## Importance

Understanding the principles underlying microbial growth is essential for the carbon and nutrient cycling in the biosphere, bioremediation technologies and biochemical engineering, as well as for natural selection and evolution. Yet fundamental questions remain about the links between mass and energy balances in metabolism and microbial growth. Guided by an out of equilibrium thermodynamic framework, we interpret many data from the literature on microbial growth. The analysis reveals how the mass and energy conversion are tightly coupled by scaling laws relating thermodynamic efficiency to the absorption rate of the electron donor and the growth efficiency. More importantly, these results appear to be universal, in that they apply to all microbial species and metabolic pathways, and pave the way for a general thermodynamic theory of microbiological systems.

## Abstract

Microbial growth is a clear example of organization and structure occurring under conditions of non-equilibrium. Due to the complexity of the microbial metabolic network, elucidating the fundamental principles governing microbial growth remains a challenge. Here, we present a systematic analysis of the thermodynamics of microbial growth, taking advantage of a large data set on the growth of energy-limited monocultures. A coherent thermodynamic framework based on reaction stoichiometry allows us to quantify the amount of available energy that microbes can efficiently convert into new biomass while dissipating remaining energy in the environment and producing entropy. We show that dissipation mechanisms can be related to the absorption rate of electron donors, which leads to the central result that thermodynamic efficiency is related to the absorption rate of electron donors by the scale law.

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and growth yield by

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. These results allow us to recalculate Pirt’s equation from a thermodynamic perspective, providing a way to calculate its coefficients, as well as a better understanding of the relationship between growth rate and yield. Our results provide rather general information on the relationship between mass and energy conversion in microbial growth with potentially wide application, particularly in ecology and biotechnology.

## Footnotes

• Accepted October 4, 2021.
• Author contributions: research designed by SC; SC, AC, SM and PVC carried out research; SC analyzed the data; SC wrote the paper; and AC, SM and PVC reviewed the project.

• The authors declare no competing interests.

• This article is a direct PNAS submission.