### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 5647-5652 |

Number of pages | 6 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 102 |

Issue number | 16 |

DOIs | |

State | Published - Apr 19 2005 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- General

### Keywords

- Delay equations
- GATA factors
- GLN3

### Cite this

*Proceedings of the National Academy of Sciences of the United States of America*,

*102*(16), 5647-5652. https://doi.org/10.1073/pnas.0501339102

}

*Proceedings of the National Academy of Sciences of the United States of America*, vol. 102, no. 16, pp. 5647-5652. https://doi.org/10.1073/pnas.0501339102

**Structure theorems and the dynamics of nitrogen catabolite repression in yeast.** / Boczko, Erik M.; Cooper, Terrante G.; Gedeon, Tomas; Mischaikow, Konstantin; Murdock, Deborah G.; Pratap, Siddharth; Wells, K. Sam.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Structure theorems and the dynamics of nitrogen catabolite repression in yeast

AU - Boczko, Erik M.

AU - Cooper, Terrante G.

AU - Gedeon, Tomas

AU - Mischaikow, Konstantin

AU - Murdock, Deborah G.

AU - Pratap, Siddharth

AU - Wells, K. Sam

PY - 2005/4/19

Y1 - 2005/4/19

N2 - 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.

AB - 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.

KW - Delay equations

KW - GATA factors

KW - GLN3

UR - http://www.scopus.com/inward/record.url?scp=17644402444&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17644402444&partnerID=8YFLogxK

U2 - 10.1073/pnas.0501339102

DO - 10.1073/pnas.0501339102

M3 - Article

C2 - 15814615

AN - SCOPUS:17644402444

VL - 102

SP - 5647

EP - 5652

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 16

ER -