Dichotomous Nature of Bistability Generated by Negative Cooperativity in Receptor-Ligand Binding

Positive cooperativity in receptor-ligand binding plays an important role in cell signaling as it generates an ultrasensitive response, a requirement for nonlinear phenomena such as bistability and oscillations in feedback regulated reaction networks. On the other hand, negative cooperativity typically produces a hyperbolic response and is thus less explored. However, recently negative cooperativity was shown to generate an ultrasensitive response under the condition of strong ligand affinity. In this work, we have used mathematical modeling to investigate the effect of negative cooperativity in receptor-ligand interaction on the bistability in a positive feedback regulatory motif. We systematically investigated the effect of negative cooperativity, modifying the two equilibrium constants of the receptor-ligand binding, on the robustness and tunability of bistability. We show that in the regime where negative cooperativity exhibits robust bistability, positive cooperativity results in poor bistability and vice versa. Further we find that the robustness and tunability of bistability depend crucially on the stability of singly and doubly engaged receptors. Our modeling highlights the ability of negative cooperativity to produce complex phenomena with potential applications in designing synthetic devices or in explaining experimental observations in cell biology.