Mathematical Models of the Generation of Radiation-induced DNA Double-strand Breaks and Misrepair Cells by Direct and Indirect Action


  • Hamizah Rashid Department of Mathematical Sciences, Faculty of Science Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia
  • Fuaada Mohd Siam Department of Mathematical Sciences, Faculty of Science Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia
  • Normah Maan Department of Mathematical Sciences, Faculty of Science Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia
  • Wan Nordiana W. Abd Rahman School of Health Sciences, Universiti Sains Malaysia, Kubang Kerian,16150, Kota Bharu, Kelantan, Malaysia
  • Mohamad Hanis Nasir Faculy of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030, Kuala Nerus, Malaysia



Indirect Effect, Reactive Oxygen Species (ROS), Double-strand break(DSB), Parameter Estimation, Linear Quadratic (LQ).


Free radical carries an unpaired electron in the outer shell which is very reactive and becomes toxic to DNA. The direct action hits cell directly, while indirect action is the interaction between ionizing radiation and water molecule which later produces free radical. Hydrated electron (e), hydroxyl radical (OH), hydrogen radical (OH), ionized water, hydroperoxyl radical and hydrogen peroxide are examples of free radical products. Among of these three free radicals, DNA damage dominantly caused by hydroxyl radical (OH) because it is found to be highly reactive compared to others. This paper aimed to develop a model by using structured population dynamics approach to study the effects of ionizing radiation by direct and indirect actions. The effects of ionizing radiation are mathematically described in a model using Ordinary Differential Equations (ODEs). The simulation results are fitted to the Linear Quadratic (LQ) formulation to give the ratio for alpha/beta . Next, the parameter estimation of the model is carried out using experimental data of human colon carcinoma cell by the aid of the MATLAB programming. The estimated parameter values can explain the biological meaning, which can support the result of the experimental design. The result showed that the sum-squared error (SSE) between simulation data and experimental data obtained is 0.0019 which indicates an excellent t to the experimental data. Thus, the model developed is in line with the experimental result. The model is able to explain the dynamics process of the direct and indirect effect of ionizing radiation on the cell population.


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