Phosphofructokinase , glycolytic oscillations

To give rise to oscillatory behavior instead of a biochemical explosion, selfamplification must, however, be coupled to a limiting process. Such a limiting process can be viewed as a form of negative feedback because it occurs as a consequence of the positive feedback that precedes it. Thus, in the case of glycolytic oscillations, the activation of phosphofructokinase by a reaction product is followed by a counteracting fall in the rate of the enzymatic reaction, due to the enhanced substrate consumption associated with enzyme activation. In Ca + pulsatile signaling, the explosive rise in cytosolic Ca + due... 

In a series of experiments we have tested the type and range of entrainment of glycolytic oscillations by a periodic source of substrate realizing domains of entrainment by the fundamental frequency, one-half harmonic and one-third harmonic of a sinusoidal source of substrate. Furthermore, random variation of the substrate input was found to yield sustained oscillations of stable period. The demonstration of the subharmonic entrainment adds to the proof of the nonlinear nature of the glycolytic oscillator, since this behavior is not observed in linear systems. A comparison between the experimental results and computer simulations furthermore showed that the oscillatory dynamics of the glycolytic system can be described by the phosphofructokinase model. 

Higgins formulated a generalized chemical mechanism for oscillating reactions. This mechanism was then used to explain glycolytic oscillations. Based on the known chemistry of phosphofructokinase (PFK) and the associated glycolytic intermediates, Higgins proposed ... 

Part I of the book is devoted to glycolytic oscillations. A two-variable allosteric model is analysed in chapter 2 for the phosphofructokinase reaction, which is responsible for the oscillations. The autocatalytic regulation of this reaction, which results from the cooperative activation of the multisubunit enzyme by one of its products, is at the core of the mechanism that produces the nonequilibrium instability beyond which... 

The role of phosphofructokinase is corroborated by the fact that inhibitors or activators of the enzyme affect periodic behaviour. This is the case, for example, for ammonium ions that activate yeast PFK their addition suppresses the oscillations (Hess Boiteux, 1968b). In muscle, where glycolytic oscillations are also observed (Frenkel, 1968 Tomheim Lowenstein, 1974, 1975 Tomheim, 1988 Tomheim, Andres Schulz, 1991 Marynissen, Sener Malaisse, 1992), the molecular mechanism is identical the enzyme responsible for the phenomenon is again PFK. Citrate ion, an inhibitor of PFK, suppresses the oscillations in muscle extracts (Frenkel, 1968). Moreover, as in yeast (Hess, 1968), the addition of purified PFK produces a phase shift of the oscillations and permits modulation of their period and amplitude above a threshold, the addition of PFK suppresses the oscillations, but these reappear when the system is supplied with hexokinase (fig. 2.7). The latter observation, together with the data from figs. 2.2-2.5, indicates that periodic behaviour in glycolysis depends on a delicate... 

Fig. 2.7. Effect of adding increasing amounts of purified phosphofructokinase (PFK) on glycolytic oscillations in muscle extracts. The quantities of PFK added are (a) 0 (b) 0.2 unit (c) 0.4 unit (d) 0.6 unit (e) 0. The addition of apyrase each time induces oscillations, because of the transformation by this enzyme of ATP into the activator ADP (Frenkel, 1968).

Each of the two enzymes thus behaves as phosphofructokinase in the model considered for glycolytic oscillations (chapter 2). To limit the study to temporal organization phenomena, the system is considered here as spatially homogeneous, as in the case of experiments on glycolytic oscillations (Hess et ai, 1969). In the case where the kinetics of the two enzymes obeys the concerted allosteric model (Monod et al, 1965), the time evolution of the model is governed by the kinetic equations (4.1), which take the form of three nonlinear, ordinary differential equations ... 

The complex oscillations predicted by the model can be related to those sometimes observed, at low values of the substrate injection rate, in glycolysing yeast extracts. Such complex glycolytic oscillations (fig. 4.31) could represent chaos resulting from the interaction between oscillating phosphofructokinase and a second instability-generating reaction, catalysed by another glycolytic enzyme, in a small range of values of the substrate injection rate. 

The analysis of the model for glycolytic oscillations based on the regulatory properties of phosphofructokinase (chapter 2) highlighted the importance of autocatalysis as a source of instability leading to periodic behaviour. The synthesis of cAMP in D. discoideum provides us with a second example of autocatalytic regulation in biochemistry. The hypothesis on which the models proposed below are based is that the autocatalytic regulation of adenylate cyclase plays a primary role in the origin of cAMP oscillations. 

Smolen, P. 1995. A model for glycolytic oscillations based on skeletal muscle phosphofructokinase kinetics. J. Theor. Biol. 174 137-48. 

Tornheim, K. J.M. Lowenstein. 1975. The purine nucleotide cycle. V. Control of phosphofructokinase and glycolytic oscillations in muscle extracts. J. Biol. Chem. 250 6304-14. 

Phosphofructokinase allosteric kinetics, 41,500 and glycolytic oscillations, 15,37 0 effect of activator and inhibitor, 71,72 periodic variation of activity, 53,55,67 role of cooperativity, 67-73 Phosphoinositidase C, 355,356 Phosphorylation of p-adrenergic receptor, 193 of Ca -dependent K channel, 346 of cAMP receptor in Dictyostelium, 19, 192-5,317... 

Glycolytic oscillations (Hess Boiteux, 1971 Goldbeter, Caplan, 1976) occur due to the allosterically controlled phosphofructokinase (PFK, EC 2.7.1.11) reaction. The simplest (perhaps oversimplified) model of glycolysis contains two variables only, namely the substrate (ATP) and the product (ADP) of the enzyme (Goldbeter Nicolis, 1976). The hierarchical regulatory mechanism of glycolysis can be described by a more detailed model (Boiteux Hess, 1984). 

The enzyme phosphofructokinase is allosteric, that is, it is made up of equivalent units that possess specific reaction sites for the fixation of the substrate and product. Each unit exists in two conformational states one active with more affinity for the substrate, and one inactive. The reaction products of phosphofructokinase (FDP and ADP) displace the conformational equilibrium in favor of the active form of the enzyme. This may create a destabilizing effect on the excess entropy production. In the glycolytic cycle, the allosteric properties of the phosphofructokinase may lead to oscillations. Consider the following simple model... 

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