A multi-stage model of cell proliferation and death: tracking cell divisions with Erlang distributions

TL;DR

This paper introduces a multi-stage model using Erlang distributions to more accurately describe cell division times in lymphocyte populations, improving upon the exponential assumption and fitting experimental data.

Contribution

The authors develop a multi-stage model with Erlang distributions for division times and compare it to data, revealing longer initial division times and the importance of multiple stages.

Findings

Multiple stages are favored in the model fitting.

Mean time to first division exceeds subsequent division times.

Model aligns well with experimental cell count data.

Abstract

Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not divide at all. If individual cells behave independently, each can be imagined as sampling from a probability density of times to division. The most convenient choice of density in mathematical and computational work, the exponential density, overestimates the probability of short division times. We consider a multi-stage model that produces an Erlang distribution of times to division, and an exponential distribution of times to die. The resulting dynamics of competing fates is a type of cyton model. Using Approximate Bayesian Computation, we compare our model to published cell counts, obtained after CFSE-labelled OT-I and F5 T cells were transferred to lymphopenic mice. The death rate is assumed to scale linearly with the generation (number of divisions) and the number of stages of undivided cells (generation $0$) is allowed to differ from that of cells that have divided at least once (generation greater than zero). Multiple stages are preferred in posterior distributions, and the mean time to first division is longer than the mean time to subsequent divisions.