Figure 4. First-passage times (FPTs) for a pair of Gag-Pol monomers to search and bind to one another reveal a clear dependence on hexamer rates and free energies.

(A) An example from a simulation of how two Gag-Pols found each other. Characterization of the edge connectivity in Figure 4—figure supplement 1. (B) The distance between all Gag-Pol pairs can be monitored in time, with this trace corresponding to the simulation in (A). The distance fluctuates and drops to the binding radius σ at 3.2 s, after which the two molecules remain bound. (C) FPTs of Gag-Pol dimerization at different reaction rates and hexamer free energies ${\displaystyle \mathrm{\Delta }{G}_{\mathrm{h}\mathrm{e}\mathrm{x}}}$. The yellow dashed line indicates the maximal length of the simulation traces. The filled-in circles report the mean FPT (MFPT) for parameter sets where all traces produce a Gag-Pol dimerization event. The open circles report a lower bound on the MFPT, because some of the traces were not long enough to observe a Gag-Pol dimerization event. The solid lines are the fits to the FPTs from usingEquation 1, using only data points that had at least 75% of the trajectories produce dimerization events. The adjusted R² measure for the fit is 0.98, which accounts for the small sample size. The leftmost red point and two leftmost cyan points are excluded from the fit because the absence of dimerization events exceeds 25% in these cases. If we fit only points with 100% of trajectories completed, we recover the same power law trends with slightly different parameters. (D) The distributions of the FPTs at different reaction rates (each row) and hexamer free energy (each column). The yellow bars and yellow numbers report the percent of traces without any Gag-Pol dimerization event over the time simulated, so they are placed at the end of the simulated time. The FPTs slow as the reaction rates decrease and as the hexamer contacts become more stabilized.

Figure 4—figure supplement 1. Characterizing bonds at the edge of the lattice.

Center-of-mass of each molecule is represented by a point. The green molecules are the molecules at the edge. A molecule is considered at the edge if it has less than 39 molecules within 15 nm. The red molecules are the molecules that have only a single bond to the lattice. The edge following our definition thus extends ~20 nm toward the interior of the lattice.