Math 536 – Final Project

Kichol Lee

Molecular Control of the Cell Cycle


In the past couple decades, molecular biologists have been able to isolate many compounds that are involved in the molecular control of the cell cycle for a collection of organisms. Since all eukaryotic organisms go through similar steps in the cell cycle, some researchers are focused on finding the minimal set of molecular reactions that are necessary for the primary control of the cell cycle. One of the simplest models is one developed by John Tyson and Bela Novak (along with some post-doctoral researchers and graduate students) for fission yeasts. The primary events for the cell cycle seem to be initiated by protein kinases whose activities depend on binding to cyclins (cyclin-dependent kinases, or Cdk's). The regulation of these key cyclins and kinases depend on whether or not they are phosphorylated. The mathematical model looks at the positive and negative feedback controls from these molecular events in an attempt to provide a minimal model that explains the major events in the cell cycle.

You will review the literature on the mathematical models for the cell cycle and discuss at least one of these models in detail. You will examine the behavior of one model through simulations, in particular showing how the model explains at least one of the genetically engineered mutants. Describe the qualitative behavior of this model in terms of bifurcations and hysteresis effects that we have studied in class. Your primary starting reference is from the webpage of one of John Tyson's students, Kathy Chen at

http://leibniz.biol.vt.edu/kathy/xen/xen.htm

References:

  1. Goldbeter, A. (1991) Proc. Natl. Acad. Sci. USA 88, 9107-9111
  2. Novak, B. and Tyson, J. J. (1995) J. Theor. Biol. 173, 283-305
  3. Novak, B. and Tyson, J. J. (1993) J. Cell Sci. 106, 1153-1168
  4. Odell, G. M. (1980) in Mathematical models in molecular and cellular biology (Segel, L. A., ed.), pp. 647-727, Cambridge Univ. Press
  5. Tyson, J. J. (1991) Proc. Natl. Acad. Sci. USA 88, 7328-7332