Detection of cellular aging in a Galton-Watson process

被引：38

作者：

Delmas, Jean-Francois ^{[1
]}

Marsalle, Laurence ^{[2
]}

机构：

[1] Univ Paris Est, CERMICS, F-77455 Champs Sur Marne, Marne La Vallee, France

[2] Univ Lille 1, Lab P Painleve, CNRS, UMR 8524, F-59655 Villeneuve Dascq, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2010年 / 120卷 / 12期

关键词：

Aging; Galton-Watson process; Bifurcating Markov process; Stable convergence; BRANCHING MARKOV-CHAINS; LIMIT-THEOREMS; MODEL; TREE; SEGREGATION;

D O I：

10.1016/j.spa.2010.07.002

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the bifurcating Markov chain model introduced by Guyon to detect cellular aging from cell lineage. To take into account the possibility for a cell to die, we use an underlying super-critical binary Galton Watson process to describe the evolution of the cell lineage. We give in this more general framework a weak law of large number, an invariance principle and thus fluctuation results for the average over all individuals in a given generation, or up to a given generation. We also prove that the fluctuations over each generation are independent. Then we present the natural modifications of the tests given by Guyon in cellular aging detection within the particular case of the auto-regressive model. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：2495 / 2519

页数：25

共 22 条

[1] Senescence in a bacterium with asymmetric division
Ackermann, M
Stearns, SC
Jenal, U
[J]. SCIENCE, 2003, 300 (5627) : 1920 - 1920
[2] On the evolutionary origin of aging
Ackermann, Martin
Chao, Lin
Bergstrom, Carl T.
Doebeli, Michael
[J]. AGING CELL, 2007, 6 (02) : 235 - 244
[3] [Anonymous], 1972, BRANCHING PROCESSES
[4] Some limit theorems for positive recurrent branching Markov chains: I
Athreya, KB
Kang, HJ
[J]. ADVANCES IN APPLIED PROBABILITY, 1998, 30 (03) : 693 - 710
[5] Athreya KB, 1998, ADV APPL PROBAB, V30, P711, DOI 10.1017/S0001867800008569
[6] BANSAYE V, 2009, LIMIT THEOREMS MARCO
[7] Proliferating parasites in dividing cells: Kimmel's branching model revisited
Bansaye, Vincent
[J]. ANNALS OF APPLIED PROBABILITY, 2008, 18 (03) : 967 - 996
[8] CELL CONTAMINATION AND BRANCHING PROCESSES IN A RANDOM ENVIRONMENT WITH IMMIGRATION
Bansaye, Vincent
[J]. ADVANCES IN APPLIED PROBABILITY, 2009, 41 (04) : 1059 - 1081
[9] Asymptotic analysis for bifurcating autoregressive processes via a martingale approach
Bercu, Bernard
de Saporta, Benoite
Gegout-Petit, Anne
[J]. ELECTRONIC JOURNAL OF PROBABILITY, 2009, 14 : 2492 - 2526
[10] THE BIFURCATING AUTOREGRESSION MODEL IN CELL LINEAGE STUDIES
COWAN, R
STAUDTE, R
[J]. BIOMETRICS, 1986, 42 (04) : 769 - 783

← 1 2 3 →