Information restriction in two-step cascade: role of fidelity and fluctuations

Information retained by the middle node X in a generic two-step cascade (TSC) motif (S → X → Y) is quantified by the metric restricted information (RI). Restricted efficiency, a normalised measure of RI, computes the ability of X in resisting the information flow from S to Y. We incorporate two types of autoregulatory edges, positive and negative, at X of the TSC framework, denoted as +TSC and −TSC, respectively. The role of autoregulatory edges (positive and negative) on the behaviour of X in information restriction is studied with reference to the TSC motif without autoregulation. Our theoretical analysis supplemented by numerical simulation shows that the information restriction imposed by X decreases (increases) with positive (negative) autoregulation. We introduce a dimensionless measure, relative fidelity, to understand the variation in RI due to autoregulatory edges. The relative fidelity is the signal-to-noise ratio for S–X regulation divided by the same for S–Y regulation. We find a specific operating range of the binding coefficient due to the autoregulatory edge at which a minimum (maximum) effect on information restriction is observed in the +TSC (−TSC) motif for high autoregulation strength.