A Stochastic Cluster Process Formalism
For Locations Along Chromosomes
of Radiation-Produced DNA Double Strand Breaks
Rainer K. Sachs, Artem L. Ponomarev, and Lynn R. Hlatky
Abstract
Ionizing radiation produces DSBs (DNA double strand breaks) in
chromosomes. For densely ionizing radiation, the DSBs are not spaced
randomly along a chromosome: recent data for size distributions of
DNA fragments indicate break clustering on kbp-Mbp scales. Different
DSB clusters on one chromosome are typically made by different,
statistically independent, stochastically structured radiation
tracks, and the average number of tracks involved can be small. We
therefore model DSB positions along a chromosome as a stationary
Poisson cluster process, i.e. a stochastic process consisting of
secondary point processes whose locations are determined by a primary
point process that is Poisson. Each secondary process represents a
break cluster, typically consisting of 1-10 DSBs in a
stochastic pattern determined by chromatin geometry and radiation
track structure. We derive theorems on the dose-dependence of
DSB patterns in the model, which we call the
"RLC" (randomly-located-clusters) formalism. The RLC dose-response
relation for DNA fragments of a given size is expressed in terms of a
dose-independent, one-cluster fragment-size distribution function.
The RLC formalism generalizes previous models, fits current data
adequately, and allows mechanistically based extrapolations from
high-dose experiments to the much lower doses of interest for most
applications.
Clusters