Primary antibodies.

<p>Primary antibodies.</p

Three MRC5 nuclei with PML locations and their corresponding F-function Test.

<p>The images are a 2-D projection but the analysis is performed in 3-D. If the observed F-function (the continuous curve) is wholly contained within the CSR envelope (the dotted curves) then the pattern is consistent with CSR (the null hypothesis). The middle nucleus rejects the null and is demonstrating PML locations that are further apart than would be expected by CSR. The right-most nucleus also rejects the null and is demonstrating locations that are more tightly clustered than would be expected by CSR.</p

Radial Analysis of PML Bodies in a 2-D projected nucleus.

<p>A binning strategy that measures only distances from the center of gravity may not respect the nucleus envelope. The dotted circles are bin boundary locations where each bin has equal area. Bin regions can occur outside of the nucleus envelope, which can affect the analysis.</p

Two-sided K-S test statistics for SDI using the F-function.

<p>For spatial point patterns generated by each type of alternative to CSR deployed, and for increasing average number of points, the summary statistic from the SDI, D, and its corresponding p-value are shown. Total number of synthetic nuclei is 200.</p

Histogram of SDI using F-function for MRC5 PML NB locations.

<p>For a CSR process we would expect the histogram to be approximately uniform, however we see concentrations in both the low and high values of SDI indictaing that there is a spatial preference for PML NBs.</p

2-D Illustrations of the alternative spatial point processes used in the construction of the synthetic data.

<p>Each of the three alternatives has a clear spatial preference. The challenge for spatial analysis is to identify such preference when the average number of points is low and potentially difficult to distinguish from CSR.</p

Modified <i>Individual</i> F-function Test using Aggregated null envelope for 3 MRC5.

<p>The distance standardized F-functions of the PML NB locations for the nuclei shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036841#pone-0036841-g001" target="_blank">Figure 1</a>. Although for these particular cells we make the same decision as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036841#pone-0036841-g007" target="_blank">Figure 7</a>, the result over the dataset is different; fewer nuclei fail to reject the null. This is likely due to the shape heterogeneity of the nucleus envelope, evidence for which is provided by the investigation of synthetic data, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036841#pone-0036841-g011" target="_blank">Figure 11</a>.</p

<i>Individual</i> F-function Test for synthetic datasets.

<p>The leftmost figure corresponds to the thick dataset and the rightmost the thin dataset. For each of 200 synthetic nuclei, in each dataset, an F-function Test is performed, where the null hypothesis is the spatial point pattern has been drawn from a CSR process. The spatial point patterns generated for these all the synthetic instances are from alternatives to CSR, hence the power of the test is equal to the proportion of instances that reject the null hypothesis.</p

Histograms of SDI using F-function for the center alternative for the thin dataset with increasing number of expected points.

<p>The expected number of points increases top left to bottom right. For a CSR process the histogram should be uniform. For 16 expected points it is difficult to distinguish the histogram from uniformity. However, as the average number of points increases we see an increase in the non-uniformity of the histogram. In particular we see a concentration for low SDI values (which is what would be expected for points that are clustered).</p

2-D Illustration of the extraction of PML locations from image data.

<p>A) Original raw image B) The boundary of the nucleus envelope and the PML bodies are segmented from an image. C) Each PML body is replaced by its center of gravity.</p