  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.
