A transport approach to relate asymmetric protein segregation and population growth

TL;DR

This paper develops a stochastic transport model to analyze how asymmetric protein segregation affects population growth in unicellular organisms, extending previous deterministic models to include randomness and providing new analytical and numerical solutions.

Contribution

It introduces a stochastic transport approach to generalize existing models, incorporating randomness in protein segregation and deriving a self-consistent equation for growth rate and protein distribution.

Findings

Stochasticity can be incorporated into the model as an effective asymmetry parameter.

The model provides both numerical and analytical solutions for population growth.

Results suggest stochastic effects influence the advantage of asymmetric segregation.

Abstract

Many unicellular organisms allocate their key proteins asymmetrically between the mother and daughter cells, especially in a stressed environment. A recent theoretical model is able to predict when the asymmetry in segregation of key proteins enhances the population fitness, extrapolating the solution at two limits where the segregation is perfectly asymmetric (asymmetry $a$ = 1) and when the asymmetry is small ($0 \leq a \ll 1$). We generalize the model by introducing stochasticity and use a transport equation to obtain a self-consistent equation for the population growth rate and the distribution of the amount of key proteins. We provide two ways of solving the self-consistent equation: numerically by updating the solution for the self-consistent equation iteratively and analytically by expanding moments of the distribution. With these more powerful tools, we can extend the previous model by Lin et al. to include stochasticity to the segregation asymmetry. We show the stochastic model is equivalent to the deterministic one with a modified effective asymmetry parameter ($a_{\rm eff}$). We discuss the biological implication of our models and compare with other theoretical models.