Slide 12 of 79
Notes:
Using a program called AUTO we have followed out solutions as a parameter is varied. The first parameter we have chosen to vary is rate constant for cyclin synthesis (k1). As we have already seen cyclin synthesis plays a key role in cell cycle regulation. Furthermore it is a parameter that is relatively easy to manipulate by experimentalists. We want to vary this parameter and look for bifurcation’s (or a qualitative change in the behavior of the solution). We begin with AUTO by following steady state solutions. The dotted lines are unstable steady states and the solid lines are stable steady states. The squares are bifurcation points where the steady state changes its stability (this is a qualitative change in behavior). These are called Hopf bifurcation’s we will have more to say about them shortly.
