The manuscript by Slepchenko presents an analysis of the cdc2-cyclin B activation pathway and explains how the presence of aggregates of cdc2-cyclin B could enhance the robustness of the activation of this pathway. This is an attempt by M. Terasaki, a cell biologist with some quantitative background, to illustrate some of the ideas presented in the manuscript for other cell biologists
The first simulations illustrate the concept of a steady state, then of bistability. The next simulations show bistability of the cdc2 pathway, but that the bistability is fragile. The last simulation shows how precipitates could make a robust bio-switch.
Steady State: This is a simple reaction in which two reactants are interconverted. No matter what the initial value of m is, the final state is the same. The initial value for m can be entered in the box. The actual values for the final state are determined by the values for k1 and k2, which are the rate constants; these can also be changed within the box. Blue button starts and red button stops the simulation.
Bistability: In this system, there are two possible steady states. The system goes to one or the other depending on the initial conditions: m < 3 goes to the lower steady state while m > 3 goes to the upper. Once the simulation is started, it is possible to push the system from the lower to upper state by clicking on the mouse within the graph; this causes an incremental increase in m.
The equation used for this simulation does not correspond to a real system of reactions but it illustrates the concept of bistability. The k values can be changed in the box - k1 is the lower steady state, k2 is the threshold, and k3 is the upper steady state.
cdc2 activation: Novak and Tyson (1993) found parameters (rate constants and total concentrations of cdc2, wee1 and cdc25) which make cdc2 activation bistable. It should be pointed out that none of the rate constants for the reactions are known, so that the k values are arbitrary. This simulation uses values similar to those found by Novak and Tyson. To see activation, start the simulation then click within the graph to cause an incremental decrease in wee1. Several clicks are necessary to reach threshold.
Fragility of cdc2 activation. This shows that bistability of the above simulation is fragile. For instance, increase cdc25 total from 1 to 1.2 -- the system activates spontaneously, i.e., the inactive state is no longer stable. Requirements for bistability are shown below the parameter boxes - click on the orange button to see whether the current parameter values meet these requirements. If the requirements are not met, the system can lose the inactive steady state, or will not make an all or none response. Yellow button resets the original values.
Cdc2 activation by increasing total mpf. This starts with the system shown above. By clicking on the mouse, there is an incremental increase in total MPF (inactive plus active). Once this passes a threshold, all of the MPF gets converted to active.