Mathematical Models of the Cell Division Cycle

细胞分裂周期是某些事件的周期性重复——DNA合成、有丝分裂和细胞质分裂——将单个细胞转化为两个子细胞。细胞分裂必须与细胞的整体生长相协调；否则，细胞可能会变得任意大或极小。通过观察细胞如何对分裂周期的扰动作出反应，细胞生物学家发现dna与蛋白质的比例在决定有丝分裂和细胞分裂的时间方面起着至关重要的作用。最近，分子研究揭示了四类蛋白在分裂控制机制中起着重要作用。两种蛋白质（cdc2和细胞周期蛋白）结合形成异源二聚体（“有丝分裂促进因子”或MPF），当被激活时，触发有丝分裂和细胞分裂的所有主要事件。MPF的活性反过来又受到蛋白激酶和蛋白磷酸酶的控制，这些蛋白激酶和蛋白磷酸酶决定MPF的磷酸化状态。本研究的长期目标是建立细胞分裂周期的数学模型，以便在来之不易的控制机制的分子细节和完整调控系统行为的经典观察之间建立安全可靠的联系。该模型将描述磷酸化对MPF活性的调节，以及MPF的磷酸化状态如何由细胞的dna -蛋白比决定。数学方法是一种工具，可以完善我们的假设，指导我们对细胞生长和分裂的基本事件进行推理。这项研究的目的是建立细胞分裂周期的数学模型。数学建模将基于这一基本生命过程中涉及的生化控制机制的最新实验证据。数学模型将有助于进一步完善实验数据的解释，并作为规划未来实验的指南，最终将导致对细胞分裂周期如何调节的透彻理解。

The cell division cycle is the periodic repetition of certain events--DNA synthesis, mitosis, and cytokinesis--that transform a single cell into two daughter cells. Cell division must be coordinated to overall cell growth; otherwise, cells could become arbitrarily large or vanishingly small. By observing how cells respond to perturbations of the division cycle, cell biologists discovered that the DNA-to-protein ratio plays an essential role in determining the timing of mitosis and cell division. Recently, molecular studies have revealed four classes of proteins that participate prominently in the division control mechanism. Two proteins, (cdc2 and cyclin) combine to form a heterodimer ("mitosis promoting factor," or MPF) that, when activated, triggers all the major events of mitosis and cell division. The activity of MPF is, in turn, controlled by protein kinases and protein phosphatases that determine the phosphorylation state of MPF. The long range goal of this research is to develop mathematical models of the cell division cycle in order to build secure, reliable connections between hard-won molecular details of the control mechanisms and classical observations of the behavior of the intact regulatory system. The model will describe the regulation of MPF activity by phosphorylation, and how the phosphorylation state of MPF is determined by the DNA-to-protein ratio of the cell. The mathematical approach is a tool to refine our assumptions and guide our reasoning about the essential events of cell growth and division. %%% The goal of this research is to develop mathematical models of the cell division cycle. The mathematical modeling will be based on recent experimental evidence concerning the biochemical control mechanisms involved in this fundamental life process. The mathematical models will be useful in further refining the interpretations of experimental data and as a guide in planning future experiments that ultimately should lead to a thorough understanding of how the cell division cycle is regulated.