Stochastic models of telomere shortening

Shortening of chromosome ends, known as telomeres, is one of the supposed m echanisms of-cellular aging and death. We provide a probabilistic analysis of the process of loss of telomere ends. The first work concerned with that issue is the paper by Levy et al. [J. Molec. Biol. 225 (1992) 951-960]. Th eir deterministic model reproduced the observed frequencies of viable cells in the in vitro experiments. Arino et al. [J. Theor. Biol. 177 (1995) 45-5 7] reformulated the model of Levy et al. (1992) in the terms of branching p rocesses with denumerable type space. In the present paper, the mathematica l results of Arino et al. (1995) are extended to the case in which cell dea th is present, in cells with telomeres above and below the critical thresho ld of length, generally with differing probabilities. Both exact and asympt otic results are provided, as well as a discussion of biological relevance of the results. (C) 1999 Elsevier Science Inc. All rights reserved.