He W et al. (2016), Dynamic heterogeneity and non-Gaussian statisti...

XB-ART-55331

Nat Commun 2016 May 26;7:11701. doi: 10.1038/ncomms11701.

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Dynamic heterogeneity and non-Gaussian statistics for acetylcholine receptors on live cell membrane.

He W , Song H , Su Y , Geng L , Ackerson BJ , Peng HB , Tong P .

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The Brownian motion of molecules at thermal equilibrium usually has a finite correlation time and will eventually be randomized after a long delay time, so that their displacement follows the Gaussian statistics. This is true even when the molecules have experienced a complex environment with a finite correlation time. Here, we report that the lateral motion of the acetylcholine receptors on live muscle cell membranes does not follow the Gaussian statistics for normal Brownian diffusion. From a careful analysis of a large volume of the protein trajectories obtained over a wide range of sampling rates and long durations, we find that the normalized histogram of the protein displacements shows an exponential tail, which is robust and universal for cells under different conditions. The experiment indicates that the observed non-Gaussian statistics and dynamic heterogeneity are inherently linked to the slow-active remodelling of the underlying cortical actin network.

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	Figure 1. Observed dynamic heterogeneity in the AChR trajectories.(a) Overall 130 representative AChR trajectories with 300 time steps (60 s). These trajectories are taken from the bottom membrane of a Xenopus muscle cell. Red trajectories indicate fast moving AChRs and black ones indicate ‘nearly immobile' AChRs. (b) A total of 52 representative trajectories of silica spheres 2.14 μm in diameter undergoing Brownian diffusion in water over a flat substrate with 1,000 time steps (47 s).
	Figure 2. Normalized histogram of the radius of gyration of AChR trajectories.Measured PDF of the normalized for the AChR trajectories taken under different sample conditions: cultured for 1 day after dissection (red circles), cultured for 4 days (magenta triangles), and cultured for 8 days (green diamonds). Each is obtained by averaging the data from 10 cells cultured under the same condition. The black circles are obtained by averaging the data from 70 cells. Their statistics is considerably improved with small error bars indicating the standard deviations. The solid black line shows the exponential function, . The dashed blue line shows the measured for silica spheres undergoing Brownian diffusion. The vertical red line indicates the cutoff value used to define the immobile trajectories.
	Figure 3. Crossover from sub-diffusion to normal diffusion observed from the MSD curve.Measured 〈Δr2(τ)〉 as a function of delay time τ for the AChR trajectories taken at two sampling rates of 80 fps (red dashed line and circles) and 5 fps (black dashed line and circles). Data from a single cell are used in the ensemble average. The red and black dashed lines are obtained when both the mobile and immobile trajectories are included in the calculation. The red and black circles are obtained when only the mobile trajectories are included in the ensemble average. The green triangles are obtained when only the immobile trajectories are included in the ensemble average. The blue solid line indicates the relationship 〈Δr2(τ)〉∼τ with a slope of unity in the log–log plot. Inset shows a linear plot of the measured 〈Δr2(τ)〉 as a function of τ and the red solid line is a linear fit to the data points.
	Figure 4. Cell-to-cell variations in the measured long-time diffusion coefficient DL and mobile ratio γ of the AChRs.Distribution of the measured DL of AChRs. Inset shows the distribution of the measured γ of the AChRs. The total number of cells used in the statistics is 365.
	Figure 5. Non-Gaussian behaviour of the normalized histogram of AChR's displacements.Measured PDFs P(Δx′) and P(Δy′) of the normalized displacements Δx′ and Δy′ for the trajectories of mobile AChRs. Data are obtained from 10 cells under each sample condition: (i) Δx′(τ) with τ=1 s (black triangles), 4 s (black circles), 10 s (black squares) and 20 s (black diamonds); (ii) Δy′(τ) with τ=4 s (blue circles) and (iii) Δx′(τ) with τ=4 s for a group of 10 cells from a different frog (green crosses). The red solid line is an exponential fit to the data points, P(Δx′)≃a exp (−β\|(Δx′)\|), with a=0.6 and β=1.4.
	Figure 6. Normalized histogram of the ‘instantaneous' diffusion coefficient of mobile AChRs.Measured PDF f(δ′) of the normalized diffusion coefficient δ′=δ/DL for the mobile AChR trajectories. Data are obtained from three groups of 10 cells each cultured for (i) 1 day (black circles), (ii) 3 days (blue triangles) and (ii) 6 days (green diamonds). The error bars show the standard deviation of the blue triangles averaged over 10 cells. The red solid line is an exponential fit to all data points, f(δ′)≃0.22 exp (−0.75δ′). The blue dashed line shows the measured f(δ′) for the silica spheres undergoing normal Brownian diffusion.

References [+] :

Alcor, Single-particle tracking methods for the study of membrane receptors dynamics. 2009, Pubmed