Detection of cellular aging in a Galton-Watson process

TL;DR

This paper extends the Galton-Watson process framework to detect cellular aging, providing new statistical laws and fluctuation results for cell lineage analysis, and adapts existing tests for this broader model.

Contribution

It introduces a Galton-Watson process model for cellular aging detection, generalizing previous bifurcating Markov chain models and deriving new fluctuation results.

Findings

Established a weak law of large numbers for the model

Proved independence of fluctuations across generations

Modified existing tests for the auto-regressive case

Abstract

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 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 one generation or up to one generation. We also prove 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.