Detection of cellular aging in a Galton–Watson process

Delmas, Jean‐François; Marsalle, Laurence

doi:10.1016/j.spa.2010.07.002

Cited by 47 publications

(86 citation statements)

References 16 publications

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“…They were introduced by Delmas and Marsalle [12] in order to take into account the death of individuals in the Escherichia coli's (E.coli) reproduction model. E.coli is a rod-shaped bacterium which reproduces by dividing in the middle, thus producing two cells.…”

Section: Introductionmentioning

confidence: 99%

“…However, in the BMC model presented by Guyon, cells are assumed to never die (a death corresponds to no more division). To take into account cells's death, Delmas and Marsalle [12], instead of a regular binary tree, used a binary GW tree to label cells. In the sequel, we will introduce the model which allowed them to study the behavior of the growth rate of cells, taking into account their possible death.…”

Section: Introductionmentioning

confidence: 99%

“…The initial individual is denoted 1. The model proposed by Delmas and Marsalle [12] is defined as follows.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, one can assume that the cells which do not divide and those which do not exist are missing or dead. In [12], Delmas and Marsalle using their results for BMC on GW tree, gave laws of large numbers and central limit theorem for the maximum likelihood estimator of the parameter…”

Section: Introductionmentioning

confidence: 99%

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Deviation inequalities for bifurcating Markov chains on Galton−Watson tree

Penda¹

2015

ESAIM: PS

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Abstract. We provide deviation inequalities for properly normalized sums of bifurcating Markov chains on Galton-Watson tree. These processes are extension of bifurcating Markov chains (which was introduced by Guyon to detect cellular aging from cell lineage) in case the index set is a binary Galton-Watson process. As application, we derive deviation inequalities for the least-squares estimator of autoregressive parameters of bifurcating autoregressive processes with missing data. These processes allow, in case of cell division, to take into account the cell's death. The results are obtained under an uniform geometric ergodicity assumption of an embedded Markov chain.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The initial individual is denoted 1. The model proposed by Delmas and Marsalle [12] is defined as follows.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Deviation inequalities for bifurcating Markov chains on Galton−Watson tree

Penda¹

2015

ESAIM: PS

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“…An asymmetric BAR model was therefore proposed by Guyon (2007), where the two sets of parameters corresponding to sister cells are allowed to be different. Inference for this model was only investigated for single-trees growing to infinity, see Guyon (2007), Bercu et al (2009) for the fully observed model or Delmas and Marsalle (2010), de Saporta et al (2011), de Saporta et al (2012 for missing data models.…”

Section: Introductionmentioning

confidence: 99%

Statistical study of asymmetry in cell lineage data

Saporta

Gégout-Petit

Marsalle

2014

Computational Statistics & Data Analysis

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A rigorous methodology is proposed to study cell division data consisting in several observed genealogical trees of possibly different shapes. The procedure takes into account missing observations, data from different trees, as well as the dependence structure within genealogical trees. Its main new feature is the joint use of all available information from several data sets instead of single data set estimation, to avoid the drawbacks of low accuracy for estimators or low power for tests on small single-trees. The data is modeled by an asymmetric bifurcating autoregressive process and possibly missing observations are taken into account by modeling the genealogies with a two-type Galton-Watson process. Least-squares estimators of the unknown parameters of the processes are given and symmetry tests are derived. Results are applied on real data of Escherichia coli division and an empirical study of the convergence rates of the estimators and power of the tests is conducted on simulated data.

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Splitting Feller Diffusion for Cell Division with Parasite Infection

Bansaye

2015

Stochastic Models for Structured Populations

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We describe the evolution of the quantity of parasites in a population of cells which divide in continuous-time. The quantity of parasites in a cell follows a Feller diffusion, which is splitted randomly between the two daughter cells when a division occurs. The cell division rate may depend on the quantity of parasites inside the cell and we are interested in the cases of constant or monotone division rate. We first determine the asymptotic behavior of the quantity of parasites in a cell line, which follows a Feller diffusion with multiplicative jumps. We then consider the evolution of the infection of the cell population and give criteria to determine whether the proportion of infected cells goes to zero (recovery) or if a positive proportion of cells becomes largely infected (proliferation of parasites inside the cells).A fragment with mass x splits with rate r(x) in two fragments whose mass are respectively equal to Θx and (1 − Θ)x. Let us notice similarities with [BD86, BD87] for splitting intervals of size x at rate r(x) = x α (α > 0), which amount to considering constant quantity of parasites within cells.We aim at determining how the infection evolves in the cell population. We stress that the results we give in this paper do not depend on the initial quantity of parasites x 0 > 0.First, in Section 3, we determine the asymptotic behavior of the quantity of parasites in a cell line (Y t : t ≥ 0). This amounts to following the infection in a cell until it divides and then choose at random one of the two daughter cells. This process is a Feller diffusion X with multiplicative jumps Θ occurring at rate r(.) and we prove the following extinction criterion.Proposition. (i) In the case where r(.) = r is constant,(ii) In the case where r is an increasing function, ⋆ If there exists x 0 such that g ≤ E(log(1/Θ))r(x 0 ), then a.s. there exists t > 0 such that Y t = 0.⋆ If g > E(log(1/Θ)) sup x∈R+ r(x), then P(lim t→∞ Y t = ∞) > 0.(iii) In the case where r is a decreasing function, ⋆ If g ≤ E(log(1/Θ)) inf x∈R+ r(x), then a.s. there exists t > 0 such that Y t = 0.

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Detection of cellular aging in a Galton–Watson process

Cited by 47 publications

References 16 publications

Deviation inequalities for bifurcating Markov chains on Galton−Watson tree

Deviation inequalities for bifurcating Markov chains on Galton−Watson tree

Statistical study of asymmetry in cell lineage data

Splitting Feller Diffusion for Cell Division with Parasite Infection

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