Some examples of the changing behavior after parameter changes

A characteristic property of coupled non-linear interactions is that the resulting pattern can change dramatically after changes in the parameters. The figure below shows an example. Fig. A shows the pattern with standard parameters. A reduction of kappaDE (which inhibits binding of MinE at high MinD concentration leads to an acceleration of the oscillation since the MinE wave can spread faster into a region of high MinD concentration.

With the parameters used, the trigger of a new MinD activation at the opposite pole occurs already before the previous activation is completely gone. This trigger reduces the availability of MinD precursors and causes the collapse of the original MinD maximum even if the MinE wave has not yet reached the pole. The MinE maximum shifts rapidly to the flank of the new MinD plateau. At lower baseline MinD association (sigmaD) to the membrane (i.e. at a lower MinD-independent MinD association) the new trigger occurs only after the collapse of the original peak, requiring also a new trigger of MinE (Fig. C). In this situation, it is absolutely essential that the new trigger is forced to the flank via an inhibition of MinE binding at high MinD concentration, since otherwise only a rapid change between MinD trigger and removal by MinE would occur (Fig. D)

 

(A): standard parameters ; (B) setting kappaDE to zero leads to a more rapid oscillation; (C) reducing baseline MinD association sigmaD from 0.05 to 0.005 leads to a new trigger only after the original peak has gone. Wave formation occurs only if kappaDE is non-zero (0.1) otherwise only very rapid oscillations occur. Wave formation is re-established almost immediately after changing kappaDE from zero to 0.1 (lower half of (D).