87.

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		2.4.4— Example of Bifurcations: Experiments of Glycolysis

		The mathematical model developed by Markus and Hess predicted that there should be a bifurcation in the output ATP concentration, from periodic to chaotic behavior, as the frequency of the input flow of sugar was varied.

		They tested their predictions using the contents from yeast cells to perform glycolysis in the solution in a glass container. They modulated the flow of sugar into the container at different frequencies. To determine how the ATP concentration varied in time, they measured the amount of blue light given off when a molecule that interacts with ATP is excited by ultraviolet light.

		At low frequencies of sugar input, the experiments showed that the concentration of ATP varied periodically with time. However, at higher frequencies of sugar input, the concentration of ATP varied chaotically with time.

		If you had found similar chaotic fluctuations in the data from your biological experiment, what do you think would happen if you tried to publish those results or get a grant to continue the work? People would look at those fluctuations and might say that you didn't know how to do those experiments properly. They might say that those fluctuations were due to experimental error. Perhaps your sensor was broken. Or they might say that the conditions were varying during the experiment. Perhaps the pH was changing in your solution. It is important to understand that the fluctuations that Markus and Hess found under certain conditions are not due to experimental error and they are not due to the conditions changing during the experiment. These variations are at the heart of what a chaotic system does all by itself.

		Are all the variations we see in experiments due to chaos? Of course not. However, we now have the mathematical tools, such as the dimension of the phase space set and bifurcation diagrams, to analyze experimental data to determine if the variations are due to chance errors or deterministic chaos.

 

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