Stochastic Gene Expression Model of Nuclear-to-Cell Ratio Homeostasis

TL;DR

This paper develops a stochastic gene expression model to analyze how nuclear-to-cell volume ratio homeostasis is maintained despite cellular variability, highlighting the roles of gene fraction and system size in controlling fluctuations.

Contribution

It introduces a stochastic model of N/C ratio regulation, extending deterministic models by incorporating gene expression noise and cell division effects.

Findings

N/C ratio homeostasis persists under stochastic fluctuations.

Gene fraction of nuclear proteins largely determines the N/C ratio.

Fluctuations decrease with increasing system size.

Abstract

Cell size varies between different cell types, and between different growth and osmotic conditions. However, the nuclear-to-cell volume ratio (N/C ratio) remains nearly constant. In this paper, we build on existing deterministic models of N/C ratio homeostasis and develop a simplified gene translation model to study the effect of stochasticity on the N/C ratio homeostasis. We solve the corresponding chemical master equation and obtain the mean and variance of the N/C ratio. We also use a Taylor expansion approximation to study the effects of the system size on the fluctuations of the N/C ratio. We then combine the translation model with a cell division model to study the effects of extrinsic noises from cell division on the N/C ratio. Our model demonstrates that the N/C ratio homeostasis is maintained when the stochasticity in cell growth is taken into account, that the N/C ratio is largely determined by the gene fraction of nuclear proteins, and that the fluctuations in the N/C ratio diminish as the system size increases.