Conditional Probabilities of Edge Lengths for Random Data.

<p>The figures illustrate how the <i>p</i>(<i>r</i>|<i>r</i>′) conditional probability looks for randomly generated point positions. Panel A. Conditional probability of points with coordinates generated according to a uniform distribution. Panel B. Conditional probability of points with coordinates generated according to a mixture of uniform distribution and clusters of Gaussian distributions. In the latter example an emphasized diagonal is observed which is the result of the Gaussian clusters. Tightly packed points tend to produce short edges, while points from the edges of the clusters mostly have longer edges.</p

Sketch of a Delaunay Triangulation.

<p>The Delaunay triangulation and its dual, the Voronoi tessellation for a random set of points. The blue lines are the segments of the Voronoi tessellation, the red ones are the edges of the Delaunay graph (triangulation).</p

Results for cells exposed to 0.5 Gy radiation.

<p>Panel A. The figure shows the radial radial distribution function for H3K4 antibodies representing euchromatin (methylated histone variants) for non-irradiated and irradiated cells. Error bars represent the standard deviation of the mean value after averaging over the sample of cells. The value for <i>g</i>(<i>r</i>) at small distances goes up to around 20, indicating the high marker densities during repair. The rapid drop off of the radial distribution function within a distance of about 50 nm shows that euchromatin forms small clustered areas. Upon exposure to 0.5 Gy γ-irradiation, a change in the correlation function can be observed in cells that were imaged after 30 min and 48 hrs. The value at small radial distances increases compared to non-irradiated cells. This indicates that the density in the euchromatic regions becomes on average higher in irradiated cells. Panel B. The distribution of edge lengths in the Delaunay triangulation of the markers confirms these observations. A sharp peak in the distribution at around 30 nm can be seen in untreated cells. In 48 h post-irradiation cells, the peak spreads slightly.</p

Conditional Probability Distribution of the Edge Lengths.

<p>Panel A. The panel shows the conditional probability distribution <i>p</i>(<i>r</i>|<i>r</i>′) of the edge lengths for the H2B markers before irradiation. The relatively prominent diagonal indicates locally a varying density. Panel B. The panel shows the conditional probability for the H2B markers 30 minutes after irradiation. Panel C. The panel shows the conditional probability for the H2B markers 48 h after irradiation. Panel D. The panel shows the difference of the conditional probabilities <i>p</i>(<i>r</i>|<i>r</i>′) measured for structures recorded before irradiation and for structures registered 30 min after irradiation. Shades towards red indicate values which are larger in the samples before irradiation, while values towards the shades of blue indicate probabilities which are larger in images registered 30 min after irradiation. The plot indicates slightly increased values along the diagonal after irradiation. This might mean a slightly increased clustering of the points. Panel E. The panel shows the differences of the conditional probability before irradiation and 48 h after irradiation. Entries in shades of red are larger in samples recorded before irradiation, while entries in shades of blue are larger in the samples recorded 48 h after irradiation. The trend is similar to that observed in panel D, however differences are less prominent. Panel F. The panel shows the differences if the conditional probability measured 30 min and 48 h after irradiation respectively. The red shades indicate larger probabilities in samples recorded 30 min after irradiation while blue shades indicate larger probabilities in samples registered 48 h after irradiation. Here a reversed trend compared to panel D was observed.</p

Conditional Probability Distribution of the Edge Lengths for Heterochromatin Markers.

<p>Panel A. The panel shows the conditional probability distribution <i>p</i>(<i>r</i>|<i>r</i>′) of the edge lengths calculated for the positions of the antibodies marking heterochromatic regions before irradiation. Panel B. The panel shows the conditional probability for the heterochromatin markers 30 min after irradiation. Panel C. The panel shows the conditional probability for the heterochromatin markers 48 h after irradiation. In all three cases the diagonal is emphasized indicating preferential spatial distribution of the edges. This may stem from the clustering of the heterochromatin markers. Note that although shades along the diagonal are darker in panel C, the value of the corresponding probabilities are very close to the probabilities along the diagonal of panel A except for small radii. Panel D. The panel shows the difference in the conditional probability distribution <i>p</i>(<i>r</i>|<i>r</i>′) before irradiation and 30 min after irradiation. A red shade of the color-map means that the probability is higher before irradiation while a blue shade means that it is higher after irradiation. The panel indicates a slightly stronger change along the diagonal indicating a more homogeneous system after irradiation. However, the change is almost independent of the value of the condition <i>r</i>′. Panel E. The panel shows the difference of the conditional probability distribution calculated for samples before and 48 h after irradiation. Shades of red indicate higher probabilities for the samples recorded before irradiation while shades of blue indicate higher probabilities in samples recorded after irradiation. Panel F. The panel illustrates the difference of the conditional probability distribution 30 min and 48 h after irradiation. Red shades correspond to higher probabilities 30 min post-irradiation while shades of blue indicate larger values 48 h after irradiation. The difference between structures observed 30 min after irradiation and 48 h after irradiation indicate a reversed trend compared to panel D.</p

Cluster analysis of the spatial distribution of heterochromatin and euchromatin after irradiation with 0.5 Gy and 3.5 Gy.

<p>The analysis was performed on non-irradiated samples, and on samples fixed 6 h and 24 h post irradiation, respectively. <b>Panel A</b> present the behaviour of heterochromatic regions irradiated with 0.5 Gy and 3.5 Gy. We observe a decrease in the ratio of the clustered points 6 h after irradiation for both doses. 24 h after irradiation these changes are reverted. This means that a few hours after irradiation the heterochromatin decondenses and after one day the decondensation is reverted. <b>Panel B</b> shows the cluster analysis result for euchromatin. These regions behave differently, compared to heterochromatin. For 0.5 Gy, the number of clustered points is increased after 6 h, and the trend continues at the 24 h timestamp. However, for 3.5 Gy, after the initial increase in the percentage of clustered points at 6 h, the ratio drops again in the 24 h measurements. The interpretation of the increase/decrease in the number of clustered points is similar in this case: when the ratio increases, the studied domains condense, when the ratio decreases, the domains relax. This means, that heterochromatin and euchromatin react to irradiation in an opposite way: This analysis, in accordance with the other results, indicates that while heterochromatin opens up soon after irradiation, euchromatin condensates. Given enough time, these processes are reverted in both cases.</p

Localization Microscopy Images.

<p>Panel A. Widefield image of a cell nucleus, as usually obtained by standard microscopy. Panel B. Pointilist image obtained after merging the acquired time series of SPDM images. Each point represents a detected blinking process during image acquisition. The green insert shows an area with a low average density, which could correspond to euchromatin and the blue area corresponds to an area with high point density, possibly belonging to heterochromatin. Panel C. This panel shows the calculated density distribution of the localized markers using a Gaussian kernel density estimation with a uniform Gaussian kernels. Panel D. The figure shows the localized points of the image. From the points, areas with very low point density, possibly corresponding to nucleoli, can clearly be made out visually. Panel E. Shown is the segmented image where only the area of interest is kept for the analysis. The segmentation was based on the density distribution; areas below a threshold density were discarded for analysis.</p

Examples of Localization Microscopy Images of Heterochromatin Markers.

<p>Panel A. Shown is the density distribution of the localized markers in a cell prior to irradiation. Small, very bright spots where markers are agglomerated can be seen. This means that heterochromatin is mainly organized in coarse areas. Panel B. Shown is the segmented image of the not irradiated cell that is used for subsequent analysis of the marker distribution. Panel C. The density distribution of a cell at 30 min after irradiation with 0.5 Gy is shown here. Differences between this cell and the not irradiated cell can be made out by visual inspection. We observe that the density has much less agglomerated and bright spots and is instead much more homogeneous. Panel D. This effect can also be seen by visual inspection of the heterochromatin markers directly. Marker positions are visibly more spread out and less strongly clustered together. Heterochromatin clearly undergoes structural changes upon irradiation.</p

Transmission electron microscopy images show GNPs being included into the cytosol but excluded from the lumina of intracellular vesicles, microbodies, the golgi apparatus and the endoplasmic reticulum.

<p>Further GNPs are preferentially accumulated in groups of varying extend. A. Overview of a group of GNPs (black arrow) inside the cytosol (Cy). The extracellular space (ES) and the nucleus (Nu) do not carry any GNP accumulations. B. Locality in the cytosol with a local GNP accumulation in the vicinity of components of the intracellular membrane apparatus (IM). C. Insert showing the homogeneous size of SmartFlares in a cluster.</p

3D image of fluorescently labelled γH2AX foci (pink) in a SkBr3 cell nucleus after irradiation of 4 Gy and incubation with 8 μl SmartFlare solution.

<p>The foci are represented with NIS-Elements. The cube’s edge length equals 20 μm. No special foci arrangement or distribution could be detected, independently from dose or GNP concentration.</p