Unravelling the Impact of Obstacles in Diffusion and Kinetics of an Enzyme Catalysed Reaction

Abstract

Lattice gas automata simulations of diffusion-limited reactions in heterogeneous media exhibit fractal-like kinetics, which is a generalised mass action kinetics with time-dependent rate constants.1,2,3 We develop a two dimensional lattice gas automata simulation of the Michaelis-Menten mechanism in diffusion-limited conditions to investigate the effect of density and size of obstacles on reactant diffusion and rate coefficients. In order to simulate more physicochemical realistic conditions, reactants rotate and interact according to their specific orientation. We also model weak interaction forces between reactants and obstacles. Our results show that obstacle density and size affect diffusion, first- and second- order rates. We also find that particle rotations and weak force interactions among particles lead to a significant decay in the fractal-like kinetic exponent h. These results suggest that the effects of fractal-like kinetics disappear under less restricted conditions than previously believed in lattice based simulations. [1] S. Schnell and T. E. Turner, Prog Biophys Mol Biol, 2004, 85, 235-260. [2] R. Kopelman, J Stat Phys, 1986, 42, 185-200. [3] R. Kopelman, Science, 1988, 241, 1620-1626.