Modelling of cell aging - system theoretic approach

• Autorzy: Świerniak, A. , Kimmel, M. , Śmieja, J. , Rzeszowska-Wolny, J.
• Języki publikacji: EN

Abstrakty

EN

We characterize the asymptotic behavior of telomeres shortening of which is supposed to be the mechanism of aging and death. The problem is described by models in the form of infinitely many differential linear first order equations, resulting from branching random walk processes used to represent the evolution of particles in this problem, under different assumptions dealing with stochastic characterization of the process. We use control theoretical machinery based on Laplace transforms, Tauberian theorems and transfer loop reduction.

Słowa kluczowe

PL

modele molekularny; błądzenie losowe rozgałęzione; telomery; transformaty Laplace'a

EN

molecular models; branching random walk; telomeres; Laplace transforms

• Czasopismo: Journal of Medical Informatics & Technologies
• Rocznik: 2001
• Tom: Vol. 2, Part. 1
• Strony: MI3--MI8
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Świerniak, A.

• Department of Automatic Control, Silesian University of Technology, Akademicka 16, 44-101 Gliwice, Poland

autor

Kimmel, M.

• Department of Statistics, Rice University, Houston TX 77251, USA

autor

Śmieja, J.

• Department of Automatic Control, Silesian University of Technology, Akademicka 16, 44-101 Gliwice, Poland

autor

Rzeszowska-Wolny, J.

• Department of Clinical and Experimental Biology, Institute of Oncology Branch Gliwice, 44-101 Gliwice, Poland

Bibliografia

• [1] ARINO O., KIMMEL M., WEBB G.F., Mathematical modeling of the loss of telomere sequences, J. Theor. Biol., Vol. 177, 45-57, 1995.
• [2] ATHREYA K. B. NEY P. E., Branching Processes, Springer, New York, 1972.
• [3] FELLER W., An Introduction to Probability Theory and Its Applications. Vol.2, Wiley, New York, 1966.
• [4] LEVY M.Z., ALLSOP R.C., FUTCHERT A. B., GRIEDER C. W., HARLEY C.B., Telomere end-replication problem and cell aging, J. Molec. Biol., Vol. 225, 951-960, 1992.
• [5] OLOFSSON P., KIMMEL M., Stochastic models of telomere shortening, Math.Biosci.. Vol. 158, 75-92, 1999.
• [6] OLOFSSON P., Mathematical modeling of telomere shortening: an overview, Arch. Contr. Sciences, Vol.9 (XLV). 133-143, 1999.