Atomic radius and charge parameter uncertainty in biomolecular solvation energy calculations

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a new method for quantifying this uncertainty in implicit solvation calculations of small molecules using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space requires compressed sensing combined with an iterative rotation method to enhance problem sparsity. We demonstrate the application of the method by presenting results for the uncertainties in small molecule solvation energies based on these approaches. The method presented in this paper is a promising approach for efficiently quantifying uncertainty in a wide range of force field parameterization problems, including those beyond continuum solvation calculations.The intent of this study is to provide a way for developers of implicit solvent model parameter sets to understand the sensitivity of their target properties (solvation energy) on underlying choices for solute radius and charge parameters

Polarizable molecular interactions in condensed phase and their equivalent nonpolarizable models

Earlier, using phenomenological approach, we showed that in some cases polarizable models of condensed phase systems can be reduced to nonpolarizable equivalent models with scaled charges. Examples of such systems include ionic liquids, TIPnP-type models of water, protein force fields, and others, where interactions and dynamics of inherently polarizable species can be accurately described by nonpolarizable models. To describe electrostatic interactions, the effective charges of simple ionic liquids are obtained by scaling the actual charges of ions by a factor of 1/sqrt(eps_el), which is due to electronic polarization screening effect; the scaling factor of neutral species is more complicated. Here, using several theoretical models, we examine how exactly the scaling factors appear in theory, and how, and under what conditions, polarizable Hamiltonians are reduced to nonpolarizable ones. These models allow one to trace the origin of the scaling factors, determine their values, and obtain important insights on the nature of polarizable interactions in condensed matter systems.Comment: 43 pages, 3 figure

Accuracy comparison of several common implicit solvent models and their implementations in the context of protein-ligand binding.

In this study several commonly used implicit solvent models are compared with respect to their accuracy of estimating solvation energies of small molecules and proteins, as well as desolvation penalty in protein-ligand binding. The test set consists of 19 small proteins, 104 small molecules, and 15 protein-ligand complexes. We compared predicted hydration energies of small molecules with their experimental values; the results of the solvation and desolvation energy calculations for small molecules, proteins and protein-ligand complexes in water were also compared with Thermodynamic Integration calculations based on TIP3P water model and Amber12 force field. The following implicit solvent (water) models considered here are: PCM (Polarized Continuum Model implemented in DISOLV and MCBHSOLV programs), GB (Generalized Born method implemented in DISOLV program, S-GB, and GBNSR6 stand-alone version), COSMO (COnductor-like Screening Model implemented in the DISOLV program and the MOPAC package) and the Poisson-Boltzmann model (implemented in the APBS program). Different parameterizations of the molecules were examined: we compared MMFF94 force field, Amber12 force field and the quantum-chemical semi-empirical PM7 method implemented in the MOPAC package. For small molecules, all of the implicit solvent models tested here yield high correlation coefficients (0.87-0.93) between the calculated solvation energies and the experimental values of hydration energies. For small molecules high correlation (0.82-0.97) with the explicit solvent energies is seen as well. On the other hand, estimated protein solvation energies and protein-ligand binding desolvation energies show substantial discrepancy (up to 10kcal/mol) with the explicit solvent reference. The correlation of polar protein solvation energies and protein-ligand desolvation energies with the corresponding explicit solvent results is 0.65-0.99 and 0.76-0.96 respectively, though this difference in correlations is caused more by different parameterization and less by methods and indicates the need for further improvement of implicit solvent models parameterization. Within the same parameterization, various implicit methods give practically the same correlation with results obtained in explicit solvent model for ligands and proteins: e.g. correlation values of polar ligand solvation energies and the corresponding energies in the frame of explicit solvent were 0.953-0.966 for the APBS program, the GBNSR6 program and all models used in the DISOLV program. The DISOLV program proved to be on a par with the other used programs in the case of proteins and ligands solvation energy calculation. However, the solution of the Poisson-Boltzmann equation (APBS program) and Generalized Born method (implemented in the GBNSR6 program) proved to be the most accurate in calculating the desolvation energies of complexes

Quantum-mechanical calculations of the stabilities of fluxional isomers of C_4H_7^+ in solution

Although numerous quantum calculations have been made over the years of the stabilities of the fluxional isomers of C4H7+, none have been reported for other than the gas phase (which is unrealistic for these ionic species) that exhibit exceptional fluxional properties in solution. To be sure, quantum-mechanical calculations for solutions are subject to substantial uncertainties, but nonetheless it is important to see whether the trends seen for the gas-phase C4H7+ species are also found in calculations for polar solutions. Of the C4H7+ species, commonly designated bisected-cyclopropylcarbinyl 1, unsym-bicyclobutonium-2, sym-bicyclobutonium 3, allylcarbinyl 4, and pyramidal structure 6, the most advanced gas-phase calculations available thus far suggest that the order of stability is 1 ≥ 2 ≥ 3 >> 4 >> 6 with barriers of only ~1 kcal/mol for interconversions among 1, 2, and 3. We report here that, when account is taken of solvation, 2 turns out to be slightly more stable than 1 or 3 in polar solvents. The pattern of the overall results is unexpected, in that despite substantial differences in structures and charge distributions between the primary players in the C4H7+ equilibria and the large differences in solvation energies calculated for the solvents considered, the differential solvent effects from species to species are rather small

O(N) continuous electrostatics solvation energies calculation method for biomolecules simulations

We report a development of a new fast surface-based method for numerical calculations of solvation energy of biomolecules with a large number of charged groups. The procedure scales linearly with the system size both in time and memory requirements, is only a few percent wrong for any molecular configurations of arbitrary sizes, gives explicit value for the reaction field potential at any point, provides both the solvation energy and its derivatives suitable for Molecular Dynamics simulations. The method works well both for large and small molecules and thus gives stable energy differences for quantities such as solvation energies of molecular complex formation.Comment: 6 pages, 4 figures, more results, examples and references adde

DFT/Solvation Continuum Electrostatic Calculations of Proton Pumping in Mammalian Cytochrome c Oxidase

With computer simulations that assess pKas of critical residues, explore electron and proton pathways, and evaluate the energetics of PT and ET processes, we can provide a more in-depth understanding of the molecular mechanism and catalytic cycle of CcO. Combining the DFT electronic structure and energy calculations with reaction and protein field contributions allows self-consistent solvation energy calculations to be iteratively performed. Moreover, valuable insights into mechanistic details and energetics of proton pumping and coupled ET/PT reactions are gained at the atomic level

Synthesis and Characterization of the k^2-acac-O,O Complex Os_(IV)(acac)_2PhCl and Study of CH Activation with Benzene

We have synthesized and fully characterized the air-stable complex (κ^2-acac-O,O)2Os^(IV)(Ph)Cl (Cl-1-Ph; acac-O,O = acetylacetonate), which reacts with C_6D_6 to generate Cl-1-Ph-d_5 in high yield and catalyzes the H/D exchange reaction between benzene and toluene-d_8 upon heating to 140 °C. To our knowledge, this is the first example of stoichiometric and catalytic, homogeneous, intermolecular CH activation of arenes by a discrete Os complex. The reactions show extended induction periods. DFT studies of Cl-1-Ph and cis-(κ^2-acac-O,O)_2Os^(III)(C_6H_5)(C_6D_6) (cis-(C_6D_6)-2-Ph) found a mechanism involving CH activation by traces of Os(III) and Cl atom transfer between Cl-1-Ph and cis-(C_6D_6)-2-Ph. Experimental data showing that addition of reductants eliminates the induction periods suggest that CH activation occurs from an oxidation state lower than Os^(IV), consistent with the DFT predictions. Consistent with a Cl atom transfer mechanism, the triflate analogue of Cl-1-Ph, OTf-1-Ph, does not undergo a stoichiometric or catalytic reaction with C_6D_6