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Image-Based Geometric Modeling and Mesh Generation pp 271–301Cite as

Finite Element Modeling of Biomolecular Systems in Ionic Solution

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Part of the book series: Lecture Notes in Computational Vision and Biomechanics ((LNCVB,volume 3))

Abstract

An accurate finite element method is introduced to solve the two most commonly used continuum models in computational biophysics: Poisson–Boltzmann (PB) equation and Poisson–Nernst–Planck (PNP) equations. They describe equilibrium and non-equilibrium (with diffusion existed) properties of ionic liquid, respectively. Both models involve two domains (solvent and solute) with distributed singular permanent charges inside biomolecules (solute domain) and a dielectric jump at the interface between solvent and solute. A stable regularization scheme is described to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and regular, well-posed PB/PNP equations are formulated. The interface conditions for electric potential are also explicitly enforced to be satisfied. An inexact-Newton method is used to solve the nonlinear elliptic PB equation and the coupled steady-state PNP equations; while an Adams–Bashforth–Crank–Nicolson method is devised for time integration for the unsteady electrodiffusion. The numerical methods are shown to be accurate and stable by various tests of real biomolecular electrostatic and diffusion problems.

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Acknowledgements

The author was supported by the State Key Laboratory of Scientific/Engineering Computing, the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, and the China NSF (NSFC10971218, NSFC11001257).

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  1. State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Benzhuo Lu

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  1. Department of Mechanical Engineering, Carnegie Mellon University, Forbes Avenue 5000, Pittsburgh, 15213, Pennsylvania, USA

    Yongjie (Jessica) Zhang

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Lu, B. (2013). Finite Element Modeling of Biomolecular Systems in Ionic Solution. In: Zhang, Y. (eds) Image-Based Geometric Modeling and Mesh Generation. Lecture Notes in Computational Vision and Biomechanics, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4255-0_14

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  • DOI: https://doi.org/10.1007/978-94-007-4255-0_14

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