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Poisson-Boltzmann equation in ℝ³

100%

Krzywicki A. , Nadzieja T.

Annales Polonici Mathematici

1991

tom 54

nr 2

125-134

The electric potential u in a solute of electrolyte satisfies the equation Δu(x) = f(u(x)), x ∈ Ω ⊂ ℝ³, $u|_{∂Ω} = 0$. One studies the existence of a solution of the problem and its properties.

Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy

100%

Nadzieja T. , Raczyński A.

Applicationes Mathematicae

2000

tom 27

nr 4

465-473

We consider the following problem: $ΔΦ = ± {M οver \int_{Ω} e^{- Φ/Θ}} e^{- Φ/Θ}, E = MΘ ∓ {1οver2}\int_{Ω} |∇Φ|^2, Φ|_{\partial Ω} = 0,$ where Φ: Ω ⊂ $ℝ^n$ → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.

A Poisson-Boltzmann Equation Test Model for Protein in Spherical Solute Region and its Applications

70%

Jiang Y. , Ying J. , Xie D.

Molecular Based Mathematical Biology

2014

tom 2

nr 1

The Poisson-Boltzmann equation (PBE) is one important implicit solvent continuum model for calculating electrostatics of protein in ionic solvent. Several numerical algorithms and program packages have been developed but verification and comparison between them remains an interesting topic. In this paper, a PBE test model is presented for a protein in a spherical solute region, along with its analytical solution. It is then used to verify a PBE finite element solver and applied to a numerical comparison study between a finite element solver and a finite difference solver. Such a study demonstrates the importance of retaining the interface conditions in the development of PBE solvers.

Progress in developing Poisson-Boltzmann equation solvers

70%

Li C. , Li L. , Petukh M. , Alexov E.

Molecular Based Mathematical Biology

2013

tom 1

42-62

This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nanoobjects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nanoobjects.

A boundary integral Poisson-Boltzmann solvers package for solvated bimolecular simulations

70%

Geng W.

Molecular Based Mathematical Biology

2015

tom 3

nr 1

Numerically solving the Poisson-Boltzmann equation is a challenging task due to the existence of the dielectric interface, singular partial charges representing the biomolecule, discontinuity of the electrostatic field, infinite simulation domains, etc. Boundary integral formulation of the Poisson-Boltzmann equation can circumvent these numerical challenges and meanwhile conveniently use the fast numerical algorithms and the latest high performance computers to achieve combined improvement on both efficiency and accuracy. In the past a few years, we developed several boundary integral Poisson-Boltzmann solvers in pursuing accuracy, efficiency, and the combination of both. In this paper, we summarize the features and functions of these solvers, and give instructions and references for potential users. Meanwhile, we quantitatively report the solvation free energy computation of these boundary integral PB solvers benchmarked with Matched Interface Boundary Poisson-Boltzmann solver (MIBPB), a current 2nd order accurate finite difference Poisson-Boltzmann solver.

SDPBS Web Server for Calculation of Electrostatics of Ionic Solvated Biomolecules

70%

Jiang Y. , Xie Y. , Ying J. , Xie D. , Yu Z.

Molecular Based Mathematical Biology

2015

tom 3

nr 1

The Poisson-Boltzmann equation (PBE) is one important implicit solvent continuum model for calculating electrostatics of protein in ionic solvent. We recently developed a PBE solver library, called SDPBS, that incorporates the finite element, finite difference, solution decomposition, domain decomposition, and multigrid methods. To make SDPBS more accessible to the scientific community, we present an SDPBS web server in this paper that allows clients to visualize and manipulate the molecular structure of a biomolecule, and to calculate PBE solutions in a remote and user friendly fashion. The web server is available on the website https://lsextrnprod.uwm.edu/electrostatics/.

Interactions of charged dust particles in clouds of charges

51%

Gundienkov V. , Yakovlenko S.

Open Physics

2004

tom 2

nr 1

35-66

Two charged dust particles inside a cloud of charges are considered as Debye atoms forming a Debye molecule. Cassini coordinates are used for the numerical solution of the Poisson-Boltzmann equation for the charged cloud. The electric force acting on a dust particle by the other dust particle was determined by integrating the electrostatic pressure on the surface of the dust particle. It is shown that attractive forces appear when the following two conditions are satisfied. First, the average distance between dust particles should be approximately equal to two Debye radii. Second, attraction takes place when similar charges are concentrated predominantly on the dust particles. If the particles carry a small fraction of total charge of the same polarity, repulsion between the particles takes place at all distances. We apply our results to the experiments with thermoemission plasma and to the experiments with nuclear-pumped plasma.