A Novel Ergodic Cellular Automaton Model of Gene-Protein Network: Theoretical Nonlinear Analyses and Efficient FPGA Implementation

A novel ergodic cellular automaton model of gene-protein network is presented. It is shown that the presented model can predict occurrences of typical nonlinear phenomena of a conventional ordinary differential equation gene-protein network model. In addition, theoretical analysis methods of the presented model are proposed. Using the analysis methods, an important advantage of the presented model is revealed: the ergodic cellular automaton is better suited to predict the occurrences of the nonlinear phenomena of the differential equation gene-protein network model compared to a regular (standard) cellular automaton. Furthermore, the presented model is implemented by a field programmable gate array and experiments validate its operations. It is then revealed that the presented model is much more hardware-efficient compared to a standard numerical integration formula of the differential equation model.