Measuring Retroactivity from Noise in Gene Regulatory Networks

Synthetic gene regulatory networks show significant stochastic fluctuations in expression levels due to the low copy number of transcription factors. When a synthetic gene network is allowed to regulate a downstream network, the response time of the regulating transcription factors increases. This effect has been termed retroactivity. In this article, we describe a method for estimating the retroactivity of a given system by measuring the stochastic noise in the transcription factor expression. We show that the noise in the output signal of the network can be affected significantly when the output is connected to a downstream module. More specifically, the output signal noise can show significantly longer correlations. We define retroactivity by the change in the correlation time. This measure of retroactivity corresponds well to the deterministic retroactivity described in another study. We provide an estimation method for measuring retroactivity from the gene expression noise by investigating its autocorrelation function. When retroactivity is defined using the decay (correlation) times from the gene expression autocorrelation functions, it is found not to depend on whether the module output is defined as either the free transcription factor or the total of the bound and free transcription factor. The frequency domain response, however, depends strongly on which output variable is considered. The proposed estimation method for measuring retroactivity, based on the gene expression noise, can serve as a practical method for characterizing interface conditions between two synthetic modules and eventually provide a step toward large-scale circuit design for synthetic biology.