Continuous Approximation of Stochastic Maps for Modeling Asymmetric Cell Division

TL;DR

This paper develops a stochastic map model for asymmetric cell division, linking it to the Ornstein-Uhlenbeck process, and derives analytical solutions for stable cell size distributions, validated through numerical simulations.

Contribution

It introduces a novel stochastic map approach for asymmetric cell division, providing analytical solutions and criteria for cell size distribution behaviors.

Findings

Derived a closed-form expression for stable cell size distribution.

Identified conditions for bi-phasic behavior in cell size distributions.

Validated analytical results with numerical simulations.

Abstract

Cell size control and homeostasis is a major topic in cell biology yet to be fully understood. Several growth laws like the timer, adder, and sizer were proposed, and mathematical approaches that model cell growth and division were developed. This study focuses on utilizing stochastic map modeling for investigating asymmetric cell division. We establish a mapping between the description of cell growth and division and the Ornstein-Uhlenbeck process with dichotomous noise. We leverage this mapping to achieve analytical solutions and derive a closed-form expression for the stable cell size distribution under asymmetric division. To validate our findings, we conduct numerical simulations encompassing several cell growth scenarios. Our approach allows us to obtain a precise criterion for a bi-phasic behavior of the cell size. While for the case of the sizer scenario, a transition from the uni-modal phase to bi-modal is always possible, given sufficiently large asymmetry at the division, the affine-linear approximation of the adder scenario invariably yields uni-modal distribution.