On the Use of the Hill Functions in Mathematical Modelsof Gene Regulatory Networks

Abstract

Hill functions follow from the equilibrium state of the reaction in which n ligands simultaneouslybind a single receptor. This result if often employed to interpret the Hill coefficient asthe number of ligand binding sites in all kinds of reaction schemes. Here, we study the equilibriumstates of the reactions in which n ligand bind a receptor sequentially, both non-cooperatively andin a cooperative fashion. The main outcomes of such analysis are that: n is not a good estimate,but only an upper bound, for the Hill coefficient; while the Hill coefficient depends quite stronglyon the cooperativity level among ligands. We finally use these results to discuss the feasibilityand constrains of using Hill functions to model the regulatory functions in mathematical models ofgene regulatory networks.