The SUPECA kinetics for scaling redox reactions in networks of mixed substrates and consumers and an example application to aerobic soil respiration
Jinyun Tang and William J. Riley
Earth and Environmental Sciences Area, Lawrence Berkeley National Laboratory, Berkeley 94720, CA, USA
Received: 24 Feb 2017 – Accepted for review: 06 Mar 2017 – Discussion started: 08 Mar 2017
Abstract. Several land biogeochemical models used for studying carbon-climate feedbacks have begun explicitly representing microbial processes. 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 here study this scaling problem by focusing on the substrate-consumer relationships for consumer mediated redox reactions of the form A + BE→ products, where products could be microbial biomass and different bio-products. Under the quasi-steady-state approximation, these substrate-consumer relationships can be formulated as the computationally difficult full Equilibrium Chemistry problem, which is then usually approximated analytically with the popular Dual Monod (DM) kinetics and Synthesizing Unit (SU) kinetics. However, we found that the DM kinetics is scaling inconsistent for reaction networks because it (1) does not incorporate substrate limitation in its derivation, (2) invokes contradictory assumptions regarding the substrate processing rate when transitioning from single substrate reactions to two-substrate redox reactions, and (3) cannot scale the product generation rate from one to multiple substrates. In contrast, the SU kinetics can consistently scale the product generation rate from one to multiple substrates, but suffers from the deficit that as the consumer abundance approaches infinity, it predicts singular infinite reaction rates even for limited substrates. We attribute this deficit to SU’s failure to incorporate the substrate limitation in its derivation and remedy SU with the proposed SUPECA (SU Plus Equilibrium Chemistry Approximation) kinetics, which consistently imposes the mass balance constraints from both substrates and consumers on consumer-substrate interactions in calculating redox reaction rates. Moreover, we show the SUPECA kinetics satisfies the partition principle as in theories like Newton's Law of motion and Dalton’s law of partial pressures, such that its mathematical manifestation is scaling invariant when transitioning from an individual reaction to a network of many reactions. We benchmarked the SUPECA kinetics with the equilibrium chemistry solution for some simple problem configurations and found SUPECA outperformed the SU kinetics. In applying the SUPECA kinetics to aerobic soil respiration, we found SUPECA predicted consistent but variable moisture response functions that agreed well to those derived from incubation data. We finally discuss how the SUPECA kinetics could help Earth System Models consistently incorporate more biogeochemical reactions to improve their biogeochemical modules.
Tang, J. and Riley, W. J.: The SUPECA kinetics for scaling redox reactions in networks of mixed substrates and consumers and an example application to aerobic soil respiration, Geosci. Model Dev. Discuss., doi:10.5194/gmd-2017-46, in review, 2017.