Pattern formation in enzyme inhibition and cooperativity with parallel cellular automata

Abstract

Enzyme reactions with inhibition and cooperativity are modelled in terms of a pair of coupled nonlinear reaction–diffusion equations. The governing equations are solved using stochastic cellular automata with local rules derived from the corresponding nonlinear partial differential equations. The parallel cellular automaton is implemented using domain decomposition according to the nature of the locality of its update rules. Numerical simulations show stable 2-D and 3-D pattern formation, and complex patterns have the interesting feature of self-organized criticality. The numerical results of cellular automata are also compared with results obtained from finite difference and finite element methods.