A modified Monod rate law for predicting variable S isotope fractionation as a function of sulfate reduction rate

Microbial sulfate reduction is associated with characteristic S isotope partitioning, which can aid in determining the rate of this ubiquitous reactive pathway in a wide variety of reducing environments. Here we introduce a new simple yet predictive model that expands the range of environmental conditions over which this functional relationship can be applied through the use of a modified Monod rate expression constrained by a novel set of experiments. A series of continuously-fed batch reactors containing an equivilant biomass of Desulfovibrio vulgaris, a sulfate reducing bacteria, were subjected to differing continuous mass addition rates of formate to precisely control the rate of sulfate reduction via electron donor limitation. Based on growth yield calculations, additional biomass accumulation was negligible. The isotopic composition (δ³⁴S) of the residual sulfate pool was measured through time for each experiment. This approach resulted in five steady state reduction rates of 2.06, 1.22, 0.83, 0.52 and 0.28 μmol * h⁻¹ that enriched the unreacted sulfate in ³⁴S by unique characteristic enrichment factors (α_obs) of 0.9976, 0.9962, 0.9938, 0.9924 and 0.9903, respectively. This relationship was used to calibrate a new coupled set of isotope-specific Monod rate laws that have been modified to incorporate (1) a minimum (α₁) and maximum (α₂) fractionation factor and (2) a rate-controlling electron donor factor (D_F). Application of these parameters in the updated model reproduce most of our data and simulate realistic shifts in the observed fractionation factor (α_obs) as a function of reduction rate in an electron donor limited system. The model was applied to our current dataset as well as three previous studies, which collectively provide a broad range in both rates and α_obs, and support validation across substantially different conditions. We show that this approach offers a reasonable approximation to more detailed microbial reactive network models, while still maintaining sufficient simplicity and versatility to allow incorporation into multi-component reactive transport simulations. Thus, the current study provides a foundation for accurate simulation of the relationship between α_obs and sulfate reduction rates in open, transient, and through-flowing systems.