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Yuichiro
Manabe
Manabe
Yuichiro
We have developed our mathematical model to study DNA mutations in cells caused by artificial radiation exposure,
accounting for the DNA damage and repair simultaneously. In our theory, the dependence of mutation frequencies on
the dose rate is critically important to predict both the time course and the stationary effect of the DNA mutation in
cell cycles. Here in this study, we derive a scaling function from our rate equations that predicts a universal feature in
the mutation frequency of living organisms in order to develop our theory. Second, we have analyzed the
experimental data of five living organisms; mouse, drosophila, chrysanthemum, maize, and Tradescantia. Despite the
difference between animal and plant, all these data reasonably fall on a single line of our scaling function. Finally,
we estimate the biological effects of long-term exposure to low dose-rate radiation by using the model. Our theory
shows the saturation of mutation frequencies, which marks a substantial difference from existing theories based on the
total dose. The mutation frequency increases linearly in time, first, i.e., it depends linearly on the total dose. Then it
starts to bend and approaches a stationary value, which is determined by the dose rate.
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1 豊田理研スカラー
ŵĸĴŁ‡|š¡ƖßƇßãßãƉíãŁʼnŅĵÚ {Žœ¡íãèĆƁâ{Žœ¡íãųðƗ
（大阪大学大学院工学研究科環境・エネルギー工学専攻量子エネルギー工学講座）
放射線生体影響数理モデルの放射線生物学・治療への展開
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ĊřƎâįƖ&#ƣ3??;BBB946604.:8,=?4.70)+ "ƗH REFERENCES
ƖƚƗD. E. Lea, Actions of Radiations on Living Cells, Cambridge University Press, Press, NY, England (1st ed. 1944: 2nd ed.1955)
ƖƛƗK. H. Chadwick and H. P. Leenhouts, Phys. Med. Biol. Vol.18, No. 1, 78 (1973).
ƖƜƗA. M. Kellerer and H. H. Rossi, Rad. Res., Vol. 75, No. 3, 471 (1978).
ƖƝƗW. L. Russell and E. M. Kelly, Proc. Natl. Acad. Sci. USA 79, 539 (1982).
ƖƞƗY. Manabe, K. Ichikawa and M. Bando, J. Phys. Soc. Jpn., 81, 104004 (2012).
ƖƟƗY. Manabe and M. Bando, J. Phys. Soc. Jpn. 82, 094004 (2013)
ƖƠƗY. Manabe, I. Nakamura and M. Bando, J. Phys. Soc. Jpn., 83, 114003 (2014)
ƖơƗY. Manabe, T. Wada, I. Nakamura, Y. Tsunoyama, H. Nakajima and M. Bando, J. Phys. Soc. Jpn., 84, 044002 (2015).
ƖƢƗT. Wada, Y. Manabe, I. Nakamura, Y. Tsunoyama, H. Nakajima and M. Bando, J. Nucl. Sci. Technol., submitted