Enzymatic reactions Oscillations in the glycolytic cycle

Example 13.11 Enzymatic reactions Oscillations in the glycolytic cycle Biochemical chains are highly likely to exhibit limit cycles and dissipative structures. Oscillations appear in living systems in a variety of ways with 

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 

Where A is the initial product glucose, F the final product glyceraldehyde 3P, D1 and D3 the active and inactive forms of the enzyme, respectively, D2 the enzymatic complex, Q and C2 the fructose IP and fructose 2P, respectively. In the conformational equilibrium step (C2 I D3 = D,) FDP activates the enzyme. Experimental results indicate that under physiological conditions, the enzyme is controlled mainly by the ATP and ADP. 

The reactant A 3 is the ATP and enters the system at constant rate of Jrl at step (a). The, l2 is the ADP, which is the product of reaction and also the activator in step (d). The factor y (y I) shows that the fixation of A 2 on the enzyme activates more than one reacting site because of the concerted conformational equilibrium. The kinetics of the model above is 

This model neglects the diffusion of the enzyme since it is much slower than for ATP and ADP. In agreement with experiments, the following conditions are assumed to hold (Glansdorff and Prigogoine, 1971) 

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Example 13.12 Enzymatic reactions—Oscillations in the glycolytic cycle... 

Example 13.11 Enzymatic reactions Oscillations in the glycolytic cycle Biochemical chains are highly likely... 

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