DSBs rejoining kinetics

Analytical-numerical models of DSB repair exist that focus on chromosome aberra- tions formation (see for exampleSachs et al.,1999a) and mis-rejoining of DNA fragments

(Radivoyevitch et al.,1998b). A novel approach that assumes initial random breakage

and supports illegitimate end-joining, based on proximity of repairable DSB ends is being developed by Hill and Johnston (unpublished). In their model, Hill and Johnston simulate low doses of sparsely-ionising radiation and the formation of several types of simple and complex aberrations, making quantitative predictions that can be tested experimentally with fluorescence in situ hybridization (FISH) techniques. Unfortunately, these sophisti- cated computer models of DSB rejoining are either too accurate for PFGE, which also does not represent the best tool for low-dose investigations of chromosome aberration formation caused by mis-repair, or are not correctly applicable to the conventional PFGE data of total DSB rejoining, because of the distortions caused to fragmentation analysis by the PFGE background damage.

As for the interpretation of experimental data of initial DNA fragmentation, in this project there has been a need to describe in simple terms, both qualitatively and quan- titatively, the results that have been collected during the experimental part of this same project. Background damage in PFGE and how to treat it has played a central role, also in fragmentation analysis of repairing DNA, hence a correct method of analysis of ex- perimental data that have not been corrected for the background damage, rather than a sophisticated rejoining kinetics model, was needed.

3.3.3.1 Modelling radiation induced DSB rejoining kinetics

Background DSBs are presumably not present as frank DSBs in viable cells, so re- joining of radiation-induced DSBs only has been considered in the computer-simulations. Part of the discussion focuses on this particular issue, §6.1. PFGE experimental data of initial DNA fragmentation do not allow us to distinguish between control and radiation- induced DSBs. If experimental data of initial fragmentation of DNA are to be used as input data to the rejoining-simulations, a method must be found to distinguish radiation- induced breaks from background breaks. To distinguish background DSBs among the to- tality of the breaks present, a ‘recognise and tag’ approach was developed and employed

first. A computer-program has been written that first reads the control fragmentation pat- tern and generates a collection of control fragments in single cells that conforms to the experimental frequency histogram, using the routines described earlier in§3.3.1.1. The procedure then generates a second collection of DNA fragments that conforms to the measured distribution of the totality of fragments, that is the fragments that are delimited by DSBs of any type, reading from the experimental data measured on the irradiated samples. This second collection is generated as described before, only the data relative to fragmentation induced by both background and radiation damage are used as input. After these two collections ofDNAfragmentsare converted to the corresponding col- lections ofDSBs (the programming objects described in§3.3.1.1and in listingA.1), an- other program procedure attempts to recognise, among the totality of the breaks present in the second collection, those that are distributed approximately like theDSBs of type ‘0’ in the first collection. These breaks are then tagged as background breaks. This type of approach has faced several practical difficulties. To make an association between background breaks in the first collection and (where only type ‘0’ breaks are present) and breaks in similar positions in the second collection was quite difficult. The number of breaks ‘tagged’ was very low, so that most of the breaks present remained attributed by exclusion to radiation, particularly those that were closely associated, and the approach has been abandoned.

The solution to the problem of distinguishing background breaks from radiation- induced breaks for the DSB rejoining kinetics simulations has been provided by the successful computer-simulations of initial DNA fragmentation based on DSB clustering (described in § 3.3.1.1 and applied to fit data in chapter 4). These simulations have in fact provided a method to generate a complete initial DNA fragmentation pattern in single cells, where DSBs of type ‘background’ and type ‘radiation’ are already well distin- guished. In these simulations there is no need to ‘recognise and tag’ background breaks, since the radiation-induced breaks have been located, in a controlled manner, and sepa- rately, on top of background DSBs that have been distributed earlier. It has been thought that the initial fragmentation pattern generated in single cells as described above could be used as the substrate for the rejoining simulation, which effectively becomes an ad- ditional program module that plugs into the existing program code for the simulation of initial DSB induction, as shown in the diagram3.6. In fact, the DSB rejoining simulation is very similar to the DSB induction simulation, but for a few extra functionalities that allow rejoining kinetics to be computer simulated for fragments of any size, so that one can compare the simulated data to measurements of rejoining kinetics evaluated in separate molecular weight regions, testing specific rejoining kinetics mechanisms. This is shown in chapter5for many experiments.

Every DSB rejoining kinetics experiment carried out in this project includes samples that have been irradiated and not incubated for repair of the damage induced. These irradiated but unrepaired samples are first analysed with the numerical extended BDRB approach described earlier (§3.3.1.1) in order to estimate the relevant parameters that describe the initial DNA fragmentation. The same parameter values (number of indepen- dent clusters, maximum cluster radius and expected cluster multiplicity) are then used in an independent DSB rejoining simulation to generate the initial DNA fragmentation pattern in single cells, which becomes the substrate of the rejoining program module.

The DSB rejoining kinetics module.

The concept of repair time is not explicitly incorporated in the DSB rejoining kinetics sim- ulation. The model does not postulate that either first or second order rejoining kinetics apply, nor single or multi-component exponential repair kinetics (§3.2.4). DSBs are re- paired one after another, according to a zero-order step-by-step process that is similar to the one suggested by Pˇridal and Lokajiˇcek (1984), at least from a practical point of view. The analogy to the model byPˇridal and Lokajiˇcekis in fact not extended to the ac- tual DSB repair mechanism, which they proposed to be based on the formation of pairs of homologous chromosomes as in the homologous recombination process, a situation that may seldom apply to repair of DSBs in human cells (see§1.4).

For a specified fraction of radiation-induced DSBs to be repaired, breaks on differ- ent chromosomes are individually selected, by randomly choosing the chromosome in which a break is about to be repaired (if there are any left to be repaired on the selected chromosome) and randomly selecting the individual break to be repaired on such chro- mosome. Every DSB is equally likely to be repaired in unit time, and breaks produced in the same cluster are not repaired in concert. The rejoining procedure may then not be viewed as the inverse operation of the DSB clustering procedure. Repair is here in- tended as restitution, or correct removal of double-strand break. Similarly, the process may be pictured with two adjacent DNA fragments, separated by one radiation-induced DSB, that join to each other to form a fragment whose length is the sum of the lengths of the former two. The fact that the breaks are selected at random for removal, during the simulation, is equivalent to saying that the probability of rejoining two fragments does not depend on size, and this rejoining mechanism has been given the name of ‘fragment size-independent rejoining kinetics’.

The rejoining simulation is repeated several times for the specified number of cells, each time removing a different fraction of the initial DSBs, ranging from 1% to 100%, for simulation of several different repair stages, up to complete repair, when all but the ir- reparable background breaks have been removed. For each simulated fraction of breaks repaired, the resulting fragmentation patterns are described quantitatively by construct-

ing a frequency histogram as described earlier. Each frequency histogram is stored in a separate data file and compared to the fragmentation patterns measured experimen- tally at all the available times of post-irradiation incubation, for the particular experiment analysed, in order to evaluate theχ2 for the goodness of the fit. For example, the exper- imental DNA fragmentation pattern measured after one hour of incubation is compared to each of the patterns obtained after simulated removal of several fractions breaks, and for each theoretical distribution obtained a χ2 value for the goodness of the fit is calcu- lated. The simulated pattern which gives the minimumχ2 _{value gives the best estimate} for the only rejoining parameter to be estimated: the fraction of DSBs repaired at that repair time, Ft. This procedure is repeated for the experimental data measured at all the repair times available for the particular experiment under analysis, so that one even- tually has an estimate, for each repair time, of how many radiation-induced DSBs have been repaired, assuming that DSBs are simply removed. Nevertheless, there is no gen- eral functional relationship between any F value and repair time, since F values are only known for the repair times available. An additional step is required to have a more complete rejoining kinetics time picture.

The computer-simulation provides a method to quantify the number of DSBs repaired as if correct repair took place. The estimates obtained for different experimental repair times may be plotted vs incubation time, in order to evaluate the more traditional to- tal DSB rejoining kinetics curve. These data can be fitted to a rejoining kinetic model, assuming for example first order repair, using single or multiple exponential decay com- ponents (§ 3.3.3). Regressions provide a functional relationship F(t), which can be inverted tot(F). It is only at this stage that computer-simulated fragmentation patterns for different fractions of DSBs rejoined may then be associated to time. The greatest advantage by far is that this allows us now to follow the kinetics, vs time, of fragments of any size, testing visually the hypothesis of fragment size-independent kinetics. This type of analysis in shown in figures5.6,5.7,5.10and5.11in chapter5.

3.3.3.2 Modelling DSB rejoining kinetics on experimental data corrected for the

background damage

Although the lack of accuracy of the subtraction procedure that corrects for the back- ground damage has been pointed out several times in this chapter, some early rejoining simulations have been run in this project to describe the rejoining kinetics of experimen- tal data that were corrected for background damage by subtraction. This analysis is re- ported in this Thesis for two experiments for illustration purposes, one for each radiation quality (see figure 5.12) merely to show how significantly different can be the results if compared to those obtained when data are not subtracted and radiation induced breaks

only are selectively rejoined, leaving the background breaks untouched.

For rejoining simulations that aim to reproduce the experimental ‘net’ (i.e. corrected for the background breaks by subtraction) frequency distributions, there is no need to distinguish between radiation-induced breaks and control breaks, since it is assumed that the experimental fragment size distributions are consequence of radiation-induced breaks only. The rest of the simulation is essentially identical to what has been described above, with breaks to be selected at random on chromosomes also selected randomly, equivalent to a fragment size-independent rejoining kinetics mechanism.