85.

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		2.4.3— Example of Bifurcations: Theory of Glycolysis

		Energy is stored in sugar molecules. Biochemical reactions in the body transfer this energy from the sugar to a molecule called ATP, adenosine triphosphate. ATP is then used as an energy source to drive many other biochemical reactions in the body. One process that accomplishes this transfer of energy from sugar to ATP is called glycolysis.

		There are a number of reactions in glycolysis. The overall speed of the reaction system is set by two steps that involve enzymes. Each enzyme speeds up one important reaction. The products produced by each of these reactions also affect the rate of the enzyme itself. Thus there is positive and negative feedback control in this reaction system.

		Markus and Hess formulated the set of equations that describe the reactions in glycolysis. They used these equations to determine how the ATP concentration in time would depend on different types of sugar input.

		For example, they studied what would happen if the flow of sugar was input into these biochemical reactions in a periodic way. The parameter they varied was the frequency at which the sugar was input into the system. They found that for some frequencies the ATP concentration fluctuated in a periodic way. For other frequencies, the ATP concentration fluctuated in a chaotic way. There was a sudden change in behavior from periodic to chaotic fluctuations as the frequency at which the sugar was input into the system changed by a small amount. This sudden change of behavior as a parameter is varied is called a bifurcation.

 

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