Appendix E
DNA Splitting by Radiation
The study and practice of medicine could benefit from an
enhanced engagement with the new perspectives provided by the
emerging areas of complexity science and systems biology.
— Geoffrey B. West
An important observable that a radiation-damage theory can predict is the distribution of fragment lengths created by a given exposure and given environment. As
another example of mathematical modeling in biology, we here present a statistical
model to predict the splitting of the DNA backbone by radiation. 1
E.1 Cleavage of Linear Molecules
Consider an initial volume of DNA molecules dispersed in a sample volume of
target material, such as a water solution. If this volume is irradiated, causing locally
deposited energy sufficient to break both backbones of the double helix (directly
or indirectly), then cleavage will have some probability of occurring. (Here, direct
break-up refers to cleavage caused by energy deposited onto the DNA from primary
and secondary radiation while indirect break-up includes energy transferred from
nearby ions and radicals created by the radiation.) To model the radiation-induced
cleavage events, assume that the molecule is made of segments of minimum length
δ, and that the initial molecules have length n δ , where n is an integer. Let N i be
the number of DNA molecule fragments present at a particular time having a length
i δ. Initially, all N i are zero except N n , which starts as the total number of DNA
molecules present in the initial volume, which is taken as N. As the molecules
are irradiated, the change in the number of molecules having length i δ comes
about from two mechanisms: an increase from cleavage of larger molecules; and
a decrease due to cleavage of the molecules of length i δ. For uniform radiation
of randomly distributed molecules all equally exposed to the radiation, the rate of
1 W.C. Parke, “Kinetic Model of DNA Cleavage by Radiation,” Phys Rev E 56, 5819–5822 (1997).
© Springer Nature Switzerland AG 2020
W. C. Parke, Biophysics, https://doi.org/10.1007/978-3-030-44146-3
647
DNA Splitting by Radiation
The study and practice of medicine could benefit from an
enhanced engagement with the new perspectives provided by the
emerging areas of complexity science and systems biology.
— Geoffrey B. West
An important observable that a radiation-damage theory can predict is the distribution of fragment lengths created by a given exposure and given environment. As
another example of mathematical modeling in biology, we here present a statistical
model to predict the splitting of the DNA backbone by radiation. 1
E.1 Cleavage of Linear Molecules
Consider an initial volume of DNA molecules dispersed in a sample volume of
target material, such as a water solution. If this volume is irradiated, causing locally
deposited energy sufficient to break both backbones of the double helix (directly
or indirectly), then cleavage will have some probability of occurring. (Here, direct
break-up refers to cleavage caused by energy deposited onto the DNA from primary
and secondary radiation while indirect break-up includes energy transferred from
nearby ions and radicals created by the radiation.) To model the radiation-induced
cleavage events, assume that the molecule is made of segments of minimum length
δ, and that the initial molecules have length n δ , where n is an integer. Let N i be
the number of DNA molecule fragments present at a particular time having a length
i δ. Initially, all N i are zero except N n , which starts as the total number of DNA
molecules present in the initial volume, which is taken as N. As the molecules
are irradiated, the change in the number of molecules having length i δ comes
about from two mechanisms: an increase from cleavage of larger molecules; and
a decrease due to cleavage of the molecules of length i δ. For uniform radiation
of randomly distributed molecules all equally exposed to the radiation, the rate of
1 W.C. Parke, “Kinetic Model of DNA Cleavage by Radiation,” Phys Rev E 56, 5819–5822 (1997).
© Springer Nature Switzerland AG 2020
W. C. Parke, Biophysics, https://doi.org/10.1007/978-3-030-44146-3
647