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 John J. Tyson Committee Co-Chair Terry L. Herdman Committee Co-Chair Eugene M. Cliff none John A. Burns none Kenneth P. Hannsgen none Keywords
- cell cycle
- MPF
- bifurcation theory
- parameter space
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 differentail 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
cyclin 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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