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Conceptualizing biogeochemical reactions with an Ohm's law analogy
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  • Jinyun Tang,
  • Jinyun Tang,
  • Riley William,
  • Gianna L Maschmann,
  • Eoin L Brodie
Jinyun Tang
Lawrence Berkeley National Laboratory

Corresponding Author:[email protected]

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Jinyun Tang
Lawrence Berkeley National Laboratory
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Riley William
Lawrence Berkeley National Laboratory
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Gianna L Maschmann
Lawrence Berkeley National Laboratory
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Eoin L Brodie
Lawrence Berkeley National Laboratory
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Abstract

In studying problems like plant-soil-microbe interactions in environmental biogeochemistry and ecology, one usually has to quantify and model how substrates control the growth of, and interaction among, biological organisms. To address these substrate-consumer relationships, many substrate kinetics and growth rules have been developed, including the famous Monod kinetics for single substrate-based growth, Liebig’s law of the minimum for multiple-nutrient co-limited growth, etc. However, the mechanistic basis that leads to these various concepts and mathematical formulations and the implications of their parameters are often quite uncertain. Here we show that an analogy based on Ohm’s law in electric circuit theory is able to unify many of these different concepts and mathematical formulations. In this Ohm’s law analogy, a resistor is defined by a combination of consumers’ and substrates’kinetic traits. In particular, the resistance is equal to the mean first passage time that has been used by renewal theory to derive the Michaelis-Menten kinetics under substrate replete conditions for a single substrate as well as the predation rate of individual organisms. We further show that this analogy leads to important insights on various biogeochemical problems, such as (1) multiple-nutrient co-limited biological growth, (2) denitrification, (3) fermentation under aerobic conditions, (4) metabolic temperature sensitivity, and (5) the accuracy of Monod kinetics for describing bacterial growth. We expect our approach will help both modelers and non-modelers to better understand and formulate hypotheses when studying certain aspects of environmental biogeochemistry and ecology.
Oct 2021Published in Journal of Advances in Modeling Earth Systems volume 13 issue 10. 10.1029/2021MS002469