Quantitative analysis of cell size control mechanisms

TL;DR

This paper develops a mathematical framework using PDEs and stochastic simulations to analyze and compare three key cell size control mechanisms, providing insights into their roles in size homeostasis.

Contribution

It introduces a PDE model with exact solutions for sizer, timer, and adder mechanisms, validated by stochastic simulations, advancing understanding of cell size regulation.

Findings

Exact solutions for size control mechanisms derived

Model shows how control parameters influence size distribution

Simulations confirm theoretical predictions

Abstract

Cell size control is crucial for maintaining cellular function and homeostasis. In this study, we develop a first-order partial differential equation model to examine the effects of three key size control mechanisms: the sizer, timer, and adder. Each mechanism is incorporated into the model through distinct boundary conditions. Exact solutions for these mechanisms are derived using the method of characteristics, allowing us to explore how the steady-state size distribution depends on control parameters. Additionally, individual-cell-based stochastic simulations are performed to validate our theoretical findings and investigate the size distribution under various conditions. This study provides new insights into the quantitative dynamics of cell size regulation, highlighting the underlying mechanisms and laying the groundwork for future theoretical and experimental work on size homeostasis in biological systems.