Susceptibilities of an irreversible Michaelis-Menten enzyme

The nonlinear response of the simplest irreversible Michaelis-Menten enzyme is considered. In the context of metabolic networks, i.e. in vivo, the enzyme is subject to sustained, frequently time-dependent, input fluxes that keep the system out of equilibrium. The connection between the fluxes and the response is investigated by means of a new sensitivity analysis. The kinetics of the enzyme is simple enough to allow for the computations to be carried out analytically. In particular, a set of sensitivities of the response with respect to the substrate influx, the susceptibilities, is derived. The susceptibilities are multivariate functions and thus are suitable for predicting complete progress curves of several variables of biochemical interest, namely, rates and concentrations. This is shown by means of an example. The relationship between the susceptibilities and the stoichiometry of the reaction is also taken into account. Moreover, all the required information comes from decay experiments of initial concentrations, which are common in enzymological setups.