Mathematical models of radiation action on living cells: From the target theory to the modern approaches. A historical and critical review.

Cell survival is conventionally defined as the capability of irradiated cells to produce colonies. It is quantified by the clonogenic assays that consist in determining the number of colonies resulting from a known number of irradiated cells. Several mathematical models were proposed to describe the survival curves, notably from the target theory. The Linear-Quadratic (LQ) model, which is to date the most frequently used model in radiobiology and radiotherapy, dominates all the other models by its robustness and simplicity. Its usefulness is particularly important because the ratio of the values of the adjustable parameters, α and ß, on which it is based, predicts the occurrence of post-irradiation tissue reactions. However, the biological interpretation of these parameters is still unknown. Throughout this review, we revisit and discuss historically, mathematically and biologically, the different models of the radiation action by providing clues for resolving the enigma of the LQ model.

The Phosphorylated ATM Immunofluorescence Assay: A High-performance Radiosensitivity Assay to Predict Postradiation Therapy Overreactions.

PURPOSE: The ability to identify, before treatment, those patients who will overreact to radiation therapy would have sound positive clinical implications. By focusing on DNA double-strand breaks recognition and repair proteins after irradiation, we recently demonstrated that the maximal number of phosphorylated ATM (pATM) nuclear foci in the first hour (pATMmax) after ex vivo irradiation correlated with postradiation therapy toxicity severity. We performed additional analyses of our whole collection of fibroblast lines to refine the predictive performance of our assay. METHODS AND MATERIALS: Immunofluorescence experiments were performed on 117 primary skin fibroblast lines irradiated at 2 Gy. The toxicity response was split into 2 binary classes: 0 if the toxicity grade was <2 and 1 otherwise. To assess the relationship between the quantity of pATMmax foci and toxicity grade, we applied a correlation and then a supervised classification analysis. Training data sets from 13 radiosensitive patients randomly drawn using a random undersampling technique were constituted. Receiver operating characteristic analyses were performed using a Monte-Carlo method to estimate the optimal threshold and discriminate the responses for each data set. The discrimination cutoff was estimated as the maximum value of the 104 thresholds computed from each training subset. RESULTS: As expected, we confirmed a quasi-linear dependence between toxicity and pATMmax (Pearson correlation coefficient -0.85; P < 2.2e-16). When taken as a binary predictive assay with the optimal cutoff value of 34.5 pATM foci/cell, our assay showed outstanding predictive performance (sensitivity, specificity, negative predictive value, positive predictive value, and area under the curve: 100%, 92%, 100%, 99%, and 0.987, respectively). CONCLUSIONS: The results of these experiments allowed us to identify pATMmax as a high-performance predictive parameter of patients with postradiation therapy overreactions. Additional studies are in progress to confirm that this radiosensitivity assay reaches the same performance level in any condition to adapt clinical practice.

Fast and Binary Assay for Predicting Radiosensitivity Based on the Theory of ATM Nucleo-Shuttling: Development, Validation, and Performance.

PURPOSE: To examine the possibility of predicting clinical radiosensitivity by quantifying the nuclear forms of autophosphorylated ATM protein (pATM) via a specific enzyme-linked immunosorbent assay (ELISA). METHODS AND MATERIALS: This study was performed on 30 skin fibroblasts from 9 radioresistant patients and 21 patients with adverse tissue reaction events. Patients were divided into 2 groups: radioresistant (toxicity grade <2) and radiosensitive (toxicity grade ≥2). The quantity of nuclear pATM molecules was assessed by the ELISA method at 10 minutes and 1 hour after 2 Gy and compared with pATM immunofluorescence data. RESULTS: The pATM ELISA data were in quantitative agreement with the immunofluorescence data. A receiver operating characteristic analysis was applied first to 2 data sets (a training set [n=14] and a validating [n=16] set) and thereafter to all the data with a 2-fold cross-validation method. The assay showed an area under the curve value higher than 0.8, a sensitivity of 0.8, and a specificity ranging from 0.75 to 1, which strongly documents the predictive power of the pATM ELISA. CONCLUSION: This study showed that the assessment of nuclear pATM quantity after 2 Gy via an ELISA technique can be the basis of a predictive assay with the highest statistical performance among the available predictive approaches.