Application of the metabolic control theory to the study of the dynamics of substrate cycles

Substrate cycles are ubiquitous structures of the cellular metabolism (e.g. Krebs cycle, fatty acids -oxydation cycles, etc... ). Moiety-conserved cycles (e.g. adenine nucleotides and NADH/NAD, etc...) are also important.The role played by such cycles in the metabolism and its regulation is not clearly understood so far. However, it was shown that these cycles can generate multistationarity (bistability), irreversible transitions, enhancement of sensitivity, temporal oscillations and chaotic motions (Hervagault & Canu, 1987; Hervagault & Cimino, 1989; Reich & Sel'kov, 1981; Ricard & Soulié, 1982). Fig. 1: Scheme of the open binary substrate cycle under study. The substrate S is converted into P with a net rate v₂. Substrate P is converted in turn into S with a net rate v₃. Step v₂ is inhibited by excess of the substrate, S. In addition, the cycle operates under open conditions, that is zero-order input of S at rates \ga₀(v₁) and first order outputs of S and P at rates \gaS and \gaP(v₄), respectively.The metabolic control theory (see also Fell, 1990), which shows how a metabolic network reacts to small perturbations in the vicinity of a steady state, and is formulated with the so-called control coefficients, was applied to such a cycle in order to get a better knowledge on the importance of each step at the regulatory point of view.The behaviour of a binary substrate cycle (fig. 1) in which one of the enzymes may be subjected to inhibition by excess of its substrate (v₂) was studied theoretically. The flux and concentration control coefficients were calculated for various steady states of the system. The evolution of the different control coefficients is compared to the evolution of the steady states. We mainly focused our study on situations for which the steady states are stable.