17 research outputs found

    Guidelines for the fitting of anomalous diffusion mean square displacement graphs from single particle tracking experiments.

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    Single particle tracking is an essential tool in the study of complex systems and biophysics and it is commonly analyzed by the time-averaged mean square displacement (MSD) of the diffusive trajectories. However, past work has shown that MSDs are susceptible to significant errors and biases, preventing the comparison and assessment of experimental studies. Here, we attempt to extract practical guidelines for the estimation of anomalous time averaged MSDs through the simulation of multiple scenarios with fractional Brownian motion as a representative of a large class of fractional ergodic processes. We extract the precision and accuracy of the fitted MSD for various anomalous exponents and measurement errors with respect to measurement length and maximum time lags. Based on the calculated precision maps, we present guidelines to improve accuracy in single particle studies. Importantly, we find that in some experimental conditions, the time averaged MSD should not be used as an estimator

    Performance of the time averaged MSD estimator for various trajectory lengths <i>L</i> and maximal time lags <i>τ</i><sub><i>M</i></sub>.

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    <p>Color bar gives the precision Φ and black lines give representative bias values, <i>B</i>. Rows give various anomalous exponents with (a–c) strong subdiffusion <i>α</i> = 0.3, (d–f) weak subdiffusion <i>α</i> = 0.7, (g–i) weak superdiffusion <i>α</i> = 1.3 and (j–l) strong superdiffusion <i>α</i> = 1.7. Measurement error changes between columns with (left) small error <i>σ</i> = 0.1, (middle) medium error <i>σ</i> = 0.5 and large error <i>σ</i> = 1. The optimal <i>τ</i><sub><i>M</i></sub> is selected as the area where Φ is maximal and ∣<i>B</i>∣ is minimal for a given trajectory length <i>L</i>.</p

    Fitting a time averaged MSD with various maximum time lags.

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    <p>A trajectory with <i>α</i> = 0.7, <i>L</i> = 2<sup>9</sup>, <i>σ</i> = 0.5 was simulated (black squares) and fitted for various <i>τ</i><sub><i>M</i></sub> values. While the small <i>τ</i><sub><i>M</i></sub> fitting (red <i>τ</i><sub><i>M</i></sub> = 10 and blue <i>τ</i><sub><i>M</i></sub> = 50) underestimated <i>α</i>, the large <i>τ</i><sub><i>M</i></sub> (green <i>τ</i><sub><i>M</i></sub> = 150) gives an overestimation. Clearly, selecting the optimal <i>τ</i><sub><i>M</i></sub> value is not trivial as both small and large values may lead to erroneous results. Graphically assessing the quality of the fit does not help select the best <i>τ</i><sub><i>M</i></sub> either.</p

    Immunofluorescence evidence of fusion of VZV-infected MeWo cells with axons.

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    <p>MeWo-GFP cells (green) infected with cell-free VZV66RFP (red) virus were plated into axonal compartments of microfluidic chambers or in glass-bottom culture dishes (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126081#pone.0126081.g001" target="_blank">Fig 1C</a>). Cultures were fixed and immunostained for the medium neurofilament subunit (NF-M, white) 1 to 3 dpi and nuclei stained with Hoechst (blue). (A–D) Control experiments with uninfected MeWo-GFP cells. No GFP was found in the NF-M+ axons. (E–H) Immunostaining of an axonal compartment where MeWo-GFP cells infected with VZV66RFP were plated 3 days prior to fixation. (E&F) Images showing GFP and ORF66RFP fluorescence, respectively. The arrow points to a syncytium of MeWo cells containing both fluorescent proteins. Arrowheads point to axons showing GFP and RFP signal. (G) shows immunocytochemical staining of this field for NF-M, the syncytium observed in E and F to contain both GFP and RFP is NF-M+ as well (white). H shows a merge of all channels, where both white (NF-M) and yellow (co-expression of GFP and RFP) staining are present in the same polykaryon. (I–L) An axonal compartment with VZV-GFP-infected ARPE cells (green) was immunostained at 4 dpi with anti-NF-H 4142 (red) and anti-VZV gI (white) antibodies. I shows GFP fluorescence and J, the immunostaining for NF-M. Many GFP+/NF-M+ axons (arrowheads) were observed. Some infected ARPE cells (arrow) became neurofilament+ after fusion with axons. The fused ARPE cells and axons were also immunopositive for glycoprotein I (K), but not several other cells that were not part of the polykaryon. Scale bar: 50μm.</p

    Transfer of protein from VZV-infected cells to axons studied using fluorescence recovery after photobleaching (FRAP).

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    <p>A–D Measurement of viral and non-viral protein diffusion coefficients in axons using FRAP 1–2hpi. VZV-GFP or VZV66RFP-infected MeWo cells were plated into axonal compartments of microfluidic chambers and the first fluorescent axons were imaged using a confocal microscope. A–D depict a FRAP analysis of a GFP-positive axon. (A) A MeWo cell and an axon before bleaching shown using an RGB-intensity look up table (LUT). Circles and polygons showing the areas that were bleached and measured: 1—bleached area, 2—area measured for determining background level, 3—area used as reference to the level of fluorescence in the input MeWo cell, 4—area measured to determine axonal fluorescence recovery. (B) The axon immediately after photobleaching (t0). (C) The same axon at the end of the recovery period. The fluorescence level recovered to a level very similar to that before bleaching. (D) The observed fluorescence recovery curve (blue) and the fitted model curve (red) of the axon shown in (A–C). The close fit of the model yields an estimate of the diffusion coefficient of the fluorescent molecule. Similar results were obtained from 10 axons where the RFP or GFP was bleached and measured. (E–H) Further evidence of diffusional transfer of fluorescent protein from non-neuronal cells to axons using FRAP at 1 to 2 hpi. An entire VZV-infected MeWo-GFP cell was photobleached (circle 1) and the GFP intensities were measured in the cell (circle 4) and the neighboring GFP-filled axon (polygon 5) for about 45s. Fluorescence intensity of the background (circle 2) and that of another MeWo cell (circle 3) were also measured. (F) The MeWo cell and the axon immediately after bleaching for 1sec (t0). (G) The same area after 46s of recovery. In contrast to the result shown in (C) above, the GFP fluorescence in the axon did not recover. (H) Graphical representation of fluorescence intensities in the MeWo cell (dashed curve) and the adjacent axon (solid line). The lack of fluorescence in the axon and the lack of recovery were apparently due to both the diffusion of GFP in the axon away from the visualized portion, and the lack of replenishment of GFP due to the bleaching of the GFP in the adjacent MeWo cell. Scale Bars: 10μm.</p
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