Brooks Emerick

The Wnt Pathway is a cascade of chemical reactions within a cell that ultimately determines the destruction or accumulation of a proliferation promoting protein called beta-catenin.  This figure shows a single trajectory in the phase space of a system of nonlinear differential equations that describes the interactions of three key proteins involved the Wnt pathway: beta-catenin, Axin, and APC.  When the concentration of Axin is relatively small, the three concentrations become periodic in time.  This indicates that a cell switches, periodically, between a proliferative and quiescent state.  The paper is here.