A quantitative robustness measure for gene regulatory networks

Biologists have known that gene regulatory networks (GRNs) are robust against mutations and the interactions between genes maybe the major mechanism that contributes to compensating the phenotypic effects of mutations. However, biologists do not know how to measure the robustness quantitatively. Therefore, it is needed to develop a quantitative robustness measure for GRNs. In this study, the dynamics of a GRN is described by a set of nonlinear coupled differential equations in power-law formalism. Based on this mathematical representation, a quantitative robustness measure for GRNs is proposed. Using the proposed robustness measure, one can quantitatively compute how the steady state of a GRN is affected by small changes of the interactions between genes due to mutations or diseases. Moreover, the proposed robustness measure could be used to quantitatively compare the robustness of different GRN topologies, which has very important applications in studying the evolution of the robustness of GRNs. In addition, the proposed robustness measure is useful for designing a robust GRN, which has very important applications in synthetic biology.