Monte Carlo methods for linear and non-linear Poisson-Boltzmann equation

Abstract : The electrostatic potential in the neighborhood of a biomolecule can be computed thanks to the non-linear divergence-form elliptic Poisson-Boltzmann PDE. Dedicated Monte-Carlo methods have been developed to solve its linearized version (see e.g.Bossy et al 2009, Mascagni & Simonov 2004}). These algorithms combine walk on spheres techniques and appropriate replacements at the boundary of the molecule. In the first part of this article we compare recent replacement methods for this linearized equation on real size biomolecules, that also require efficient computational geometry algorithms. We compare our results with the deterministic solver APBS. In the second part, we prove a new probabilistic interpretation of the nonlinear Poisson-Boltzmann PDE. A Monte Carlo algorithm is also derived and tested on a simple test case.
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https://hal.inria.fr/hal-01088930
Contributor : Mireille Bossy <>
Submitted on : Saturday, November 29, 2014 - 10:57:51 AM
Last modification on : Monday, April 8, 2019 - 1:30:03 AM

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Mireille Bossy, Nicolas Champagnat, Helene Leman, Sylvain Maire, Laurent Violeau, et al.. Monte Carlo methods for linear and non-linear Poisson-Boltzmann equation. ESAIM: Proceedings, EDP Sciences, 2015, CEMRACS 2013, 48, pp.420-446. ⟨http://www.esaim-proc.org/⟩. ⟨10.1051/proc/201448020 ⟩. ⟨hal-01088930⟩

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