Multistability equivalence between gene regulatory networks of different dimensionality with application to a differentiation network

Abstract

SummaryThis paper formulates and addresses the problem of equivalence in terms of multistability properties between nonlinear models of gene regulatory systems of different dimensionality. Given a nonlinear dynamical model of a gene regulatory network and the structure of another higher‐dimensional gene regulatory network, the aim is to find a dynamical model for the latter that has the same equilibria and stability properties as the former. We propose construction rules for the dynamics of a high‐dimensional system, given the low‐dimensional system and the high‐dimensional network structure. These construction rules yield a multistability‐equivalent system, as we prove in this work. We demonstrate the value of our method by applying it to an example of a multistable gene regulatory network involved in mesenchymal stem cell differentiation. Here, differentiation is described by a core motif of three genetic regulators, but the detailed network contains at least nine genes. The proposed construction method allows to transfer the multistability based differentation mechanism of the core motif to the more detailed gene regulatory network. Copyright © 2016 John Wiley & Sons, Ltd.