Asymptotic analysis of noisy fitness maximization, applied to metabolism and growth

TL;DR

This paper models population dynamics with cell growth and metabolic phenotype diffusion, solving a non-linear Fokker-Planck equation asymptotically to reveal how populations respond to perturbations.

Contribution

It introduces an asymptotic analysis of a population model coupling growth and metabolism, providing new scaling laws for fluctuations and response times.

Findings

Suboptimal populations respond faster to perturbations.

Scaling laws for growth rate fluctuations derived.

Steady state solutions obtained via WKB approximation.

Abstract

We consider a population dynamics model coupling cell growth to a diffusion in the space of metabolic phenotypes as it can be obtained from realistic constraints-based modelling. In the asymptotic regime of slow diffusion, that coincides with the relevant experimental range, the resulting non-linear Fokker-Planck equation is solved for the steady state in the WKB approximation that maps it into the ground state of a quantum particle in an Airy potential plus a centrifugal term. We retrieve scaling laws for growth rate fluctuations and time response with respect to the distance from the maximum growth rate suggesting that suboptimal populations can have a faster response to perturbations.