Existence of Solutions to Synthesis Problem of Gene Regulatory Networks for Realizing Separatrices

Abstract

Recently, synthesis of gene regulatory networks having desired behavior has become of interest to many researchers and several studies have been done. We have proposed synthesis methods of gene regulatory networks in which desired behavior are given by expression pattern sequences. For realizing more complex behavior synthesizing more complex networks is needed. Realizing separatices in the state space of gene regulatory networks is helpful in order to synthesize gene regulatory networks having simpler structures. Therefore we have proposed a synthesis method for realizing separatrices. The purpose of this paper is to proof the existence of solutions to a synthesis problem of gene regulatory network for realizing separatrices. The proof is based on the procedure for finding a solution of the problem. Hence the proof also gives a synthesis method of gene regulatory networks for realizing separatirices.