# Applied Mathematics Colloquium: Dr. Alexandra Jilkine

## University of Notre Dame

Friday, November 10, 2017

2:00 PM - 3:00 PM

2:00 PM - 3:00 PM

Mathematics/Psychology : 103

**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.