Applied Mathematics Colloquium: Dr. Alexandra Jilkine
University of Notre Dame
Location
Mathematics/Psychology : 103
Date & Time
November 10, 2017, 2:00 pm – 3:00 pm
Description
Title: Modeling the Dynamics of Cdc42
Oscillation in Fission Yeast
Speaker: Alexandra Jilkine, University of Notre Dame
Abstract: Regulation of polarised cell growth is essential
for many cellular processes, including spatial coordination of cell morphology
changes during growth and division. We present a mathematical model of the core
mechanism responsible for the regulation of polarised growth dynamics in
fission yeast. The model is based on the competition of growth zones of
polarity protein Cdc42 localised at the cell tips for a common substrate
(inactive Cdc42) that diffuses in the cytosol. We consider several
potential ways of implementing negative feedback between Cd42 and its GEF
regulator in this model that would be consistent with the observed oscillations
of Cdc42 in fission yeast. We analyse the bifurcations in this model as the
cell length increases, and total amount of Cdc42 and GEF increase. Antiphase
oscillations at two tips emerge via saddle--homoclinic bifurcations or Hopf
bifurcations. We find that a stable oscillation and a stable steady state can
coexist, which is consistent with the experimental finding that only 50% of
bipolar cells oscillate. The mean amplitude and period can be tuned by
parameters involved in the negative feedback. We link modifications in the
parameters of the model to observed mutant phenotypes. Our model suggests that
negative feedback is more likely to be acting through inhibition of GEF
association rather than upregulation of GEF dissociation.
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