Reduction and elimination of phase shift between Cdc42-GTP and Pak1 with increased Pak1 attachment/detachment rate constants in the model. (A) Incrementally increasing the detachment rate constant of Pak1 () from 0.3 to 2 leads to a gradual reduction in the phase shift between Cdc42-GTP and Pak1. As nears 2, this shift becomes less pronounced, culminating in dampened oscillations that eventually subside. (B) A simultaneous elevation of both the attachment rate constant () from 1 to 10 and from 0.3 to 2 induces a progressive decrease in the phase shift between Cdc42-GTP and Pak1. This shift declines as the pair (, ) reaches (10, 2), whereupon the oscillations are increasingly attenuated and ultimately extinguished. The separation between the dashed black lines illustrates the phase discrepancy between Cdc42-GTP and Pak1. (C) A comparison between model results with and without Pak1-dependent endocytosis.
