A single formula to describe radiation-induced protein relocalization: Towards a mathematical definition of individual radiosensitivity

Immunofluorescence with antibodies against DNA damage repair and signaling protein is revolutionarising the estimation of the genotoxic risk. Indeed, a number of stress response proteins relocalize in nucleus as identifiable foci whose number, pattern and appearance/disappearance rate depend on several parameters such as the stress nature, dose, time and individual factor. Few authors proposed biomathematical tools to describe them in a unified formula that would be relevant for all the relocalizable proteins. Based on our two previous reports in this Journal (. Foray et al., 2005; Gastaldo et al., 2008), we considered that foci response to stress is composed of a recognition and a repair phase, both described by an inverse power function provided from a Euler's Gamma distribution. The resulting unified formula called "Bodgi's function" is able to describe appearance/disappearance kinetics of nuclear foci after any condition of genotoxic stress. By applying the Bodgi's formula to DNA damage repair data from 45 patients treated with radiotherapy, we deduced a classification of human radiosensitivity based on objective molecular criteria, notably like the number of unrepaired DNA double-strand breaks and the radiation-induced nucleo-shuttling of the ATM kinase.