Cell cycle dynamics The process of cell division is periodic, with repeated growth and division phases as the cell population multiplies. It has been suggested that the division phase is triggered by high concentrations of a molecule called MPF (maturation promoting factor). The production of this factor is stimulated by another molecule called cyclin, and MPF eventually inhibits its own production.

Using M and C to denote the concentrations of these two biomolecules (in mgymL), a simple model for their interaction is dM dt

− C 1 CM2 2

M 1 1 M dC dt

−  2 M

(a) Suppose that  − 2,  − 1,  − 10, and  − 1. Construct the phase plane, including all nullclines, equilibria, and arrows indicating the direction of movement in the plane.

(b) From your answer to part (a), what is the qualitative nature of the dynamics of M predicted by this model?

What does this predict about the dynamics of cell division?

(c) For any equilibrium found in part (a), specify whether it is locally stable, unstable, or if the information is inconclusive.