Membrane Diffusion Occurs by Continuous-Time Random Walk Sustained by Vesicular Trafficking

Abstract

Diffusion in cellular membranes is regulated by processes that occur over a range of spatial and temporal scales. These processes include membrane fluidity, interprotein and interlipid interactions, interactions with membrane microdomains, interactions with the underlying cytoskeleton, and cellular processes that result in net membrane movement. The complex, non-Brownian diffusion that results from these processes has been difficult to characterize, and moreover, the impact of factors such as membrane recycling on membrane diffusion remains largely unexplored. We have used a careful statistical analysis of single-particle tracking data of the single-pass plasma membrane protein CD93 to show that the diffusion of this protein is well described by a continuous-time random walk in parallel with an aging process mediated by membrane corrals. The overall result is an evolution in the diffusion of CD93: proteins initially diffuse freely on the cell surface but over time become increasingly trapped within diffusion-limiting membrane corrals. Stable populations of freely diffusing and corralled CD93 are maintained by an endocytic/exocytic process in which corralled CD93 is selectively endocytosed, whereas freely diffusing CD93 is replenished by exocytosis of newly synthesized and recycled CD93. This trafficking not only maintained CD93 diffusivity but also maintained the heterogeneous distribution of CD93 in the plasma membrane. These results provide insight into the nature of the biological and biophysical processes that can lead to significantly non-Brownian diffusion of membrane proteins and demonstrate that ongoing membrane recycling is critical to maintaining steady-state diffusion and distribution of proteins in the plasma membrane.

Figure 1

CD93 Diffusion is non-Brownian. The diffusion of CD93-GFP ectopically expressed on CHO cells was studied by single-particle tracking. (A) A portion of CD93 undergoing corralled versus free diffusion is shown. (B) The distribution of CD93 confinement zone sizes is shown. (C) Diffusion coefficients determined using lag times of less than 100 ms of freely diffusing CD93 and CD93 corralled in corrals of 100–500 nm diameter are shown. (D) The effect of time on the ensemble-averaged MSD of CD93-GFP is shown. (E) The effect of lag time on the EA-TAMSD of freely diffusing CD93 and CD93 in 100 and 200 nm corrals is shown. n = mean ± SEM of a minimum of three independent experiments (A–C) or the mean of a track ensemble containing 31,633 trajectories collected over three experiments. ^∗p < 0.05. The paired t-test (A) or ANOVA with Tukey correction (B and C) is compared to freely diffusing CD93. To see this figure in color, go online.

Figure 2

CD93 diffusional anomalies revealed by time-averaged MSD. Time-averaged MSD curves were calculated for individual CD93-GFP for trajectory lengths Τ = 2.0 s (free CD93) and 5.0 s (CD93 in 200 nm corrals). (A and B) Log-log plots of time-averaged MSD curves for 40 randomly selected CD93-GFP molecules that were freely diffusing (A) or corralled in 200 nm corrals are shown (B). (C) The distribution shows the power-law index α_τ of time-averaged MSD plots for freely diffusing and corralled CD93. The power-law indices of free CD93 were normally distributed with a mean slightly less than the value of 1 expected for Brownian diffusion; α_τ for CD93 in 200 nm corrals was not normally distributed and had a much smaller mean value. Data are representative of (A) and (B) or are an ensemble obtained from three independent experiments (C).

Figure 3

CD93 diffusion is consistent with CTRW. Mean maximal excursion analysis of freely diffusing CD93 was performed to identify the model that best describes the diffusion of CD93. (A) The effect of trajectory length on the EA-TAMSD is shown. (B) The effect of experimental time on the EA-MSD (regular) and second MME (MME) moments is shown. (C) The effect of experimental time on the ratios between the second and fourth EA-MSD moments (regular) and the second and fourth MME moments (MME) is shown. Horizontal lines indicate the regular (dotted line) and MME (dashed line) moment ratios predicted for Brownian motion; ratios above these values are expected for CTRW. Data are the ensemble of three independent experiments.

Figure 4

Time-averaged MSDs evolve over experimental time. Power-law indices were determined from the TAMSDs of freely diffusing and corralled CD93 for trajectory lengths from 2 to 8 s. (A) The distribution shows power-law indices α_τ for corralled CD93 at Τ = 2.0, 6.0, and 8.0 s. (B) The distribution shows α_τ for freely diffusing CD93 at Τ = 2.0, 5.0, and 6.0 s. The two peaks centered at exponent values μ₁ and μ₂ indicate the presence of two distinct populations that diffuse at different rates. (C) The mean and SE of α_τ values for the more diffusive (μ₁) and less diffusive (μ₂) populations of CD93 originally identified as uncorralled are shown, calculated by fitting the distribution of power-law indices to the sum of two Gaussians for total measurement times from 5 to 8 s. (D) The fraction of CD93 initially classified as freely diffusing appears in the less-diffusive population as a function of T. n = 3, Data are presented as mean ± SEM (error bars) or mean ± SD (shaded areas).

Figure 5

CD93 diffusion is sustained by membrane recycling. (A) The number of particle tracks for corralled CD93 classified as stabile corralled (stable), undergoing hop diffusion (hop), transiently escaping confinement (transient), or totally escaping confinement (escaped) is shown. (B) The number of newly exocytosed CD93 tracks measured after treatment with brefeldin A, N-ethylmaleimide (NEA), or fixation of the cell with PFA (fixed) is shown. (C) A portion of CD93 exocytosed during imaging classified as freely diffusing and corralled is shown over the course of the experiment. (D) A portion of CD93 present on the cell surface before imaging is classified as freely diffusing and corralled over the course of the experiment (E–G) Representative images (E and F) and quantification (G) of colocalization of HA-CD93 present on the cell surface at the beginning of the experiment (Cy3-CD93) are shown as well as recently exocytosed CD93 (647-CD93) with Arf6-GFP or Rab11-GFP after a 1 h incubation. Arrows indicate vesicles positive for Cy3-CD93 and Arf6 or Rab11. Scale bars, 10 μm. (H) Superresolution images show the distribution of CD93 in untreated versus brefeldin-A-treated cells. Scale bars, 500 nm. Images are presented as heat maps. (I) The effect of brefeldin A on the fraction of CD93 located in puncta (point) versus web-like structures (web) is shown. Data are presented as mean (A) or mean ± SEM (B–D and G), n = 5. ^∗p < 0.05 compared to the same group at 20 min (C and D, ANOVA with Tukey correction) or to Cy3-CD93 in the same cells (G, paired t-test). ND, none detected.