Impact of bioavailability restrictions on microbially induced stable isotope fractionation. 1. Theoretical calculation

The microbial degradation of organic substrates often exhibits a fractionation of stable isotopes which leads to an enrichment of the heavier isotope in the remaining substrate. The use of this effect to quantify the amount of biodegraded substrate in contaminated aquifers requires that the isotope fractionation factor is constant in time and space. In many natural and engineered systems the bioavailable concentration at the location of the enzymes differs from the average bulk concentration of the substrate. When enzymatically driven substrate degradation is coupled to a preceding transport step controlling the bioavailability of the substrate, the observed isotope fractionation becomes a function of the bulk substrate concentration. The sensitivity of the observed isotope fractionation factor toward such substrate concentration changes depends on the ratio of bulk substrate concentration and Michaelis-Menten constant and on the ratio between the specific affinity of the microorganisms toward the substrate and the first order rate constant of the bioavailability limiting transport process. Highest sensitivities toward substrate concentration were found for combinations of high substrate concentration with low substrate bioavailability (i.e., high ratios of substrate concentration and Michaelis-Menten constant, and high ratios of specific affinity and transport rate constant). As a consequence, changes in concentration and isotopic composition of a bioavailability limited substrate in batch experiments should not exhibit a linear relation in a Rayleigh plot, and the slope of the Rayleigh plot should show a decreasing trend with concentration decrease. When using isotope fractionation to quantify biodegradation along groundwater flow paths, changes in observed isotope fractionation might occur while contaminant concentration decreases along a flow path.