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We have carried out a comparative study of the lateral motion of ganglioside GM1, which is a glycosphingolipid residing on the outer leaflet of the plasma membrane, and acetylcholine receptor (AChR), which is a well-characterized ion channel. Both the lipid molecules and the transmembrane proteins reside on the plasma membranes of live Xenopus muscle cells. From a thorough analysis of a large volume of individual molecular trajectories obtained from more than 300 live cells over a wide range of sampling rates and long durations, we find that the GM1s and AChRs share the same dynamic heterogeneity and non-Gaussian statistics. Our measurements with the ATP-depleted cells reveal that the diffusion dynamics of the GM1s and AChRs is uniformly affected by the intracellular ATP level of the living muscle cells, further demonstrating that membrane diffusion is strongly coupled to the dynamics of the underlying cortical actin network, as predicted by the dynamic picket-fence model.
FIGURE 1:. Explanation of the dynamic picket-fence model. (a) Cortical actin network with anchored proteins (blue), which form a continuous random network, partitioning the membrane into corrals of different sizes. (b) The motion of mobile proteins (red) is confined to corrals, whose lift time is determined by the slow dynamics of the cortical network. As a result, the diffusion of the mobile proteins is strongly influenced by the size of the corrals, giving rise to a broad distribution of the local diffusion coefficient δ.
FIGURE 2:. (a) One hundred forty-three representative GM1 trajectories with 400 time steps (80 s). (b) One hundred sixty-two AChR trajectories with 400 time steps (80 s). All the trajectories are obtained from the bottom membrane of a Xenopus muscle cell with a viewing area 68 × 68 μm2. Red trajectories indicate fast-moving GM1s/AChRs and black ones indicate nearly immobile GM1s/AChRs.
FIGURE 3:. Measured PDF (normalized histogram) h(Rg′) of the normalized radius of gyration Rg′ for the GM1 trajectories taken at 5 fps (black circles) and 80 fps (green diamonds). The red triangles are obtained from the AChR trajectories taken at 5 fps. Each h(Rg′) is obtained by averaging the data from 70 cells under the same condition. The error bars indicate the SD of the measurements. The black solid line shows the exponential function h(Rg′) ≃ 1.5 exp (–1.25 Rg′). The red vertical line indicates the cutoff value (Rg′)c = 0.3 used to define the immobile trajectories.
FIGURE 4:. (a) Measured MSD 〈Δr2(τ)〉 as a function of delay time τ for the mobile GM1 trajectories taken at two sampling rates of 80 fps (red circles) and 5 fps (black circles). The green triangles are obtained from the immobile GM1 trajectories. Data from a single cell are used in the ensemble average. The blue diamonds are obtained from the immobile QDs, which are physically stuck on a coverslip. The blue solid line indicates the relationship 〈Δr2(τ)〉 with a slope of unity in the log–log plot. (b) A linear plot of the measured 〈Δr2(τ)〉 as a function of τ for the mobile GM1 trajectories taken from a single cell with a sampling rate of 0.25 fps. The red solid line is a linear fit to the data points with τ < 45 s.
FIGURE 5:. (a) Comparison of the distribution of the measured long-time diffusion coefficients DL of GM1s (black bars) and AChRs (red bars) (b) Comparison of the distribution of measured mobile ratios γ of the GM1s (black bars) and AChRs (red bars).
FIGURE 6:. Measured PDFs P (Δx′) and P (Δy′) of the normalized displacements Δx′ and Δy′ for the mobile trajectories of GM1s. The data are obtained from 10 cells under different sample conditions: 1) Δx′ (τ) with τ = 1 s (black triangles), 4 s (black circles), and 10 s (black squares); 2) Δy′ (τ) with τ = 4 s (blue circles); and 3) Δx′ (τ) with τ = 4 s for the mobile trajectories of AChRs from 10 cells (green diamonds). The error bars show the SD of the black circles averaged over 10 cells. The red solid line is an exponential fit to the black circles, P (Δx′) ≃ aexp (–β|Δx′|), with a = 0.53 and β =1.26.
FIGURE 7:. Measured PDF f (δ′) of the normalized diffusion coefficient δ′ = δ/DL for the mobile GM1 trajectories. The data are obtained from two groups of 10 cells each cultured for 1 day (black circles) and 6 days (blue triangles), respectively. The green diamonds are obtained from the mobile AChR trajectories taken from a group of 10 cells cultured for 1day. The error bars indicate the SD of the black circles averaged over 10 cells. The red solid line is an exponential fit to the black circles, f (δ′) ≃ 0.45 exp (–0.82δ′).
FIGURE 8:. (a) Changes of the mean value of the long-time diffusion coefficient DL for GM1s (black bars) and AChRs (red bars) after ATP depletion (DATP). (b) Changes of the mean value of the mobile ratio γ for GM1s (black bars) and AChRs (red bars) after DATP. The statistics of all the data sets for GM1s in a and b were obtained from 30 ATP-depleted cells in three separate experiments and those for AChRs were obtained from 40 ATP-depleted cells in three separate experiments. The error bars indicate the SD of the measurements. The effect of ATP depletion is shown with the shaded bars in comparison with the data from the untreated (normal) cells shown in solid bars.
FIGURE 9:. (a) Measured PDF P ( Δx′) of the normalized displacement Δx′ (τ) with τ = 4 s for the mobile trajectories of GM1s (black circles) and AChRs (red triangles) after ATP depletion (DATP). The blue dashed line indicates the exponential fit, P ( Δx′) ≃ 0.53 exp (–1.26|x′|), to the black circles shown in Figure 6. (b) Measured PDF f (δ′) of the normalized instantaneous diffusion coefficient δ′ = δ/DL for the mobile trajectories of GM1s (black circles) and AChRs (red triangles) after DATP. The blue dashed line indicates the exponential fit, f (δ′) ≃ 0.45 exp (–0.82δ′), to the black circles shown in Figure 7. The green dashed line shows the measured f (δ′) for the silica spheres undergoing normal Brownian diffusion. The statistics of all the data sets for GM1s in a and b were obtained from 30 ATP-depleted cells in three separate experiments and those for AChRs were obtained from 40 ATP-depleted cells in three separate experiments. All the cells used were cultured within the first two days. The error bars show the SD of the measurement for the black circles.
FIGURE 10:. Microscope images of the rhodamine–phalloidin stained F-actin filaments in a cultured Xenopus muscle cell. (a) Large view of an untreated (normal) cell; (b) enlarged view of a portion of the normal muscle cell; (c) large view of an entire cell (top portion of the image) after the ATP depletion; (d) enlarged view of a portion of the muscle cell after the ATP depletion, showing the local feature of F-actin filaments. All of the scale bars are 20 µm. The blue and red boxes in b and d show, respectively, a sampled cortical region and an adjacent bulk region further away from the cell boundary. Each box covers an area of 5 × 5 μm2, and they are aligned along the normal direction of the cell boundary, as indicated by the two parallel yellow lines.
FIGURE 11:. Changes in the measured fluorescent intensity ratio R after the ATP depletion. The value of R is averaged over different parts of 20 muscle cells for both the ATP-depleted and control cell sets. Sixty data points are used in the statistics under each condition. The error bars show the SD of the measurements.
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