Deterministic Mechanical Model of T-Killer Cell Polarization Reproduces the Wandering of Aim between Simultaneously Engaged Targets
Figure 3
Quantitative analysis of centrosome reorientation.
(A) The time it takes the model centrosome to reorient by one-half of the initial angular separation, as a function of this initial separation, plotted for the indicated values of the microtubule length. The segments of the broken lines connect the points corresponding to the actual simulation results; where the segments are dashed, it indicates that they connect two data points between which a data point is missing because the half-reorientation could not be achieved. Pulling force density, 40 pN/µm; effective cytoplasm viscosity, 2 pN s/µm2. (B) Qualitatively different predictions obtained with the different microtubule length and initial angular separation between the centrosome and the middle of the synapse. Regions in the two-dimensional parameter space are color-coded and numbered. In region 1, the complete reorientation is achieved. In region 2, the reorientation is “jammed” at around 30° of remaining angular separation. In region 3, the reorientation is “jammed” at the characteristic angular separation of 100°. In region 4, reorientation does not commence because the microtubules are too short to contact the synapse. In region 5, complete reorientation is achieved after a catastrophic stability loss of the “locked” configuration of antiparallel microtubules overlapping at the synapse. In region 6, the same happens but the final reorientation is as incomplete as in region 2. In region 7, the “locked” overlapping configuration is stable and no reorientation occurs. Pulling force density, 40 pN/µm; effective cytoplasm viscosity, 2 pN s/µm2. (C) Effect of microtubule dynamic instability on the stability of the “locked” configuration such as predicted in region 7 of (B). Angular position of the centrosome is plotted vs. time as predicted by the purely deterministic model analyzed throughout the paper (black curve) and with an additional assumption of stochastic microtubule dynamic instability (colored curves). The three stochastic simulations are independent (in the sense of pseudo-random number generation on a computer) repetitions of a simulation which was otherwise set up the same way as the deterministic one. The angle plotted is defined as the angle formed by the lines drawn from the nucleus center to the centrosome and to the middle of the synapse. The deterministic prediction is that the centrosome, having started facing the opposite side of the cell from the synapse, will not be able to reorient to the synapse. The stochastic predictions differ between runs: one is similar to the deterministic prediction, in the other two the centrosome was able to reorient. Pulling force density, 40 pN/µm; microtubule length (starting microtubule length in stochastic simulations), 21.5 µm; effective cytoplasm viscosity, 2 pN s/µm2.