Hysteresis, alternative stationary states and auto-oscillations in an open futile cycle one of the reactions of which is substrate inhibited]

In connection with the problem of regulation of futile (energy-dissipating) cycles in cell metabolism, a kinetic model has been investigated of an open cycle S1 (see article) S2, in which one of the enzymes (E-) is inhibited by the excess of its substrate S2. The quasi-stationary net velocity of the utilization of substrate S1 in the cycle as a function of its concentration is shown to be of a hysteretic character. Owing to this the alternative stationary states and self-oscillations may occur in the cycle. Under certain conditions the transition from one alternative state to another may reverse the direction of the net flux of conversion from S1 to S2 or vice versa. The self-oscillations are associated with a periodical change in the net flux direction. It is suggested the participation of glycogen (starch) in the self-oscillatory mechanism of the futile cycle formed by the phosphofructokinase and fructose bisphosphatase reactions may give rise to oscillations with the period of 10(3)-10(4) min, which may serve as the basis for the cell clock.