Before revision:  we reveal a quantitative relation between stochastic fluctuations and feedback regulation at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations ] . Based on such relation, we also develop an effective method to extract the topological information of gene regulatory networks from single-cell gene expression data  .
After revision:  we reveal a quantitative relation between stochastic fluctuations and feedback regulation at the single-molecule level, which provides novel insights into how and to what extent a feedback loop can enhance or suppress molecular fluctuations ]. In negative-feedback networks, we find a fundamental inequality similar to the Carnot theorem in classical thermodynamics . Based on such relation, we also develop an effective method to extract the topological information of gene regulatory networks from single-cell gene expression data .