Multistability equivalence between gene regulatory networks of different dimensionality

This paper formulates and addresses the problem of equivalence in terms of multistability properties between gene regulatory systems of different dimensionality. Given a dynamical system of a gene regulatory network, and the structure of another, higher-dimensional gene regulatory network, the aim is to find a dynamical system for the latter which has the same 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. The usefulness of our method is illustrated with an exemplary gene regulatory network, for which we construct a dynamical system which has the same multistability properties as a given, low-dimensional model of gene regulation.