[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.

[Oscillations and trigger phenomena in fructose-2,6-bis-phosphate metabolism. A mathematical model].

A mathematical model describing metabolism of fructose-2,6-bisphosphate (F2, 6P2), which is a powerful mediator in glycolysis, is investigated. The model takes into account inhibitory effect of F2, 6P2 and fructose-6-phosphate (F6P) on protein kinase, which phosphorylates the bifunctional enzyme fructose-6-phosphate-2-kinase/fructose-2,6-bisphosphatase. Such a mechanism of enzyme chemical modification in the presence of F2, 6P outflow from the F6P in equilibrium with F2, 6P2 cycle, caused by nonspecific phosphatases, can display trigger phenomena and sustained oscillations in F2, 6P2 metabolism and in the whole glycolytic system.

[Characteristics of the stoichiometric regulation of glycolysis in prokaryotic cells. A model].

A model is developed to investigate the steady state of the glycolytic system of procaryotic cells which have the hexose transport into the cell coupled with phosphoenolpyruvic acid-dependent phosphorylation. Analysis of the model shows that this phosphorylation results: 1) in stoichiometric connection between the rate of hexose consumption and the utilization of ATP and 2) the stoichiometric positive feedback. The latter can be the cause of bistability, oscillations and other nonlinear phenomena.

[Parametric resonance and amplification of periodic disturbances in membranes containing ion channels with inactivation].

Parametric resonance and amplification of periodic perturbations in the membrane transport of ions through channels with inactivation was studied in computational experiments. It has been shown that a periodic change in the membrane capacitance or in the applied electric current with a frequency approximately 2 omega 0 (omega 0--the own angular frequency of the membrane) may excite stable self-oscillations in the membrane with a frequency of approximately omega 0. For this to occur, the degree of the capacitance modulation m or the amplitude of the applied current i0 must exceed some critical values mcr and i0cr.

[Resonance phenomena in membranes containing ion channels with inactivation].

A mathematical model of the ion transport across a membrane containing channel with inactivation has been analysed. Under certain conditions, such a membrane has been shown to behave as a selfoscillating circuit of a very high quality, its own frequency ranging for a variety of natural channels between 10(-1)-10(3) cycles. When exposed to an alternating electric field with a frequency approximating f0, the membrane displays resonance changes in its potential and channel conductivity.

[resonant events in membranes having ion channels with two conformational states].

A study was carried out of a mathematical model of ion transport through biological membranes along the channels capable of conformational transitions between two states (R, T) with different conductivities. The model describes changes in time of te membrane potential and surface concentration of channels in one of the states (R). It has been shown that there may exist extinguishing oscillations with the frequency close to f0 on such a system may induce the resonance changes of the membrane potential.

[Kinetic resonance in open biochemical reactions with genetic induction of enzyme biosynthesis].

It has been shown that the genetic induction of enzyme synthesis by the substrate, like the kinetic induction, may bring about resonance responses in an open biochemical reaction at periodic external disturbances. Joint action of genetic and kinetic inductions broadens the range of the system parameters, where the resonance phenomena are possible. Under the joint action of genetic and kinetic inductions the resonance frequency may be independent of the amplitude of external periodic disturbance.

Flux regulation in glycogen-induced oscillatory glycolysis in cell-free extracts of Saccharomyces carlsbergensis.

To localise the controlling point of the glycolytic system, the temporal changes in concentrations of glycolytic intermediates have been analysed after addition of glycogen to a substrate-depleted yeast extract. Three sequential metabolic states are clearly observable: a transition state at which there is continuous accumulation of the intermediates before the glyceraldehydephosphate dehydrogenase (GAPDH, EC 1.2.

[Self-oscillations in an open biochemical substrate-inhibited reaction interacting with the enzyme-producing system].

An open biochemical reaction with substrate inhibition is analysed under conditions of a continuous turnover of its enzyme maintained by the enzyme-producing system (EPS). In this reaction, self-oscillations of a long period may occur in addition to the resonance phenomena found in a simple biochemical reaction with the EPS. A distinctive property of this reaction is also superadaptation with which the total enzyme concentration increases as a square of the substrate influx rate.

[Oscillations and resonance phenomena in the simple, open enzymatic reaction--S-E-P-- reacting with an enzyme-forming system].

Resonance phenomena in a simple open biochemical reaction were studied under conditions of a continuous enzyme flow through the reaction maintained by the enzyme-producing system (EPS). Periodical disturbance of the rate of substrate influx may bring about a resonance effect in the reaction, the amplitude of forced sustained oscillations being maximal at a frequency close to that of the system itself. Additional resonance effects may appear due to nonlinearity of the system at frequencies multiple (or close to multiple) of the own frequency, as well as at subfrequencies.

[Analysis of a simple open biochemical reaction S leads to P by means of E interacting with an enzyme-producing system].

A mathematical model of an open enzymic reaction S leads to P by means of E is analysed. The enzyme E of this reaction undergoes a continuous turnover in the enzyme--producing system (EPS) involving two opposing processes, formation of the enzyme at a constant velocity upsilon e and its irreversible degradation or removal at a rate constant kappa e. In the derivation of the model it was assumed that the substrate S prevents the enzyme from degradation.

[Analysis of allosteric mechanisms of suppressing parasitic recirculation in the futile cycle fructose-6-P--fructose-1,6-P2].

The uncontrollable substrate recirculation in the central futile cycle (FC) in the carbohydrate energy metabolism fructose-6-P (F6P) in equilibrium or formed from fructose-1,6-P2 (FBP), makes it impossible to maintain a stable level of ATP because of its wasteful expenditure in the cycle reactions which are equivalent to the ATPase reaction and also because of the diversion of FBP from glycolytic phosphorylation of ADP. It follows from the analysis of a mathematical model of the carbohydrate energy metabolism that the allosteric inhibition of fructosebisphosphatase (FBPase) by FBP and AMP leads to suppression of the recirculation in the FC and recovery of the ability of glycolysis to stabilize the level of ATP with high accuracy. The allosteric activation of phosphofrucktokinase (PFK) by AMP couples the expenditure of ATP and F6P in the FC with ATP consumption by a load.

[Mathematical model for carbohydrate energy metabolism. Mechanism of the Pasteur effect].

The simple mathematical model based on the stoichiometric structure of carbohydrate metabolism and the only allosteric regulation presented, i. e. activation of phosphofructokinase by AMP, was used to study the mechanism of the Pasteur effect, e.

[Multiplicity of auto-oscillations and steady states in an open reaction catalyzed by E. coli phosphofructokinase. Quantitative model].

A quantitative mathematical model of two-substrate reaction catalized by phosphofructokinase from E. coli has been investigated. The model takes into account the tetrameric enzyme structure and resulting kinetic peculiarities of the reaction catalized, in particular, iso-and alosteric effects of ADP on enzyme activity.

[Mathematical model of carbohydrate energy metabolism. Interaction between glycolysis, the Krebs cycle and the H-transporting shuttles at varying ATPase load].

A simple mathematical model for carbohydrate energy metabolism based on the stoichiometic structure of glycolysis, the Krebs cycle and oxidative phosphorylation is proposed. The only allosteric regulation involved in the model is phosphofructokinase activation by AMP. Simple as it is, the model can explain the following properties of carbohydrate metabolism: a drastic rise of the rate of glucose consumption during transition to a higher level of ATPase load; stabilization of ATP and an increase of the steady state rates of glycolysis and oxidation of cytoplasmic NADH by the H-transporting shuttles and of pyruvate in the Krebs cycle with increasing rate of the ATPase load; activation of glycolysis and a decrease of the rate of oxidative phosphorylation following an inhibition of the H-transporting shuttles.

[Theoretical evidence for the need to suppress parasitic recirculation in the futile cycle fructose-6-P--fructose-1,6-P2].

In connection with the discussion of a possible role of the futile cycle fructose-6-P in equilibrium or formed from fructose-1,6,-P2 in the regulation of the carbohydrate energy metabolism, simple stoichiometric models of glycolysis and gluconeogenesis are examined which take account of substrate recirculation in the cycle. The recirculation is shown to involve wasteful expenditure of ATP and to divert fructose-1,6-P2 from glycolytic phosphorylation ADP and fructose-6-P from glucose or glycogen resynthesis. As a result, the glycolytic system loses its capacity to stabilize the level of ATP, while gluconeogenesis proves to be not efficient.

[Allosteric regulation in the open futile cycle fructose-6-P--fructose-1,6-P2].

The effect of fructosebisphosphatase inhibition and phosphofructokinase activation by fructose-1,6-bisphosphate on a parasite recirculation of substrates in the futile (energy-dissipating) cycle fructose-6-P in equilibrium fructose-1,6-P2 has been studied. Both the inhibition and activation have been shown to produce self-oscillations in the cycle under flow-through conditions. The common recirculation with both regulatory mechanisms present is about half as high as with only one of them.

[Qualitative study of a mathematical model of the open futile cycle fructose-6-P--fructose-1,6-P2].

A simple mathematical model of the open futile cycle fructose-6-P in equilibrium fructose-1,6-P2 in which the fructose bisphosphatase reaction is inhibited by excess of its substrate has been analysed. A detailed qualitative investigation of the model shows that it possesses all properties characteristic of any other dynamical system of the second order which has a hysteretic major null-cline, 1 to 3 steady states and is capable of generating self-oscillations.