Role of feedback inhibition in stabilizing the classical operon |
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| Authors: | Richard D. Bliss Page R. Painter Allen G. Marr |
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| Affiliation: | Department of Biology, University of California, Riverside, California, U.S.A.;Department of Bacteriology, University of California, Davis, California 95616, U.S.A.;Department of Bacteriology, University of California, Davis, California, U.S.A. |
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| Abstract: | The Goodwin equations for a repressible operon (Goodwin, 1965) are modified (1) to describe a time lag between genetic regulation and appearance of functional enzyme, (2) to describe consumption of endproduct in protein synthesis, and (3) to describe feedback inhibition of enzyme activity. The stability of the modified equations is determined by a method outlined in the appendix which treats a class of negative feedback systems with time delays. With parameters estimated from experimental data on the tryptophan operon of Escherichia coli, we conclude that the operon becomes unstable as normal feedback inhibition is lost. Numerical solution of the modified equations shows that an example with a partial loss of feedback inhibition can have a period of oscillation less than the cell generation time, and the numerical solutions are shown to be in qualitative agreement with experiments showing oscillations in tryptophan operon expression. |
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| Keywords: | To whom correspondence and reprint requests should be addressed. |
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