ADAPTATION OF SIMPLE MOLECULAR NETWORKS TO TIME-DEPENDENT STIMULUS

Adaptation is the ability by which signaling systems reset themselves after responding to a stimulus. Incoherent feedforward loops and negative feedback loops are the only two types of three-node topologies showing adaptation to constant stimuli. In this study, adaptation of these two types of topologies to time-dependent stimuli are discussed. Through analytical calculation and numerical simulations, it is found that they may show adaptation when the pulse duration and internal are properly assigned. In particular, for incoherent feedforward loops, two kind of models, i.e., logic approximation piecewise-linear equations and Hill-type equations are considered. When adaptation to time-dependent stimulus is considered, analytical solutions for logic approximation piecewise-linear equations and numerical simulation for Hill-type equations are in substantial agreement. The study on adaptation to time-dependent stimulus could serve as a manual providing different possible solutions to develop intelligent therapeutic strategies and to build biological circuits with specified functions.