Stochastic models of telomere shortening.

Shortening of chromosome ends, known as telomeres, is one of the supposed mechanisms 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]. Their deterministic model reproduced the observed frequencies of viable cells in the in vitro experiments. Arino et al. [J. Theor. Biol. 177 (1995) 45-57] reformulated the model of Levy et al. (1992) in the terms of branching processes with denumerable type space. In the present paper, the mathematical results of Arino et al. (1995) are extended to the case in which cell death is present, in cells with telomeres above and below the critical threshold of length, generally with differing probabilities. Both exact and asymptotic results are provided, as well as a discussion of biological relevance of the results.

[1]  Charles J. Mode,et al.  Multitype Branching Processes. , 1973 .

[2]  J. Skurnick,et al.  Shortened telomere length in white blood cells of patients with IDDM. , 1998, Diabetes.

[3]  B L Levine,et al.  Human naive and memory T lymphocytes differ in telomeric length and replicative potential. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[5]  C B Harley,et al.  Telomere loss: mitotic clock or genetic time bomb? , 1991, Mutation research.

[6]  Niels Schaft,et al.  T Cell Telomere Length in HIV-1 Infection: No Evidence for Increased CD4+ T Cell Turnover , 1996, Science.

[7]  A M Olovnikov,et al.  A theory of marginotomy. The incomplete copying of template margin in enzymic synthesis of polynucleotides and biological significance of the phenomenon. , 1973, Journal of theoretical biology.

[8]  Alan S. Perelson,et al.  Multitype Branching Processes , 1985 .

[9]  P. Jagers.  General branching processes as Markov fields , 1989 .

[10]  Upendra Dave,et al.  Applied Probability and Queues , 1987 .

[11]  William Feller,et al.  An Introduction to Probability Theory and Its Applications, Vol. 2 , 1967 .

[12]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[13]  Peter Olofsson,et al.  A branching process model of telomere shortening , 2000 .

[14]  R. Holliday.  Growth and death of diploid and transformed human fibroblasts. , 1975, Federation proceedings.

[15]  C B Harley,et al.  Telomere end-replication problem and cell aging. , 1992, Journal of molecular biology.

[16]  A. W. Kemp,et al.  Applied Probability and Queues , 1989 .

[17]  M Kimmel,et al.  Mathematical modeling of the loss of telomere sequences. , 1995, Journal of theoretical biology.

[18]  J. Steitz,et al.  Telomere shortening associated with chromosome instability is arrested in immortal cells which express telomerase activity. , 1992, The EMBO journal.