On the Emergence of the Deviation from a Poisson Law in Stochastic Mathematical Models for Radiation-Induced DNA Damage: A System Size Expansion

Abstract

In this paper, we study the system size expansion of a stochastic model for radiation-induced DNA damage kinetics and repair. In particular, we characterize both the macroscopic deterministic limit and the fluctuation around it. We further show that such fluctuations are Gaussian-distributed. In deriving such results, we provide further insights into the relationship between stochastic and deterministic mathematical models for radiation-induced DNA damage repair. Specifically, we demonstrate how the governing deterministic equations commonly employed in the field arise naturally within the stochastic framework as a macroscopic limit. Additionally, by examining the fluctuations around this macroscopic limit, we uncover deviations from a Poissonian behavior driven by interactions and clustering among DNA damages. Although such behaviors have been empirically observed, our derived results represent the first rigorous derivation that incorporates these deviations from a Poissonian distribution within a mathematical model, eliminating the need for specific ad hoc corrections.

Across the stages: a multiscale extension of the generalized stochastic microdosimetric model (MS-GSM2) to include the ultra-high dose rate

“…The target considered is bigger than the cell nucleus, so the energy deposited by tracks passing near the cell nucleus, i.e., the ionization penumbra of the tracks, is also accounted for by the MS-GSM 2 . The resulting model is an extremely general biophysical model, able to provide a mechanistically grounded description of several effects of random processes in space and time [34,39].…”

Mathematical Modeling in Systems Biology

“…The authors put forward a hypothesis that cell death can be controlled by a singular, highly integrated cell death decision network that enables cells to choose alternative cell death execution pathways within a single control network of cell death. Francesco Cordoni's work presents a macroscopic deterministic approximation of microscopic systems, which is represented by a stochastic model for radiation-induced DNA damage kinetics and repair [6]. The approximation is used to compute the distribution of the number of DNA damages that result in cell death.…”