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Conceptualizing Biogeochemical Reactions With an Ohm's Law Analogy


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 (and abiotic factors, e.g., adsorptive mineral soil surfaces). 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 and Liebig's law of the minimum for multiple-nutrient-colimited growth. 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 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 (a) multiple-nutrient-colimited biological growth, (b) denitrification, (c) fermentation under aerobic conditions, (d) metabolic temperature sensitivity, and (e) the legitimacy of Monod kinetics for describing bacterial growth. We expect that our approach will help both modelers and nonmodelers to better understand and formulate hypotheses when studying certain aspects of environmental biogeochemistry and ecology.

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