On the Dynamical Approach of Quantitative Radiation Biology

A quantitative approach in radiation biology based on the clonogenic method and cell survival curves in various conditions are introduced. The cell survival curves seem to have universality with regard to its functional form; in other words, functional form of survival curve seems to be unchanged under various conditions including different species. Various factors affecting the radiosensitivity have been introduced to find macroscopic nature of living organisms. Mathematical models that describe cell survival curves have been presented for discussing the derivation of the mathematical form based on biological mechanism. Finally, the possibility that the structural change of chromosome affects the repair process is discussed

A Framework for Analysis of Abortive Colony Size Distributions Using a Model of Branching Processes in Irradiated Normal Human Fibroblasts

<div><p>Background</p><p>Clonogenicity gives important information about the cellular reproductive potential following ionizing irradiation, but an abortive colony that fails to continue to grow remains poorly characterized. It was recently reported that the fraction of abortive colonies increases with increasing dose. Thus, we set out to investigate the production kinetics of abortive colonies using a model of branching processes.</p><p>Methodology/Principal Findings</p><p>We firstly plotted the experimentally determined colony size distribution of abortive colonies in irradiated normal human fibroblasts, and found the linear relationship on the log-linear or log-log plot. By applying the simple model of branching processes to the linear relationship, we found the persistent reproductive cell death (RCD) over several generations following irradiation. To verify the estimated probability of RCD, abortive colony size distribution (≤15 cells) and the surviving fraction were simulated by the Monte Carlo computational approach for colony expansion. Parameters estimated from the log-log fit demonstrated the good performance in both simulations than those from the log-linear fit. Radiation-induced RCD, i.e. excess probability, lasted over 16 generations and mainly consisted of two components in the early (<3 generations) and late phases. Intriguingly, the survival curve was sensitive to the excess probability over 5 generations, whereas abortive colony size distribution was robust against it. These results suggest that, whereas short-term RCD is critical to the abortive colony size distribution, long-lasting RCD is important for the dose response of the surviving fraction.</p><p>Conclusions/Significance</p><p>Our present model provides a single framework for understanding the behavior of primary cell colonies in culture following irradiation.</p></div

Reproductive cell death probability <i>P₁</i> (0, 2 and 8 Gy) and the excess <i>P₁</i> (2, 4 and 8 Gy) at 0 to 5 generations.

<p><i>P₁</i> was calculated with the simultaneous equations <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0070291#pone.0070291.e005" target="_blank">Equation 1</a>, using the regression curves in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0070291#pone-0070291-g004" target="_blank">Figure 4a–4f</a>. IR-induced excess of <i>P₁</i> was estimated by <i>P₁</i> of abortive colonies derived from non-irradiated cells minus that from irradiated ones. Dotted lines show the 95% confidence limit.</p

Parameter values obtained from the log-linear (log y = a x+b) or log-log (log y = a log x+b) fits to the experimental data set.

<p><i>R²</i> denotes the correlation coefficient square.</p

Mock examination of the branching dynamics with a probability of reproductive cell death (<i>P₁</i>) on the log-linear plot (a) and log-log plot (b).

<p>The same <i>P₁</i> value at all branch points of the cell lineage was assumed, and <i>Freq</i> (occurrence frequency of abortive colony with <i>n</i> cells) was calculated. <i>P₁</i> ranged from 0.1 to 0.9.</p

Empirical colony size distribution.

<p>Circles indicate the experimentally determined data at 0, 2, 4 and 8 Gy of ⁶⁰Co γ-rays. “Frequency” represents the frequency of a colony with <i>n</i> cells in all abortive and clonogenic colonies.</p

Simulated colony size distribution of irradiated abortive clones.

<p>The abortive colony size distributions at 2, 4 and 8 Gy are shown in panels (a), (b) and (c), respectively. Circles demonstrate the experimentally determined size of colonies, and lines represent the simulated colony size distribution with the specific slope <i>c</i> (0.1, 0.2 and 0.4) using the parameters of the log-log fit. The data of the fixed <i>P₁</i> shows the result of the simulation using the <i>P₁</i> (<i>g</i> = 0) at all generations.</p

Regression analysis of experimental colony size distribution of abortive colonies at 0, 2 and 8 Gy.

<p>Two regression analyses on the log-linear (a, c and e) and log-log (b, d and f) plots were tested. Here, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0070291#pone.0070291.e005" target="_blank">Equation 1</a> was used to estimate the frequency of 1-cell colony size (solid circle) from that of 2-cell colonies, assuming the similar probability of reproductive cell death for 1- and 2-cell colonies. The straight lines show the linear regression curves, and the dotted lines show the curves of a 95% confidence limit. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0070291#pone-0070291-t001" target="_blank">Table 1</a> lists the numerical values of parameters obtained from the regression analysis of the data set.</p