[Comparative analysis of the mechanism of metabolism of storage compounds in the cell clock].

The effect of the autooscillation period Td of various kinetic mechanisms for D in equilibrium with S exchange (D storage form of the compound S) was theoretically studied in a system of the D in equilibrium with S in equilibrium with G1 type, where G = S in equilibrium with G1 is a relaxation autooscillator. The kinetics studied were linear, hyperbolic and cooperative. With a rapid D in equilibrium S exchange all the three kinetic mechanisms were shown to yield approximately equal values of Td.

Parametric resonance and amplification in excitable membranes. The Hodgkin-Huxley model.

It has previously been shown by different investigators that the excitable membrane shows a resonant sensitivity to periodic external perturbations, but its Q-factor is, as a rule, low. The present paper analyses the possible ways of increasing the membrane Q, using a model of the Hodgkin-Huxley type. It is found, in particular, that it can be increased considerably by modulating periodically the membrane capacitance or the activation and inactivation rate constants of ionic channels, with a frequency of about 2 fo (fo being the fundamental frequency of damped oscillations in the membrane), the extent of modulation not exceeding the critical value 2/Q.

[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.

[The key role of fructose-2,6-bis-phosphate in the temporal organization of carbohydrate metabolism. An auto-oscillating mathematical model].

A mathematical model describing the periodical temporal organization of the open futile cycle fructose-6-phosphate in equilibrium fructose-1,6-bisphosphate (F6P in equilibrium F1,6P2) is investigated. The oscillations in this cycle are caused by the regulatory cycle F6P in equilibrium fructise-2,6-bisphosphate (F2,6P2), catalyzed by phosphofructokinase-2 (PFK-2) with a cascade of covalent chemical modification. The apparent product activation of PFK-2 by F2,6P2 together with the F2,6P2 outflux from the regulatory cycle create square-shaped oscillations in the concentration of F2,6P2, a powerful reciprocal regulator of the enzymes of the futile cycle F6P in equilibrium F1,6P2.

[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.