title: Structure theorems and the dynamics of nitrogen catabolite repression in yeast.
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.
authors.affiliation: Department of Biomedical Informatics Vanderbilt University, Nashville, TN 37232, USA. erik.boczko@vanderbilt.edu
authors.forename: Erik M
authors.initials: EM
authors.lastname: Boczko
authors.forename: Terrance G
authors.initials: TG
authors.lastname: Cooper
authors.forename: Tomas
authors.initials: T
authors.lastname: Gedeon
authors.forename: Konstantin
authors.initials: K
authors.lastname: Mischaikow
authors.forename: Deborah G
authors.initials: DG
authors.lastname: Murdock
authors.forename: Siddharth
authors.initials: S
authors.lastname: Pratap
authors.forename: K Sam
authors.initials: KS
authors.lastname: Wells
mesh_terms: D005979:Glutathione Peroxidase; D005982:Glutathione Transferase / Q000235:genetics / Q000378:metabolism; D008433:Mathematics; D008954:Models, Biological; D009584:Nitrogen / Q000378:metabolism*; D011328:Prions / Q000235:genetics / Q000378:metabolism; D012097:Repressor Proteins / Q000235:genetics / Q000378:metabolism; D012441:Saccharomyces cerevisiae / Q000235:genetics* / Q000378:metabolism*; D029701:Saccharomyces cerevisiae Proteins / Q000235:genetics / Q000378:metabolism; D014157:Transcription Factors / Q000235:genetics / Q000378:metabolism
chemical_list: C071664:GLN3 protein, S cerevisiae; D011328:Prions; D012097:Repressor Proteins; D029701:Saccharomyces cerevisiae Proteins; D014157:Transcription Factors; D005979:Glutathione Peroxidase; C067020:URE2 protein, S cerevisiae; D005982:Glutathione Transferase; D009584:Nitrogen