A transfer-function representation for regulatory responses of a controlled metabolic pathway

A transfer-function representation for the response of a controlled metabolic pathway to the changes in influx and efflux rates of metabolites is formulated to describe analytically and approximately the regulatory behavior of the pathway around a steady state. The pathway model analysed is an open and homogeneous system which consists of two consecutive enzymatic reactions catalyzed by an allosteric enzyme of Monod-Wyman-Changeux (MWC) dimeric model and a Michaelis-Menten-type enzyme, respectively, and undergoes the feedback inhibition by the end product. The rate equation for the system (a system of ordinary differential equations) is linearized about a steady state, so that the responses of the reaction rates to the changes in influx rate of the substrate and efflux rate of the end product are expressed in a form of transfer function. The formulation leads to the transfer function for the response of production rate of the end product to the change in its efflux rate to clarify the regulatory response of feedback mechanism in controlled metabolic pathways. The relationship among the chemical species in the system at steady stete also supports a reasonable assumption that the regulatory mechanisms in metabolic pathways are to control the production of end product against the change in its demand from the cellular environments.