Bifurcation analysis of a model of the frog egg cell cycle Herdman, Terry L.
ISBN: 0599133368
Summary:
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 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.
Notes:
Co-Chairmen: John J. Tyson; Terry L. Herdman.
Thesis (Ph.D.)--Virginia Polytechnic Institute and State University,
1997.
Electronic reproduction.Ann Arbor, MI: ProQuest Information and
Learning Company,2007.System requirements: Adobe Acrobat
Reader.Available via World Wide Web.Digital version of: Bifurcation
analysis of a model of the frog egg cell cycle.
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