Response to Biophysical Journal comment to the editor by Skóra regarding the article entitled: Vast heterogeneity in cytoplasmic diffusion rates revealed by nanorheology and Doppelgänger simulations

Abstract

In a Comment to the Editor, Skóra raises a concern that the modeling framework implemented in Garner et al. (Biophysical Journal, 2023) neglects a potentially important term in the Brownian dynamics simulation of diffusion. Omission of this diffusivity gradient term may lead to an underestimation of the mean and overestimation of the variance of the cytoplasmic viscosity. In this response, we directly address this concern by incorporating this term into our model and showing that for this data set, its effect is negligible and does not alter the conclusions of this work.

Figure 1

The diffusivity gradient term has no measurable effect on the mean or variance of the particle diffusivity distribution. (a) Original modeling framework (#1). Doppelgänger simulation of an example cell showing variation in cytoplasmic viscosity with a 1000 nm characteristic domain size (Garner and Molines et al., Biophysical Journal, 2023) (1). (b) New modeling framework (#2). Doppelgänger simulation of the same example cell shown in (a), now with a smoothed viscosity profile generated by interpolation into 10 nm bins. (c) New modeling framework (#3). In addition to a smoothed viscosity profile, the diffusivity gradient term suggested by Dr. Skóra (2) drives particles toward regions with high diffusivity (i.e., low viscosity). To demonstrate the effect of the diffusivity gradient term on its own, representative initial particle positions (red dots with black outlines) and tracks (red lines) are shown for particles following the diffusivity gradient in the absence of Brownian motion. As expected, particles flow up the diffusivity gradient (lighter areas in yellow). For results shown in (d-i), the Brownian motion is included. (d-f) Comparison of representative particle tracks (red lines) for the original (#1, d), smoothed (#2, e), and smoothed + diffusivity gradient term (#3, f) models. In each simulation, five particles were allowed to diffuse for 10 s (significantly longer than the typical experimental trajectory, to demonstrate the bias in localization). Models were all initiated with the same random number generator seed, and so have identical initial particle positions (red dots with black outline) and Brownian steps. (g-i) Heatmap of the 2D probability distribution of the particle position for 3681 simulated particles in each of the three modeling frameworks. In the model with the diffusivity gradient term (#3, i) particles are uniformly distributed, compared to the models without the diffusivity gradient term (#1 and #2, g-h) ‒ demonstrating that the diffusivity gradient term is implemented correctly. (j-l) Comparison of the particle diffusivity distribution between the experimental data, the original model (#1), the updated model with a smoothed viscosity profile (#2), or the updated model with a smoothed viscosity profile and the diffusivity gradient term suggested by Skóra (#3). Addition of the gradient term (#3) has no effect on the mean or variance of the particle diffusivity distribution. (j) Median apparent diffusivity (averaged across all tracks) plotted for the experimental data as well as each model. Error bars represent the SE of the median. Wilcoxon rank sum test for equality of the medians shows differences are not significant (n.s., p ≥ 0.05). (k-l) Distributions of apparent diffusivities calculated from fits of the track-wise (k) or cell-wise (l) MSD curves displayed for the experimental data as well as each of the models. Note the logarithmic scale along the y axis. Levene’s test for equality of variance shows differences are not significant (n.s., p ≥ 0.05).