Development of a robust DNA damage model including persistent telomere-associated damage with application to secondary cancer risk assessment

Mathematical modelling has been instrumental to understand kinetics of radiation-induced DNA damage repair and associated secondary cancer risk. The widely accepted two-lesion kinetic (TLK) model assumes two kinds of double strand breaks, simple and complex ones, with different repair rates. Recently, persistent DNA damage associated with telomeres was reported as a new kind of DNA damage. We therefore extended existing versions of the TLK model by new categories of DNA damage and re-evaluated those models using extensive data. We subjected different versions of the TLK model to a rigorous model discrimination approach. This enabled us to robustly select a best approximating parsimonious model that can both recapitulate and predict transient and persistent DNA damage after ionizing radiation. Models and data argue for i) nonlinear dose-damage relationships, and ii) negligible saturation of repair kinetics even for high doses. Additionally, we show that simulated radiation-induced persistent telomere-associated DNA damage foci (TAF) can be used to predict excess relative risk (ERR) of developing secondary leukemia after fractionated radiotherapy. We suggest that TAF may serve as an additional measure to predict cancer risk after radiotherapy using high dose rates. This may improve predicting risk-dose dependency of ionizing radiation especially for long-term therapies.


Model Formulation
The models are implemented in systems of differential equations with events: where c determines the percentage of initial complex DSBs, k DSB and k TAF determine the number of DSBs and TAF per absorbed irradiation dose D [Gy], respectively, square brackets [] indicate optional parameters/variables, and <,> indicate alternatives. The characteristics of the candidate models are listed in Table 1, where column names indicate alternative parameters and components. Bold model components indicate the corresponding free parameters that were either fitted to data or set to zero, depending on the model candidate. All other components were either set or calculated. At > 0 T AF , S i and C i were discretely set from their initial values to new values using respective events. The state variables have the unit 'average number per cell'.     14. The SSR after parameter estimation is plotted versus scanned parameter values. 95% confidence region is calculated by F-ratio test (grey solid line). The minimum objective value reached is shown at bottom (grey dashed line) and the corresponding estimated parameter value is shown by a bold dot. Parameter identifiability analysis results showed no structural non-identifiability, absence of a flat SSR profile, in model Nr. 14. It also indicates that 4 parameters out of 13 are practically identifiable. Figure S4: Profile likelihood-based parameter identifiability analysis for models Nr. 8. The SSR after parameter estimation is plotted versus scanned parameter values. 95% confidence region is calculated by F-ratio test (grey solid line). The minimum objective value reached is shown at bottom (grey dashed line) and the corresponding estimated parameter value is shown by a bold dot. Parameter identifiability analysis results showed no structural nonidentifiability, absence of a flat SSR profile, in model Nr. 8. This indicates that 5 parameters out of 7 are practically identifiable.

Quantification of H2AX foci time series from published papers
We quantified the experimental results already published by Hewitt et al. [1] abd Fumagalli et al.
[2] using the free software "Plot Digitizer" under the terms of the GNU General Public License.

Data scaling
The absolute number of quantified foci is hardly comparable among experiments from different laboratories, because of differences in the technical equipment, staining protocols and actual foci counting procedures. To make our data comparable to the data from Hewitt et al. (2012) we assumed that the total number of foci 24h after 10Gy radiation was the same in both experiments ( Figure 2D) and scaled our data accordingly, excluding the initial time points, which were left unchanged. For scaling our 2.5 Gy time series we used the same approach, using a linear interpolation between measured H2AX foci 24h after1 Gy and 5 Gy irradiation ( Figure 2D, closed square).

Extended consensus H2AX foci time series for 20 Gy
The  Figure S2 therein). Therefore, we reasoned that especially the longterm data from Fumagalli's BJ cells can used for MRC5 cells as well. Moreover, there was no remarkable difference in absolute numbers between Hewitt's MRC5 data and Fumagalli's BJ data at later time points: for 10 days after 20 Gy both measured approximately 9 foci per nucleus on average. Therefore, we combined the two time series taking the average of both in case of overlapping measurements. Table S3 shows the combined time series with indicated data sources.

Quantification of H2AX foci time series from fluorescent microscopy
The H2AX  foci quantification was performed automatically using custom written algorithm implemented in MatlabR2008b (see http://www.mathworks.com). In addition, we utilized Image Processing Toolbox of Matlab and ImageJ 1.45s as plug-in. ImageJ is a freely available image processing program that we obtained from http://imagej.nih.gov/ij/. For bi-directional communication and data exchange between Matlab and ImageJ we used a Java package MIJ obtained from the web page http://bigwww.epfl.ch/sage/soft/mij/.
The algorithm used for foci quantification includes following steps: 1. Convert an RGB image with both nuclei and foci to double precision and split into two channels: blue channel for getting nuclei image, green channel for getting foci image. 2. Create a nuclei mask applying following procedures to the nuclei image: 2.1. correct possible non-uniform illumination using top-hat filtering (imtophat with structuring element 'disk' of radius 3 pixels in Matlab In Figure S7 and Figure S8 we visualized the result of foci count in nuclei cropped from representative images. Images were selected from three experimental repetitions. Foci, which were recognized and counted by the algorithm, are marked by red frames. Figure S7: The visualization of foci count in nuclei of immunofluorescent stained MRC5 cells after 1, 3, 6, 24, 48, 72, 168 hours post 2.5 Gy irradiation. Images of nuclei were picked from three experiment repetitions. Foci, which were recognized and counted by the algorithm, are marked by red frames. Figure S8: The visualization of foci count in nuclei of immunofluorescent stained MRC5 cells after 1, 3, 6, 24, 48, 72, 168 hours post 10 Gy irradiation. Images of nuclei were picked from three experiment repetitions. Foci, which were recognized and counted by the algorithm, are marked by red frames.