Boltzmann statistics are underlying microbial growth

Elie Desmond-Le Quéméner (1) , Théodore Bouchez (2)

1 BIOMIC
2 UR HBAN - Hydrosystèmes et Bioprocédés

Microbes are the most abundant living forms on earth and major contributors to the biogeochemical cycles. However, our ability to model their dynamics only relies on empirical laws, fundamentally restricting our understanding and predictive capacity in many environmental systems. Preeminent physicists such as Schrödinger and Prigogine have introduced a thermodynamic interpretation of life, paving the way for a quantitative theory. From these seminal contributions have emerged microbial thermodynamics, which allows the prediction of microbial energy allocation. Nevertheless, the link between energy balances and growth dynamics is still not understood. Here we demonstrate a microbial growth equation relying on an explicit theoretical ground sustained by Boltzmann statistics, thus establishing a flux-force relationship between microbial growth rate and exergy. Historical data from Monod are used to illustrate the ability of our law to represent the classical sigmoidal relationship between growth rate and substrate concentration. More importantly, we derived a theoretical interpretation of microbial isotopic fractionation phenomenon and made associated predictions such as the existence of two classes of fractionation behavior depending on the thermodynamic properties of isotopomers. Using recent reports, we then show how these predictions are supported by experimental evidences. Our work opens the door to the modeling of microbial population dynamics through a thermodynamic state analysis of environmental systems. We anticipate that this flux-force relationship could improve the design and control of biotechnological processes and applications. The contribution of microbial reactions to earth biogeochemical cycles could also be more accurately modeled. More fundamentally, we believe that our theory offers a mathematical framework to assess the consistency of ecological and evolutionary concepts.

Mots clés: growth rate; exergy; Gibbs energy; statistical physics; flux force relationship; microbial division

Domaines: Ecologie, Environnement; Biophysique [physics.bio-ph]; Microbiologie et Parasitologie

Elie Desmond-Le Quéméner, Théodore Bouchez. Boltzmann statistics are underlying microbial growth. 2013. ⟨hal-00825781v2⟩