Restricted information in a two-step cascade

A cell must sense extracellular and intracellular fluctuations and respond appropriately to survive for optimal cellular functioning. Accordingly, a cell builds up biochemical networks which can transduce information of extracellular and intracellular fluctuations accurately. We consider a generic two-step cascade as a model gene regulatory network containing three regulatory proteins S, X, and Y connected as S→X→Y. The intermediate node X is a stochastic variable, acts as an obstacle, and impedes the information flow from S to Y. We quantify the information that is restricted by X using the tools of information theory and term this as restricted information. In this context, we further propose two measurable quantities, restricted efficiency and information transfer efficiency. The former determines how efficiently X restricts the upstream information coming from S, while the latter computes the efficiency of X to pass the upstream information toward Y. We also quantify the information that is being uniquely transferred from X to Y, which determines the extent of the ability of X to act as a source of information. Our analysis shows that when the signal strength (or mean population of S, 〈s〉) is low, the intermediate X can carry forward the upstream information reliably as well, as it acts as a better source of information, thereby increasing the fidelity of the network. But at the high signal strength, X restricts most of the upstream information, and its ability to act as a source of information gets reduced. This leads to a loss of fidelity of the network.