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\begin{document}

\title{Conceptualizing biogeochemical reactions with an Ohm's law analogy}



\author[1]{Jinyun Tang}%
\author[1]{Jinyun Tang}%
\author[1]{Riley William}%
\author[1]{Gianna L Maschmann}%
\author[1]{Eoin L Brodie}%
\affil[1]{Lawrence Berkeley National Laboratory}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{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.%
\end{abstract}%



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