A generalized cellular automata approach to modeling first order enzyme kinetics

Biochemical processes occur through intermediate steps which are associated with the formation of reaction complexes. These enzyme-catalyzed biochemical reactions are inhibited in a number of ways such as inhibitors competing for the binding site directly, inhibitors deforming the allosteric site or inhibitors changing the structure of active substrate. Using an in silico approach, the concentration of various reaction agents can be monitored at every single time step, which are otherwise difficult to analyze experimentally. Cell-based models with discrete state variables, such as Cellular Automata (CA) provide an understanding of the organizational principles of interacting cellular systems to link the individual cell (microscopic) dynamics with a particular collective (macroscopic) phenomenon. In this study, a CA model representing a first order enzyme kinetics with inhibitor activity is formulated. The framework of enzyme reaction rules described in this study is probabilistic. An extended von Neumann neighborhood with periodic boundary condition is implemented on a two-dimensional (2D) lattice framework. The effect of lattice-size variation is studied followed by a sensitivity analysis of the model output to the probabilistic parameters which represent various kinetic reaction constants in the enzyme kinetic model. This provides a deeper insight into the sensitivity of the CA model to these parameters. It is observed that cellular automata can capture the essential features of a discrete real system, consisting of space, time and state, structured with simple local rules without making complex implementations but resulting in complex but explainable patterns.