Mathematical Models of the Cell Division Cycle

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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.