Modelling post-bleaching diffusion inside a sphere: Monte-Carlo simulations and direct calculations.

<p><i>A</i>, Graphical representation of the bleaching experiment, showing an impermeable sphere of unit radius, in which the horizontal polar axis distance <i>µ</i> = cos(<i>θ</i>) and the normalised radius <i>r</i> are spherical coordinates describing fluorophore concentration distribution. A bleached region covering the horizontal axis interval <i>α</i>≤<i>µ</i>≤1 is shown in white, the rest of the sphere contains fluorophore (grey). <i>B–C</i> Monte-Carlo FRAP recovery simulations. <i>B,</i> Concentration profiles for simulated redistribution of 20000 particles, initially positioned at time <i>τ</i> = 0 s in the left hemisphere (black trace). Recovery times are coded by the trace colours. Simulation parameters were: sphere radius <i>R</i>₀ = 1 µm, prescribed diffusion coefficient <i>D</i> = 3 µm²/s, bleaching parameter <i>α</i> = 0, simulation step 5·10⁻⁴s. Profiles were constructed from images representing the 2D projections of the sphere, each simulated particle was represented by a pixel of value 1. The plot of normalised moment kinetics is shown in <i>C</i>. Red line- monoexponential fit, the fitted time constant <i>τ</i> = 83 ms corresponds to the <i>D</i> value of 2.79 µm²/s (Eq.8). <i>E–F,</i> Analysis of the same problem from images representing projections of concentration distributions calculated using Eq.10. <i>E</i>, Concentration profiles for simulated distributions, time-dependent colour coding as in <i>B</i>. Oscillating patterns (Gibb’s phenomena) at short times (black trace) are due to approximation of discontinuity by finite Legendre sums. <i>F,</i> The normalised moment kinetics fitted either by a single exponent (red trace, <i>τ</i> = 66 ms, evaluated <i>D</i> = 3.5 µm²/s) or by a sum of two exponents (blue trace, <i>τ</i>₁ = 3.5 ms, <i>τ</i>₂ = 75 ms, <i>D</i> evaluated from <i>τ</i>₂ was 3.1 µm²/s; the amplitude of fast component was 0.105 of that for slow component). <i>D,</i> The relationship between the values of <i>D</i> prescribed in Monte-Carlo simulations and results obtained from fits as in <i>C</i> and <i>F.</i> The results were compared with identity line (red). The slopes of the best fits were: for Monte-Carlo simulations (as in <i>B–C</i>) 0.93±0.009 (circles), for the best monoexponential fit to calculated values 1.18±0.0006 (open triangles), for the slower mode of bi-exponential fit (as in <i>E–F</i>) 1.03±0.0004 (filled blue triangles).</p

Post-fusion WPBs acquire plasma membrane components by membrane mixing.

<p><i>A</i>, Image of a HUVEC expressing EGFP-Rab35 membrane protein (green) and immunolableled for endogenous VWF (red). Greyscale images are from the region indicated by the white box. Scale bar, 10 µm. <i>B</i>, Top, a montage of colour-merged images of a Pro-mRFP-labelled WPB (red) from a confocal live cell video of HUVEC co-expressing Pro-mRFP- and EGFP-Rab35- (green) and undergoing histamine-evoked exocytosis. <i>B</i>, Bottom, the EGFP-Rab35 component alone. Scale bar, 2 µm. The images show entry of plasma membrane EGFP-Rab35 into the membrane of the fusing WPB. <i>C</i>, The kinetics of EGFP-Rab35 fluorescence accumulation in the WPB shown in <i>B</i> (radius of the ROI used for measurements was 0.75 µm). The time constant of the exponential fit to the protein transfer process was 3.16 s. <i>D,</i> Confocal images of rounded WPB found inside HUVEC after being stimulated in the presence of the extracellular fluid phase marker Alexa-647. Plasma membrane-derived EGFP-Rab35 (green) is found in the limiting membrane of the post-fusion WPB structure containing Alexa-647 dye (blue) and positive for Pro-mRFP (red). Scale bar, 1 µm. Experiments <i>B</i>–<i>D</i> were performed at 37°C. <i>E–F,</i> Membrane dye vDiI transfers from plasma membrane to the post-fusion WPB. <i>E</i>, Right, confocal fluorescence of vDiI in a HUVEC containing Pro-EGFP-labelled WPBs (left image). Scale bar, 2 µm. <i>F</i>, Confocal images of a post-fusion WPB expressing Pro-EGFP (green) showing the presence of vDiI (red) after stimulation in the presence of the extracellular fluid phase marker Alexa-647 (blue). Scale bar, 1 µm.</p

Comparison of mobilities of WPB proteins in NH₄Cl-rounded and post-fusion WPBs.

a<p><i>n</i>_mob and <i>n</i>_im are numbers of WPB experiments where mobile or immobile behaviour was observed, correspondingly.</p>b<p><i>D</i> and MF (mobile fraction) values as calculated for all experiments, immobile values regarded as 0s.</p>c<p>the values in square brackets single out mobile cases only.</p><p>Comparison of mobilities of WPB proteins in NH₄Cl-rounded and post-fusion WPBs.</p

Differential changes in intra-WPB mobilities of soluble cargo proteins in post-fusion WPBs.

<p><i>A–B</i>, Images of extracellular Alexa-647-containing (right panels) post-fusion WPBs expressing Pro-EGFP (<i>A</i>, green) or VWF-EGFP (<i>B</i>, green). <i>A1–B1</i>, Left, images and right, image profiles for selected FRAP times (as indicated) for a Pro-EGFP- (<i>A1</i>) or VWF-EGFP-containing (<i>B1</i>) post-fusion WPBs. Here and in subsequent images the bleaching frames are marked in yellow. <i>A2–B2</i>, The lack of recovery of normalised first moment for Pro-EGFP (<i>A2</i>) and VWF-EGFP (<i>B</i>2) indicating that both are immobile within the post-fusion structures. Scale bars, 1 µm. <i>C</i>, Image of an Eotaxin-3-EGFP- and mRFP-Rab27A-co-expressing WPB rounded by preincubation in NH₄Cl. Both scale bars, 1 µm. <i>C1</i>, Top, images and bottom, fluorescence profiles for Eotaxin-3-EGFP fluorescence during a FRAP experiment. <i>C2</i>, The change of average fluorescence in the rounded structure (moment <i>µ</i>₀). The symbols corresponding to the frames shown in the images <i>C1</i> above are coloured red. <i>C3</i>, The plot of the normalised first moment <i>µ</i>₁/<i>µ</i>₀ and an exponential fit to its kinetics (blue dotted line). The time constant of the fit, 48 ms, is unreliable as it is based only on 2–3 measured points. With mean frame interval 41 ms, <i>R</i>₀ = 49 µm we estimate <i>D</i>_crit = 1.49 µm²/s, meaning the diffusion in this experiment is faster than this value.</p

Cumulative fusion involving post-fusion WPB.

<p>Selected images from a live cell epifluorescence video (see also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0108093#pone.0108093.s001" target="_blank">Movie S1</a>) of an EGFP-CD63-expressing HUVEC stimulated with 100 µM histamine. Scale bar, 2 µm. <i>A</i>, Left, approximate positions of ROIs corresponding to two EGFP-CD63-labelled WPBs participating in the cumulative fusion. <i>A</i>, Right, images showing the change in shape of the first, dimmer WPB (ROI ‘1’) due to fusion. Arrow in frame 2 of <i>A</i> indicates a WPB that fuses to form initial rounded structure, indicated by arrows in frames 4–6 and frame 1 of <i>B</i>. Here and below the colour-coded bars above the images correspond to the marked time intervals in the graph <i>D</i>. <i>B</i>, Two rows of images showing the fusion of the second WPB ‘2’ with the rounded WPB ‘1’ indicated in <i>A.</i> The time of this second fusion was set to 0 s. Note the redistribution of fluorescence between the two structures. <i>C</i>, Loss of EGFP-CD63 fluorescence of the compound structure (arrow) upon fusion with the plasma membrane. <i>D</i>, The time course of the fluorescence changes within ROI ‘1’ (blue) and ROI ‘2’ (black) in control (black bar), during the cumulative fusion event (red bar) and after fusion with plasma membrane (blue bar). The average intensities of images were normalised to the beginning of experiment. The slow residual decline of fluorescence is due to uncompensated photobleaching of EGFP.</p

Post-fusion WPBs swell.

<p><i>A</i>, Example of the WPB shape change seen during stimulated (1 µM ionomycin) fusion in a HUVEC expressing EGFP-CD63. Scale bar, 2 µm. <i>B–C</i>, The distributions of the pre-fusion WPB lengths <i>L</i> (<i>B,</i> mean 1.56±0.06 µm) and of maximal radii of the resulting spheroid structures <i>R</i>₀ seen soon after fusion (<i>C,</i> mean 0.49±0.01 µm) for all WPBs measured when undergoing exocytosis (labelled with EGFP-CD63, <i>n</i> = 99 and with P-selectin-EGFP, <i>n = </i>41). <i>D,</i> The radius of rounded structure (<i>C</i>) plotted against the corresponding length of the parent WPB (<i>B</i>) in the same fusion event (points), double logarithmic scale. The solid line is the best power function fit to the dependence, <i>R</i>₀ = 0.384·<i>L</i>^0.573, the dashed line is the best √<i>L</i> fit: <i>R</i>₀ = 0.399·√<i>L</i>. The dotted line represents radius prediction for the model of rounding preserving the WPB surface, <i>R</i>₀ = 0.194·√<i>L,</i> the dash-dot line represents the constant-volume rounding model, <i>R</i>₀ = 0.162·<i>L</i>^1/3. In calculations the average diameter of WPBs was assumed to be 0.15 µm. <i>E</i>, the distribution of radii for all rounded fluorescent WPBs found persisting after stimulation and containing extracellular Alexa-647 (mean radius 0.61±0.02 µm, <i>n</i> = 150).</p

Mobilities of membrane proteins in post-exocytosis rounded WPBs.

<p><i>A</i>, Image of a post-fusion P-selectin-EGFP-labelled WPB (left, green) containing the extracellular fluid phase marker Alexa–647 (right). <i>A1</i>, Left, images and right, image profiles measured at selected FRAP times (as indicated). <i>A2</i>, The time course of normalised moment kinetics fitted by exponent (red line), time constant <i>τ</i> = 2.44 s, with the radius <i>R</i>₀ = 0.69 µm yielding the <i>D</i> value of 0.098 µm²/s (Eq. 1). <i>B</i>, Image of a post-fusion WPB co-expressing EGFP-CD63 (left, green) and Pro-mRFP (right, red) and labelled with the extracellular fluid phase marker Alexa-647 (middle). <i>B1</i>, Images and image profiles for EGFP-CD63 during FRAP. <i>B2</i>, Exponential fit to the normalised moment change, <i>τ</i> = 1.0 s, <i>R</i>₀ = 0.78 µm, <i>D</i> = 0.29 µm²/s. <i>C,</i> Image of a post-fusion WPB co-expressing EGFP-Rab27A (left, green) and Pro-mRFP (right, red) and containing the extracellular fluid phase marker Alexa-647 (middle). <i>C1</i>, Images and image profiles for EGFP-Rab27A during FRAP. <i>C2</i>, Analysis of moment kinetics, exponential fit <i>τ</i> = 0.32 s, <i>R</i>₀ = 0.62 µm, <i>D</i> = 0.58 µm²/s. All scale bars, 1 µm.</p

Additional file 1: TableS1. of TuberOus SClerosis registry to increase disease Awareness (TOSCA) – baseline data on 2093 patients

Age and Gender Distribution of TSC manifestations reported in TOSCA. (DOCX 13 kb