Electronic Journal of Statistics

Cox Markov models for estimating single cell growth

Federico Bassetti, Ilenia Epifani, and Lucia Ladelli

Full-text: Open access

Abstract

Recent experimental techniques produce thousands of data of single cell growth, consequently stochastic models of growth can be validated on true data and used to understand the main mechanisms that control the cell cycle. A sequence of growing cells is usually modeled by a suitable Markov chain. In this framework, the most interesting goal is to infer the distribution of the doubling time (or of the added size) of a cell given its initial size and its elongation rate. In the literature, these distributions are described in terms of the corresponding conditional hazard function, referred as division hazard rate. In this work we propose a simple but effective way to estimate the division hazard by using extended Cox modeling. We investigate the convergence to the stationary distribution of the Markov chain describing the sequence of growing cells and we prove that, under reasonable conditions, the proposed estimators of the division hazard rates are asymptotically consistent. Finally, we apply our model to study some published datasets of E-Coli cells.

Article information

Source
Electron. J. Statist. Volume 11, Number 2 (2017), 2931-2977.

Dates
Received: September 2016
First available in Project Euclid: 11 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1502416820

Digital Object Identifier
doi:10.1214/17-EJS1306

Zentralblatt MATH identifier
1372.60100

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces 62N02: Estimation 62P10: Applications to biology and medical sciences
Secondary: 62F12: Asymptotic properties of estimators 62M05: Markov processes: estimation

Keywords
Asymptotic consistency cell size growth in bacteria Cox partial likelihood division hazard rate extended Cox model positive Harris recurrent Markov chains

Rights
Creative Commons Attribution 4.0 International License.

Citation

Bassetti, Federico; Epifani, Ilenia; Ladelli, Lucia. Cox Markov models for estimating single cell growth. Electron. J. Statist. 11 (2017), no. 2, 2931--2977. doi:10.1214/17-EJS1306. https://projecteuclid.org/euclid.ejs/1502416820


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