Stochastic multicellular modeling of x-ray irradiation, DNA damage induction, DNA free-end misrejoining and cell death

The repair or misrepair of DNA double-strand breaks (DSBs) largely determines whether a cell will survive radiation insult or die. A new computational model of multicellular, track structure-based and pO2-dependent radiation-induced cell death was developed and used to investigate the contribution to cell killing by the mechanism of DNA free-end misrejoining for low-LET radiation. A simulated tumor of 1224 squamous cells was irradiated with 6 MV x-rays using the Monte Carlo toolkit Geant4 with low-energy Geant4-DNA physics and chemistry modules up to a uniform dose of 1 Gy. DNA damage including DSBs were simulated from ionizations, excitations and hydroxyl radical interactions along track segments through cell nuclei, with a higher cellular pO2 enhancing the conversion of DNA radicals to strand breaks. DNA free-ends produced by complex DSBs (cDSBs) were able to misrejoin and produce exchange-type chromosome aberrations, some of which were asymmetric and lethal. A sensitivity analysis was performed and conditions of full oxia and anoxia were simulated. The linear component of cell killing from misrejoining was consistently small compared to values in the literature for the linear component of cell killing for head and neck squamous cell carcinoma (HNSCC). This indicated that misrejoinings involving DSBs from the same x-ray (including all associated secondary electrons) were rare and that other mechanisms (e.g. unrejoined ends) may be important. Ignoring the contribution by the indirect effect toward DNA damage caused the DSB yield to drop to a third of its original value and the cDSB yield to drop to a tenth of its original value. Track structure-based cell killing was simulated in all 135306 viable cells of a 1 mm3 hypoxic HNSCC tumor for a uniform dose of 1 Gy.

Let the number of breaks (DSBs, or cDSBs in the current work) in the nucleus be N ∈ [2, ∞). The number of misrejoinings involving these breaks is N mr ∈ [0, N ]. It will be demonstrated that this equation for P surv(mr) is true (given the assumptions above) for N = 2 and all N mr ∈ {0, 1, 2} and for N ≥ 3 provided N mr = N . For N ≥ 3 and N mr = N , one of the misrejoinings was counted that should not have been, i.e., P surv(mr) would have been correct if a value of N mr → N mr − 1 had been used in the formula instead. Thus, the cell killing was overestimated in these cases (though they did not contribute appreciably in the current work -see Discussion). Lastly, it will be shown that the equation for P surv(mr) extends to a nucleus containing multiple independent groups of breaks with misrejoinings. N = 2 2 breaks on 2 chromosomes (1 break on each chromosome) If there were no misrejoinings (N mr = 0), both breaks were rejoined faithfully (assumption 1) and P surv(mr) = 1, which the formula gives for N mr = 0.

break on each arm of a chromosome
If N mr = 0, same as in the previous example.

breaks on the same arm of a chromosome
If N mr = 0, same as above.

• paracentric inversion (2 ways) → viable
Lethal and viable outcomes were equally likely (2 ways each), so P surv(mr) = 0.5, which the formula gives for N mr = 1. As above, if the 2 misrejoinings were simulated explicitly, the second misrejoining was not counted toward N mr (assumption 3), so N mr = 1 and the formula correctly gives P surv(mr) = 0.5.
If the second misrejoining was not between the same pair of breaks as the first (N mr = 2), then the options are (after the third misrejoining; by assumption 2): • 1 dicentric (no sticky ends), 1 symmetric translocation (no sticky ends) and 1 acentric fragment (no sticky ends) (36 ways) → lethal • 3 symmetric translocations (no sticky ends) (12 ways) → viable There are 36 ways for a lethal outcome and 12 ways for a viable outcome, giving P surv(mr) = 0.25, which the formula correctly gives for N mr = 2. If the 3 misrejoinings were simulated explicitly, the situation is as described above, with P surv(mr) = 0.25. In the current algorithm, the third misrejoining was mistakenly counted (N mr = 3), so the formula incorrectly gave P surv(mr) = 0.125. This will be fixed in future iterations of the algorithm.

Independent groups of breaks in a nucleus
Consider a nucleus containing one group of breaks with N mr,1 and corresponding P surv(mr),1 and a second group of breaks with N mr,2 and corresponding P surv(mr),2 : P surv(mr),1 = 0.5 Nmr,1 (1) P surv(mr),2 = 0.5 Nmr,2 For the cell to be viable, both groups of breaks must have a viable outcome: P surv(mr) = P surv(mr),1 P surv(mr),2 = 0.5 Nmr,1 0.5 Nmr,2 (4) = 0.5 Nmr,1+Nmr,2 So P surv(mr) is given by the same formula but using the total number of misrejoinings in the nucleus.