Competitor Sizes and Diffusion Determine Kinetics that Best Approximate Biogeochemical Reaction Rates

ECA kinetics best describes enzymatic depolymerization and microbial substrate uptake.

The Science

The debate on which kinetic formulation should be used to model soil biogeochemical processes (e.g., enzymatic depolymerization and microbial substrate uptake) has accelerated over the past decade. In this project, U.S. Department of Energy (DOE) scientists at Lawrence Berkeley National Laboratory (LBNL) combine the century-old Smoluchowski model of chemical reactions to infer how the sizes of microbes, enzymes, polymer particles, and monomer substrates together determine the mathematical formulations of biogeochemical process rates. They show that neither the popular forward Michaelis-Menten (fMM) kinetics nor the reverse Michaelis-Menten (rMM) kinetics is able to describe these biogeochemical processes that include entities physically varying over orders of magnitude in size. Fortunately, the equilibrium chemistry approximation (ECA) kinetics they recently derived can seamlessly scale over a wide range of biogeochemical reactions.

The Impact

The analysis (1) explains why fMM and rMM kinetics can describe certain biogeochemical processes well, but not others; (2) provides approaches to scale from geometric sizes to kinetic parameters used in soil biogeochemical models; and (3) explains why different sizes of organisms need to be considered explicitly in biogeochemical models.


Substrate kinetics are essential mathematical tools to model biogeochemistry in various ecosystem processes. However, scientists have been debating which formulations to use to describe the biogeochemical reactions that often involve entities varying over orders of magnitude in physical sizes. The fMM and rMM kinetics are two popular formulations used to interpret and model many biogeochemistry experiments. However, neither of them can perform satisfyingly over the wide range of size scales found in soils. LBNL scientists combined the Smoluchowski model of chemical reactions and a mathematical description of physical sizes to derive relationships that explain why fMM and rMM kinetics performed better in one case and worse in another. In particular, the researchers show that both fMM and rMM kientics are special approximations to the ECA kinetics and that the measurable information of entity sizes and reaction rates provides a good way to parameterize the ECA kinetics. Following their early studies, the team says these results are paving the way to develop a first principles–based model of soil biogeochemistry.

Principal Investigator(s)

William Riley
Lawrence Berkeley National Laboratory

Jinyun Tang
Lawrence Berkeley National Laboratory


This research is supported as part of the Soil Warming Scientific Focus Area (SFA; Contract No. DE-AC02-05CH11231) at Lawrence Berkeley National Laboratory and the Next-Generation Ecosystem Experiments (NGEE)–Arctic project in the Terrestrial Ecosystem Science program of the Office of Biological and Environmental Research (BER), within the U.S. Department of Energy (DOE) Office of Science.


Tang, J.-Y., and W. J. Riley. “Competitor and substrate sizes and diffusion together define enzymatic depolymerization and microbial substrate uptake rates.” Soil Biology and Biogeochemistry 139, 107624 (2019). DOI:10.1016/j.soilbio.2019.107624