A Markov formulation of the repair-misrepair model of cell survival

Abstract

Tobias' repair-misrepair (RMR) model of cell survival is formulated as a Markov process, a sequence of discrete repair steps occurring at random times, and the probability of a sequence of viable repairs is calculated. The Markov formulation describes the time evolution of the probability distribution for the number of lesions in a cell. The probability of cell survival is calculated from the distribution of the initial number of lesions and the probabilities of the repair events. The production of lesions is formulated in accordance with the principles of microdosimetry, and the distribution of the initial number of lesions is obtained as an approximation for high and low linear energy transfer cases. The Markov formulation of the RMR model uses the same biological hypotheses as the original version with two statistical approximations deleted. These approximations are the neglect of the effect of statistical fluctuations in calculating the average rate of repair of lesions and the assumption that the final number of unrepaired and lethally misrepaired lesions has a Poisson distribution. The quantitative effect of these approximations is calculated, and a basis is provided for an alternative approach to calculating survival probabilities.