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19th GAMM-Seminar Leipzig on
High-dimensional problems - Numerical treatment and applications

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
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  19th GAMM-Seminar
January, 23th-25th, 2003
 
     
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  Abstract P. Lötstedt, Fri, 11.30-11.55 Previous Contents Next  
  Fokker-Planck approximation of the master equation in molecular biology
P. Lötstedt (Uppsala University)

The stochastic character of the molecular devices in single cells cannot be neglected, since the number of macromolecules of the different species involved often is limited to tens or hundreds. This makes mesoscale modelling of the chemical reactions based on the master equation mandatory.

The master equation is a scalar, linear difference-differential equation for how the probability distribution of the number of molecules of the species in the reactions varies with time.

Each different molecule species corresponds to one dimension.

The equations are approximated numerically by a finite difference discretization of the multidimensional Fokker-Planck equation.

The number of grid points for a two dimensional system for the Fokker-Planck equation is reduced by more than 300 compared to the master equation. The steady state solution of a four dimensional problem illustrates the efficiency of the method. Comparisons are made with solutions obtained with Gillespie's Monte Carlo method.

This talk presents joint work with Johan Elf and Paul Sjöberg.
 

 
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Last updated:
30.11.2004 Impressum
 
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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