Skip to main content
SpringerLink
Log in

A reaction–diffusion model for radiation-induced bystander effects

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

We develop and analyze a reaction–diffusion model to investigate the dynamics of the lifespan of a bystander signal emitted when cells are exposed to radiation. Experimental studies by Mothersill and Seymour 1997, using malignant epithelial cell lines, found that an emitted bystander signal can still cause bystander effects in cells even 60 h after its emission. Several other experiments have also shown that the signal can persist for months and even years. Also, bystander effects have been hypothesized as one of the factors responsible for the phenomenon of low-dose hyper-radiosensitivity and increased radioresistance (HRS/IRR). Here, we confirm this hypothesis with a mathematical model, which we fit to Joiner’s data on HRS/IRR in a T98G glioma cell line. Furthermore, we use phase plane analysis to understand the full dynamics of the signal’s lifespan. We find that both single and multiple radiation exposure can lead to bystander signals that either persist temporarily or permanently. We also found that, in an heterogeneous environment, the size of the domain exposed to radiation and the number of radiation exposures can determine whether a signal will persist temporarily or permanently. Finally, we use sensitivity analysis to identify those cell parameters that affect the signal’s lifespan and the signal-induced cell death the most.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Notes

  1. The word “delay” in a biological context often refers to the fact that a process is slower than normal. It does not necessarily refer to a delay term as would arise in a delay equation.

References

  • Alexandre J, Hu Y, Lu W, Pelicano H, Huang P (2007) Novel action of paclitaxel against cancer cells: bystander effect mediated by reactive oxygen species. Cancer Res 67(8):3512–3517

    Article  Google Scholar 

  • Antonelli F, Belli M, Cuttone G, Dini V, Esposito G, Simone G, Sorrentino E, Tabocchini MA (2005) Induction and repair of DNA double-strand breaks in human cells: dephosphorylation of histone H2AX and its inhibition by calyculin a. Radiat Res 164(4):514–517

    Article  Google Scholar 

  • Azzam EI, de Toledo SM, Little JB (2001) Direct evidence for the participation of gap junction-mediated intercellular communication in the transmission of damage signals from \(\alpha \)-particle irradiated to nonirradiated cells. Proc Nat Acad Sci 98(2):473–478

    Google Scholar 

  • Ballarini F, Alloni D, Facoetti A, Mairani A, Nano R, Ottolenghi A (2006) Modelling radiation-induced bystander effect and cellular communication. Radiat Prot Dosim 122(1–4):244–251

    Google Scholar 

  • Bishayee A, Hill HZ, Stein D, Rao DV, Howell RW (2001) Free radical-initiated and gap junction-mediated bystander effect due to nonuniform distribution of incorporated radioactivity in a three-dimensional tissue culture model. Radiat Res 155(2):335–344

    Article  Google Scholar 

  • Blyth BJ, Sykes PJ (2011) Radiation-induced bystander effects: what are they, and how relevant are they to human radiation exposures? Radiat Res 176(2):139–157

    Article  Google Scholar 

  • Brenner DJ (2008) The linear-quadratic model is an appropriate methodology for determining isoeffective doses at large doses per fraction. Semin Radiat Oncol 18(4):234–239

    Article  Google Scholar 

  • Cai J, Yang J, Jones D (1998) Mitochondrial control of apoptosis: the role of cytochrome c. Biochim Biophys Acta (BBA) Bioenerg 1366(1):139–149

    Article  Google Scholar 

  • Curtis SB (1986) Lethal and potentially lethal lesions induced by radiation—a unified repair model. Radiat Res 106(2):252–270

    Article  Google Scholar 

  • Cusato K, Ripps H, Zakevicius J, Spray D (2006) Gap junctions remain open during cytochrome c-induced cell death: relationship of conductance to bystander cell killing. Cell Death Differ 13(10):1707–1714

    Article  Google Scholar 

  • Frank DK, Szymkowiak B, Josifovska-Chopra O, Nakashima T, Kinnally KW (2005) Single-cell microinjection of cytochrome c can result in gap junction-mediated apoptotic cell death of bystander cells in head and neck cancer. Head Neck 27(9):794–800

    Article  Google Scholar 

  • Gao CF, Ren S, Zhang L, Nakajima T, Ichinose S, Hara T, Koike K, Tsuchida N (2001) Caspase-dependent cytosolic release of cytochrome c and membrane translocation of bax in p53-induced apoptosis. Exp Cell Res 265(1):145–151

    Article  Google Scholar 

  • Gong J, dos Santos MM, Finlay C, Hillen T (2013) Are more complicated tumour control probability models better? Math Med Biol 30(1):1–19

    Article  MathSciNet  MATH  Google Scholar 

  • Goodman J, Weare J (2010) Ensemble samplers with affine invariance. Commun Appl Math Comput Sci 5(1):65–80

    Article  MathSciNet  MATH  Google Scholar 

  • Goyanes-Villaescusa V (1971) Chromosomal abnormalities in lymphocytes of children and baby rabbits born from mothers treated by X-irradiation before pregnancy. A transplacentary plasmatic chromosome-damaged factor? Blut 22(2):93–96

    Article  Google Scholar 

  • Hauri D, Spycher B, Huss A, Zimmermann F, Grotzer M, von der Weid N, Weber D, Spoerri A, Kuehni CE, Röösli M et al (2013) Domestic radon exposure and risk of childhood cancer: a prospective census-based cohort study. Environ Health Perspect 121(10):1239–1244

    Google Scholar 

  • Hu B, Wu L, Han W, Zhang L, Chen S, Xu A, Hei TK, Yu Z (2006) The time and spatial effects of bystander response in mammalian cells induced by low dose radiation. Carcinogenesis 27(2):245–251

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Khvostunov IK, Nikjoo H (2002) Computer modelling of radiation-induced bystander effect. J Radiol Prot 22(3A):A33

    Article  Google Scholar 

  • Kim JK, Jackson TL (2013) Mechanisms that enhance sustainability of p53 pulses. PLoS ONE 8(6):e65242

    Article  Google Scholar 

  • Kohandel M, Kardar M, Milosevic M, Sivaloganathan S (2007) Dynamics of tumor growth and combination of anti-angiogenic and cytotoxic therapies. Phys Med Biol 52(13):3665

    Article  Google Scholar 

  • Kovalchuk A, Mychasiuk R, Muhammad A, Hossain S, Ilnytskyy S, Ghose A, Kirkby C, Ghasroddashti E, Kovalchuk O, Kolb B (2016) Liver irradiation causes distal bystander effects in the rat brain and affects animal behaviour. Oncotarget 7(4):4385

    Google Scholar 

  • Lambin P, Marples B, Fertil B, Malaise E, Joiner M (1993) Hypersensitivity of a human tumour cell line to very low radiation doses. Int J Radiat Biol 63(5):639–650

    Article  Google Scholar 

  • Lara PC, López-Peñalver JJ, de Araújo Farias V, Ruiz-Ruiz MC, Oliver FJ, de Almodóvar JMR (2015) Direct and bystander radiation effects: a biophysical model and clinical perspectives. Cancer Lett 356(1):5–16

    Article  Google Scholar 

  • Leuraud K, Richardson DB, Cardis E, Daniels RD, Gillies M, O’Hagan JA, Hamra GB, Haylock R, Laurier D, Moissonnier M et al (2015) Ionising radiation and risk of death from leukaemia and lymphoma in radiation-monitored workers (INWORKS): an international cohort study. Lancet Haematol 2(7):e276–e281

    Article  Google Scholar 

  • Lintott R, McMahon S, Prise K, Addie-Lagorio C, Shankland C (2014) Using process algebra to model radiation induced by stander effects. In: Mendes P, Dada JO, Smallbone K (eds) Computational methods in systems biology, CMSB 2014. Lecture Notes in computer science, vol 8859. Springer, Cham

  • Marples B (2004) Is low-dose hyper-radiosensitivity a measure of G2-phase cell radiosensitivity? Cancer Metastasis Rev 23(3–4):197–207

    Article  Google Scholar 

  • Marples B, Joiner M (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

    Article  Google Scholar 

  • McMahon S, Butterworth KT, Trainor C, McGarry CK, O’Sullivan JM, Schettino G, Hounsell AR, Prise KM (2013) A kinetic-based model of radiation-induced intercellular signalling. PloS ONE 8(1):e54526

    Article  Google Scholar 

  • Mothersill C, Seymour C (1997) Medium from irradiated human epithelial cells but not human fibroblasts reduces the clonogenic survival of unirradiated cells. Int J Radiat Biol 71(4):421–427

    Article  Google Scholar 

  • Mothersill C, Seymour C (2006) Radiation-induced bystander effects: evidence for an adaptive response to low dose exposures? Dose-Response 4(4):283–290

    Article  Google Scholar 

  • Nagasawa H, Little JB (1992) Induction of sister chromatid exchanges by extremely low doses of \(\alpha \)-particles. Cancer Res 52(22):6394–6396

    Google Scholar 

  • Nikjoo H, Khvostunov IK (2003) Biophysical model of the radiation-induced bystander effect. Int J Radiat Biol 79(1):43–52

    Article  Google Scholar 

  • Pant GS, Kamada N (1977) Chromosome aberrations in normal leukocytes induced by the plasma of exposed individuals. Hiroshima J Med Sci 26(2–3):149–154

    Google Scholar 

  • Powathil GG, Munro AJ, Chaplain MA, Swat M (2016) Bystander effects and their implications for clinical radiation therapy: insights from multiscale in silico experiments. J Theor Biol 401:1–14

    Article  MATH  Google Scholar 

  • Prise K (1998) Studies of bystander effects in human fibroblasts using a charged particle microbeam. Int J Radiat Biol 74(6):793–798

    Article  Google Scholar 

  • Prise KM, O’Sullivan JM (2009) Radiation-induced bystander signalling in cancer therapy. Nat Rev Cancer 9(5):351–360

    Article  Google Scholar 

  • Prise KM, Schettino G, Folkard M, Held KD (2005) New insights on cell death from radiation exposure. Lancet Oncol 6(7):520–528

    Article  Google Scholar 

  • 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 Nat Acad Sci 100(9):5057–5062

    Article  Google Scholar 

  • Ryan LA, Smith RW, Seymour CB, Mothersill CE (2008) Dilution of irradiated cell conditioned medium and the bystander effect. Radiat Res 169(2):188–196

    Article  Google Scholar 

  • Schuler M, Bossy-Wetzel E, Goldstein JC, Fitzgerald P, Green DR (2000) p53 induces apoptosis by caspase activation through mitochondrial cytochrome c release. J Biol Chem 275(10):7337–7342

    Article  Google Scholar 

  • Seymour CB, Mothersill C (2004) Radiation-induced bystander effects—implications for cancer. Nat Rev Cancer 4(2):158–164

    Article  Google Scholar 

  • 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):847–855

    Article  Google Scholar 

  • Short S, Woodcock M, Marples B, Joiner M (2003) Effects of cell cycle phase on low-dose hyper-radiosensitivity. Int J Radiat Biol 79(2):99–105

    Article  Google Scholar 

  • Short SC, Kelly J, Mayes CR, Woodcock M, Joiner MC (2001) Low-dose hypersensitivity after fractionated low-dose irradiation in vitro. Int J Radiat Biol 77(6):655–664

    Article  Google Scholar 

  • Wouters BG, Sy AM, Skarsgard LD (1996) Low-dose hypersensitivity and increased radioresistance in a panel of human tumor cell lines with different radiosensitivity. Radiat Res 146(4):399–413

    Article  Google Scholar 

Download references

Acknowledgements

We are particularly grateful to G. Powathil for inspiration and discussions about bystander effects, and we thank an anonymous referee for helpful suggestions. We are grateful to helpful suggestions of W. Roda on the implementation of the Goodman and Weare Affine invariant ensemble MCMC sampler for data fitting. We are also grateful for the feedback from the Journal Club of the Center for Mathematical Biology at the University of Alberta. OO is supported by the President’s International Doctoral Award, GdeV and TH are supported by NSERC.

Author information

Authors and Affiliations

  1. Centre for Mathematical Biology, Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G2G1, Canada

    Oluwole Olobatuyi, Gerda de Vries & Thomas Hillen

Authors
  1. Oluwole Olobatuyi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gerda de Vries
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Thomas Hillen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oluwole Olobatuyi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Olobatuyi, O., de Vries, G. & Hillen, T. A reaction–diffusion model for radiation-induced bystander effects. J. Math. Biol. 75, 341–372 (2017). https://doi.org/10.1007/s00285-016-1090-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00285-016-1090-5

Keywords

Mathematics Subject Classification

Search

Navigation