Synthesis method of gene regulatory networks having desired periodic expression pattern sequences

Recently, synthesis of gene regulatory networks having desired behavior has become of interest to many researchers and several studies have been done. There exist periodic phenomena in cells and these periodic phenomena are considered to be generated by gene regulatory networks. We already proposed a synthesis method of gene regulatory networks having desired cyclic expression pattern sequences. In this paper, we propose a synthesis method for realizing not only desired cyclic expression pattern sequences but also desired periods. In the proposed method we derive a representation of periods and introduce Poincare map for realizing periodic solution trajectories with desired periods. We also introduce a discrete-time network which represent transition of expression pattern. In the problem, gene regulatory network model is given by differential equations. However, in order to synthesize gene regulatory networks we solve only the discrete-time network. Therefore desired behavior are realized efficiently. Numerical experiments are carried out to illustrate the performance of the proposed method.