Getting on Torus, Turning to Singular:
Ask Also What Biology Can Do For Mathematics

Hong Qian, University of Washington

Motivated by the recent development in motor proteins and in cellular phosphorylation-dephosphorylation signaling, this talk will discuss two abstract mathematical models: (1) A model for motor protein in terms of nonlinear stochastic dynamics on a torus, and (2) a model for two-step phosphorylation-dephosphorylation cycle kinetics in terms of singular mathematical equations. We shall show how the mathematical concept of rotation number defines the biophysics of "power stroke" and "Brownian rachet" in (1), and a canonical competition behavior in (2) might have implications to cancer biology. Both models demand non-conventional techniques in their analysis.