Glycolysis oscillations

It is interesting to note that this sigmoidal character of enzyme kinetics plays an essential role in regulation. Most of the regulatory enzymes in the metabolic pathways of amino acid biosyntheses and in carbohydrate metabolism exhibit such behavior, with the result that the kinetics can change in the presence of effectors (intermediary metabolities) from sigmoid to hyperbolic (see glycolysis oscillations. Sect. 5.2.1). 

In addition to bistability and hysteresis, the minimal model of glycolysis also allows nonstationary solutions. Indeed, as noted above, one of the main rationales for the construction of kinetic models of yeast glycolysis is to account for metabolic oscillations observed experimentally for several decades [297, 305] and probably the model system for metabolic rhythms. In the minimal model considered here, oscillations arise due to the inhibition of the first reaction by its substrate ATP (a negative feedback). Figure 24 shows the time courses of oscillatory solutions for the minimal model of glycolysis. Note that for a large... 

Figure 24. The nullclines (upper panels, gray lines) and time courses (lower panels) for oscillatory solutions of the minimal model of glycolysis. Left panels Damped oscillations. The...

Figure 29 Bifurcation diagram of the minimal model of glycolysis as a function of feedback strength and saturation 6 of the ATPase reaction. Shown are the transitions to instability via a saddle node (SN) and a Hopf (HO) bifurcation (solid lines). In the regions (i) and (iv), the largest real part with in the spectrum of eigenvalues is positive > 0. Within region (ii), the metabolic state is a stable node, within region (iii) a stable focus, corresponding to damped transient oscillations.

The negative feedback in glycolysis, induced by substrate inhibition of lumped PFK HK reaction, thus fulfills an important functional role but concomitantly opens the possibility of sustained oscillations. In particular, because glycolytic oscillations have no obvious physiological role and are only observed under rather specific experimental conditions, it is plausible that they are merely an unavoidable side effect of regulatory interactions that are optimized for other purposes. 

A. Boiteux, A. Goldbeter, and B. Hess, Control of oscillating glycolysis of yeast by stochastic, periodic, and steady source of substrate A model and experimental study. Proc. Natl. Acad. Sci. 72(10), 3829 3833 (1975). 

Y. Termonia and J. Ross, Oscillations and control features in glycolysis Numerical analysis of a comprehensive model. Proc. Natl. Acad. Sci. USA 78, 2952 2956 (1981). 

K. Nielsen, P. G. Sprensen, F. Hynne, and H. G. Busse, Sustained oscillations in glycolysis An experimental and theoretical study of chaotic and complex periodic behavior and of quenching of simple oscillations. Biophys. Chem. 72, 49 62 (1998). 

Some of the main types of cellular regulation associated with rhythmic behavior are listed in Table III. Regulation of ion channels gives rise to the periodic variation of the membrane potential in nerve and cardiac cells [27, 28 for a recent review of neural rhythms see, for example, Ref. 29]. Regulation of enzyme activity is associated with metabolic oscillations, such as those that occur in glycolysis in yeast and muscle cells. Calcium oscillations originate... 

The molecular mechanism of glycolytic oscillations has been discussed for long [31, 38, 40-42]. Because glycolysis represents a system of enzymatic reactions coupled through different intermediates such as ATP and NADH,... 

H. F. Chou, N. Berman, and E. Ipp, Oscillations of lactate released from islets of Langerhans Evidence for oscillatory glycolysis in P-cells. Am. J. Physiol. 262, E800-E805 (1992). 

MEYERHOF OXIDATION QUOTIENT See also specific enzyme of glycolysis GLYCOLYTIC OSCILLATION GLYCOSIDASES,... 

A typical chemical system is the oxidative decarboxylation of malonic acid catalyzed by cerium ions and bromine, the so-called Zhabotinsky reaction this reaction in a given domain leads to the evolution of sustained oscillations and chemical waves. Furthermore, these states have been observed in a number of enzyme systems. The simplest case is the reaction catalyzed by the enzyme peroxidase. The reaction kinetics display either steady states, bistability, or oscillations. A more complex system is the ubiquitous process of glycolysis catalyzed by a sequence of coordinated enzyme reactions. In a given domain the process readily exhibits continuous oscillations of chemical concentrations and fluxes, which can be recorded by spectroscopic and electrometric techniques. The source of the periodicity is the enzyme phosphofructokinase, which catalyzes the phosphorylation of fructose-6-phosphate by ATP, resulting in the formation of fructose-1,6 biphosphate and ADP. The overall activity of the octameric enzyme is described by an allosteric model with fructose-6-phosphate, ATP, and AMP as controlling ligands. 

I would like to comment on the theoretical analysis of two systems described by Professor Hess, in order to relate the phenomena discussed by Professor Prigogine to the nonequilibrium behavior of biochemical systems. The mechanism of instability in glycolysis is relatively simple, as it involves a limited number of variables. An allosteric model for the phosphofrucktokinase reaction (PFK) has been analyzed, based on the activation of the enzyme by a reaction product. There exists a parameter domain in which the stationary state of the system is unstable in these conditions, sustained oscillations of the limit cycle type arise. Theoretical... 

Glycolysis in yeast has been intensively studied especially under anaerobic conditions. Here, one of these previous kinetic studies is augmented by the core reactions of the xenobiotic ketone. The used model of glycolysis was devised by Hynne et al. and contains 22 variables for concentrations of involved metabolites and 24 reactions [53]. This model quantitatively accounts for most known details of enzyme regulation in order to precisely describe the supercritical onset of oscillations as observed experimentally [49, 82]. The following extensions have been introduced to the literature model (Fig. 3.4) ... 

Models for Oscillating Reactions in Glycolysis Model 1 Back Activation Model Reference Higgins (1967). 

IIIF) 1968-2 Sel kov, E. E. Self-Oscillations in Glycolysis. Simple Single-Frequency Model, Molecular Biology, vol. 2, 208-221 (Molekulyarnaya Biologiya 252-266)... 

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