Before revision:  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 .
After revision:  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  . 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 .