Extending the Rayleigh equation to allow competing isotope fractionating pathways to improve quantification of biodegradation

The Rayleigh equation relates the change in isotope ratio of an element in a substrate to the extent of substrate consumption via a single kinetic isotopic fractionation factor (α). Substrate consumption is, however, commonly distributed over several metabolic pathways each potentially having a different α. Therefore, extended Rayleigh-type equations were derived to account for multiple competing degradation pathways. The value of α as expressed in the environment appears a function of the α values and rate constants of the various involved degradation pathways. Remarkably, the environmental or apparent α value changes and shows non-Rayleigh behavior over a large and relevant concentration interval if Monod kinetics applies and the half-saturation constants of the competing pathways differ. Derived equations were applied to previously published data and enabled (i) quantification of the share that two competing degradation pathways had on aerobic 1,2-dichloroethane (1,2-DCA) biodegradation in laboratory batch experiments and (ii) calculation of the extent of methyl tert-butyl ether (MTBE) biodegradation shared over aerobic and anaerobic degradation at a field site by means of an improved solution to two-dimensional (carbon and hydrogen) compound-specific isotope analysis (CSIA).