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. 2023 Feb 3;122(5):767–783. doi: 10.1016/j.bpj.2023.01.040

Figure 4.

Figure 4

Weak nonergodicity of GEM diffusion can be explained by heterogeneity in viscosity. (a) GEM particle MSD versus time, calculated either by ensemble averaging over all particle tracks (EA MSD, red line), or by first time averaging over each track and then ensemble averaging over all particles (TEA MSD, black line). 95% CIs of the EA MSD were calculated by bootstrapping and are plotted as a red shaded region around the EA MSD. Note the logarithmic scale along the x and y axes. (b) The TEA and EA MSD calculated for a representative Doppelgänger simulation for Model #1: uniform viscosity (see Fig. 3b). (c) The TEA and EA MSD calculated for a representative Doppelgänger simulation for Model #4: spatial and cellular heterogeneity in viscosity (see Fig. 3b), using a 100 nm spatial domain size. (d–f) The percent difference between the EA and the TEA MSD ((EA-TEA)∗100/EA) displayed in (a–c), respectively, plotted as a function of time interval. The best fit of the data to an exponential decay plus a constant: y = Ae(-Bt)+C is plotted as a thick dashed black line. (g) The percent difference between the EA and TEA MSD for Model #4: spatial and cellular heterogeneity in viscosity, where each subplot represents a different choice for the domain size of the spatial heterogeneity. x and y axes for all subplots are identical. Each light orange line represents an individual simulation, equivalent to the entire experimental data set. Fifty replicate simulations are superimposed onto the plot. Each curve was individually fit to an exponential decay plus a constant: y = Ae(-Bt)+C, and the best fit parameters were averaged across all 50 simulations to produce the best fit line (thick dashed orange line). The best fit to the experimental data shown in (d) is overlaid as a thick dashed purple line. Of the domain sizes sampled, simulations using the 100 nm domain gives the closest agreement to the experimental data, with the experimental data best fit line lying well within the range of outcomes among replicate simulations. On average, the 100 nm simulation best fit line lies slightly below the experimental best fit line, and the 300 nm simulation best fit line lies slightly above the experimental best fit line. Thus, we estimate the domain size of the cytoplasm is on the order of ∼100–300 nm.