PR^major and PR^minor are differentially affected by thresholding and clustering.

<p>Cells were simulated to be: i) symmetric non-clustered; ii) asymmetric non-clustered; iii) symmetric clustered; iv) asymmetric clustered. (<b>A</b>) Examples of simulated cells and approach to hemisphere separation. Blue and red lines describe the major and minor axes respectively, and the magenta contour shows the separation that gave an equal number of pixels to each hemisphere (slightly shifted from the major axis). (<b>B</b>) PR^major and PR^minor values for 10 simulated cells were plotted against T value (<b>C</b>) M^major and M^minor values for 10 simulated cells were plotted against T value. Note that in the asymmetric cells, some fluorescence values were reduced to 0 for the higher threshold settings, causing misleading values of 1 in (B) and infinite (unplottable) values in (C). Input for simulations: θ = 0, R = 22 pixels, number of clusters in D1 and D2 was 20 in the symmetric and 20 and 30 in asymmetric</p

Ratio coefficients from synthetic data are dependent on the threshold value.

<p>10 images of cells simulated to have symmetric fluorescence partitioning with non-clustered (<b>A</b>) and clustered localization (<b>B</b>) were simulated to quantify the effect of background subtraction on ratio coefficients. The horizontal axis represents the Threshold value. The vertical axis represents the PR. The possible range varies between -1 to 1, where 0 is maximum symmetry and high absolute ratios indicate maximum asymmetry. Different colors represent different simulated divisions. Black crosses represent the ratio and T value of illustrative images below. Input for simulation: θ = 0, R = 22 pixels, number of clusters in both D1 and D2 was 20.</p

Axial subdivision for polarization analysis.

<p>(<b>A</b>) An approach for quantification of polarity. Black arrows represent the major and its perpendicular minor axis. Splitting the image into two allows a direct comparison of fluoresce intensity across the minor or major axes. The major axis is derived from the longest diameter of an ellipse that overlaps the cell. The minor axis is defined as the perpendicular to the major axis. Blue and red colors show the areas from which pixel intensities were collected, and represent the two halves of the cell that would, if the cell divided, become daughter 1 and 2. The left and right sides of the cells are bright and dim respectively. (<b>B</b>) Polarization ratios are extracted by integrating pixel intensities across the major or minor axis: i) Ratio along the major axis (using segments divided by the minor axis). ii) PR^major: Normalized ratio along the major axis (across the minor axis). iii) PR^minor: Normalized ratio along the minor axis (across the major axis).</p

Ratio coefficients from experimental data are dependent on the threshold value.

<p>Fluorescence intensity ratios were extracted from images of dividing MLA cells expressing GFP, and for a random selection of 10 events, ratios plotted again threshold setting. Ratios were calculated using Proportion (<b>A</b>) and PR (<b>B</b>). Different colors represent different events.</p

The effect of cluster number on the accuracy of PR measurements.

<p>Divisions were simulated to have increasing numbers of clusters ranged from 1 to 100 in increments of 1 for one of the daughter cells. The number of clusters in the second daughter was the number of clusters in daughter 1 multiplied with its corresponding ratio. Ratios vary from1 to 2 with increments of 0.1, and were calculated under 0%, 20%, 40%, 60%, and 80% threshold. (<b>A</b>) The PR^major and PR^minor for each event are shown in heat maps, where the PR ranging from 0 to 1 are represented in "jet" colors (blue to red). The ratios were binarized using (<b>B</b>) cut-off value of 1.5 or (<b>C</b>) by equation 5. Blue pixels represent events in which PR^major was larger than PR^minor; white pixels represent events in which PR^major was smaller than PR^minor.</p

Sensitivity test from simulations.

<p>Cell divisions were simulated in increasing ratios from 1 to 1.5 with even increments of 0.05, giving n = 1100 divisions in total. PR^major was plotted against PR^minor for non-clustered (<b>A</b>) and clustered (<b>B</b>) data. Data is showed as major/minor plot, under a range of thresholds from T = 0%, to T = 80% in increments of 20%. The magenta line shows gating exclusion of 10% of data with the highest PR^minor. The gate shifts right as T value increase. The colours in the figure legend represent different ratios and corresponding to the ratio colour of each data dot. Input for simulations: θ was chosen randomly varying from 0 to 90 degrees, distribution of parental radius and total intensity were selected randomly from a real distribution from real data, number of clusters in one of the daughter cells was 20 to 100, and the number of clusters in the other daughter cell was multiplied in the simulated ratio giving a possible range from 30 to 150.</p

Suggested workflow for optimal analysis of ACD.

<p>A method of analysis that avoids some pitfalls of polarity measurement as illustrated in this study begins with (<b>1</b>) extraction and segmentation of images, including demarcation of major and minor axes (either using the long axis as demonstrated here, or alternative strategies). (<b>2</b>) A randomly selected sample set of the data should be used to plot PR^major and PR^minor against a range of processing settings, and used to (<b>3</b>) determine the optimal processing settings that avoid artificially high PR values (as indicated by PR^minor analysis) but provide good dynamic range of PR^major(see the discussion of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099885#pone-0099885-g004" target="_blank">Fig 4</a> for an illustration of this process) (<b>4</b>) The optimal processing settings are used to plot PR^major against PR^minor for the entire population. (<b>5</b>) PR^major vs. PR^minor is utilized for exploration of the quality of the data. Firstly, assuming that polarization occurs only along one axis, the two parameters should be independent of each other and this can be evaluated from the plot both visually (as is common in flow cytometric analysis where correlations can indicate errors in cross-spectral compensation) and by regression analysis. If the plots are still linked to the original data, any outliers can be readily examined to determine possible causes of error. For instance, using an interface such as provided by the TACTICS Toolbox <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099885#pone.0099885-Pham2" target="_blank">[23]</a>, clicking on the dots can bring up the specific frame or movie associated with that data point and possible exclusion of aberrant data such as problems with the focus. Secondly, gating for cells with low PR^minor values on the plots enables exclusion of noisy data and simultaneous assessment of the extent, range and variance of PR^major. (<b>6</b>) The gated PR^major can then be plotted as a histogram or scatter plot, enabling comparison with control data or between test populations. These plots represent an endpoint of the analysis, but can also be used to determine whether additional values such as mean or median PR, range, variance or proportion in different PR values would be informative and could be extracted from the data. (<b>7</b>)(<b>Optional</b>) Depending upon the quality of the data and the goals of the analysis, binarization of the events into ACD and SCD could be achieved by either cut-off or comparison of PR^major and PR^minor values as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099885#pone-0099885-g005" target="_blank">Figure 5</a>.</p

Gating based on PR^minor in simulated data.

<p>Cell divisions were simulated with ratio 1 (blue color) or 1.5 (red color), 100 divisions for each, with 10% of out of focus "bad data" and PR^major (y-axis) was plotted against PR^minor (x-axis) (<b>A</b>) for non-clustered (i) and clustered (ii) fluorescence. The magenta line show the gating border that to removes 10% outliers of the minor axis polarization, to remove "bad data". PR^major of the gated events were plotted as a (<b>B</b>). Input for simulations: θ was chosen randomly varying from 0 to 90 degrees, distribution of parental radius and total intensity were selected randomly from real distribution from real data, number of clusters in one of the daughter cells was 20 to 100, and the number of clusters in the other daughter cell was multiplied in the simulated ratio giving possible range from 30 to 150.</p

Additional file 3: Figure S2. of Delivery of VEGFA in bone marrow stromal cells seeded in copolymer scaffold enhances angiogenesis, but is inadequate for osteogenesis as compared with the dual delivery of VEGFA and BMP2 in a subcutaneous mouse model

A limited number of blood capillaries, only in ad-VEGFA scaffold explants, were weakly positive for anti-CD31 antibody targeting human CD31 protein. (B–G) No CD31-positive staining was observed in the capillary/vessel-like structures (black arrows) in the entire scaffold explants from all groups both at 2 and 8 weeks, except for a few capillaries in the ad-VEGFA explants at 8 weeks (E, green arrows). (A) Positive control (normal human oral mucosa) showed multiple CD31-positive capillary-like structures. (TIF 14626 kb

Additional file 1: of Countdown to 2015 country case studies: what can analysis of national health financing contribute to understanding MDG 4 and 5 progress?

Health Financing Analysis for Countdown Case Studies: A Guide. (PDF 1459 kb