A theory of effective microbial substrate affinity parameters in variably saturated soils and an example application to aerobic soil heterotrophic respiration

Affinity parameters are essential for substrate kinetics‐based modeling of soil biogeochemistry. These parameters were originally defined for well‐mixed aqueous solutions to represent enzyme substrate binding. For variably saturated soils, they are often calibrated and highly uncertain. Here we develop a predictive theory of effective substrate affinity parameters to account for other processes that affect microbial substrate acquisition, so that the substrate kinetics for well‐mixed aqueous solutions can be similarly applied to variably saturated soils. The theory is based on an analytical approximation of how diffusive substrates are intercepted by soil microbial cells and integrates microbial characteristics, microsite structure, and soil physical properties. The predicted effective substrate affinity thus closely integrates the physical substrate limitation in soils with the intrinsic substrate affinity parameter. The theory predicts that, as moisture changes, the effective diffusive substrate delivery rates vary by orders of magnitude, resulting in highly variable effective affinity parameters for substrates like oxygen, methane, and nonvolatile solutes. As an example, we apply the theory with three substrate kinetics to aerobic soil incubations. Our models accurately reproduced observations of 32 soil incubations in four soil classes, demonstrating that the soil moisture versus respiration relationship varies with maximum respiration rate, soil texture, soil carbon content, and microbial biomass. This example suggests that the traditional use of a single static multiplicative function to parameterize how soil respiration depends on moisture is inappropriate. Because of its capability to integrate microbial traits and soil physical properties, our theory will help develop more robust soil biogeochemistry models.