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

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.

24 pages, 6 figures

References in corpus (3)

• The ODE/IM Correspondence
• Scaling laws governing stochastic growth and division of single bacterial cells
• Bethe Ansatz and the Spectral Theory of affine Lie algebra-valued connections I. The simply-laced case

Cited by in corpus (5)

• Statistical mechanics for metabolic networks during steady-state growth
• Initial cell density encodes proliferative potential in cancer cell populations
• Exploration-exploitation tradeoffs dictate the optimal distributions of phenotypes for populations subject to fitness fluctuations
• Counting monster potentials
• Relationship between fitness and heterogeneity in exponentially growing microbial populations