Ohm’s Law for Biogeochemical Modeling
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. We here first showed that simple enzyme kinetics can be interpreted using Ohm’s law. We then used Ohm’s law to formulate various biogeochemical reactions. This approach allowed us to obtain insights on 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. We 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. We thus recommend the application of Ohm’s law to all sorts of biogeochemical problems in ecosystem models.
Our 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, we 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. Start-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. We here 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. We showed that 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. We 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. We expect Ohm’s law to find a wide range of applications in ecosystem modeling.