Parameter optimization in differential geometry based solvation models

Differential geometry (DG) based solvation models are a new class of variational implicit solvent approaches that are able to avoid unphysical solvent-solute boundary definitions and associated geometric singularities, and dynamically couple polar and nonpolar interactions in a self-consistent framework. Our earlier study indicates that DG based nonpolar solvation model outperforms other methods in nonpolar solvation energy predictions. However, the DG based full solvation model has not shown its superiority in solvation analysis, due to its difficulty in parametrization, which must ensure the stability of the solution of strongly coupled nonlinear Laplace-Beltrami and Poisson-Boltzmann equations. In this work, we introduce new parameter learning algorithms based on perturbation and convex optimization theories to stabilize the numerical solution and thus achieve an optimal parametrization of the DG based solvation models. An interesting feature of the present DG based solvation model is that it provides accurate solvation free energy predictions for both polar and nonploar molecules in a unified formulation. Extensive numerical experiment demonstrates that the present DG based solvation model delivers some of the most accurate predictions of the solvation free energies for a large number of molecules.Comment: 19 pages, 12 figures, convex optimizatio

Theoretical studies of 31P NMR spectral properties of phosphanes and related compounds in solution

Selected theoretical methods, basis sets and solvation models have been tested in their ability to predict 31P NMR chemical shifts of large phosphorous-containing molecular systems in solution. The most efficient strategy was found to involve NMR shift calculations at the GIAO-MPW1K/6-311++G(2d,2p)//MPW1K/6-31G(d) level in combination with a dual solvation model including the explicit consideration of single solvent molecules and a continuum (PCM) solvation model. For larger systems it has also been established that reliable 31P shift predictions require Boltzmann averaging over all accessible conformations in solution

Interface of the polarizable continuum model of solvation with semi-empirical methods in the GAMESS program

An interface between semi-empirical methods and the polarized continuum model (PCM) of solvation successfully implemented into GAMESS following the approach by Chudinov et al (Chem. Phys. 1992, 160, 41). The interface includes energy gradients and is parallelized. For large molecules such as ubiquitin a reasonable speedup (up to a factor of six) is observed for up to 16 cores. The SCF convergence is greatly improved by PCM for proteins compared to the gas phase

Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

Octanol/water distribution coefficients of the C~1~ through C~7~ perfluoro-n-alkyl sulfonates: Comparison of the IEFPCM-UFF, CPCM, and SMD solvation models

The octanol/water distribution coefficients (log D~ow~) of the C~1~ through C~7~ perfluoro-n-alkyl sulfonates (PFSAs) were calculated using the M062X/6-311++G(d,p) and MP2/6-311++G(d,p)//M062X/6-311++G(d,p) levels of theory and the IEFPCM-UFF, CPCM, and SMD solvation models. At both levels of theory with all solvation models, absolute log D~ow~ calculated for the straight chain C~1~ through C~7~ PFSAs display a substantial negative bias against available experimental data and expected trends by several log units. However, the SMD solvation model achieves accurate relative log D~ow~ accuracy, yielding fragmental contributions of a -CF~2~- group towards the log D~ow~ of 0.51+/-0.02 to 0.54+/-0.01 units (-3.0+/-0.1 to -3.1+/-0.1 kJ/mol), in good agreement with the experimental value of 0.61 units (-3.4+/-0.1 kJ/mol). In contrast, the IEFPCM-UFF and CPCM solvation models exhibit either invariant log D~ow~ with increasing perfluoro-n-alkyl chain length (CPCM) or a modestly decreasing trend (IEFPCM-UFF)

Accurate Evaluation of Charge Asymmetry in Aqueous Solvation

Charge hydration asymmetry (CHA)--a characteristic dependence of hydration free energy on the sign of the solute charge--quantifies the asymmetric response of water to electric field at microscopic level. Accurate estimates of CHA are critical for understanding hydration effects ubiquitous in chemistry and biology. However, measuring hydration energies of charged species is fraught with significant difficulties, which lead to unacceptably large (up to 300%) variation in the available estimates of the CHA effect. We circumvent these difficulties by developing a framework which allows us to extract and accurately estimate the intrinsic propensity of water to exhibit CHA from accurate experimental hydration free energies of neutral polar molecules. Specifically, from a set of 504 small molecules we identify two pairs that are analogous, with respect to CHA, to the K+/F- pair--a classical probe for the effect. We use these "CHA-conjugate" molecule pairs to quantify the intrinsic charge-asymmetric response of water to the microscopic charge perturbations: the asymmetry of the response is strong, ~50% of the average hydration free energy of these molecules. The ability of widely used classical water models to predict hydration energies of small molecules correlates with their ability to predict CHA