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2020 | OriginalPaper | Buchkapitel

Stochastic Models of Cell Proliferation Kinetics Based on Branching Processes

verfasst von : Nikolay M. Yanev

Erschienen in: Statistical Modeling for Biological Systems

Verlag: Springer International Publishing

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Abstract

The aim of this memorial survey paper is to present some joint work with Andrei Yu. Yakovlev (http://​www.​biology-direct.​com/​content/​3/​1/​10) focused on new ideas for the theory of branching processes arising in cell proliferation modeling. The following topics are considered: some basic characteristics of cell cycle temporal organization, distributions of pulse-labeled discrete markers in branching cell populations, distributions of a continuous label in proliferating cell populations, limiting age and residual lifetime distributions for continuous-time branching processes, limit theorems and estimation theory for multitype branching populations and relative frequencies with a large number of ancestor, age-dependent branching populations with randomly chosen paths of evolution. Some of the presented results have not been published yet.

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Nächstes Kapitel Age-Dependent Branching Processes with Non-homogeneous Poisson Immigration as Models of Cell Kinetics
Fußnoten
Literatur
1.
Athreya, K. B., & Ney, P. E. (1972). Branching processes. Berlin: Springer.CrossRef
2.
Dion, J.-P., & Yanev, N. M. (1997). Limit theorems and estimation theory for branching processes with an increasing random number of ancestors. Journal of Applied Probability, 34, 309–327.MathSciNetCrossRef
3.
Feller, W. (1951). Diffusion processes in genetics. Proceedings of Second Berkeley Symposium on Mathematical Statistics and Probability (pp. 227–246). Berkeley: University of California Press.
4.
Guttorp, P. (1991). Statistical inference for branching processes. New York: Wiley.MATH
5.
Haccou, P., Jagers, P., & Vatutin, V. A. (2005). Branching processes: Variation, growth and extinction of populations. Cambridge: Cambridge University Press.CrossRef
6.
7.
Hyrien, O., Mayer-Proschel, M., Noble, M., & Yakovlev, A. Yu. (2005). Estimating the life-span of oligodendrocytes from clonal data on their development in cell culture. Mathematical Biosciences, 193, 255–274.MathSciNetCrossRef
8.
Hyrien, O., Mayer-Proschel, M., Noble, M., & Yakovlev, A. Yu. (2005). A stochastic model to analyze clonal data on multi-type cell populations. Biometrics, 61, 199–207.MathSciNetCrossRef
9.
Jagers, P. (1969). The proportions of individuals of different kinds in two-type populations. A branching process problem arising in biology. Journal of Applied Probability, 6, 249–260.MathSciNetCrossRef
10.
Jagers, P. (1975). Branching processes with biological applications. London: Wiley.MATH
11.
Kimmel, M., & Axelrod, D. E. (2002). Branching processes in biology. New York: Springer.CrossRef
12.
Kolmogorov, A. N. (1938). Zur Lösung einer biologischen Aufgabe. Proceedings of Tomsk State University, 2, 1–6.
13.
Kolmogorov, A. N. (1941). On the lognormal distribution of the particle sizes in splitting (in Russian). Doklady Akademii Nauk (Proceedings of the Academy of Sciences USSR), 31, 99–101.
14.
Kolmogorov, A. N., & Dmitriev, N. A. (1947). Branching random processes (in Russian). Doklady Akademii Nauk (Proceedings of the Academy of Sciences USSR), 56, 7–10.
15.
Kolmogorov, A. N., & Sevastyanov, B. A. (1947). Calculation of final probabilities of branching random processes (in Russian). Doklady Akademii Nauk (Proceedings of the Academy of Sciences USSR), 56, 783–786.
16.
Lamperti, J. (1967). Limiting distributions for branching processes. In Proceedings of Fifth Berkeley Symposium on Mathematical Statistics and Probability (pp. 225–241). Berkeley: University of California Press.
17.
Mode, C. J. (1971). Multitype branching processes: Theory and applications. New York: Elsevier.MATH
18.
Mode, C. J. (1971). Multitype age-dependent branching processes and cell cycle analysis. Mathematical Biosciences, 10, 177–190.CrossRef
19.
Sevastyanov, B. A. (1971). Branching processes (in Russian). Moscow: Nauka.
20.
Yakovlev, A. Yu., Boucher, K., Mayer-Proschel, M., & Noble, M. (1998). Quantitative insight into proliferation and differentiation of oligodendrocyte type 2 astrocyte progenitor cells in vitro. Proceedings of the National Academy of Sciences of the United States of America, 95, 14164–14167.
21.
Yakovlev, A. Yu., Stoimenova, V. K., & Yanev, N. M. (2008). Branching processes as models of progenitor cell populations and estimation of the offspring distributions. Journal of the American Statistical Association, 103, 1357–1366.MathSciNetCrossRef
22.
Yakovlev, A. Yu., & Yanev, N. M. (1980). The dynamics of induced cell proliferation within the models of branching stochastic processes: 1. Numbers of cells in successive generations. Cytology, 22, 945–953.
23.
Yakovlev, A. Yu., & Yanev, N. M. (1989). Transient processes in cell proliferation kinetics.Lecture notes in biomathematics (Vol. 82). New York: Springer.CrossRef
24.
Yakovlev, A. Yu., & Yanev, N. M. (2006). Branching stochastic processes with immigration in analysis of renewing cell populations. Mathematical Biosciences, 203, 37–63.MathSciNetCrossRef
25.
Yakovlev, A. Yu., & Yanev, N. M. (2006). Distributions of continuous labels in branching stochastic processes. Proceedings of Bulgarian Academy of Sciences, 60, 1123–1130.
26.
Yakovlev, A. Yu., & Yanev, N. M. (2007). Age and residual lifetime distributions for branching processes. Statistics & Probability Letters, 77, 503–513.MathSciNetCrossRef
27.
Yakovlev, A. Yu., & Yanev, N. M. (2007). Branching populations of cells bearing a continuous label. Pliska Studia Mathematica Bulgarica, 18, 387–400.MathSciNet
28.
Yakovlev, A. Yu., & Yanev, N. M. (2009). Relative frequencies in multitype branching processes. The Annals of Applied Probability, 19, 1–14.MathSciNetCrossRef
29.
Yakovlev, A. Yu., & Yanev, N. M. (2010). Limiting distributions in multitype branching processes. Stochastic Analysis and Applications, 28, 1040–1060.MathSciNetCrossRef
30.
Yanev, N. M. (1975). On the statistics of branching processes. Theory of Probability and its Applications, 20, 612–622.MathSciNet
31.
Yanev, N. M. (2008). Statistical inference for branching processes. In M. Ahsanullah & G. P. Yanev (Eds.), Records and branching processes (pp. 143–168). New York: NOVA Science Publishers.
32.
Yanev, N. M., & Yakovlev, A. Yu. (1983). The dynamics of induced cell proliferation within the models of branching stochastic processes: 2. Some characteristics of cell cycle temporal organization. Cytology, 25, 818–825.
33.
Yanev, N. M., & Yakovlev, A. Yu. (1985). On the distributions of marks over a proliferating cell population obeying the Bellman-Harris branching processes. Mathematical Biosciences, 75, 159–173.CrossRef
34.
Yanev, N. M., Yakovlev, A. Yu., & Tanushev, M. S. (1987). Bellman-Harris branching processes and distribution of marks in proliferating cell populations. Proceedings of the 1stWord Congress of the Bernoulli Society, 2, 725–728.
35.
Zorin, A. V., Yakovlev, A. Yu., Mayer-Proschel, M., & Noble, M. (2000). Estimation problems associated with stochastic modeling of proliferation and differentiation of O-2A progenitor cells in vitro. Mathematical Biosciences, 67, 109–121.CrossRef
Metadaten
Titel
Stochastic Models of Cell Proliferation Kinetics Based on Branching Processes
verfasst von
Nikolay M. Yanev
Copyright-Jahr
2020
Buch
Statistical Modeling for Biological Systems

Print ISBN: 978-3-030-34674-4

Electronic ISBN: 978-3-030-34675-1

Copyright-Jahr: 2020

DOI
https://doi.org/10.1007/978-3-030-34675-1_1

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