Analysis of substrate competition in regulatory network motifs: Stimulus–response curves, thresholds and ultrasensitivity

Abstract

In the simplest case, substrate competition arises if two ligands compete for access to a single binding site of a receptor protein (or enzyme). If the two ligands exhibit different binding affinities the competition becomes biased: as long as the receptor concentration remains lower than that of the high-affinity ligand the latter blocks all of the available binding sites so that the concentration of the complex comprising the low-affinity ligand remains low. The latter only rises if the receptor concentration is increased beyond that of the high-affinity ligand. Depending on the binding affinity of the low-affinity ligand this increase may then occur in an ultrasensitive manner. Similar behavior has been observed in a phosphorylation/dephosphorylation cycle involved in cell-cycle regulation. However, a steady state analysis shows that in this case the threshold concentration is modulated by the catalytic rate constants for phosphorylation and dephosphorylation of the high-affinity substrate. As a consequence, there exists a trade-off between the dynamic range of the system as measured by the maximal phosphorylation level of the substrate and the sensitivity of the system as measured by the position of the threshold. Using the ratio of the binding affinities as a small parameter we derive explicit expressions for the stimulus–response curves as a function of the receptor (or enzyme) concentration as well as conditions for the occurrence of ultrasensitivity. Interestingly, the network motifs investigated in this study are described by structurally similar steady state equations indicating that the analysis presented here may be extendable for analyzing substrate competition in more complex regulatory networks.