Single Molecule Localization Microscopy Analyses of DNA-Repair Foci and Clusters Detected Along Particle Damage Tracks

High-LET (Linear Energy Transfer) particle irradiation as being provided from heavy ion accelerator facilities has an increasing impact on bio-medical research and cancer treatment. Nevertheless, there are a lot of open questions concerning the understanding of damaging mechanisms and repair processes within the light of radio-sensitivity and thus, individualized medical applications. The three-dimensional architecture of genomes on the meso- and nano-scale acts in combination with epigenetic gene activation as an important player of gene regulation and fundamental biological processes such as DNA damage response and repair. So far only little is known about the impact of high-LET particles on the chromatin architecture along the passing track when they are “lumbering” through the cell nucleus. How does a cell nucleus manage such complex damages and re-organize the chromatin toward functionally intact units? Is there a radio-sensitivity related difference in this reaction? Here, we present some approaches to investigate spatial and topological parameters of chromatin to glimpse some aspects related to these questions. Two cell lines, a radio-resistant glioblastoma and a radio-sensitive fibroblast cell line, were used and irradiated by 15N-ions in 90° and 10° radiation beam geometry. Nano-probing of particle induced damage sites along particle tracks, and the recruited DNA repair proteins (as presented here for 53BP1 and Rad51) in combination with super-resolution Single Molecule Localization Microscopy (SMLM) are powerful methods for geometric and topological analyses to study particle related mechanisms of chromatin conformation and repair complexes in single cells. We used variable tools for such investigations based on image free high precision SMLM, nano-scaled molecule distribution analyses, appropriate metrics following Ripley’s distance frequencies and cluster formation analyses, as well as topological quantifications employing persistence homology. The data reveal a cell type specific nano-architecture of DNA damage foci along particle tracks and their dynamic molecular re-arrangements during repair. Comparing the topology of repair foci by persistence homology suggests similarities of repair cluster formation along given particle tracks. Our studies contribute to the molecular understanding of cellular radiation response at sub-light microscopic chromatin levels; thereby showing how chromatin architecture around complex damage sites and repair foci nano-architecture may contribute to ongoing repair processing. The methodological approach presented here may give a basis for improved biological dosimetry or radiotherapies in the future.

High-LET (Linear Energy Transfer) particle irradiation as being provided from heavy ion accelerator facilities has an increasing impact on bio-medical research and cancer treatment. Nevertheless, there are a lot of open questions concerning the understanding of damaging mechanisms and repair processes within the light of radiosensitivity and thus, individualized medical applications. The three-dimensional architecture of genomes on the meso-and nano-scale acts in combination with epigenetic gene activation as an important player of gene regulation and fundamental biological processes such as DNA damage response and repair. So far only little is known about the impact of high-LET particles on the chromatin architecture along the passing track when they are "lumbering" through the cell nucleus. How does a cell nucleus manage such complex damages and re-organize the chromatin toward functionally intact units? Is there a radio-sensitivity related difference in this reaction? Here, we present some approaches to investigate spatial and topological parameters of chromatin to glimpse some aspects related to these questions. Two cell lines, a radio-resistant glioblastoma and a radio-sensitive fibroblast cell line, were used and irradiated by 15 N-ions in 90°and 10°r adiation beam geometry. Nano-probing of particle induced damage sites along particle tracks, and the recruited DNA repair proteins (as presented here for 53BP1 and Rad51) in combination with super-resolution Single Molecule Localization Microscopy (SMLM) are powerful methods for geometric and topological analyses to study particle related mechanisms of chromatin conformation and repair complexes in single cells. We used variable tools for such investigations based on image free high precision SMLM, nanoscaled molecule distribution analyses, appropriate metrics following Ripley's distance frequencies and cluster formation analyses, as well as topological quantifications employing persistence homology. The data reveal a cell type specific nano-architecture of DNA damage foci along particle tracks and their dynamic molecular re-arrangements during repair. Comparing the topology of repair foci by persistence homology suggests similarities of repair cluster formation along given particle tracks. Our studies contribute to INTRODUCTION All over the Universe, matter is subjected to extreme conditions as for instance high temperatures, pressures, and densities. Stellar collisions and explosions prepare ultra-fast heavy ions interacting with any material crossing their ways. With mankind´s quest to discover space and our planetary system not only by vehicles but also by manned space missions, an understanding of interactions of these heavy ions with biological and especially cellular systems has become an urgent demand to science [1]. Modern nuclear accelerators enable researchers to create radiation conditions of space in the earth-based laboratory. Particle beams of various elements at different intensities and qualities can be generated and applied on cells, tissues, organs or organisms. While protective systems to control or even to avoid accidental exposure of humans on space missions are under development [2,3], targeted applications as for instance the powerful treatment tool against aggressive tumors especially brain tumors, have been established worldwide in medicine [4,5].
Up to now research has delivered a huge amount of knowledge and findings of biological, epigenetic response to low-LET (Linear Energy Transfer) photon and high-LET particle irradiation; thereby a lot of questions concerning damaging profiles and repair response remain unanswered [6][7][8][9][10]. Scientific results improving the understanding of mechanisms behind damaging and repair are demanded in order to optimize space mission planning or to individualize radiation treatment [11]. Therefore not only defined radiation experiments in accelerator facilities are required but also novel tools to elucidate components of epigenetic control and their impact on radiation response.
Radiation induced DNA damages are depending on the dose, dose rate, LET, radiation type, cell radio-sensitivity, DNA repair capacity, etc. In contrast to low-LET photon irradiation which induces DNA damages in a coarse gain pattern, high-LET particles (e.g., protons, α-particles, heavy ions) pass the chromatin in linear tracks [12] along which a complex damaging process happens, which locally may lead to an overload of single (SSB) and double strand breaks (DSB) [13][14][15]. The most severe damages being created are complex double-stranded breaks (DSBs) of the DNA molecule [16]. These complex lesions consist of several SSBs and DSBs generated in close mutual proximity in combination with other types of DNA damages [17] and highly challenge all repair mechanisms being available for cellular survival [18][19][20]. Multiple complex DSBs often remain unrepaired which leads to cell death, the treatment effect envisaged in successful radiation cancer therapy.
On the other hand, escaping cell death, the complexity of lesions increases the risks of dysfunctional cells with mutations and chromosome aberrations, a serious problem, which medical radiation treatment schemes always have to avoid [21][22][23]. In contrast to cell death being required for heavy ion radiation therapy, radiation protection in the field of long-term space missions planned [2] should save the cells in their best functional conditions. These extremely opposite demands show the urgent need for further investigations in order to better understand the mechanisms of DNA damaging and repair.
In general, the genome is responding to DSBs by specific phosphorylation of histone H2AX in a 2 Mbp region surrounding the chromatin damage site, which can be visualized in form of socalled γH2AX foci [24,25] against which specific antibodies are available. Inside these foci, the cell starts to repair the damage by recruiting and releasing a complex network of proteins along given repair pathways. The main repair pathways are the canonic non-homologous end-joining (c-NHEJ), the homologous recombination (HR) and the less precisely classified alternative (or backup) pathways, such as Ku-independent non-homologous end-joining (a-NHEJ), single-strand annealing (SSA) or microhomology-mediated end-joining (MMEJ) [26][27][28][29][30].
All these repair pathways are functioning differently and recruit different series and amounts of repair proteins to the initially induced γH2AX damage foci. The main differences in the chosen pathways are the speed and quality of repair. HR is very precise in maintaining the base sequence of the damaged region exactly; thereby it is slow since an appropriate DNA sequence template has to be arranged, the damaged sites have to be resected correctly, and nucleotide by nucleotide has to be reconstructed. In contrast to HR, c-NHEJ is fast but tolerates the loss of some nucleotides in the new strand after trimming and "sticking" the broken ends together. a-NHEJ and other alternative pathways only seem to play a significant role after multiple damaging by high dose exposure. Due to a lack of availability of enough repair proteins, broken ends are repaired under omitting some typical c-NHEJ proteins with the consequence of being slow and more error prone. Repair errors also occur due to illegitimate recombination between short homologous sequences or repeats.
At a first glimpse, it appears that a cell decides individually or even randomly which repair pathway is used at a given damage site. However, a more detailed view on repair processes reveals that repair pathway selection is depending on several conditions like the phase of the cell cycle, the chromatin structure and compaction at the site of damage, the complexity and multiplicity of DSBs, the general radiation sensitivity of the cell type, and potentially several other factors [19,[31][32][33][34][35][36][37][38][39][40][41][42]. All these factors contributing to repair pathway choice at a given damage site in a given cell type require a complex epigenetic controlling system [9,10] that may interact according to so far not fully understood rules.
Beyond the "classical" epigenetic systems following so far known epigenetic protein pathways, another level of epigenetic function and control appears to be relevant for further consideration especially in case of complex damaging processes. This epigenetic system, not pushed into the focus of investigations, yet, is the chromatin architecture. Chromatin architecture is known to be functionally organized [43,44] on the micro-, meso-and nano-scale, and its relaxation and precisely regulated re-arrangements were observed at damage sites [6,45]; reviewed in Ref. 8 [9,10]. On the sub-micro scale, local chromatin architecture changes after DNA-damage induction and along repair processes. In the context of chromatin architecture, two perspectives have to be considered: a) the broken chromatin strands with their chemically different ends, environment of H2AX phosphorylation and variable mobility [6]; [8], and b) the spatial organization of repair protein during formation and release of repair complexes (visible as repair foci). Understanding how spatial arrangements of chromatin and recruited proteins impact DNA repair, requires a precise analysis of geometry and topology of single molecules of γH2AX as well as of by repair proteins forming foci, e.g., MRE11, 53BP1, RAD51, etc. Counting of these foci, generally known as Ionizing Radiation-Induced Foci (IRIFs), by means of light microscopy has become a well established measure for intra-cellular dosimetry [14,46,47]. Until recently, the investigations of nano-architecture of chromatin and repair complexes had to rely on electron microscopy [48][49][50], which, however, suffers from serious limitations and disadvantages. A breakthrough in the field was brought about by the development of super-resolution light microscopy techniques [51,52], based on specific labeling of the target molecules that allowed to overcome Abbes' diffraction limit [15,45,[53][54][55][56].
For low-LET radiation, the numbers of DSBs and labeled γH2AX foci are directly correlated, although it is still under debate whether and how many DSBs are joined together within one IRIF. For high-LET radiation, it has become obvious that foci are enlarged and their number is considerably below the predicted number of DSBs [14,57,58]. This phenomenon can be explained by overlapping and aggregation of several foci in a not well defined way. The internal architecture and complexity of repair foci after high-LET particle traversing, however, have not been systematically and thus satisfyingly investigated. The spatial structure, organization, and topology of IRIF thus remain to be intensively discussed. Open questions such as the arrangement of elementary or functional foci sub-units call for further research on the nature and typical parameters (shape, size, quantitative composition, etc.) of these still mysterious structures and their relationship to particular repair pathways.
Investigations using super-resolution light microscopy or electron microscopy revealed sub-structures like clusters within γH2AX or repair protein (e.g., 53BP1, MRE11, Rad51, pATM etc.) foci. These cluster can be observed independently of nature or the LET of radiation [49,54,56,[59][60][61][62][63][64][65]. For low-LET irradiation, the number of repair-focus sub-units (clusters) seems to better correlate with the number of DSBs and damage complexity than the number of IRIFs detected at the microscale [54]. In addition, after low-LET irradiation, γH2AX cluster sub-units were found to show high topological similarity provided they were closely associated to heterochromatin [66].
For high-LET irradiation, beyond the analyses of γH2AX foci and sub-units [15,16], it has become obvious that the architecture and topology of the clusters of the follow-up recruited repair proteins is important with respect to the question of spatial organization of molecules as epigenetic control systems. 53BP1 foci were analyzed in more detail [15,55,56] after high-LET radiation exposure. 53BP1 is involved in NHEJ and acts as a stabilizing factor during HR [67]. 53BP1 binds to methylated regions of histones where it interacts with other repair proteins, for instance to promote NHEJ. During such interactions, 53BP1 could be displaced from the primary damaged sites [68,69] opening them for instance for access of BRCA1 or CtIP.
SMLM [70,71] has been successfully applied to study DNA repair and cluster formation of γH2AX molecules under low-LET radiation condition [53,54,72] and during long-term cell culture under folate deficiency [73]. Foci and sub-focus clusters of repair proteins were also investigated after particle irradiation [15,55,56].
SMLM of fluorescently tagged 53BP1 molecules was performed and clusters of these tags were determined as subunits of repair foci, so that the formation and relaxation of these clusters could be studied during the repair period [15,55].
In the article presented here, we continue in the analysis of 53BP1 clustering after 15 N particle irradiation with the focus on cluster size and environment during repair. In addition, we will show that persistent homologies of clusters as being calculated by topological methods of mathematics show different degrees of similarities in cell lines of high and low radio-sensitivity. These tools exemplarily presented here may be used to classify foci with respect of their follow-up repair mechanisms. Nitrogen ions were used as they are relevant for both space research and radiotherapy. They are present in galactic and solar cosmic radiation [74] and are extensively produced when cosmic radiation interacts with the atmosphere [75]. Interestingly, Pioneer 10 spacecraft have revealed increased (up to the factor of 20) amounts of N (and O) ions relative to their abundance in galactic or solar cosmic rays, pointing to specific sources of this component of cosmic radiation in the Universe [76]. N-ions are also generated during hadron radiation therapy and may significantly contribute to the patients' absorbed dose [77]. Nitrogen ion beams have been also studied as promising particles for radiotherapy [78].

Cell Culture and Specimen Preparation
Cell culturing and specimen preparation has been described in detail elsewhere [14,15,55]. In brief: Primary neonatal human dermal fibroblasts (NHDF) and human U87 glioblastoma cells . This approach ensured that cells of the same condition (proliferation phase, cell cycle distribution, and physiological status) were analyzed at all post irradiation time point. For fluorescence labeling, the cells were washed twice in 1x PBS, permeabilized in 0.2% Triton X-100 at RT, washed again three times in 1× PBS, and incubated in 2% bovine serum albumin (BSA) for 60 min at RT. Primarily rabbit anti-53BP1 (ab21083, Abcam) antibodies or rabbit anti-Rad51 (ab63801, Abcam) antibodies, respectively, were added to the cells and the cells were rinsed with 0.2% Triton X-100 and washed three times with 1× PBS for 5 min at RT. The secondary antibodies, AlexaFluor 594-conjugated goat anti-rabbit (Johnson Laboratories) (53BP1), or Alexa Fluor 568-conjugated donkey anti-rabbit (ThermoFisher Scientific) (Rad51), respectively, were applied to the cells for 30 min and again the cells were washed three times in 1× PBS for 5 min and counterstained with DAPI. After washing the slides three times in 1× PBS for 5 min each, the cover slips were air dried, and the cells were embedded in ProLong Gold ® (ThermoFisher Scientific) for SMLM. Prolong Gold was left to polymerize for 24 h in the dark at RT before the slides were sealed with nail polish and stored.

Specimen Irradiation
As described in detail elsewhere [14] 15 N ions were accelerated using a U 400M isochronous cyclotron in the Flerov Laboratory of Nuclear Reaction at the Joint Institute for Nuclear Research (JINR, Dubna) [79]. The radiation conditions applied are summarized in Table 1.
In the experiments, cells were exposed to an average of about 2 and 25 particles per nucleus for 10°and 90°irradiation, respectively. This corresponds to the doses of 1.3 Gy (10°i rradiation) and 4.0 Gy (90°irradiation). The values were calculated as described in Ref. 80; for the average nuclear area of 186 μm 2 . The non-homogeneity within the irradiation field of 14 mm in diameter was less than 5%, as monitored using five identical flow-type ionization chambers; the central chamber served as the monitor of the radiation dose [79]. The energy and corresponding LET values of ions at the plane of the cell monolayer were calculated using LISE++ software [81].
The cells were irradiated on glass coverslips at Petri dish bottoms tangentially or perpendicularly. The side of the coverslips covered with cells was oriented toward the ion beam so that the cells were hit by the particles before the beam entered the culture medium in the Petri dish. During irradiation, the cells were kept in a thermostable box, ensuring a constant temperature of 37°C and prevention from infection during the whole procedure. After irradiation, the cells were immediately placed back into the incubator until fixation. For microscopic analyses, the cell nuclei were fixed at numerous periods of time after irradiation (5 min-24 h PI), as explained in detail in paragraph Cell Culture and Specimen Preparation.

Single Molecule Localization Microscopy
A detailed description of the SMLM instrument has been published elsewhere [53,54,64,82]. In brief: The microscope has an oil-objective (100×/NA 1.46) and four lasers 405 nm/ 491 nm, respectively. Measurements were done with the 561 nm wavelength laser. An in-built electron multiplier (EM-gain) enhances signals detected by the EmCCD camera (80 nm/px). The microscope was installed on a Smart- Table compensating for vibrations, and provided with a water-cooling system to keep constant temperature and to minimize drifts. Lasers were controlled using the "Omicron Control Center" program and image acquisition was carried out using "Live Acquisition v. 2.6.0.14" software. For thermal stabilization, first measurements with the microscope were performed 1 h after booting.
A protocol for automatized localization image acquisition was used. In brief, an initial excitation switched most fluorophores into a reversibly bleached state; then 2,000 single image frames were taken at maximum laser power with an exposure time of 100 ms per image frame. Wide-field images were always taken before localization image acquisition. For each time point during the repair period, a minimum of 23 cells was imaged. The image data stacks were stored as *.tif stacks and subjected to further computational analysis as described below.

Data Evaluation and Image Processing
The local positions of the detected dye molecules of the antibodies were obtained from registration of molecular blinking events according to an algorithm described elsewhere [82], which is based on subtraction of the brightness values of two successive frames. This method enables the differentiation of the blinking events from the background. A so-called "Orte-Matrix" was produced, which contained information about the signal amplitude, the lateral x-and y-coordinates, the standard deviations in the x-and y-direction, position errors, etc. This "Orte-Matrix" was the starting data set for all further evaluation procedures and for the construction of artificial images of the cell nuclei.
Mathematical procedures and algorithms were applied on these raw coordinate data of the detected labeling points instead on processed images. The data analysis program is modularly built up and was programmed in Python (https:// www.python.org) (Gote, Neitzel et al., manuscript in preparation). Several algorithms developed are based on Ripley's point-to-point distance frequency measure structure information [84] or use DBSCAN [85]) in order to obtain information whether the fluorophores were localized in clusters. The point-to-point distances were measured by distances from each given central point to its peripheral ones. Without regarding absolute position information, the graphical display of absolute and relative distance frequencies makes it possible to discriminate between specimen structure signals and background signals. The envelope function of the distance frequency histogram is correlating to functional arrangements of points [53].
A homogeneous point-to-point distance distribution leads to a linear increase in the distance frequency histogram. The slope of the straight line is scaled with the number of detected points. If the points appear in clusters, smaller distances are more frequent resulting in a peak. The width of the peak gives the maximum distance between two points in the cluster and thus the cluster diameter. The area under the peak is a measure relative to the point density in a cluster. The shape of the peak gives a measure of the homogeneity of the distribution of points in the cluster. If clusters are embedded in a pointillist background, the result consists of three parts: a) a homogeneous distribution (linear increase); b) a cluster distribution (peak) and c) a cross term or additional peak, which contains the distances between the points of two neighboring clusters.
According to the DBSCAN algorithm [85], clusters are compact regions of increased local density of points. The amount of all points inside a given radius around a point must have a minimum value to define a cluster. If any points inside such a cluster also meet the cluster definition they are attributed to the same cluster. The cluster size is the maximum area in which all points meet the cluster criteria. Inside clusters various characteristics can be examined and compared to the point distributions outside the clusters.
The following cluster parameters describing the minimum number of points within a given radius were interactively determined ( Table 2).
Novel analytical methods for 53BP1 cluster characterization were applied using procedures of persistence homology [66]. This method, using established calculations and mathematical operations, allows two point distributions, here the point distributions of 53BP1 clusters of two irradiation schemes, to be compared to each other in a cell-independent manner, thereby giving a mathematical measure of their similarity [86].
The major principle of this analysis for persistent topologies is to record properties of point patterns, which are invariant under certain deformations of the object. Mathematically these deformations correspond to continuous transformations of the topological space defined by the structures. For 53BP1 clusters, the attention was focused on two properties: a) the number of "components", which are independent from each other in such sense that connections between points only exist within the respective components; b) the number of "holes" of the structures inside the components. In algebraic topology, these properties are called the Betti numbers for zero-and one-dimensional simplicial complexes. They are the topological invariants that distinguish between different topological spaces.
SMLM data sets of repair foci are clustered point-sets for which components and holes can be defined [66]. In the following, this procedure is briefly described: A geometric relationship among cluster points is obtained by growing spheres of radius α around each point. Whenever two of these spheres mutually embed each-other's center, these centers are connected by a line. The connected points belong to the same component. With increasing radii of the spheres, more and more points are connected to previously disjoint components. Thus, the number of components is decreasing with increasing of the radius α. At the end of the procedure, a single component is remaining. For the definition of holes, the simplest polygon, the triangle, is appropriate. Whenever a component of three connecting lines of points forms a triangle, the area of the triangle is considered as a hole. With reducing the number of disjunct components, the number of holes is increasing and decreasing again.
The amounts of components and holes are depending on the value of α. For the formation of each component and each hole, a bar of a barcode pattern starts. The end of the respective bar is fixed at the disappearance of components and holes with increasing α [87]. The mathematical transfer of the spatially organized pattern of labeling points into barcodes contains information about components and holes in a compact and illustrative way. The sets of barcodes for each 53BP1 cluster were compared with each other and their similarity was calculated. The procedure used for quantification of the barcodes similarity is based on the Jaccard index [88]. A detailed description and illustration is presented in Refs. 66 and 86. The result of this normalized similarity measure is a value between 0 and 1, where a value of 0 means no overlap of two bars and 1 the identity of two bars. The similarity of barcodes of different dimensions is defined as the average of the individual similarity values of the bars of a cluster. Such topological comparisons are independent of the scale and the perspective on the clusters so that it is possible to compare variably large foci randomly orientated to the microscopic detection system.

RESULTS
The Neonatal Human Dermal Fibroblast (NHDF) line was studied as model of normal (non-transformed) cells with relatively higher radio-sensitivity while U87 glioblastoma cells were selected for their high radio-resistance [55] and aggressive cancer phenotype. In addition, forming the skin, NHDF fibroblasts are always irradiated by external radiation sources. Glioblastoma (U87 cells) then represents a tumor treated by radiation but with poor results only due to its high radioresistance. Both cell types were exposed to high-LET 15 N ions in two different geometries (i.e., under the angle of 10°and 90°as described in Materials and Methods) and IRIF formed by γH2AX and selected repair proteins (53BP1 and Rad51) were studied with SMLM in different periods of time post-irradiation (PI), ranging from 5 min PI to 24 h PI. Within the first minutes after irradiation, 53BP1 proteins were recruited to the damaged sites, visualized as γH2AX foci. 53BP1 foci provide information of the early recruitment of proteins for repair. In the previous studies [15,55], we have shown that DSB repair proceeds much slower in cells exposed to (high-LET) 15 N ions than in cells irradiated with low-LET γ-rays. Also, it emerged obvious that 53BP1 repair foci differ in their parameters for NHDF and U87 cells. Here, the 53BP1 data sets already investigated by SMLM [55] were further analyzed for structural clustering and topological similarity. In addition, data sets of the same cell types and radiation conditions were prepared also for Rad51 protein, which is, unlike 53BP1, selectively involved in DSB repair via homologous recombination. The first data of Rad51 labeling and spatial organization of Rad51 foci were elucidated and compared to results obtained for 53BP1 repair protein participating both in NHEJ and HR. Focus formation and clustering, persistent homologies, and structural changes during the post-irradiation (PI) period of repair were analyzed at several repair relevant time points (5, 15 min (10°only), 30, 45 min (10°only), 1, 2, 4, 8, 24 h).
In contrast to U87 cells, NHDF fibroblasts quickly recruited the majority of the 53BP1 proteins (∼60%) to the damaged chromatin sites along the particle tracks so that clusters have already been visible and well developed at 5 min PI, though their number progressively increased within the first 30 min PI. In both cell types, the cluster numbers were maintained until 8 h and then started to decrease; thereby a considerable proportion of clusters persisted even after 24 h PI (Figure 1).
U87 cells contained 53BP1 clusters also prior to irradiation (control samples) which was not observed in NDHF cells. In U87 cells, the formation of 53BP1 clusters in tracks was delayed up to 30 min PI and the relative number of recruited 53BP1 proteins was always less than 40% of the protein pool available. These results thus confirmed our previous observations [55]. In Figure 1, illustrative examples of SMLM images of 53BP1 foci/clusters are shown for the two cell lines, the two radiation schemes, and different periods PI. The left images show wide-field images of DAPI-stained nuclei with inserted point signals of individual 53BP1 molecules acquired with SMLM. The right columns then provide the corresponding SMLM images of the 53BP1 foci after cluster area determination. For the 10°i rradiation angle, the specimens of both cell lines showed characteristic tracks highlighted by dense arrangements of labeling tags. At later periods PI, the tracks partly dissolved and separated protein cluster units became visible dispersed, over the cell nuclei. In contrast to the 10°irradiation experiments, the 90°irradiation experiments showed more clusters irregularly dispersed over the cell nucleus. Since the dose was higher in these experiments, all these clusters may represent a separate particle track perpendicular to the image plain.
The following investigations are reasoned by the hypothesis that repair proteins form characteristic, similarly sized clusters at the damaged chromatin sites. These proteins are recruited to and released from clusters during the repair period; thereby their spatial topology can be expected to show high similarity provided the chromatin environment around the damage sites is also similar and the same repair mechanism has been activated. The correct topological arrangement is assumed to be required for the downstream repair steps so that the follow-up repair protein molecules could correctly access the damaged chromatin sites. The results presented here support these ideas and show by which mathematical operations the biophysical verification of the hypothesis could be approached.
To further investigate the dynamics and cluster formation of tagged 53BP1 molecules, Ripley distance analysis was applied that is based on relative frequency histograms of pairwise point distances. The distance frequency histograms were compared for all repair time points of each cell type and each radiation condition. In Figure 2, the results are presented. The controls of both cell lines showed a peak at smaller distances, which indicates these small distances occur very frequently, i.e., the labeled proteins are often arranged in such closely adjacent conformations ( cluster conformations). These clusters are embedded in a random distribution of points which can be concluded from the linearly increasing frequency of larger distances. Note that the histograms show the relative frequency of distances but do not give information about the absolute number of distances or clusters.
Shortly after irradiation, the formation of clusters increases in NHDF cells but not in U87 cells. Subsequently, from 1 h PI, the absolute cluster frequency was decreasing in NHDF cells. For longer periods PI (2-24 h), some clusters remained while the rest of protein labeling points followed a strong random distribution (Figures 2A,B). This behavior was found for both, the 10°and 90°i rradiation schemes, though it was less pronounced for 90°( compare Figure 2A vs. 2B).
The cluster and labeling point dynamics appeared to be different in U87 cell nuclei (Figures 2C,D). Significant clusters were found also in the non-irradiated controls, embedded within a random labeling point pattern. For the 10°irradiation scheme, the amount of labeling points was increasing and larger clusters were formed after 5 min PI ( Figure 2C). From 15 min PI until the end of the period of investigation (24 h), the clusters kept their size and remained. Some minor fluctuations within some randomly dispersed labeling points were observed. For the 90°i rradiation scheme, the control showed the same behavior as for the 10°irradiation scheme, separate clusters within an Frontiers in Physics | www.frontiersin.org November 2020 | Volume 8 | Article 578662 environment of randomly dispersed labeling points. However, after irradiation with the high dose (4 Gy), the situation was different as fluctuations in cluster formation and size appeared until 2 h PI ( Figure 2D). Between 2 and 24 h PI, a low clustering frequency within a strong random distribution of labeling points could be seen. These measurements, in conclusion, indicate that 53BP1 clusters are quickly formed after irradiation. With the progress of the early repair period (ending at about 30 min or 1 h PI) one part of the clusters becomes dispersed while the other part persists within a growing amount of randomly distributed proteins. These persistent clusters remained in cell nuclei until the end of the investigation period (24 h PI).
In the next step, we decided to analyze "remaining" 53BP1 clusters at 2 h PI in terms of the persistent homology and determined the degree of their mutual topological similarity.
Based on the pointillist information obtained by SMLM, we used this new analytical method for 53BP1 cluster characterization after high-LET 15 N ion irradiation for the first time. A cell independent, pairwise comparison of point distributions (here the point distributions of two 53BP1 clusters) with each other was elaborated for a selected ensample of clusters. For the evaluation, the following total numbers of clusters were considered ( Table 3): The resulting barcodes of 0 (components) and 1 (holes) dimensions were compared in both directions and a mathematical measure of their similarity was calculated and visualized in heatmap descriptions (Figure 3). For both cell types the similarity measure as being determined by the Jaccard index was very high for the components (>0.9) independent of the irradiation scheme ( Figures 3A,B, a). This indicates that the complex, ion-induced damages are marked with a specific repair cluster setup. On the other hand the similarity measure for the holes was below 0.5 for both cell types and radiations schemes (Figures 3A,B, b). Interestingly the similarity of holes was on average higher for NHDF ( Figure 3A, b) than for U87 cells (Figure 3B, b).
The similarity values obtained by averaging of components and holes values for each 53BP1 cluster are presented in Figures  3A,B, c. When the clusters of the 10°irradiations scheme were  compared, the Jaccard indices laid between 0.55 and 0.82 for both cell types. The frequency distribution was broad without a peak for NHDF cells whereas U87 showed a clear peak at 0.64 ( Figure 4). Comparing the clusters of the 90°irradiation scheme, the peak was at 0.63 for U87 cells. This value was also obtained for the comparison of the 10°with the 90°i rradiation scheme. For these two comparisons (90°vs. 90°, 10°v s. 90°), NHDF cells showed a bimodal peak distribution with one peak at 0.67 and another peak at 0.72 ( Figure 4). In general it can be concluded that the more radio-sensitive NHDF cells revealed a higher topological similarity in 53BP1 clustering than the more radio-resistant U87 cells. 53BP1 is known to be preferentially involved in NHEJ but it could also act as a stabilizing factor during HR. So in a very first approach we wanted to see whether under harsh damaging conditions occurring during high-LET ion irradiation, HR is used for DNA damage repair. Therefore we labeled γH2AX and Rad51 simultaneously in cell nuclei of the two cell lines under the 10°irradiation scheme. In Figure 5A, a typical example is shown. It was obvious that also HR was employed as a repair pathway for broken chromatin in the track. In these cases, the Rad51 signals were always completely embedded in a γH2AX environment. However, the frequency of Rad51 clusters was very different for the cells analyzed. For both cell types, nearly no Rad51 cluster was found in the control. An increase of Rad51 clusters emerged between 1 and 8 h PI for NHDF and between 2 and 8 h PI for U87. The number of Rad51 clusters at 24 h PI was again on the level of the non-irradiated control specimen ( Figure 5B).

DISCUSSION
High-LET particle radiation has a Janus-faced nature. On one side it is highly dangerous and risky, as for instance during space mission. Even single particles could have a significant damaging effect on individual cells, with an unpredictable outcome for astronauts on space missions. On the other hand, high-LET particles can inactivate cells deeply inside the patients' bodies, making them an ideal tool for radiation treatment, especially of brain tumors or tumors embedded in very sensitive (and potentially vital) tissues. Therefore radio-protection as well as radio-therapy require a better understanding of the processes which the cells employ to repair complex damage events along the particle track. Heavy ion accelerator facilities offer defined high-LET radiation conditions as for instance in terms of the particle type, dose, irradiation angle etc. Hence, particle accelerators allow precise and defined experiments on given cell models, which are a prerequisite for sophisticated systematic analyses of DNA damaging and repair upon specific irradiation conditions. Research opportunities offered by these facilities have therefore rocketed bio-medical research.
High-LET particles lumbering through the chromatin of a cell nucleus induce a very complex damage pattern highlighted by γH2AX foci and other foci of recruited repair proteins. So far it is neither known how many damaged sites associate and are eventually repaired within one focus (visible at the microscale), nor whether the foci have an internal nanostructure composed of smaller sub-units (clusters), representing a single damage each, which are potentially functionally organized. A correct repair of the associated broken DNA ends indicates that the relevant repair units may be smaller clusters, for some reason aggregated in foci. Otherwise, multiple damage concentrated within one repair focus, would promote miss-repair in a much higher extent than it is observed. Hence, it cannot be excluded that the hypotheses of "repair factories", postulated but not confirmed to explain DSB repair and formation of chromosomal aberrations at the microscale (reviewed in Ref. 8), will be revitalized at the nanoscale. Therefore, it is of high interest to better understand the spatial organization of repair foci and consequently the repair mechanism resulting from defined spatial arrangements of repair protein clusters. This has motivated us to perform sophisticated microscopy studies of repair protein foci along particle damage tracks by means of super-resolution SMLM. Systematic investigations have been started using the radiation facility at JINR Institute (Dubna, Russia) by applying different doses of various high-LET particle radiation types at different doses and under different irradiation angles to well established cell systems of different radio-sensitivity. In Ref. 55; we analyzed the abundance and recruitment dynamics of 53BP1 repair protein, which indicated significant differences in IRIF nanoarchitecture between radiosensitive normal fibroblasts (NHDF) and cancerous, highly radioresistant U87 cells. Here, we have continued these studies with a special focus on cluster formation and topological cluster similarity. Ripley distance frequency analysis in combination with calculations of similarity values after evaluation of persistent homology provided novel insights into the nano-architecture of repair foci that form at damaged sites in different cell types. For normal NHDF fibroblasts, our data on 53BP1 molecules within IRIF revealed cluster formation and relaxation that was comparable for the two different radiations schemes and doses applied. In contrast, U87 cells showed a more variable cluster formation with fluctuations during the repair time. Moreover, independently of dose and irradiation angle the topology of the clusters was highly similar for NHDF cells in comparison to U87 cells. The high topological similarity of 53BP1 clusters in NHDF may indicate that, for both applied irradiation schemes, the 53BP1 clusters forming along the ion-induced chromatin damage have a specific, thus potentially functional setup. One reason for the existence of this setup may be the presence of several complex damage sites within the clusters instead of one single DSB. Further, with 53BP1 being located in the perichromatin and interchromatin [61], the specific arrangement of 53BP1 may be caused by the chromatin structure. Similar to our findings, the presence of resembling substructures of 53BP1 foci has also been observed by Reindl et al., who found that 53BP1 foci are subdivided into nano-foci of a constant size, thence no difference was observable in the setup of the nano-foci after low-LET proton and high-LET carbon ion irradiation [63,89].
In addition, the comparison of the two cell lines (NHDF and U87) indicated that the loss of radio-sensitivity may be associated with a reduction of topological similarity of 53BP1 clusters. One possible explanation for this may be that, due to defects in DNA damage repair, U87 cells fail to build up clusters in a standard structured manner. In that case, the increased radio-resistance may originate from a "radiation adaptation" leading to cell survival with an unrepaired genome instead of more efficient repair [53]. As cancer cells often have modifications in their chromatin structure, another option would be that the characteristics in the repair cluster setup of U87 cells and their increased radio-resistance may be associated with chromatin re- arrangements characteristic for carcinogenesis in general or specifically for this cell type. Nevertheless, a combination of several phenomena seems to be the most probable explanation. In Ref. 55; we observed that the more complex 53BP1 clusters disappeared much faster from U87 cells compared to NHDF fibroblasts though the overall repair kinetics of both cell types was more similar. This could mean that while some repair pathways are defective, the others are augmented.
Here, we wanted to introduce novel technical and mathematical approaches. The results of 53BP1 SMLM analysis revealed the potential of these proposed approaches. Future investigations will therefore be directed not only to further analyses of the clustering and topological similarity of 53BP1 at other time points PI but also to systematic investigations on γH2AX foci that directly indicate the reaction of chromatin to (low-LET vs. high-LET) radiation damage.
In general, the structure of the chromatin and the arrangement of proteins involved in repair may influence repair process and even the pathway choice by determining the accessibility of the damage site for follow-up proteins [55,66,90]. It has been proposed that 53BP1 is excluded from the center of the repair region and relocated to the outer part, if the DSB repair is directed to HR. This reposition opens space for loading of particular HR proteins, such as Rad51 [63,67,69,91]. Hence, the structure of 53BP1 clusters may have a direct impact on the pathway selection. This correlation remains to be studied in future. As the first attempt to investigate the relationship between a specific topology of 53BP1 clusters, chromatin architecture at the damage sites, and initiation of HR, we have checked whether the HR marker, Rad51, is recruited to the damage track. In order not to find a Rad51 cluster or focus just by chance somewhere in the nucleus, we irradiated the cells in a sharp (10°) angle, which allowed us to visualize particle tracks trough the nucleus (using γH2AX as the damage marker) in the x-y plane of the microscope with much better resolution compared to 90°irradiation [14]. Indeed, during later repair times we found a considerable increase of Rad51 clusters that colocalized with γH2AX, indicating an increase in HR activity. This may be surprising since the harsh complex damage generated by high-LET particles could be expected to be a very challenging target for HR. On the other hand there seems to be special chromatin conditions that favor HR repair at high-LET damage sites. So far this data on the repair pathway selection at specific DSB sites are preliminary but indicate the need of further investigations in order to better understand how chromatin architecture affects chromatin functionality in relation to DNA damage repair. As presented here, powerful mathematical procedures applicable to SMLM data of repair processes are available that will shed new light into the shadow of complex damage events along particle tracks. As well, modern particle accelerators offer systematic evaluation of damage events induced by different types of precisely defined high-LET particle radiation.

DATA AVAILABILITY STATEMENT
All datasets presented in this study are included in the article.