Monte-Carlo simulation of an inhomogeneous reaction-diffusion system in the biophysics of receptor cells

Abstract

The numerical simulation of Markov processes is usually performed by means of the minimal process method or Gillespie algorithm. In reaction-diffusion systems including extremely inhomogeneous situations, the direct application of this algorithm meets with severe difficulties which eventually cause extremely large computing times. We present a modification of the minimal process method which make it applicable to such situations even on small size computers within moderate computing times. Our modifications include the use of logarithmic classes for transition probabilities in order to increase the acceptance rate of von Neumann rejection methods, a non-local storage of the lattice state, hash tables and dynamical storage management in order to save memory capacity. Our actual example for demonstrating our modified algorithm is signal transduction in biological receptor cells where transmitter molecules are released on a two-dimensional structure (cell membrane) after a quantum reception event, e.g. a photon capture in photoreceptor cells, and interact with ionic transport channels. We find satisfying agreement of our simulation results with the experimental data for the ventral nerve photoreceptor of Limulus.