Analysis of the late response time. (*A*) Kymograph depicts the change in the lamellipodium directed by the gradient and dimming seen in the cell body during the late polarization time. The image preceding the kymograph illustrates the gradient (red), visualized with Alexa 594, received by the cell. The green color visualizes expression of YF-TIAM1. Red dotted lines indicate where the fluorescent values in *C* are taken from. Times are given in minutes. (Scale bar, 10 μm.) (*B*) Simulations show response strength vs. input (s_{o}) for two gradient levels (s_{1}); note bifurcations at distinct s_{o} values. Response strength is defined as the ratio of Rac activity at the front vs. the back in the model cell. (*C*) Intensity of the cell body normalized to the initial time point. Intensity values are taken as the mean of the fluorescence intensity of the area enclosed by the red trace in *A*. The drop line indicates the late polarization time, with a circle highlighting the inversion of response used to define this time. (*D*) Three-dimensional reconstruction of confocal slices of the same cell taken before and after rapamycin addition. The “post” cell image was taken 240 min after treatment. (Scale bars, 10 μm.) (*E*) Cell body volume before and after rapamycin addition. The data show the mean of *n* = 9 cells, and error bars show the SEM. The asterisk denotes a statistically significant difference (*P* = 0.019), using a two-sided Student’s *t* test. (*F*) Late response time as a function of mean concentration: state I, green (*n* = 29); state II, blue (*n* = 37); and state III, red (*n* = 27). The response times of other states are superimposed on each plot in gray. The pink drop line in the state III plot demarcates the separation point between unresponsive cells and responsive cells. Pearson correlation coefficient of linear regressions: state I = −0.608, state II = −0.783, and state III = −0.698. The red asterisk denotes a statistically significant difference (state II vs. state I, *P* < 1e-4; state II vs. state III, *P* < 1e-4) between the *y* intercept of the linear regression for state II vs. the *y* intercepts of the regression data from other states. There is no significant difference between the *y* intercept of state I vs. state III (*P* = 0.13). Both statistical analyses were carried out using an ANCOVA test.

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