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

Mireille Bossy 1 Nicolas Champagnat 2, 1 Helene Leman 3 Sylvain Maire 1, 4 Laurent Violeau 1 Mariette Yvinec 5
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
2 Probabilités et statistiques
IECL - Institut Élie Cartan de Lorraine
5 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
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.
Type de document :
Article dans une revue
ESAIM: Proceedings, EDP Sciences, 2015, CEMRACS 2013, pp.27. 〈http://www.esaim-proc.org/〉
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https://hal.inria.fr/hal-01088930
Contributeur : Mireille Bossy <>
Soumis le : samedi 29 novembre 2014 - 10:57:51
Dernière modification le : jeudi 10 mai 2018 - 02:04:11

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  • HAL Id : hal-01088930, version 1
  • ARXIV : 1411.2304

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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, pp.27. 〈http://www.esaim-proc.org/〉. 〈hal-01088930〉

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