Figure 4. Estimation of vesicle diffusion coefficients D_short and D_long.

(A) Parameter search for the best match between the average drift-corrected control FRAP data (Figure 2C) and Monte Carlo (MC) simulations (Figure 3C,D) across a range of D_short and % immobile vesicles, expressed as log(${\displaystyle {\chi }^2}$). Black star denotes smallest ${\displaystyle {\chi }^2}$ (D_short = 0.060 µm²/s, 25% immobile vesicles). Ellipse denotes 68.3% confidence region for two degrees of freedom (${\displaystyle {\chi }^2}$ < 2.30). The vesicle step size (dr = 2 nm) was sufficiently small to avoid discretization error and the simulation space (a 2 µm cube) was sufficiently large to avoid boundary effects (Figure 4—figure supplement 1). (B) Best-match simulation (red) compared to control FRAP data (open circles). Gray denotes 68.3% confidence. (C) D(t) for best-match conditions in A with steady-state value (D_long = 0.025 µm²/s; black dashed line) computed from a double-exponential fit for t > 10 ms. Inset, D(t) on a logarithmic timescale with average time to first collision (gray dashed line, 0.46 ms) when steric interactions start to reduce vesicle mobility. (D) Same as B but with added best-match finite-difference (FD) simulation with D_long = 0.028 µm²/s (blue). Log(${\displaystyle {\chi }^2}$) = 0.8 (MC) and 0.5 (FD).

DOI: http://dx.doi.org/10.7554/eLife.15133.016

Figure 4—figure supplement 1. Comparison of Monte Carlo FRAP curves for different vesicle step size and simulation cube size.

(A) Average FRAP curves for vesicle step size dr = 1 and 2 nm (blue and red; see Equation 3) for best-match conditions in Figure 4B (2 µm cube geometries) showing a close overlap and therefore little discretization error for the simulation with dr = 2 nm. (B) The simulation in A for dr = 2 nm inside a 2 µm cube (red) was repeated inside a 3 µm cube (green), with both FRAP curves also showing a close overlap. Hence, a 2 µm cube is sufficiently large to avoid boundary effects and simulate the large interior of a MFT.

DOI: http://dx.doi.org/10.7554/eLife.15133.018