Controller design method of gene regulatory networks for realizing cyclic expression pattern sequences

Recently, synthesis of gene regulatory networks having desired functions has become of interest to many researchers because it is a complementary approach to understanding gene regulatory networks, and it could be the first step in controlling living cells. There exist several periodic phenomena in cells, e.g. circadian rhythm. These phenomena are considered to be generated by gene regulatory networks. In this paper we propose a controller design method of gene regulatory networks, in which desired behavior are given by cyclic expression pattern sequences. In order that objective gene regulatory networks have desired cyclic expression pattern sequences, it is required that expression pattern sequences of the controller gene regulatory network are cyclic. Moreover, the solution trajectories corresponding to the desired expression pattern sequences are need to be periodic. The proposed method consists of two steps. Firstly, we design a controller gene regulatory network such that the objective one has desired cyclic expression pattern sequences. Secondly, we design controller gene regulatory networks such that the objective one has desired expression pattern sequences together with their corresponding solution trajectories being periodic. Numerical experiments are carried out to illustrate the performance of the proposed method.