SUPECA kinetics for scaling redox reactions in networks of mixed substrates and consumers and an example application to aerobic soil respiration

Abstract

Abstract. Several land biogeochemical models used for studying carbon-climate feedbacks have begun explicitly representing microbial dynamics. However, to our knowledge, there has been no theoretical work on how to achieve a consistent scaling of the complex biogeochemical reactions from microbial individuals to populations, communities, and interactions with plants and mineral soils. We focus here on developing a mathematical formulation of the substrate-consumer relationships for consumer-mediated redox reactions of the form A+B E → products, where products could be, e.g., microbial biomass or bioproducts. Under the quasi-steady-state approximation, these substrate-consumer relationships can be formulated as the computationally difficult full equilibrium chemistry problem or approximated analytically with the dual Monod (DM) or synthesizing unit (SU) kinetics. We find that DM kinetics is scaling inconsistently for reaction networks because (1) substrate limitations are not considered, (2) contradictory assumptions are made regarding the substrate processing rate when transitioning from single-to multi-substrate redox reactions, and (3) the product generation rate cannot be scaled from one to multiple substrates. In contrast, SU kinetics consistently scales the product generation rate from one to multiple substrates but predicts unrealistic results as consumer abundances reach large values with respect to their substrates. We attribute this deficit to SU's failure to incorporate substrate limitation in its derivation. To address these issues, we propose SUPECA (SU plus the equilibrium chemistry approximation -ECA) kinetics, which consistently imposes substrate and consumer mass balance constraints. We show that SUPECA kinetics satisfies the partition principle, i.e., scaling invariance across a network of an arbitrary number of reactions (e.g., as in Newton's law of motion and Dalton's law of partial pressures). We tested SUPECA kinetics with the equilibrium chemistry solution for some simple problems and found SU-PECA outperformed SU kinetics. As an example application, we show that a steady-state SUPECA-based approach predicted an aerobic soil respiration moisture response function that agreed well with laboratory observations. We conclude that, as an extension to SU and ECA kinetics, SUPECA provides a robust mathematical representation of complex soil substrate-consumer interactions and can be applied to improve Earth system model (ESM) land models.

A reanalysis of the foundations of the macromolecular rate theory

“…where 𝐸 ' is the concentration of free enzymes whose conformation structure is in the native state (i.e., able to carry out the catalysis), 𝑃 is the concentration of product molecules, 𝑆 is concentration of the substrate, 𝐸 ' 𝑆 is concentration of the enzymesubstrate complex, and 𝑘 ( ) , 𝑘 ( * , and 𝑣 +,-are temperature (𝑇) dependent kinetics parameters. Although it is not necessary for 55 the validity of the Michaelis-Menten kinetics (Briggs and Haldane, 1925), for scaling purpose, 𝑣 +,-(the maximum enzymatic catalysis rate) is often assumed to be much greater than 𝑘 ( * (Tang and Riley, 2017;Kooijman, 2009;Holling, 1959;Aksnes and Egge, 1991;Van Slyke and Cullen, 1914). Moreover, throughout this study, we take all variables to be in ISO units.…”

An Introduction to the E3SM Special Collection: Goals, Science Drivers, Development, and Analysis

“…Building from CLM4.5, E3SM Land Model (ELM v1) includes new options for representing soil hydrology and biogeochemistry, featuring a variably saturated flow model (Bisht et al 2018) and a new module for phosphorus dynamics (Yang et al 2019). To understand the effects of nutrient limitations on carbon-climate feedbacks and their sensitivity to model structural uncertainty, two biogeochemistry approaches are included in ELM v1 to contrast a mechanistic (Equilibrium Chemistry Approximation or ECA; Tang, 2015;Tang and Riley, 2017;Zhu et al, 2016;Zhu et al, 2017) and a conceptual (Converging Trophic Cascade or CTC; Mao et al, 2016;Raczka et al, 2016;Duarte et al, 2017) framework for representing nutrient competition between microbes, plants, and abiotic processes. The MOSART river model replaces the River Transport Model (RTM) used in CESM1 as the river component of E3SM.…”

Linear two-pool models are insufficient to infer soil organic matter decomposition temperature sensitivity from incubations

“…When bio-diversity is further integrated with known ecological principles (e.g., competition and symbiosis), the many parameters can compensate each other to reduce predictive uncertainty and meanwhile enhance the models' resilience to perturbations (see Sect. 6 of Tang and Riley (2017) for a discussion of this concept).…”