January 10, 2023

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New Model Resolves Non-Monotonic Tradeoff Between Microbial Carbon Use Efficiency and Growth Rates

Revised dynamic energy budget model consistently and conceptually upscales from intracellular chemical reactions to the growth of microbial populations.

The dynamic energy budget (DEB) model (red) can predict that the same carbon use efficiency (CUE) can be realized with two substrate uptake rates, while popular empirical models (cyan, black) predict CUE as a monotonic function of substrate uptake rate.

[Reprinted under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0) from Tang, J., and W. J. Riley. "Revising the Dynamic Energy Budget Theory with a New Reserve Mobilization Rule and Three Example Applications to Bacterial Growth." Soil Biology and Biochemistry 178 108954 (2023). DOI:10.1016/j.soilbio.2023.108954.]

The Science

To better model microbial growth, a team of researchers developed a revised dynamic energy budget model (rDEB) that represents reserve dynamics using equilibrium chemistry approximation (ECA) kinetics. The rDEB model is consistent with a single biochemical reaction and growth of microbial populations. The rDEB model also includes several widely used microbial models as special cases. This study shows that only DEB models reasonably capture that the same microbial carbon use efficiency (CUE; i.e., the fraction of carbon retained as biomass per unit carbon uptake) can happen at both high and low growth and substrate uptake rates

The Impact

This study’s theoretical analysis and observational benchmarks indicate that (1) a thermodynamically consistent description of microbial CUE dynamics requires biological growth to be represented explicitly as a function of intracellular metabolism; (2) popular empirical models are unable to represent the microbial CUE dynamics correctly, especially for its tradeoff for growth and substrate uptake rates; and (3) a consistent mathematical upscaling from single enzymatic chemical reactions to microbial population growth is feasible. This study supports the long-held hypothesis that enzyme kinetics can be upscaled to model microbial growth.


Modeling environmental biogeochemistry requires a robust mathematical representation of biological growth. The dynamic energy budget theory provides an opportunity to develop a unified mathematical representation of biomass growth for microbes, plants, and even animals. By partitioning biomass into reserve, kinetic, and structural compartments, researchers developed the rDEB model that links a single enzymatic reaction to microbial population biomass growth. The rDEB model better explains proteomic control of biological growth and includes the standard DEB (sDEB) model and many popular empirical models as special cases. Moreover, the rDEB model identifies limitations of the sDEB model and resolves tradeoffs between microbial CUE and growth and substrate uptake rates. The rDEB model also reveals that soil water stress on microbial growth is exerted primarily through diffusion limitation of substrate uptake, with smaller effects from turgor pressure and intracellular macromolecular crowding. If kinetic biomass is further partitioned, the rDEB model will be able to resolve the dynamic proteomic control of microbial growth. Insights from this study can guide microbial model development to consistently organize trait regulation of microbial dynamics and thus obtain more robust predictions of microbial and climate control of soil carbon and nutrient dynamics.

Principal Investigator

William J. Riley
Lawrence Berkeley National Laboratory
[email protected]

Program Manager

Daniel Stover
U.S. Department of Energy, Biological and Environmental Research (SC-33)
Environmental System Science
[email protected]


This research was supported by the Biological and Environmental Research (BER) Program within the U.S. Department of Energy’s (DOE) Office of Science under contract no. DE-AC02-05CH11231 as part of the Belowground Biogeochemistry Science Focus Area and the Next-Generation Ecosystem Experiments-Arctic project.


Tang, J., and W. J. Riley. "Revising the Dynamic Energy Budget Theory with a New Reserve Mobilization Rule and Three Example Applications to Bacterial Growth." Soil Biology and Biochemistry 178 108954  (2023). https://doi.org/10.1016/j.soilbio.2023.108954.