Modular systems approach to understanding the interaction of adaptive and monostable and bistable threshold processes

Adaptive signalling is a common and important element in cellular systems. Threshold processes are also ubiquitous in signal transduction. This study takes a modular systems approach to systematically understand the interaction of adaptive modules and threshold modules (both monostable and bistable). The authors employ representative modules of adaptive and threshold elements and use these to examine and analyse various aspects of their interaction including the order of interconnection, the role of relative time scales, the difference between monostable and bistable thresholds in this context and how threshold modules may act as a switch induced by transient signals. Numerical simulations, bifurcation analysis and analytical work are employed to address these questions. Overall, the authors´ analysis is a first step towards a detailed systems engineering understanding of the different kinds of interactions between these ubiquitous elements in cellular signal transduction.