Ohm’s Law for Biogeochemical Modeling

  • November 15, 2021
  • Home Page Feature,Science and Technical Highlights
  • Top: Circuit schema for the Michaelis-Menten kinetics, with the example (in red box) depicting the conversion of pyruvate into acetyl-coA and CO2 by the enzyme complex pyruvate dehydrogenase complex; Bottom: Series resissubstratetor-based schema for an enzyme chain and its reaction on 𝑆_1, where dotted lines indicate multiple resistors 𝑟_(𝐸,𝑗) concatenated in series. Symbols are explained in the main text. The example for b depicts the metabolic pathway of glycolysis.

    Ohm’s law was shown to be able to formulate most biogeochemical reactions, providing a unified formulation between biogeochemistry and biogeophysics in land biogeochemical models.


    Consistent and coherent formulation of biogeochemical reactions is important for the design of mathematically and mechanistically well-posed ecosystem biogeochemistry models. Usually, biogeochemical models rely on an intuitive extension of Monod kinetics and application of the law of the minimum, as manifested in the modeling of photosynthesis and multiple substrate co-limited growth. Scientists first showed that simple enzyme kinetics can be interpreted using Ohm’s law. Then they used Ohm’s law to formulate various biogeochemical reactions. This approach allowed obtaining insights into several important biogeochemical processes, such as the power-efficiency tradeoff for metabolic pathways, the preference of anaerobic respiration to aerobic respiration in a high carbon substrate environment by facultative microbes, the temperature sensitivity of biogeochemical reactions, and multiple-substrate-co-limited growth. Researchers evaluated Ohm’s law for modeling aerobic respiration and multiple-substrate-co-limited growth and found very good performance in terms of goodness of fit to observations. The scientists thus recommend the application of Ohm’s law to all sorts of biogeochemical problems in ecosystem models.


    The theoretical analysis and observational benchmarks indicate that Ohm’s law can provide (1) coherent formulations for many commonly encountered biogeochemical processes, such as microbial substrate uptake, multiple-substrate-co-limited biological growth, photosynthesis, etc., (2) important insights on the temperature sensitivity of biogeochemical reactions (for example, and show that the popular macromolecular rate theory is a crude approximation to the thermodynamic based formulation), and (3) unified formulation of biogeochemistry and biogeophysics in ecosystem models.


    Ecosystem biogeochemical modeling requires robust and coherent mathematical formulations of the biogeochemical processes. State-of-the-art approaches have largely relied on the intuitive application of the Monod kinetics and law of the minimum. Although more rigorous approaches such as the SUPECA (synthesize unit plus equilibrium chemistry approximation) kinetics exist, they have been difficult to implement. Researchers show that Ohm’s law that is taught in high school physics and widely adopted by land models for biogeophysics provides a coherent interpretation and formulation of the many biogeochemical processes that biogeochemical modelers strive to resolve. The application of Ohm’s law resulted in satisfying performance in modeling aerobic soil respiration from incubation experiments and two-substrate-limited plant and microbial growth from observations. It was further demonstrated that Ohm’s law provides insights to many important observations, including why microbial growth often follows the Mond kinetics, why facultative microbes do fermentation under high carbon substrate conditions when the environment is aerobic, and why the macromolecular rate theory emerges from thermodynamics but may have inaccuracies when modeling the temperature sensitivity of biogeochemical reactions. Ohm’s law is expected to find a wide range of applications in ecosystem modeling.



    • This work was supported by No. DE-AC02-05CH11231 as part of the NGEE Arctic project, TES warming project, and the Energy Exascale Earth System Model (E3SM) project.


    • William J. Riley, Lawrence Berkeley National Laboratory
    Send this to a friend