Mathematical modeling of telomere shortening: an overview

• Autorzy: Olofsson P.
• Języki publikacji: EN

Abstrakty

EN

Shortening of telomeres is one of the supposed mechanisms of aging and death. This paper reviews the attempts to model and analyze this process with mathematical methods. The emphasis is put on branching process models where the main features are irreducibility and polynomial growth.

Słowa kluczowe

EN

branching process; population dynamics; cell population; telomeres

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 1999
• Tom: Vol. 9, no. 1/2
• Strony: 133--141
• Opis fizyczny: Bibliogr. 13 poz., wzory

Twórcy

autor

Olofsson P.

• Department of Statistics, Rice University, Houston, USA

Bibliografia

• [1] O. Arino M. Kimmel and G. F. Webb: Mathematical modeling of the loss of telomere sequences. J. Theor. Biol. 177 (1995), 45-57.
• [2] O. Arino, E. Sanchez and G. F. Webb: Polynomial growth dynamics of telomere loss in a heterogeneous cell population. Dynam. Contin. Discrete Impuls. Systems 3 (1997), 262-282.
• [3] S. Asmussen: Applied Probability and Queues. Wiley, New York, 1987.
• [4] W. Feller: An Introduction to Probability Theory and its Applications. Vol 2. Wiley, New York, 1971.
• [5] P. Jagers: General branching processes as Markov fields. Stoch. Proc. Appl., 32 (1989), 183-212.
• [6] R. B. Jones, R. G. Whitney and J. R. Smith: Intramitotic variation in proliferative potential: stochastic events in cellular aging. Mech. Ageing. Dev., 29 (1985), 143-149.
• [7] D. D. Larson, E. A. Spangler and E. H. Blackburn: Dynamics of telomere length variation in tetrahymena thermophila. Cell, 50 (1987), 477-483.
• [8] M. Z. Levy, R. C. Allsopp, A. B. Futcher, C. W. Greider and C. B. Harley: Telomere end-replication problem and cell Aging. J. Molec. Biol., 225 (1992), 951-960.
• [9] C. Mode: Multitype Branching Processes. American Elsevier, New York, 1971.
• [10] P. Olofsson: A Branching Process Model of Telomere Shortening. Communications in Statistics-Stochastic Models, 16(1) (2000), 167-177.
• [11] P. Olofsson and M. Kimmel: Stochastic models of telomere shortening. Math. Biosci., 1 (1999), 75-92.
• [12] I. Rubelj and Z. Vondracek: Stochastic Mechanism of Cellular Aging-Abrupt Telomere Shortening as a Model for Stochastic Nature of Cellular Aging. J. Theor Biol., 197 (1999), 425-438.
• [13] Z. Tan: Intramitotic and Intraclonal Variation in Proliferative Potential of Human Diploid Cells: Explained by Telomere Shortening. J. Theor Biol., 198 (1999), 259-268.