Sensitivities of Regulation Intensities in Feed-Forward Loops with Multistability

Gene regulatory networks depict the interactions among genes, proteins, and other components of the cell. These interactions are stochastic when large differences in reaction rates and small copy number of molecules are involved. Discrete Chemical Master Equation (dCME) provides a general framework for understanding the stochastic nature of these networks. Here we used the Accurate Chemical Master Equation method to directly compute the exact steady state probability landscape of the feed-forward loop motif (FFL). FFL is one of the most abundant gene regulatory networks motifs where the regulation is carried out from the top nodes to the bottom ones. We examine the behavior of stochastic FFLs under different conditions of various regulation intensities. Under the conditions with slow promoter binding, we show how FFL can exhibit different multistabilities in their landscapes. We also study the sensitivities of regulations of FFLs and introduce a new definition of stochastic sensitivity to characterize how FFLs respond in their probability distributions at the steady state to perturbations of system parameters. We show how change in gene expression under FFL regulations are sensitive to system parameters, including the state of multistability in FFLs.