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Communicated by Avner Friedman, Ohio State University, Columbus, OH, February 18, 2005 (received for review May 25, 2004)
Abstract
By using current biological understanding, a conceptually simple, but mathematically complex, model is proposed for the dynamics of the gene circuit responsible for regulating nitrogen catabolite repression (NCR) in yeast. A variety of mathematical “structure” theorems are described that allow one to determine the asymptotic dynamics of complicated systems under very weak hypotheses. It is shown that these theorems apply to several subcircuits of the full NCR circuit, most importantly to the URE2–GLN3 subcircuit that is independent of the other constituents but governs the switching behavior of the full NCR circuit under changes in nitrogen source. Under hypotheses that are fully consistent with biological data, it is proven that the dynamics of this subcircuit is simple periodic behavior in synchrony with the cell cycle. Although the current mathematical structure theorems do not apply to the full NCR circuit, extensive simulations suggest that the dynamics is constrained in much the same way as that of the URE2–GLN3 subcircuit. This finding leads to the proposal that mathematicians study genetic circuits to find new geometries for which structure theorems may exist.
Footnotes
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↵ † To whom correspondence should be addressed. E-mail: erik.boczko{at}vanderbilt.edu.
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Author contributions: E.M.B., T.G.C., T.G., K.M., D.G.M., and K.S.W. designed research; E.M.B., T.G., K.M., and S.P. performed research; E.M.B., T.G.C., T.G., K.M., D.G.M., S.P., and K.S.W. analyzed data; and E.M.B., T.G.C., T.G., K.M., and K.S.W. wrote the paper.
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Abbreviation: NCR, nitrogen catabolite repression.
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↵ †† Note that the word monotone in this setting refers to the fact that solutions to the dynamical system observe a certain ordering property. This concept is different from the monotonicity assumption referred to in the cyclic feedback systems that refers to the rate of response function between species within the system.
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Freely available online through the PNAS open access option.
- Copyright © 2005, The National Academy of Sciences
Structure theorems and the dynamics of nitrogen catabolite repression in yeast
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