3:30 pm Thursday, October 8, 2009
Math/ICES Center of Numerical Analysis Seminar: Mathematical model of the nonlocal electrostatics by Sergej Rjasanow (Saarland University) in ACE 6.304
Protein-protein interaction belongs to the most important processes in the body. Today many diseases can be and treated at the protein, i.e. biomolecular level. Prediction and scoring of possible protein-protein interaction is an important prerequisite for efficient drug design on a computer. In recent years significant interest has been focused on the determination of electrostatic potentials of large biomolecules. However, the standard continuum approach ultimately becomes inaccurate when used to determine electrostatic properties on atomic scales [1]. In the papers [2], [4], we have proposed a novel formulation of nonlocal electrostatics allowing numerical solutions for the nontrivial molecular geometries. Some rather simple examples were solved and demonstrated correct physical behaviour. However, the mathematical model presented in these two papers is not completely equivalent to the physical model formulated in terms of Maxwell equations with nonlocal material relationship in the exterior domain, see [3]. In the recent paper [5], we present new system of four partial differential equations for nonlocal electrostatic which is formally equivalent to the physical model, shows its ellipticity, derive a simple analytical solution in the case of the unit sphere, find the fundamental solution of this system in an explicit analytical form and by the use of this, rewrite the interface problem in form of boundary integral equations. References: [1] T. Simonson. Macromolecular electrostatics: continuum models and their growing pains. Curr. Op. Struct. Biol., 11:243–252, 2001. [2] A. Hildebrandt, R. Blossey, S. Rjasanow, O. Kohlbacher, and H.-P. Lenhof. A novel formulation of nonlocal electrostatics. Phys. Rev. Let., 93(10):104–108, 2004. [3] A. A. Kornyshev, A. I. Rubinstein and M. A. Vorotyntsev. Model nonlocal electrostatics.1. J. Phys. C: Solid State Phys. 11:3307–3322, 1978. [4] A. Hildebrandt, H.-P. Lenhof, R. Blossey, S. Rjasanow, and O. Kohlbacher. Electrostatic potentials of proteins in water: A structured continuum approach. Bioinformatics, 23(2):99–103, 2007. [5] C. Fasel, S. Rjasanow, and O. Steinbach. A boundary integral formulation for nonlocal electrostatics. In K. Kunisch, G. Of, and O. Steinbach, editors, Numerical Mathematics and Advanced Applications. Proceedings of ENUMATH 2007, pages 117–124. Springer, Heidelberg, 2008. Submitted by
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