Fluctuation-feedback relation, Carnot theorem, and feedback topology inference in stochastic gene expression with nonlinear feedback

Understanding the relationship between spontaneous stochastic fluctuations and the topology of the underlying gene regulatory network is fundamental for the study of single-cell stochastic gene expression. Here by solving the analytical steady-state protein distribution in a general model of stochastic gene expression with nonlinear feedback regulation, we reveal a quantitative relation between stochastic fluctuations and feedback topology, perfecting the results in [Phys. Rev. Lett. 113:268105, 2014]. In negative-feedback networks, we find a fundamental inequality similar to the Carnot theorem in classical thermodynamics. Based on the fluctuation-feedback relation, we also develop an effective method to extract the topological information of a gene regulatory network from single-cell gene expression data via only three statistical quantities: the mean, variance, and decaying rate of the steady-state protein distribution. The theory is demonstrated by numerical simulations and, more importantly, validated quantitatively by single-cell data analysis of a synthetic gene circuit integrated in human kidney cells.