Simulation of stochastic reaction-diffusion processes on lower dimensional manifolds with application in molecular biology

Abstract: In this thesis, we simulate stochastically the reaction-diffusion processes in a living cell. The simulation is done in three dimension (3D) by MATLAB. The one dimensional (1D) polymers are embedded in the 3D space. The reaction and diffusion events occur both in the space and on the polymers. There is also a possibility for the molecule to jump between the 3D space and 1D polymers. Two simulation levels are used: mesoscopic and microscopic. An accurate and efficient algorithm is developed for the mesoscopic simulation. The corresponding microscopic Smoluchowski equation is solved numerically by a finite difference method in a specific coordinate system adapted to its boundary conditions. The comparison between the result of the mesoscopic simulation and the solution of the microscopic Smoluchowski equation is provided. Good agreement is observed in the experiments.