Signal duration and the time scale dependence of signal integration in biochemical pathways

Signal duration (e.g. the time scales over which an active signaling intermediate persists) is a key regulator of biological decisions in myriad contexts such as cell growth, proliferation, and developmental lineage commitments. Accompanying differences in signal duration are numerous downstream biological processes that require multiple steps of biochemical regulation. Here, we present an analysis that investigates how simple biochemical motifs that involve multiple stages of regulation can be constructed to differentially process signals that persist at different time scales. We compute the dynamic gain within these networks and resulting power spectra to better understand how biochemical networks can integrate signals at different time scales. We identify topological features of these networks that allow for different frequency dependent signal processing properties. Our studies suggest design principles for why signal duration in connection with multiple steps of downstream regulation is a ubiquitous control motif in biochemical systems.