Simple, realistic models of complex biological processes: positive feedback and bistability in a cell fate switch and a cell cycle oscillator.

Here we review some of our work over the last decade on Xenopus oocyte maturation, a cell fate switch, and the Xenopus embryonic cell cycle, a highly dynamical process. Our approach has been to start with wiring diagrams for the regulatory networks that underpin the processes; carry out quantitative experiments to describe the response functions for individual legs of the networks; and then construct simple analytical models based on chemical kinetic theory and the graphical rate-balance formalism. These studies support the view that the all-or-none, irreversible nature of oocyte maturation arises from a saddle-node bifurcation in the regulatory system that drives the process, and that the clock-like oscillations of the embryo are built upon a hysteretic switch with two saddle-node bifurcations.