SIMULATION AND SENSITIVITY ANALYSIS ON THE PARAMETER OF NON-TARGETED IRRADIATION EFFECTS MODEL
DOI:
https://doi.org/10.11113/jt.v81.12448Keywords:
Bystander effects, double-strand breaks, survival fraction, sensitivity analysis, structured ordinary differential equationAbstract
Real-life situations showed damage effects on non-targeted cells located in the vicinity of an irradiation region, due to danger signal molecules released by the targeted cells. This effect is widely known as radiation-induced bystander effects (RIBE). The purpose of this paper is to model the interaction of non-targeted cells towards bystander factors released by the irradiated cells by using a system of structured ordinary differential equations. The mathematical model and its simulations are presented in this paper. In the model, the cells are grouped based on the number of double-strand breaks (DSBs) and mis-repair DSBs because the DSBs are formed in non-targeted cells. After performing the model's simulations, the analysis continued with sensitivity analysis. Sensitivity analysis will determine which parameter in the model is the most sensitive to the survival fraction of non-targeted cells. The proposed mathematical model can explain the survival fraction of non-targeted cells affected by the bystander factors.
References
Mothersill, C., Fernandez-Palomo, C., Fazzari, J., Smith, R., Schültke, E., Bräuer-Krisch, E., Laissue, J., Schroll, C. and Seymour, C. 2014. Transmission of Signals from Rats Receiving High Doses of Microbeam Radiation to Cage Mates: An Inter-Mammal Bystander Effect. Dose-Response. 12(1): 72-92.
DOI: http://dx.doi.org/10.2203%2Fdose-response.13-011.Mothersill.
Nasir, M. H. and Siam, F. M. 2017. Mini-review: Recent Updates on the Mathematical Modelling of Radiation-induced Bystander Effects. Malaysian Journal of Fundamental and Applied Sciences. 13(2): 103-108.
DOI: http://dx.doi.org/10.11113/mjfas.v13n2.563.
Lin, X., Wei, F., Major, P., Al-Nedawi, K., Al Saleh, H. A., and Tang, D. 2017. Microvesicles Contribute to the Bystander Effect of DNA Damage. International Journal of Molecular Sciences. 18(4): 788-800.
DOI: http://dx.doi.org/10.3390/ijms18040788.
Wang, H., Yu, K. N., Hou, J., Liu, Q. and Han, W. 2015. Radiation-induced Bystander Effect: Early Process and Rapid Assessment. Cancer Letters. 356(1): 137-144.
DOI: https://doi.org/10.1016/j.canlet.2013.09.031.
Najafi, M., Fardid, R., Hadadi, G. and Fardid, M., 2014. The Mechanisms of Radiation-induced Bystander Effect. Journal of Biomedical Physics & Engineering. 4(4): 163-172.
Nikitaki, Z., Mavragani, I.V., Laskaratou, D.A., Gika, V., Moskvin, V.P., Theofilatos, K., Vougas, K., Stewart, R.D. and Georgakilas, A.G., 2016, June. Systemic Mechanisms and Effects of Ionizing Radiation: A New “Old†Paradigm of How the Bystanders and Distant Can Become the Players. Seminars in Cancer Biology. 37: 77-95. Academic Press.
DOI: https://doi.org/10.1016/j.semcancer.2016.02.002
Havaki, S., Kotsinas, A., Chronopoulos, E., Kletsas, D., Georgakilas, A., & Gorgoulis, V. G. 2015. The Role of Oxidative DNA Damage in Radiation Induced Bystander Effect. Cancer Letters. 356(1): 43-51.
DOI: https://doi.org/10.1016/j.canlet.2014.01.023.
Desouky, O., Ding, N. and Zhou, G. 2015. Targeted and Non-Targeted Effects of Ionizing Radiation. Journal of Radiation Research and Applied Sciences. 8(2): 247-254.
DOI: https://doi.org/10.1016/j.jrras.2015.03.003.
Sprung, C. N., Ivashkevich, A., Forrester, H.B., Redon, C.E., Georgakilas, A. and Martin, O.A. 2015. Oxidative DNA Damage Caused by Inflammation May Link to Stress-induced Non-Targeted Effects. Cancer Letters. 356(1): 72-81.
DOI: https://doi.org/10.1016/j.canlet.2013.09.008.
Lintott, R., McMahon, S., Prise, K., Addie-Lagorio, C. and Shankland, C. 2014. Using Process Algebra to Model Radiation Induced Bystander Effects. International Conference on Computational Methods in Systems Biology. Springer, Cham. 196-210.
DOI: https://doi.org/10.1007/978-3-319-12982-2_14.
Siam, F.M. 2014. Modelling Effects of Ionising Radiation. Doctoral Dissertation. University of Strathclyde.
F. M. Siam, M. Grinfeld. 2014. Modeling ATM DNA Damage Sensor Mechanism. Advances in Mathematics Modeling. Ed. Yusof Yaacob. Penerbit UTM Press. 15-36.
Ivanov, V. N., Zhou, H., Ghandhi, S. A., Karasic, T. B., Yaghoubian, B., Amundson, S. A. and Hei, T. K. 2010. Radiation-induced Bystander Signaling Pathways in Human Fibroblasts: A Role for Interleukin-33 in the Signal Transmission. Cellular Signaling. 22(7):1076-1087.
DOI: https://doi.org/10.1016/j.cellsig.2010.02.010.
Sokolov, M. V., Smilenov, L. B., Hall, E. J., Panyutin, I. G., Bonner, W. M. and Sedelnikova, O. A. 2005. Ionizing Radiation Induces DNA Double-Strand Breaks in Bystander Primary Human Fibroblasts. Oncogene. 24(49): 7257-7265.
DOI: https://doi.org/10.1038/sj.onc.1208886.
Sedelnikova, O. A., Nakamura, A., Kovalchuk, O., Koturbash, I., Mitchell, S. A., Marino, S. A., Brenner, D. J. and Bonner, W. M. 2007. DNA Double-strand Breaks Form in Bystander Cells after Microbeam Irradiation of Three-dimensional Human Tissue Models. Cancer Research. 67(9): 4295-4302.
DOI: https://doi.org/10.1158/0008-5472.CAN-06-4442.
Hu, B., Han, W., Wu, L., Feng, H., Liu, X., Zhang, L., Xu, A., Hei, T.K. and Yu, Z. 2005. In situ Visualization of DSBs to Assess the Extranuclear/Extracellular Effects Induced by Low-Dose α-particle Irradiation. Radiation Research. 164(3): 286-291.
DOI: https://doi.org/10.1667/RR3415.1.
Hall, E. J. and Giaccia, A. J. 2006. Radiobiology for the Radiologist. Lippincott Williams & Wilkins.
Stein, G. S. and Pardee, A. B. 2004. Cell Cycle and Growth Control: Biomolecular Regulation and Cancer. John Wiley & Sons.
Prise, K. M., Schettino, G., Folkard, M. and Held, K. D. 2005. New Insights on Cell Death from Radiation Exposure. The Lancet Oncology. 6(7): 520-528.
DOI: https://doi.org/10.1016/S1470-2045(05)70246-1.
Siam, F. M., Grinfeld, M., Bahar, A., Rahman, H. A., Ahmad, H. and Johar, F. 2018. A Mechanistic Model of High Dose Irradiation Damage. Mathematics and Computers in Simulation. 151: 156-168.
DOI: https://doi.org/10.1016/j.matcom.2016.02.007.
Hattori, Y., Yokoya, A. and Watanabe, R. 2015. Cellular Automaton-based Model for Radiation-induced Bystander Effects. BMC Systems Biology. 9(1): 90.
DOI: https://doi.org/10.1186/s12918-015-0235-2.
Kundrát, P. and Friedland, W. 2012. Non-Linear Response of Cells to Signals Leads to Revised Characteristics of Bystander Effects Inferred from Their Modelling. International Journal of Radiation Biology. 88(10): 743-750.
DOI: https://doi.org/10.3109/09553002.2012.698029.
Powathil, G. G., Munro, A. J., Chaplain, M. A. and Swat, M. 2016. Bystander Effects and Their Implications for Clinical Radiation Therapy: Insights from Multiscale in silico Experiments. Journal of Theoretical Biology. 401: 1-14.
DOI: https://doi.org/10.1016/j.jtbi.2016.04.010.
Olobatuyi, O., de Vries, G. and Hillen, T. 2017. A Reaction–Diffusion Model for Radiation-Induced Bystander Effects. Journal of Mathematical Biology. 75(2): 341-372.
DOI: https://doi.org/10.1007/s00285-016-1090-5.
McKibben, M. and Webster, M. D. 2014. Differential Equations with MATLAB: Exploration, Applications, and Theory. CRC Press.
Borgonovo, E. and Plischke, E., 2016. Sensitivity Analysis: A Review of Recent Advances. European Journal of Operational Research. 248(3): 869-887.
DOI: https://doi.org/10.1016/j.ejor.2015.06.032.
Zi, Z., Zheng, Y., Rundell, A. E. and Klipp, E. 2008. SBML-SAT: A Systems Biology Markup Language (SBML) Based Sensitivity Analysis Tool. BMC Bioinformatics. 9(1): 342-355.
DOI: https://doi.org/10.1186/1471-2105-9-342.
Arthur, J. G., Tran, H. T. and Aston, P. 2017. Feasibility of Parameter Estimation in Hepatitis C Viral Dynamics Models. Journal of Inverse and Ill-Posed Problems. 25(1): 69-80.
DOI: https://doi.org/10.1515/jiip-2014-0048.
Shirvan, K.M., Mamourian, M., Mirzakhanlari, S. and Ellahi, R. 2017. Numerical Investigation of Heat Exchanger Effectiveness in A Double Pipe Heat Exchanger Filled with Nanofluid: A Sensitivity Analysis by Response Surface Methodology. Powder Technology. 313: 99-111.
DOI: https://doi.org/10.1016/j.powtec.2017.02.065.
Ingalls, B. 2013. Mathematical Modelling in Systems Biology: An Introduction. MIT Press.
Cooper, G. M. The Cell: A Molecular Approach. 2nd Edition. Sugarland (MA): Sinauer Associate. The Eukaryotic Cell Cycle., 2000. Available from: <https://www.ncbi.nlm.nih.gov/books/NBK9876/>accessed on June 30, 2018.
Belchior, A., Balásházy, I., Gil, O. M., Vaz, P. and Almeida, P. 2014. Does the Number of Irradiated Cells Influence the Spatial Distribution of Bystander Effects? Dose-Response. 12(4): 525-539.
DOI: https://doi.org/10.2203/dose-response.14-001.Belchior.
Li, R. and Mather, J. P. 1997. Lindane, An Inhibitor of Gap Junction Formation, Abolishes Oocyte Directed Follicle Organizing Activity in vitro. Endocrinology. 138(10): 4477-4480.
DOI: https://doi.org/10.1210/endo.138.10.5567.
Bazak, J., Fahey, J. M., Wawak, K., Korytowski, W. and Girotti, A. W. 2017. Enhanced Aggressiveness of Bystander Cells in an Anti-Tumor Photodynamic Therapy Model: Role of Nitric Oxide Produced by Targeted Cells. Free Radical Biology and Medicine. 102: 111-121.
DOI: https://doi.org/10.1016/j.freeradbiomed.2016.11.034.
Han, W., Chen, S., Yu, K. N. and Wu, L. 2010. Nitric Oxide Mediated DNA Double Strand Breaks Induced in Proliferating Bystander Cells after α-particle Irradiation. Mutation Research/Fundamental and Molecular Mechanisms of Mutagenesis. 684(1): 81-89.
DOI: https://doi.org/10.1016/j.mrfmmm.2009.12.004.
Kamran, M. Z., Ranjan, A., Kaur, N., Sur, S. and Tandon, V. 2016. Radioprotective Agents: Strategies and Translational Advances. Medicinal Research Reviews. 36(3): 461-493.
DOI: http://dx.doi.org/10.1002%2Fmed.21386.
Siam, F. M., Kamal, M. H. A. and Johar, F. 2016. Parameter Estimation for a Mechanistic Model of High Dose Irradiation Damage Using Nelder-Mead Simplex Method and Genetic Algorithm. Jurnal Teknologi. 78(12-2): 87-92.
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