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E E Sel'kov

Publications and source records attributed to E E Sel'kov.

At least 19 recordsLinked to original sources
PubMed1989

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. In this case, a significant parametric amplification of the membrane current takes place. If the modulation coefficient is above 2/Q, the membrane can display a parametric resonance that causes stable self-oscillations in the potential with a frequency approximately fo. The conditions for the realization of parametric amplification and resonance in biological membranes are discussed.

Cell Membrane↗
PubMed1982

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 1.2.1.12) step; a stationary state with all glycolytic intermediates having concentrations oscillating at nearly stationary mean values; and a depletion state at which the intermediates before the GAPDH step are being depleted due to the exhaustion of glycogen. In all these states, the mean ethanol production rate and the concentration of ATP and the intermediates beyond the GAPDH-step are maintained fairly constant, while the glycogen consumption rate and intermediate concentrations of the upper part of the glycolytic system changes considerably: the glycogen consumption rate varies 4-fold and fructose-bis-phosphate concentration more than 10-fold. Doubling of the initial glycogen concentration and the addition of a great excess of fructose-bis-phosphate do not affect the ethanol production rate and the mean glycerate-3-phosphate (3-PGA) and pyruvate levels. By contrast, ethanol production was accelerated by an increase of the net ATP consumption rate resulting from either the addition of apyrase or by substitution of trehalose for glycogen. Neither the mean absolute ATP level nor the adenylate energy charge were measurably affected, however, all this data can be interpreted in terms of a very strong stoichiometric regulation and stabilization of the lower part of the glycolytic system.

Adenosine Triphosphate↗
PubMed1980

[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. The mechanisms of the coordinated changes in the steady state rates of glycolysis, the H-transporting shuttles and the Krebs cycle at varying ATPase load in the cell are discussed.

Adenosine Triphosphatases↗
PubMed1980

[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. g. interrelationship of glycolysis, the Krebs cycle and H-transporting shuttles at varying rates of oxidative phosphorylation and ATPase load. It was shown that the mechanism of the Pasteur effect is based on the presence of two negative feed-back mechanisms in carbohydrate metabolism, namely by the level of ATP in glycolysis and by the level of mitochondrial NADH in the Krebs cycle and H-transporting shuttles. It was also shown that the value and sign of the Pasteur effect depend on the level of ATPase load. The role of this phenomenon in stabilization of ATP in the cell is discussed. The effects of changes in the allosteric properties of phosphofructokinase and low activity of H-transporting shuttles on the Pasteur effect was studied. It was shown that the low values of the pasteur effect in tumour tissues are mainly determined by an insufficient activity of oxidative phosphorylation.

Adenosine Triphosphatases↗
PubMed1977

[Effect of NAD recirculation on the mechanism of ATP stabilization in cytoplasm. Mathematical models].

A mathematical model of the glycolytic system with the cytoplasmic coenzymes NAD+ and NADH as essential variables is proposed. It has been shown that any increase in the steady-state concentration of NADH will reduce the range of activity of the "generalized" ATPase, wherein the level of ATP is stabilized. Such a reduction in the range of ATP stabilization may be caused by an increasing rate of the pyruvate loss into non-glycolytic pathways, in particular, into mitochondria. This effect may be compensated by increasing oxidation of NADH by the dehydrogenases of H+-transferring cytosol-mitochondrial shuttles (malate-aspartate or alpha-glycerophosphate). The properties of the complete model were compared with those of its simplified version, which takes account only of the phosphotransferase reactions of glycolysis. The effects of various factors, which do not alter the level of NADH in the system, may be studied within the scope of the simplified model.

Adenosine Triphosphatases↗
PubMed1977

[Substrate inhibition as a cause of oscillations in an open irreversible enzymic reaction S1 + S2 in the presence of E(R,T) leads to S1' + S2'. A mathematical model].

A mathematical model of an open irreversible reaction S1 + S2 (formula: see text) catalysed by an olygomeric enzyme E(R, T) has been analysed. It is assumed that the enzyme undergoes the concerted conformational transitions R in equilibrium T in conformity with the theory of Monod, Wyman and Changeux, and one of the substrates (S2) produces inhibition of the enzyme, thus shifting the equilibrium between the two enzyme forms in the direction of T formation. A simple graphical explanation is given to the hysteresis of the input characteristic approximately v ([S1]) (approximately v is the reaction rate at d[S2]/dt=O) which gives rise to self--oscillations. The hysteresis occurs both in the case of allosteric and isosteric substrate inhibition.

Allosteric Regulation↗
PubMed1976

[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.

Adenylate Kinase↗
PubMed1975

Stabilization of energy charge, generation of oscillations and multiple steady states in energy metabolism as a result of purely stoichiometric regulation.

A simple kinetic model of cell energy metabolism with autocatalytic reaction sequences has beepn analysed. The model accounts for the fact that part of energy produced in the form of ATP, or any other equivalent form, is utilized in "sparking" reactions to activate initial substrates. Analysis of the model shows that energy metabolism, in the absen-e of all non-stoichiometric (i.e. isosteric, cooperative, and allosteric) regulations, is capable of (a) stabilizing, to a high degree of accuracy, the relative concentration of the "charged form" of the energy-transferring cofactor (ATP); (b) alternating between two stable stationary states by means of hysteretic transitions; (c) generating self-oscillations in energy production. It is proposed that energy metabolism can be a source of very slow, in particular circadian (of about a one-day period), oscillations which may serve as the basis for temporal organization of the cell.

Cells↗
PubMed1975

Time hierarchy, equilibrium and non-equilibrium in metabolic systems.

A metabolic system consists of cooperating biochemical reactions. The motion is described by differential equations in the metabolites. The right-hand sides of these equations are linear combinations of the velocities of the individual reactions. These velocities depend in a non-linear manner on the metabolite concentrations (according to the law of mass action). A characteristic "metabolic" time may be defined for the motion of the whole system. It scales the essential metabolic events whose evolution time is comparable to this metabolite time unit. The constituent reactions of the metabolic system have an individual characteristic time which need not coincide with the general metabolic time. The individual time characterises the approach to the individual equilibrium of the isolated undisturbed reaction. According to the ratio of these two time scales, a single reaction may be fast, or slow, or essential, as compared with the metabolic events. Characteristic time of a single reaction and its steady-state deviation from equilibrium are closely related. It can be shown that the relative deviation from equilibrium of a reaction within the metabolic network is of the same numerical order as the ratio between individual time to metabolic time. The interaction of many reactions with different characteristic times introduces a time hierarchy into the system. This can be made transparent by appropriate scaling and by linear transformation of the system. The subsystem of fast cooperating reactions (dehydrogenases, phosphotransferases) attains a state which is near to the individual equilibrium and reestablishes this state after perturbation. The equilibration is fast; an ultrarapid phase of cofactor equilibrium can be distinguished from the fast phase of substrate equilibrium (exchange of metabolic material between different pathways). During the slower metabolic phase these near-equilibria manifest themselves as stoichiometric linkage between unrelated metabolites. The latter cease to be independent variables and combine to metabolic pools. It can be strictly shown that the essential variables at the metabolic time scale are carrier pools and the degree of occupancy of these carriers by metabolic groups. Chemically different types of carrier pools may be functionally linked together by fast reactions. A consequence of such an arrangement of reactions are distance effects: Changes at one end of a metabolic map may be directly conveyed to other pathways via stoichiometric linkage brought about by fast equilibration of cofactor reactions.

Enzymes↗
PubMed1970

Stable circadian rhythms as a property of cell populations.

Our paper analyzes the main difficulties which the theory of circadian rhythms encounters in an attempt to explain the mechanisms of biological clocks. It is shown that the assumption of a small concentration of the enzymes involved in the cell-clock mechanism allows explaining such well-known properties of biological clocks as: 1) a large period of the circadian oscillation; 2) insignificant energy consumption; 3) insensitivity to inhibitors; 4) temperature independence; 5) initiation of circadian oscillations in response to a short single external impulse; 6) a limited possibility of synchronization by periodic external factors. It is shown also that the self-oscillating clock mechanism may exist at the level of cell populations. This mechanism is considered to be a temperature-dependent component of the circadian clocks in multicellular organisms.

Cell Physiological Phenomena↗
PubMedDate not supplied

[Generalization of the Monod-Wyman-Changeux model for the case of multisubstrate reactions].

A general equation is derived for the rate of multisubstrate reaction catalyzed by oligomeric enzyme E(R, T) liable to concerted transitions Ro in equilibrium To or Ro in equilibrium 2To. It is shown that with some assumptions about the enzymes the rate equations can be constructed from the rates of corresponding reactions catalyzed by a single active site. These single active site rate equations are known for the majority of catalysis mechanisms, otherwise they can be easily deduced. As an example the rate equation is derived for the reaction S1 + S2 + S3 in equilibrium S4 + S5 catalyzed by an oligomeric enzyme according to the ordered ter-bi mechanism.

Binding Sites↗
PubMedDate not supplied

[Hysteresis and multiplicity of dynamic states in open 2-substrate enzyme reactions with substrate inhibition].

A mathematical model of an open two-substrate enzymic with substrate inhibition has been analyzed. The hysteretic form of the reaction input characteristics resulting in the appearance of three alternative stationary states, O1, O2 and O3, has been obtained. The region of existence of a stable limit cycle has been determined within the framework of linear approximation. Analysis of the model to a non-linear approximation shows that close to the boundary of the stability region the unstable or stable limit cycle can surround O1 or O3 as well as the only stationary state O.

Enzymes↗
PubMedDate not supplied

[Hysteresis, multiplicity of stationary states and auto-oscillations in the reversible flow-through reaction].

A mathematical model has been investigated of a reversible flow-through reaction S1 reversible S2 catalyzed by an olygomeric enzyme E(R,T) the protomers of which undergo concerted conformational transitions R reversible T. The isosteric activation of olygomer E by product S2 binding preferably to protomer active sites in conformation R is shown to be a possible cause of hysteresis in the quasi-stationary input characteristic of the reaction, v (s2). The latter determines the rate law of the reaction, provided the concentration of S2 is a quasi-stationary one. The hysteresis of the characteristic v (s1) gives rise to multiple steady states and self-oscillations in the reaction.

Catalysis↗