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首页> 外文期刊>Proceedings of the National Academy of Sciences of the United States of America >Structure theorems and the dynamics of nitrogen catabolite repression in yeast
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Structure theorems and the dynamics of nitrogen catabolite repression in yeast

机译：酵母中结构定理和氮分解代谢物阻遏的动力学

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摘要

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 sub-circuit 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.
机译：通过使用当前的生物学理解，提出了一种概念上简单但数学上复杂的模型，用于负责调节酵母中氮分解代谢物阻遏（NCR）的基因回路的动力学。描述了各种数学上的“结构”定理，这些定理使人们能够在非常弱的假设下确定复杂系统的渐近动力学。结果表明，这些定理适用于整个NCR电路的几个子电路，最重要的是适用于URE2-GLN3子电路，该电路与其他成分无关，但在氮源变化的情况下控制了整个NCR电路的开关行为。在与生物学数据完全一致的假设下，已证明该子电路的动力学是与细胞周期同步的简单周期性行为。尽管当前的数学结构定理不适用于整个NCR电路，但大量的模拟表明，动力学的约束方式与URE2-GLN3子电路的约束方式几乎相同。这一发现导致了一个建议，即数学家研究遗传回路以寻找可能存在结构定理的新几何形状。

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