Title page for ETD etd-1115202339731121


Type of Document Dissertation
Author Borisuk, Mark T.
Author's Email Address borisuk@math.vt.edu
URN etd-1115202339731121
Title Bifurcation Analysis of a Model of The frog Egg Cell Cycle
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Burns, John A.
Cliff, Eugene M.
Hannsgen, Kenneth B.
Herdman, Terry L. Committee Co-Chair
Tyson, John J. Committee Co-Chair
Keywords
  • parameter space
  • cell cycle
  • MPF
  • bifurcation theory
Date of Defense 1997-04-21
Availability unrestricted
Abstract
Fertilized frog eggs (and cell-free extracts) undergo periodic oscillations in the activity of "M-phase promoting factor" (MPF), the crucial triggering enzyme for mitosis (nuclear division) and cell division. MPF activity is regulated by a complex network of biochemical reactions. Novak and Tyson, and their collaborators, have been studying the qualitative and quantitative properties of a large system of nonlinear ordinary differential equations that describe the molecular details of this system as currently known. Important clues to the behavior of the model are provided by bifurcation theory, especially characterization of the codimension-1 and -2 bifurcation sets of the differential equations. To illustrate this method, I have been studying a system of 9 ordinary differential equations that describe the frog egg cell cycle with some fidelity. I will describe the bifurcation diagram of this system in a parameter space spanned by the rate constants for cyclin synthesis and cycling degradation. My results suggest either that the cell cycle control system should show dynamical behavior considerably more complex than the limit cycles and steady states reported so far, or that the biochemical rate constants of the system are constrained to avoid regions of parameter space where complex bifurcation points unfold.

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