrochemical and electrocatalytic processes of molecules and cluster models with accurate electronic structure methods

Continuous dielectric permittivity I: Specific features of the dielectric continuum solvation model with a position-dependent permittivity function

We consider a modified formulation for the recently developed new approach in the continuum solvation theory (Basilevsky, M. V., Grigoriev, F. V., Nikitina, E. A., Leszczynski, J., J. Phys. Chem. B 2010, 114, 2457), which is based on the exact solution of the electrostatic Poisson equation with the space-dependent dielectric permittivity. Its present modification ensures the property curl E = 0 for the electric strength field E inherent to this solution, which is the obligatory condition imposed by Maxwell equations. The illustrative computation is made for the model system of the point dipole immersed in a spherical cavity of excluded volume.Comment: 31 pages, 4 figure

Beyond Poisson-Boltzmann: Numerical sampling of charge density fluctuations

We present a method aimed at sampling charge density fluctuations in Coulomb systems. The derivation follows from a functional integral representation of the partition function in terms of charge density fluctuations. Starting from the mean-field solution given by the Poisson-Boltzmann equation, an original approach is proposed to numerically sample fluctuations around it, through the propagation of a Langevin like stochastic partial differential equation (SPDE). The diffusion tensor of the SPDE can be chosen so as to avoid the numerical complexity linked to long-range Coulomb interactions, effectively rendering the theory completely local. A finite-volume implementation of the SPDE is described, and the approach is illustrated with preliminary results on the study of a system made of two like-charge ions immersed in a bath of counter-ions

Modeling Electrostatics and Geometrical Quantities in Molecular Biophysics Using a Gaussian-Based Model of Atoms

Electrostatic and geometric factors are critical to modeling the interactions and solvation effects of biomolecules in the aqueous environments of biological cells as they respectively influence the polar and non-polar components of the associated free energies. Conventional protocols use a hard-sphere model of atoms to devise and study the underlying thermodynamics. But this traditional model tends to overlook some of the important biophysical aspects at the cost of oversimplification of the representation of the solute-solvent environments. Here an alternative and physically appealing model of atoms – a Gaussian-based model, is presented which replaces the hard-sphere model with a smooth density-based description of atoms. This dissertation explains the derivation of a physically appealing dielectric distribution from the Gaussian schematic to model the electrostatics of biomolecules using the implicit-solvent/Poisson-Boltzmann (PB) formalism. It also demonstrates the advantages of using it for computing geometric properties of a molecule such as its volume and surface area (SA) for estimating non-polar portions of the free energy. While highlighting the qualitative importance of the Gaussian-based model, it offers conceptual proofs towards its validity through computational investigations of explicit solvent simulations. It also reports the key features of the Gaussian-based model, which impart to it the capacity of accurately capturing the crucial biophysical factors that characterize biomolecular properties, namely – the effect of intrinsic conformational flexibility and salt distribution. The non-triviality of these factors and their portrayal through the Gaussian models are meticulously discussed. A major theme of this work is the implementation of the Gaussian model of dielectric distribution and volume/SA estimation into the PB solver package called Delphi. These developments illustrate the manner in which the utility of Delphi has been expanded and its reputation as a popular tool for modeling solvation effects with appreciable time-efficacy and accuracy has been enhanced

Developing and validating Fuzzy-Border continuum solvation model with POlarizable Simulations Second order Interaction Model (POSSIM) force field for proteins

The accurate, fast and low cost computational tools are indispensable for studying the structure and dynamics of biological macromolecules in aqueous solution. The goal of this thesis is development and validation of continuum Fuzzy-Border (FB) solvation model to work with the Polarizable Simulations Second-order Interaction Model (POSSIM) force field for proteins developed by Professor G A Kaminski. The implicit FB model has advantages over the popularly used Poisson Boltzmann (PB) solvation model. The FB continuum model attenuates the noise and convergence issues commonly present in numerical treatments of the PB model by employing fixed position cubic grid to compute interactions. It also uses either second or first-order approximation for the solvent polarization which is similar to the second-order explicit polarization applied in POSSIM force field. The FB model was first developed and parameterized with nonpolarizable OPLS-AA force field for small molecules which are not only important in themselves but also building blocks of proteins and peptide side chains. The hydration parameters are fitted to reproduce the experimental or quantum mechanical hydration energies of the molecules with the overall average unsigned error of ca. 0.076kcal/mol. It was further validated by computing the absolute pKa values of 11 substituted phenols with the average unsigned error of 0.41pH units in comparison with the quantum mechanical error of 0.38pH units for this set of molecules. There was a good transferability of hydration parameters and the results were produced only with fitting of the specific atoms to the hydration energy and pKa targets. This clearly demonstrates the numerical and physical basis of the model is good enough and with proper fitting can reproduce the acidity constants for other systems as well. After the successful development of FB model with the fixed charges OPLS-AA force field, it was expanded to permit simulations with Polarizable Simulations Second-order Interaction Model (POSSIM) force field. The hydration parameters of the small molecules representing analogues of protein side chains were fitted to their solvation energies at 298.15K with an average error of ca.0.136kcal/mol. Second, the resulting parameters were used to reproduce the pKa values of the reference systems and the carboxylic (Asp7, Glu10, Glu19, Asp27 and Glu43) and basic residues (Lys13, Lys29, Lys34, His52 and Lys55) of the turkey ovomucoid third domain (OMTKY3) protein. The overall average unsigned error in the pKa values of the acid residues was found to be 0.37pH units and the basic residues was 0.38 pH units compared to 0.58pH units and 0.72 pH units calculated previously using polarizable force field (PFF) and Poisson Boltzmann formalism (PBF) continuum solvation model. These results are produced with fitting of specific atoms of the reference systems and carboxylic and basic residues of the OMTKY3 protein. Since FB model has produced improved pKa shifts of carboxylic residues and basic protein residues in OMTKY3 protein compared to PBF/PFF, it suggests the methodology of first-order FB continuum solvation model works well in such calculations. In this study the importance of explicit treatment of the electrostatic polarization in calculating pKa of both acid and basic protein residues is also emphasized. Moreover, the presented results demonstrate not only the consistently good degree of accuracy of protein pKa calculations with the second-degree POSSIM approximation of the polarizable calculations and the first-order approximation used in the Fuzzy-Border model for the continuum solvation energy, but also a high degree of transferability of both the POSSIM and continuum solvent Fuzzy Border parameters. Therefore, the FB model of solvation combined with the POSSIM force field can be successfully applied to study the protein and protein-ligand systems in water

Proteins in Mixed Solvents: A Molecular-level Perspective

We present a statistical mechanical approach for quantifying thermodynamic properties of proteins in mixed solvents. This approach, based on molecular dynamics simulations which incorporate all atom models and the theory of preferential binding, allows us to compute transfer free energies with experimental accuracy and does not incorporate any adjustable parameters. Specifically, we applied our approach to the model proteins RNase A and T1, and the solvent components water, glycerol, and urea. We found that the observed differences in the binding of glycerol and urea to RNase T1 and A are predominantly a consequence of density differences in the first coordination shell of the protein with the cosolvents, but the second solvation shell also contributes to the overall binding coefficients. The success of this approach in modeling preferential binding indicates that it incorporates the important underlying physics of proteins in mixed solvent systems and that the difficulty in quantitative prediction to date can be surmounted by explicitly incorporating the complex protein-solvent and solvent-solvent interactions.Singapore-MIT Alliance (SMA