Figure 4. Presence and consequence of biphasic dose responses in cellular signaling arising from enzyme-mediated substrate modification: Top left hand panel: Schematic representation of the study.

The basic mechanism of enzyme-mediated substrate modification (when present in different reversible modification cycles) allows for simple biochemical systems to present biphasic dose-response behavior. This is analyzed in a series of commonly encountered biochemical building blocks of cell signaling (M0-M8, see Figure 1—figure supplement 1 for detailed schematic). In each case, we assess whether the system exhibits biphasic behavior with respect to variation of total amounts of enzyme and substrate as doses, and if it does so robustly. The table below provides a classification system to determine the different possibilities of biphasic responses (enzyme/substrate) vis-a-vis the desirability/undesirability of biphasic responses. This provides a framework (in synthetic biology) for determining what changes need to be made to a system, to obtain desirable characteristics. We then extend the study to consider the consequence of such biphasic dose responses in network motif structures (either within nodes, or in interactions–colored in red) and study how biphasic interactions can alter expected outcomes from these systems (N1–N5). Top right hand panel: Case study: Extracellular signal-regulated kinase (Erk) Regulation. The ERK regulatory network is capable of both exhibiting substrate and enzyme biphasic response in the double phosphorylated Erk (pYpTErk) in the steady state dose response with ${\displaystyle Me{k}_{Total}}$ (Enzyme biphasic) and ${\displaystyle Er{k}_{Total}}$ (Substrate biphasic). A-B shows an instance of enzyme and substrate biphasic response, respectively. (C) shows how the steady state concentration of pYpTErk changes with ${\displaystyle Me{k}_{Total}}$ and ${\displaystyle Er{k}_{Total}}$ (for a fixed kinetic parameter set). This indicates the presence of simultaneous substrate and enzyme biphasic response in the system (red and blue lines indicate the peak concentration of pYpTErk achieved for a given amount of total substrate and total enzyme amounts, respectively). Bottom panel. Table: Detailed summary of the various results discussed in the manuscript, including the possibility and impossibility of specific dose-response behaviors in a model, and the different ways in which the expected outcome of a network motif structure is undercut by biphasic responses within interactions. Note: These results discuss analytical results which can be found in Supplementary file 1.