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Exploring a coarse-grained distributive strategy for finite-difference Poisson-Boltzmann calculations.

ABSTRACT: We have implemented and evaluated a coarse-grained distributive method for finite-difference Poisson-Boltzmann (FDPB) calculations of large biomolecular systems. This method is based on the electrostatic focusing principle of decomposing a large fine-grid FDPB calculation into multiple independent FDPB calculations, each of which focuses on only a small and a specific portion (block) of the large fine grid. We first analyzed the impact of the focusing approximation upon the accuracy of the numerical reaction field energies and found that a reasonable relative accuracy of 10(-3) can be achieved when the buffering space is set to be 16 grid points and the block dimension is set to be at least (1/6)(3) of the fine-grid dimension, as in the one-block focusing method. The impact upon efficiency of the use of buffering space to maintain enough accuracy was also studied. It was found that an "optimal" multi-block dimension exists for a given computer hardware setup, and this dimension is more or less independent of the solute geometries. A parallel version of the distributive focusing method was also implemented. Given the proper settings, the distributive method was able to achieve respectable parallel efficiency with tested biomolecular systems on a loosely connected computer cluster.

SUBMITTER: Hsieh MJ

PROVIDER: S-EPMC3143316 | biostudies-literature | 2011 Aug

REPOSITORIES: biostudies-literature

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Exploring a coarse-grained distributive strategy for finite-difference Poisson-Boltzmann calculations.

Hsieh Meng-Juei MJ Luo Ray R

Journal of molecular modeling 20101203 8

We have implemented and evaluated a coarse-grained distributive method for finite-difference Poisson-Boltzmann (FDPB) calculations of large biomolecular systems. This method is based on the electrostatic focusing principle of decomposing a large fine-grid FDPB calculation into multiple independent FDPB calculations, each of which focuses on only a small and a specific portion (block) of the large fine grid. We first analyzed the impact of the focusing approximation upon the accuracy of the numer ...[more]

PMID: 21127924

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Project description:We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first provably convergent discretization, and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this two-term regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a priori L(∞) estimates to establish quasi-orthogonality. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme are demonstrated with FETK through comparisons with the original regularization approach for a model problem. The convergence and accuracy of the overall AFEM algorithm is also illustrated by numerical approximation of electrostatic solvation energy for an insulin protein.

Dataset Information

Exploring a coarse-grained distributive strategy for finite-difference Poisson-Boltzmann calculations.

Publications

Exploring a coarse-grained distributive strategy for finite-difference Poisson-Boltzmann calculations.

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