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On regularization of charge singularities in solving the Poisson-Boltzmann equation with a smooth solute-solvent boundary.

ABSTRACT: Numerical treatment of singular charges is a grand challenge in solving the Poisson-Boltzmann (PB) equation for analyzing electrostatic interactions between the solute biomolecules and the surrounding solvent with ions. For diffuse interface PB models in which solute and solvent are separated by a smooth boundary, no effective algorithm for singular charges has been developed, because the fundamental solution with a space dependent dielectric function is intractable. In this work, a novel regularization formulation is proposed to capture the singularity analytically, which is the first of its kind for diffuse interface PB models. The success lies in a dual decomposition - besides decomposing the potential into Coulomb and reaction field components, the dielectric function is also split into a constant base plus space changing part. Using the constant dielectric base, the Coulomb potential is represented analytically via Green's functions. After removing the singularity, the reaction field potential satisfies a regularized PB equation with a smooth source. To validate the proposed regularization, a Gaussian convolution surface (GCS) is also introduced, which efficiently generates a diffuse interface for three-dimensional realistic biomolecules. The performance of the proposed regularization is examined by considering both analytical and GCS diffuse interfaces, and compared with the trilinear method. Moreover, the proposed GCS-regularization algorithm is validated by calculating electrostatic free energies for a set of proteins and by estimating salt affinities for seven protein complexes. The results are consistent with experimental data and estimates of sharp interface PB models.

SUBMITTER: Wang S

PROVIDER: S-EPMC9871984 | biostudies-literature | 2021 Jan

REPOSITORIES: biostudies-literature

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On regularization of charge singularities in solving the Poisson-Boltzmann equation with a smooth solute-solvent boundary.

Wang Siwen S Alexov Emil E Zhao Shan S

Mathematical biosciences and engineering : MBE 20210101 2

Numerical treatment of singular charges is a grand challenge in solving the Poisson-Boltzmann (PB) equation for analyzing electrostatic interactions between the solute biomolecules and the surrounding solvent with ions. For diffuse interface PB models in which solute and solvent are separated by a smooth boundary, no effective algorithm for singular charges has been developed, because the fundamental solution with a space dependent dielectric function is intractable. In this work, a novel regula ...[more]

PMID: 33757190

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Dataset Information

On regularization of charge singularities in solving the Poisson-Boltzmann equation with a smooth solute-solvent boundary.

Publications

On regularization of charge singularities in solving the Poisson-Boltzmann equation with a smooth solute-solvent boundary.

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