DNA double-strand breaks (DSBs) can be induced by ionizing radiation and are known to be the most severe damages in the genome of a cell nucleus. The amount of DSBs simultaneously occurring is dependent on the radiation dose, the LET (Linear Energy Transfer) of radiation, the cell type, the radio-sensitivity of the cell, etc. Recent investigations have shown that DNA damaging is accompanied by an instant spatial reorganization of chromatin at and around the damaged site [1
] and an activation of the repair machinery. One of the first steps of chromatin modification after DSB induction is phosphorylation of the histone variant H2AX [4
] to γH2AX within a given neighborhood of the damaged site [5
]. Such foci seem to “tag” the locations of damaged DNA for the recruitment of proteins that are starting and processing the follow-up repair [8
]. At that point, a decision about the next procedure has to be made by the cell [10
]. Several factors such as cell cycle state, functional activity of genes, break position along the DNA sequence, temporal state of DNA compaction, number of simultaneously occurring DSBs, etc., are known to influence this decision and the consequences for a cell nucleus and the genome [10
At a very first glimpse, the cell has to decide between fast or error-free repair for each DSB within the first minutes after damaging by irradiation. One choice may be homologous recombination repair (HRR) [11
], which is a rather slow but error-free repair process. HRR needs an intact DNA sequence template of the homologous chromosome, along which a complementary strand can be reconstructed. In contrast to HRR, non-homologous end joining (NHEJ), a very frequently used repair process, may cause errors in the DNA base sequence but works much faster than HRR. Several specific proteins process the broken DNA ends by strand resection and re-connection of the broken ends at appropriately complimentary bases. HRR and NHEJ are the most often chosen pathways (for review, see [12
]). HRR may sometimes be suppressed within repetitive DNA units if the damaged DNA side is not relocated to the heterochromatin periphery. In these cases, single-strand annealing (SSA) takes place instead [14
]. It has also been shown that especially in cases of irradiation at higher doses (>2 Gy) and consequently more DBSs, the conventional NHEJ (c-NHEJ) may fail at some breakage sites and an alternative NHEJ process (a-NHEJ) is applied, which is a slow and error-prone repair process [13
On the one hand, HRR may be the first choice and preferentially used to keep the genome as preserved as possible. Only if HRR is insufficient (e.g., due to too many DSBs at higher doses) then NHEJ saves the situation since it is much faster. Recently, it has been shown that in G1 resection dependent NHEJ is possible, which seems to be different from resection processes in HRR [16
]. On the other hand in G2, most DSBs are repaired by NHEJ. So some people believe that NHEJ is always the first choice and only in those cases where NHEJ fails, HRR saves the repair [17
Each of these different repair processes requires a different cascade of proteins that are time dependent recruited and decruited during the repair process and are responsible for DNA strand end clipping and processing, end-to-end fixation, or correct sequence re-association [18
]. Although many steps of DNA strand processing and its relevant proteins are known and the interaction of proteins during the different pathways are often well understood, the question as to what makes up the cell’s decision for a certain pathway at a certain damage site remains insufficiently answered. Considering all the major factors that influence the repair pathway choice and the quickness of the cell response, this may suggest a still unknown or not sufficiently understood central mechanism behind the pathway choice. This mechanism should work at each damaged side individually. This means that physical as well as topological parameters of the DNA strand break environment may determine the repair pathway choice together with epigenetic conditions [8
]. This assumption has been recently supported by investigations showing that radio-sensitivity can be modulated by chromatin remodeling in daughter cells of irradiated samples [20
Assuming that the genome architecture and the architecture of repair complexes on the micro-and especially on the nano-scale become important for a repair focus region, not only novel techniques for a detailed analysis of spatial foci organization are required but also methods to categorize foci or sub-foci (clusters) and to compare each focus/cluster with each other independently of the cell or cell nucleus. Nano-scaled analysis has reasoned several transmission electron and super-resolution light microscopic studies in order to elucidate the spatio-temporal internal organization of repair foci and their chromatin surroundings with molecular resolution [3
]. Recently, it has been shown by super-resolution light microscopy, that γH2AX foci are built up by clusters that form nano-foci with different repair activities [23
] and that inside these nano-foci repair proteins are well organized [23
] whereas the chromatin environment is interacting in a characteristic arrangement [28
]. In addition, it has been shown that after radiation exposure and DNA damaging, Alu heteroduplexes may undergo Alu/Alu recombination into a single chimeric Alu element by NHEJ [32
]. This may reason a dose dependent accessibility of ALU-sequence specific oligonucleotides (17mer uniquely binding to the ALU consensus sequence) as detected by SMLM [33
During recent years, it has been demonstrated that single molecule localization microscopy (SMLM) [35
] is an appropriate technique to elucidate conformations of molecular arrangements and their functional relevance in cell nuclei, cytosol, and on cell membranes [1
]. An embodiment of SMLM [39
] as being used in this article, applies standard fluorescent dyes for specific labeling that can be switched between spectral “on” and “off” states [40
] to spatial separation of molecules (“reversible photo-bleaching”). From a reversible dark state, the fluorescent molecules randomly return to the emission state and cause blinking events that can be separated from a continuously fluorescent background. Each position of an emitting fluorophore is represented by an Airy disc and can precisely be located as the center-of-mass (barycenter) of such a disc. This also allows the precise calculation of spatial distances between fluorescent molecules in the 10 nm regime [34
]. Using the matrix of the coordinates of fluorescent tags, all acquired positions can be visualized by an artificial “pointillist”, super-resolution image. In the images representing the point distribution, the effective resolution is only depending on the localization precision [43
]. Moreover, the images can also encode results of distance analysis evaluations or density measurements.
However, localization data sets (e.g., labeling molecules of γH2AX or methylation sides of heterochromatin such as H3K9me3) consist of tens or even some tens of thousands of individual point coordinates and their visualization and analysis is a separate challenge, since a point pattern does not automatically reveal a characteristic conformation or shape. In that way SMLM data fundamentally differ from conventional microscope images. While a conventional microscope provides an image with contours resolved with a scale of the order of 100 nm, SMLM is only producing a coordinate matrix with the positions of the fluorophores in the nanometer range. Such a pointillist representation requires a new approach to extract the relevant conformational information, in such a way that the point distribution is unequivocally transferred into a certain shape or better topology that may be also maintained under different perspectives and different deformations. This requires quantitative analysis using mathematical concepts.
Approaches for a quantitative point density, distance, or cluster analysis exist for SMLM [23
]. The analysis is restricted in scale to a certain order of magnitude and does not consider shape deformation. Quantifications on several orders of magnitude (for example in the range of a few nanometers up to several hundred nanometers) are hardly possible and cannot be easily compared according to typical characteristics. In order to overcome these restrictions, a novel mathematical approach is presented here, which analyzes SMLM data with methods of persistent homology [44
]. This has the advantage that both the geometric and the topological properties of given point distributions are considered [45
] and a parameter-free quantification of the structural arrangement of a point distribution over several orders of magnitude is possible. Thus, the accuracy achieved by state-of-the-art SMLM can be used, not only for a point pattern analysis, but also for a structural analysis of molecular arrangements. The point distributions and thus the underlying structures (e.g., heterochromatin distributions or γH2AX foci/clusters) can now be directly compared independently of a cell nucleus whereby both nano-scale and micro-scale level differences are considered. Mors theory and set theory allow for a quantitative comparison of two point distributions and a categorization according to a similarity measure. This higher degree of abstraction compared to image visualization achieves a higher degree of information and functionally relevant insights.
In order to demonstrate the power of this new mathematical approach for SMLM data, a proof of principle has been applied to analyze and categorize clusters of γH2AX repair foci according to their structure and chromatin vicinity. The packaging degree of the DNA has consequences for the repair process. This is especially true for the densely packed heterochromatin because the damaged DNA has to be histone free for the repair and must also be accessible for the repair protein complexes [46
]. It has been shown that DSBs in the heterochromatin region are usually be repaired at the border of heterochromatic chromatin regions [1
] whereby the methylation degree typical for heterochromatin remains unchanged. Re-organization within heterochromatic regions is necessary to make the damage accessible for repair proteins. Therefore the proximity to heterochromatin was the parameter that was correlated to the internal topology by means of the topological data analysis (TDA). The topological representation of each focus was compared to each other and the degree of similarity was determined.
DNA double strand repair uses fascinating mechanisms that have been developed during evolution towards two different directions fast and error tolerable or slow and exact [12
]. After having induced a DSB by ionizing radiation, chromatin re-arranges and H2AX phosphorylation occurs in the damage environment [1
] within a few minutes accompanied by the recruitment of proteins specific for a certain repair mechanism. During the last decades modern techniques applied in radiation biology and radiation biophysics, have offered detailed insights into the protein interactions and cascades along the different repair pathways [8
]. These investigations have completed our understanding about repair processes and boundary conditions that favor repair towards either end-joining processes such as NHEJ or recombination processes such as HRR. The better our understanding has become the more the question becomes urgent how a cell can decide which repair pathway should be the appropriate one at a certain damage side. Cells can simultaneously use all repair pathways in a cell nucleus at different damaged sites.
The repair pathway choice could be random for instance. This, however, is not convincing since it has been shown that whenever it is functionally relevant for cell survival a fast repair process is addressed.
Assuming a non-random pathway choice at a given damaged side raises the question for a fast, easy and therefore always functionally available, and everywhere implemented mechanism for the cell’s decision. Beyond several epigenetic approaches, people have started to discuss whether such a mechanism may be encoded in the architecture of chromatin around the damaged site (key note) lectures and discussions at the joint ERRS (European Radiation Research Society) and GBS (Gesellschaft für Biologische Strahlenforschung) conference 2017 in Essen, Germany). This would, however, require deeper insights into the internal structural organization of a repair focus of a typical order of size of about the resolution limit of a light microscope (about 200 nm).
Recent applications of electron-microscopy [25
] and super-resolution light microscopy such as SMLM, STED or GSDIM [1
] have demonstrated that it is feasible to study single molecular arrangements within a repair focus. With improving resolution of microscopy and data evaluation of structures on the meso- and nano-scale, the question for best suited analysis parameters and potentially useful classification criteria of repair foci and damaged chromatin sites has become important.
Here, we have introduced a rather unconventional approach for SMLM data analysis of γH2AX foci and their chromatin environment. This approach makes use of the advantage that SMLM data can be evaluated without image production and image processing [34
]. This novel approach combines a geometrical evaluation based on Ripley’s distance and cluster analysis with persistence homology for similarity classification of repair cluster loci. Although the mathematical principles behind this approach are well established, it is the first time that topology has been used as biologically relevant criteria. This may allow to circumvent locally occurring deformations in the analysis and to extract a parameter pattern that is scale independent and can categorize repair foci into structural classes. Here we have demonstrated a very first proof-of-concept experiment, in which we could show that the category of HC associated γH2AX clusters are highly similar in terms of both topology and geometry whereas nHC associated clusters are completely dissimilar. This topological similarity was independent of the irradiation doses. However, only one early repair time was considered. In future experiments other later repair times may also be considered in order to find out whether a change in topology occurs during repair.
In addition clusters that do not fit in size could be ruled out also by the topological similarity measure. Here, however, the practicability of this method has been demonstrated; therefore, the foci selected by the presented method have not been sorted out. The number of 400 clusters used for this analysis has been large enough that outliers, such as the mentioned foci, are not significant. On the other hand 400 clusters are manageable by interactive control of the experiment.
The aim of this article was to demonstrate the methodological approach. In future experiments systematic studies for further parameters such as other chromatin types (e.g., euchromatin, ALU sequence regions etc.) in the environment or assignment to the follow-up proteins in the repair pathway (e.g., MRE11, Ku70, Ku80, 53BP1, Rad51, etc.) are necessary in order to understand the correlation of γH2AX clusters and other clusters formed by further recruited proteins during repair. Furthermore the application to other cell types, different repair times and radiation types (e.g., high LET ions, α-particles, β-particles etc.) would contribute to a conclusive knowledge of pathway choice and the correlation to structure and topology. This will be subject of next years’ investigations.