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 beta-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). [formula: see text] 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 alpha 0(v1) and first order outputs of S and P at rates alpha S and alpha P(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.(ABSTRACT TRUNCATED AT 250 WORDS)