Fig. 3.

Spatiotemporal dynamics of the model in a 2D square domain representing the cell in the absence of a gradient. (A) Heat-maps of inactive/active Rac, inactive/active Rho and unphosphorylated/phosphorylated paxillin at steady state (at the end of the simulation), as indicated by the legend in each panel, in the absence of gradients in Rac and Rho activation rates. The heat-maps were colour-coded according to the colour-bar to the right of each panel. (B) Averaged total number of phosphorylated paxillin (top), active Rho (middle) and active Rac (bottom) molecules over the entire 2D domain in the absence of gradients in Rac and Rho activation rates. The model exhibits a hysteresis, a hallmark of bistability, consisting of non-coinciding jumps between two co-existing states representing the induced (high active Rac/low active Rho) and uninduced (low active Rac/high active Rho) states, depending on where the simulations were initiated. Blue/orange lines correspond to model responses when maximum paxillin phosphorylation rate, $B$, was increased/decreased while starting the simulations from the uninduced/induced state. Although the model exhibits bistability at the whole-cell level, stochastic dynamics were insufficient to produce polarity in the absence of a gradient in reaction rates. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)