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Biochemical and biophysical rhythms are ubiquitous characteristics of living organisms, from rapid oscillations of membrane potential in nerve cells to slow cycles of ovulation in mammals. One of the first biochemical oscillations to be discovered was the periodic conversion of sugar to alcohol (“glycolysis”) in anaerobic yeast cultures (Chance et al. 1973). The oscillation can be observed as periodic changes in fluorescence from an essential intermediate, NADH; see Figure 9.1. In the laboratories of Britton Chance and Benno Hess, these oscillations were shown to arise from a curious property of the enzyme phosphofructokinase (PFK), which catalyzes the phosphorylation of fructose-6-phosphate to fructose-1,6-bisphosphate using ATP as the phosphate donor; Figure 9.1B. Although PFK consumes ATP, the glycolytic pathway produces more ATP than it consumes. To properly regulate ATP production, ATP inhibits PFK and ADP activates PFK. Hence, if the cell is energy “rich” (ATP high, ADP low), then PFK activity is inhibited, and the flux of sugars into the glycolytic pathway is shut down. As ATP level drops and ADP level increases, PFK is activated and glycolysis recommences. In principle, this negative feedback loop should stabilize the energy supply of the cell. However, because ATP is both a substrate of PFK and an inhibitor of the enzyme (likewise, ADP is both a product of PFK and an activator of the enzyme), the steady-state flux through the glycolytic pathway can be unstable, as we shall see, and the regulatory system generates sustained oscillations in all intermediates of the pathway.
KeywordsCircadian Rhythm Hopf Bifurcation Negative Feedback Loop Limit Cycle Oscillation Hopf Bifurcation Point
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Suggestions for Further Reading
- •Jospeh Higgins published the first comprehensive theory of biochemical oscillators, and it is still valuable reading today (Higgins 1967).Google Scholar
- •The earliest collection of articles on biological and biochemical oscillators was edited by Chance, Pye, Ghosh, and Hess, B. (Chance et al. 1973).Google Scholar
- •For a comparative survey of cellular oscillators see (Berridge and Rapp 1979).Google Scholar
- •Sol Rubinow’s 1980 chapter is one of the best summaries of the kinetics of regulatory enzymes (Rubinow 1980).Google Scholar
- •Although not easy reading, Albert Goldbeter’s 1996 book Biochemical Oscillators and Cellular Rhythms is comprehensive, authoritative, and well motivated (Goldbeter 1996).Google Scholar