A generalized cellular automata approach to modeling first order enzyme kinetics

Abstract

Abstract. 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 twodimensional (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.

A generalized neighborhood for cellular automata

“…Rdiamond (0, r) = 0, r > 0 There are also other known ways for extending von Neumann's neighborhood using radius r > 1; for example the scheme outlined in [4]. This only allows differences with absolute value equal to r in a single coordinate and is illustrated in Figure 3 for the 2-dimensional case.…”

A Comparative Study of Multi Objective Optimization Algorithms for a Cellular Automata Model

“…The Cellular Automata (CA) model used in this study has been developed and validated in earlier works (Kar et al, 2010;Kar et al, 2014;Dutta et al, 2015). The model representation is made in a two-dimensional grid with periodic boundary conditions and the consideration of a von-Neumann neighborhood.…”

“…The grid size of the CA model is fixed at 50×50. Its number of update iterations has been fixed to 1000 based on the observation of attainment of steady state when running with the standard values for the probability rules (Dutta et al, 2015). The reaction agents used in the model are Substrate (S), Product (P), Enzyme (E), Inhibitor (I) and Water (W).…”