Temporal dose inversion properties of adaptive biomolecular circuits

Cells have the capacity to encode and decode information in the temporal features of molecular signals. Many pathways, for example, generate either sustained or pulsatile responses depending on the context, and such diverse temporal behaviors have a profound impact on cell fate. Here we focus on how molecular pathways can convert the temporal features of dynamic signals, in particular how they can convert transient signals into persistent downstream events and vice versa. We describe this type of behavior as temporal dose inversion, and we demonstrate that it can be achieved through adaptive molecular circuits. We consider motifs known as incoherent feedforward loop (IFFL) and negative feedback loop (NFL), and identify parametric conditions that enable temporal dose inversion. We next consider more complex versions of these circuits that could be realized using enzymatic signaling and gene regulatory networks, finding that both circuits can exhibit temporal dose inversion. Finally, we consider a generalized IFFL topology, and we find that both the time delay in the inhibition pathway and the relative signal intensities of the activation and inhibition signals are key determinants for temporal dose inversion. Our investigation expands the potential use of adaptive circuits as signal processing units and contributes to our understanding of the role of adaptive circuits in nature.