[Homeostasis of the auto-oscillation period in a model of a cellular circadian clock].

A mathematical model was numerically investigated which describes the autooscillatory temporal organization of futile cycles of the carbohydrate branch of energy metabolism. Using an optimization method we found a region in the parametric space of the model in which the circadian oscillation period was practically constant, although the major eight parameters varied in a wide range. Such homeostasis of the period is due to synergistic effects of the four feed-back mechanisms regulating activities of the key enzymes.

[Mathematical model of stabilization of circadian rhythm in cell energy metabolism].

A mathematical model for circadian self-oscillation in the carbohydrate branch of energy metabolism (CEM) was analysed. The self-oscillations are due to the reciprocal regulation of the activities of 6-phosphofructokinase and fructose-1,6-bisphosphatase by fructose-1,6-bisphosphate. The circadian period was shown to be insensitive to metabolic disturbances because of the presence in CEM of negative feedback mechanisms regulating the activities of the key enzymes 6-phosphofructokinase, fructose-1,6-bisphosphatase, pyruvate kinase and phosphoenolpyruvate carboxykinase.