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A strategy for reducing gross errors in the generalized Born models of implicit solvation.

ABSTRACT: The "canonical" generalized Born (GB) formula [C. Still, A. Tempczyk, R. C. Hawley, and T. Hendrickson, J. Am. Chem. Soc. 112, 6127 (1990)] is known to provide accurate estimates for total electrostatic solvation energies ?G(el) of biomolecules if the corresponding effective Born radii are accurate. Here we show that even if the effective Born radii are perfectly accurate, the canonical formula still exhibits significant number of gross errors (errors larger than 2k(B)T relative to numerical Poisson equation reference) in pairwise interactions between individual atomic charges. Analysis of exact analytical solutions of the Poisson equation (PE) for several idealized nonspherical geometries reveals two distinct spatial modes of the PE solution; these modes are also found in realistic biomolecular shapes. The canonical GB Green function misses one of two modes seen in the exact PE solution, which explains the observed gross errors. To address the problem and reduce gross errors of the GB formalism, we have used exact PE solutions for idealized nonspherical geometries to suggest an alternative analytical Green function to replace the canonical GB formula. The proposed functional form is mathematically nearly as simple as the original, but depends not only on the effective Born radii but also on their gradients, which allows for better representation of details of nonspherical molecular shapes. In particular, the proposed functional form captures both modes of the PE solution seen in nonspherical geometries. Tests on realistic biomolecular structures ranging from small peptides to medium size proteins show that the proposed functional form reduces gross pairwise errors in all cases, with the amount of reduction varying from more than an order of magnitude for small structures to a factor of 2 for the largest ones.

SUBMITTER: Onufriev AV

PROVIDER: S-EPMC3100913 | biostudies-literature | 2011 Apr

REPOSITORIES: biostudies-literature

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A strategy for reducing gross errors in the generalized Born models of implicit solvation.

Onufriev Alexey V AV Sigalov Grigori G

The Journal of chemical physics 20110401 16

The "canonical" generalized Born (GB) formula [C. Still, A. Tempczyk, R. C. Hawley, and T. Hendrickson, J. Am. Chem. Soc. 112, 6127 (1990)] is known to provide accurate estimates for total electrostatic solvation energies ΔG(el) of biomolecules if the corresponding effective Born radii are accurate. Here we show that even if the effective Born radii are perfectly accurate, the canonical formula still exhibits significant number of gross errors (errors larger than 2k(B)T relative to numerical Poi ...[more]

PMID: 21528947

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Project description:The ion atmosphere around highly charged nucleic acid molecules plays a significant role in their dynamics, structure, and interactions. Here we utilized the implicit solvent framework to develop a model for the explicit treatment of ions interacting with nucleic acid molecules. The proposed explicit ions/implicit water model is based on a significantly modified generalized Born (GB) model and utilizes a non-standard approach to define the solute/solvent dielectric boundary. Specifically, the model includes modifications to the GB interaction terms for the case of multiple interacting solutes-disconnected dielectric boundary around the solute-ion or ion-ion pairs. A fully analytical description of all energy components for charge-charge interactions is provided. The effectiveness of the approach is demonstrated by calculating the potential of mean force for Na+-Cl- ion pair and by carrying out a set of Monte Carlo (MC) simulations of mono- and trivalent ions interacting with DNA and RNA duplexes. The monovalent (Na+) and trivalent (CoHex3+) counterion distributions predicted by the model are in close quantitative agreement with all-atom explicit water molecular dynamics simulations used as reference. Expressed in the units of energy, the maximum deviations of local ion concentrations from the reference are within k B T. The proposed explicit ions/implicit water GB model is able to resolve subtle features and differences of CoHex distributions around DNA and RNA duplexes. These features include preferential CoHex binding inside the major groove of the RNA duplex, in contrast to CoHex biding at the "external" surface of the sugar-phosphate backbone of the DNA duplex; these differences in the counterion binding patters were earlier shown to be responsible for the observed drastic differences in condensation propensities between short DNA and RNA duplexes. MC simulations of CoHex ions interacting with the homopolymeric poly(dA·dT) DNA duplex with modified (de-methylated) and native thymine bases are used to explore the physics behind CoHex-thymine interactions. The simulations suggest that the ion desolvation penalty due to proximity to the low dielectric volume of the methyl group can contribute significantly to CoHex-thymine interactions. Compared to the steric repulsion between the ion and the methyl group, the desolvation penalty interaction has a longer range and may be important to consider in the context of methylation effects on DNA condensation.

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A strategy for reducing gross errors in the generalized Born models of implicit solvation.

Publications

A strategy for reducing gross errors in the generalized Born models of implicit solvation.

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