Measuring the degree of modularity in gene regulatory networks from the relaxation of finite perturbations

In gene regulatory networks, transcription factors regulate downstream sites by binding or unbinding to specific promoter regions. It is known that the binding-unbinding process can affect factor life times, and thus response times. This change in the dynamical properties depends on the number of sites that the transcription factor binds to as well as the factor concentration level. To estimate how the dynamics of a given transcription factor will be affected by the number of binding sites, we previously devised a measure called the fan-out - complimentary measure to retroactivity - that indicates the maximum number of the binding sites before the dynamic response is significantly affected. We provided an efficient method to measure the fan-out and retroactivity experimentally by exploiting gene expression noise. In this presentation, we provide another efficient measurement method for retroactivity and fan-out at the population level. The method resorts to finite-size perturbations in system parameters or concentrations. The equivalent analysis method at the single cell level that is based on gene expression noise is also presented.