A Time-Varying Branching Process Approach to Model Self-Renewing Cells

TL;DR

This paper introduces a continuous time branching process model with time-dependent offspring distribution to analyze stem cell proliferation, providing analytical expressions and inference methods to estimate dynamic division probabilities.

Contribution

It develops a novel time-varying branching process model for stem cell dynamics, including likelihood-based inference and a forward algorithm for unobserved cell types.

Findings

Estimates time-dependent division probabilities accurately.

Derives analytical expressions for mean, variance, and autocovariance.

Demonstrates effectiveness through simulation studies.

Abstract

Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the proliferation process not only uncovers proliferative properties of stem cells, but also offers insight into tissue development under both normal conditions and pathological disruption. In this paper, we develop a continuous time branching process model with time-dependent offspring distribution to characterize stem cell proliferation process. We derive analytical expressions for mean, variance, and autocovariance of the stem cell counts, and develop likelihood-based inference procedures to estimate model parameters. Particularly, we construct a forward algorithm likelihood to handle situations when some cell types cannot be directly observed. Simulation results demonstrate that our estimation method recovers the time-dependent division probabilities with good accuracy.