Enzymes as molecular automata: a stochastic model of self-oscillatory glycolytic cycles in cellular metabolism.

A stochastic model based on the molecular automata approach was developed to simulate the cyclic dynamics of glycolysis-gluconeogenesis in cell energy metabolism. The stochastic algorithm, based on Gillespie's method, simulates the master equation associated with any network of enzymatically controlled reactions. This model of the glycolytic-gluconeogenetic cycle was developed by assembling the stochastic kinetic reactions controlled by two enzymes: phosphofructokinase (PFKase) and fructose-1, 6-biphosphatase (FBPase). In order to obtain the hysteresis behaviour predicted by classical Sel'kov analysis, a minimum complexity is required in the allosteric regulations. This implies that the FBPase cannot have a single binding site for its transition to the inactive state (a minimum of two or three binding sites is necessary). Given the multimeric structure of this enzyme, this kinetic hypothesis is tenable. Other possible applications of the stochastic automata approach for different cases of channels, receptors and enzymatic control are suggested.