A mathematical model for the effect of low-dose radiation on the G2/M transition. (English) Zbl 1427.92021
Summary: We develop a mathematical model to study the immediate effect of low-dose radiation on the G2 checkpoint and the G2/M transition of the cell cycle via a radiation pathway (the ATM-Chk2 pathway) of an individual mammalian cell. The model consists of a system of nonlinear differential equations describing the dynamics of a network of regulatory proteins that play key roles in the G2/M transition, cell cycle oscillations, and the radiation pathway. We simulate the application of a single pulse of low-dose radiation at different intensities \((\sim 0-0.4\) Gy) and times during the latter part of the G2-phase. We use bifurcation analysis to characterize the effect of radiation on the G2/M transition via the ATM-Chk2 pathway. We show that radiation between 0.1 and 0.3 Gy can delay the G2/M transition, and radiation higher than 0.3 Gy can fully activate the G2 checkpoint. Also, our results show that radiation can be low enough to neither delay the G2/M transition nor activate the G2 checkpoint \((\sim 0.1\) Gy). Our model supports the idea that the cell response to radiation during G2-phase explains hyper-radiosensitivity and increased radioresistance (HRS/IRR) observed at low dose.
Keywords:
G2 checkpoint; G2/M transition; ionizing radiation; HRS; IRR; radiation pathway; ATM; Chk2; cell cycle modelling; regulatory dynamics; cell physiologyReferences:
| [1] | Bartek J, Falck J, Lukas J (2001) CHK2 kinase—a busy messenger. Nat Rev Mol Cell Biol 2(12):877-86 · doi:10.1038/35103059 |
| [2] | Bezanson J, Edelman A, Karpinski S, Shah VB (2017) Julia: a fresh approach to numerical computing. SIAM Rev 59(1):65-98 · Zbl 1356.68030 · doi:10.1137/141000671 |
| [3] | Bodgi L, Foray N (2016) The nucleo-shuttling of the ATM protein as a basis for a novel theory of radiation response: resolution of the linear-quadratic model*. Int J Radiat Biol 92(3):117-131 · doi:10.3109/09553002.2016.1135260 |
| [4] | Bodgi L, Canet A, Pujo-menjouet L, Lesne A (2016) Mathematical models of radiation action on living cells: from the target theory to the modern approaches. A historical and critical review. J Theor Biol 394:93-101 · Zbl 1343.92120 · doi:10.1016/j.jtbi.2016.01.018 |
| [5] | Burma S, Chen BP, Murphy M, Kurimasa A, Chen DJ (2001) ATM phosphorylates histone H2AX in response to DNA double-strand breaks. J Biol Chem 276(45):42462-42467 · doi:10.1074/jbc.C100466200 |
| [6] | Buscemi G, Savio C, Zannini L, Miccichè F, Masnada D, Nakanishi M, Tauchi H, Komatsu K, Mizutani S, Khanna K, Chen P, Concannon P, Chessa L, Delia D (2001) Chk2 activation dependence on Nbs1 after DNA damage. Mol Cell Biol 21(15):5214-5222 · doi:10.1128/MCB.21.15.5214-5222.2001 |
| [7] | Deckbar D, Birraux J, Krempler A, Tchouandong L, Beucher A, Walker S, Stiff T, Jeggo P, Löbrich M (2007) Chromosome breakage after G2 checkpoint release. J Cell Biol 106(6):749-755 · doi:10.1083/jcb.200612047 |
| [8] | Deckbar D, Jeggo PA, Löbrich M (2011) Understanding the limitations of radiation-induced cell cycle checkpoints. Crit Rev Biochem Mol Biol 46(4):271-283 · doi:10.3109/10409238.2011.575764 |
| [9] | Donzelli M, Draetta GF (2003) Regulating mammalian checkpoints through Cdc25 inactivation. EMBO Rep 4(4):671-677 · doi:10.1038/sj.embor.embor887 |
| [10] | Enns L, Rasouli-Nia A, Hendzel M, Marples B, Weinfeld M (2015) Association of ATM activation and DNA repair with induced radioresistance after low-dose irradiation. Radiat Prot Dosimetry 166(1-4):131-6 · doi:10.1093/rpd/ncv203 |
| [11] | Ermentrout GB, Kopell N (1986) Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM J Appl Math 46(2):233-253 · Zbl 0594.58033 · doi:10.1137/0146017 |
| [12] | Gérard C, Tyson JJ, Coudreuse D, Novák B (2015) Cell cycle control by a minimal Cdk network. PLOS Comput Biol 11(2):e1004056 · doi:10.1371/journal.pcbi.1004056 |
| [13] | Glass L, Mackey MC (1988) From clocks to chaos: the rhythms of life. Princeton University Press, Princeton · Zbl 0705.92004 |
| [14] | Godin M, Delgado FF, Son S, Grover WH, Bryan AK, Tzur A, Jorgensen P, Payer K, Grossman AD, Kirschner MW, Manalis SR (2010) Using buoyant mass to measure the growth of single cells. Nat Methods 7(5):387-390 · doi:10.1038/nmeth.1452 |
| [15] | Goldbeter A, Koshland DE (1981) An amplified sensitivity arising from covalent modification in biological systems. Proc Natl Acad Sci USA 78(11):6840-6844 · doi:10.1073/pnas.78.11.6840 |
| [16] | Goodarzi AA, Noon AT, Deckbar D, Ziv Y, Shiloh Y, Löbrich M, Jeggo PA (2008) ATM signaling facilitates repair of DNA double-strand breaks associated with heterochromatin. Mol Cell 31(2):167-177 · doi:10.1016/j.molcel.2008.05.017 |
| [17] | Haince JF, Kozlov S, Dawson VL, Dawson TM, Hendzel MJ, Lavin MF, Poirier GG (2007) Ataxia telangiectasia mutated (ATM) signaling network is modulated by a novel poly(ADP-ribose)-dependent pathway in the early response to DNA-damaging agents. J Biol Chem 282(22):16441-16453 · doi:10.1074/jbc.M608406200 |
| [18] | Hanahan D, Weinberg RA (2000) The hallmarks of cancer. Cell 100(1):57-70 · doi:10.1016/S0092-8674(00)81683-9 |
| [19] | Hartwell L, Weinert T (1989) Checkpoints: controls that ensure the order of cell cycle events. Science 246(4930):629-634 · doi:10.1126/science.2683079 |
| [20] | Iliakis G, Wang Y, Guan J, Wang H (2003) DNA damage checkpoint control in cells exposed to ionizing radiation. Oncogene 22:5834-5847 · doi:10.1038/sj.onc.1206682 |
| [21] | Ishikawa A, Yamauchi M, Suzuki K, Yamashita S (2010) Image-based quantitative determination of DNA damage signal reveals a threshold for G2 checkpoint activation in response to ionizing radiation. Genome Integr 1:1-10 · doi:10.1186/2041-9414-1-10 |
| [22] | Joiner MC, Marples B, Lambin P, Short SC, Turesson I (2001) Low-dose hypersensitivity: current status and possible mechanisms. Int J Radiat Oncol Biol Phys 49(2):379-389 · doi:10.1016/S0360-3016(00)01471-1 |
| [23] | Kozlov SV, Graham ME, Jakob B, Tobias F, Kijas AW, Tanuji M, Chen P, Robinson PJ, Taucher-Scholz G, Suzuki K, So S, Chen D, Lavin MF (2011) Autophosphorylation and ATM activation: additional sites add to the complexity. J Biol Chem 286(11):9107-9119 · doi:10.1074/jbc.M110.204065 |
| [24] | Löbrich M, Jeggo PA (2007) The impact of a negligent G2/M checkpoint on genomic instability and cancer induction. Nat Rev Cancer 7(11):861-869 · doi:10.1038/nrc2248 |
| [25] | Marples B (2004) Is low-dose hyper-radiosensitivity a measure of G2-phase cell radiosensitivity? Cancer Metastasis Rev 23(3-4):197-207 · doi:10.1023/B:CANC.0000031761.61361.2a |
| [26] | Marples B, Collis SJ (2008) Low-dose hyper-radiosensitivity: past, present, and future. Int J Radiat Oncol Biol Phys 70(5):1310-1318 · doi:10.1016/j.ijrobp.2007.11.071 |
| [27] | Marples B, Joiner MC (1993) The response of Chinese hamster V79 cells to low radiation doses: evidence of enhanced sensitivity of the whole cell population. Radiat Res 133(1):41-51 · doi:10.2307/3578255 |
| [28] | Matsuoka S, Huang M, Elledge SJ (1998) Linkage of ATM to cell cycle regulation by the Chk2 protein kinase. Science (New York, NY) 282(5395):1893-1897 · doi:10.1126/science.282.5395.1893 |
| [29] | Medema RH, Macůrek L (2012) Checkpoint control and cancer. Oncogene 31(21):2601-13 · doi:10.1038/onc.2011.451 |
| [30] | Miciak J, Bunz F (2017) Understanding the pluses of pulses. Cell Cycle 16(14):1325 · doi:10.1080/15384101.2017.1337979 |
| [31] | Morgan DO (2007) The cell cycle: principles of control. New Science Press Ltd, London |
| [32] | Murray D, McEwan AJ (2007) Radiobiology of systemic radiation therapy. Cancer Biother Radiopharm 22(1):1-23 · doi:10.1089/cbr.2006.531 |
| [33] | Novák B, Tyson JJ (1993) Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos. J Cell Sci 106:1153-1168 |
| [34] | Novák B, Tyson JJ (2008) Design principles of biochemical oscillators. Nat Rev Mol Cell Biol 9(12):981-991 · doi:10.1038/nrm2530 |
| [35] | Novák B, Pataki Z, Ciliberto A, Tyson JJ (2001) Mathematical model of the cell division cycle of fission yeast. Chaos 11(1):277-286 · Zbl 0992.92022 · doi:10.1063/1.1345725 |
| [36] | Olobatuyi O, de Vries G, Hillen T (2017) A reaction-diffusion model for radiation-induced bystander effects. J Math Biol 75(2):341-372 · Zbl 1377.92026 · doi:10.1007/s00285-016-1090-5 |
| [37] | Olobatuyi O, de Vries G, Hillen T (2018) Effects of G2-checkpoint dynamics on low-dose hyper-radiosensitivity. J Math Biol 77(6-7):1969-1997 · Zbl 1404.92101 · doi:10.1007/s00285-018-1236-8 |
| [38] | Park K, Millet LJ, Kim N, Li H, Jin X, Popescu G, Aluru NR, Hsia KJ, Bashir R (2010) Measurement of adherent cell mass and growth. Proc Natl Acad Sci 107(48):20691-20696 · doi:10.1073/pnas.1011365107 |
| [39] | Rackauckas C, Nie Q (2017) DifferentialEquations.jl—a performant and feature-rich ecosystem for solving differential equations in Julia. J Open Res Softw 5(15):15 · doi:10.5334/jors.151 |
| [40] | Rothkamm K, Löbrich M (2003) Evidence for a lack of DNA double-strand break repair in human cells exposed to very low X-ray doses. Proc Natl Acad Sci USA 100(9):5057-62 · doi:10.1073/pnas.0830918100 |
| [41] | Scott BR (2010) Multicellular signalling model for DNA double-strand break repair kinetics after low-dose radiation. Int J Low Radiat 7(5):347-358 · doi:10.1504/IJLR.2010.036959 |
| [42] | Short S, Mayes C, Woodcock M, Johns H, Joiner MC (1999) Low dose hypersensitivity in the T98G human glioblastoma cell line. Int J Radiat Biol 75(7):847-55 · doi:10.1080/095530099139908 |
| [43] | Taleei R (2018) Modelling Dsb repair kinetics for DNA damage induced by proton and carbon ions. Radiat Prot Dosim 183:75-78 · doi:10.1093/rpd/ncy304 |
| [44] | Taleei R, Nikjoo H (2013) The non-homologous end-joining (NHEJ) pathway for the repair of DNA double-strand breaks: I. A mathematical model. Radiat Res 179(5):530-9 · doi:10.1667/RR3123.1 |
| [45] | Tyson JJ, Novák B (2001) Regulation of the eukaryotic cell cycle: molecular antagonism, hysteresis, and irreversible transitions. J Theor Biol 210(2):249-263 · doi:10.1006/jtbi.2001.2293 |
| [46] | Tyson JJ, Novák B (2015) Models in biology: lessons from modeling regulation of the eukaryotic cell cycle. BMC Biol 13(1):46 · doi:10.1186/s12915-015-0158-9 |
| [47] | Tyson JJ, Csikasz-Nagy A, Novák B (2002) The dynamics of cell cycle regulation. BioEssays 24(12):1095-1109 · doi:10.1002/bies.10191 |
| [48] | Tyson JJ, Chen KC, Novák B, Novak B (2003) Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. Curr Opin Cell Biol 15(2):221-231 · doi:10.1016/S0955-0674(03)00017-6 |
| [49] | Vitale I, Galluzzi L, Castedo M, Kroemer G (2011) Mitotic catastrophe: a mechanism for avoiding genomic instability. Nat Rev Mol Cell Biol 12(6):385-392 · doi:10.1038/nrm3115 |
| [50] | Zhang P, Wang B, Chen X, Cvetkovic D, Chen L, Lang J, Ma CM (2015) Local tumor control and normal tissue toxicity of pulsed low-dose rate radiotherapy for recurrent lung cancer. Dose Response 13(2):155932581558850 · doi:10.1177/1559325815588507 |
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