Quantification of isotope fractionation in experiments with deuterium-labeled substrate.

Abstract

Isotope analysis is a potentially sensitive method to trace in situ degradation of organic contaminants. In a recent paper, Morasch et al. (3) investigated the mechanism of isotope fractionation during toluene biodegradation using deuterium-labeled toluene. The authors overlooked that the Rayleigh equation that is normally used to evaluate isotope fractionation at natural abundance level (2) is not applicable to studies with labeled substrate, particularly if large isotope fractionation occurs. For several of their experiments they obtained negative hydrogen isotope fractionation factors (see Table 1 in reference 3), which contradict the definition of the fractionation factor (see below). Since labeled compound will likely be used in further investigations to study isotope fractionation, it is important to demonstrate why the commonly used Rayleigh equation is usually not applicable in such studies and to provide an alternative method to quantify isotope fractionation. The magnitude of isotope fractionation is normally characterized by the fractionation factor, which is defined as follows for kinetic isotope fractionation: (1) where H and L are the concentrations of the substrate with heavy and light isotopes, respectively, at a given time and dHp and dLp are increments of product with heavy or light isotopes, respectively, that appear in an infinitely short time (instantaneous product). In some studies, the fractionation factor is defined by the inverse ratio (2). Since all terms in equation 1 are positive, α has to be positive. For mass balance reasons, (2) Combining equations 1 and 2 and rearrangement leads to Integration of equation 3 from L0 to L and H0 to H gives (4) Dividing both sides by L/L0 yields (5) where R and R0 are the isotope ratios (H/L) at a given time t and at time zero, respectively. The fraction of substrate that has not reacted yet, f, at time t is given by (6) Equations 5 and 6 are analogous to those given by Bigeleisen and Wolfsberg (1), except that here they were derived without any specific assumption about the reaction kinetics and using a different definition of α and f. The crucial point is that L/L0 in equation 5 can only be approximated by f if either (i) the concentrations of the heavy isotopes, H and H0, are small, as common for studies at natural abundance level, or (ii) 1 + R ≈ 1 + R0. In the first case, the first expression for f in equation 6 approaches L/L0; in the second case, the second expression can be approximated by L/L0. If one of these two conditions is fulfilled, equation 5 can be simplified to (7) which corresponds to the Rayleigh equation as used by the authors of the study (3). However, in the experiments with labeled compound presented in the study, condition i is not fulfilled since the compound with deuterium accounts for 50% of the total toluene concentration. Condition ii is not fulfilled either. For example, for the experiment illustrated in Fig. 1 in reference 3, R0 is 1 and R varies between 1 and about 12 and thus, the assumption that 1 + R ≈ 1 + R0 holds true is not valid. In other experiments, even higher R values of up to about 54 were observed (see Fig. 2 in reference 3). By combining equations 5 and 6, an accurate equation is obtained that relates R, R0, f, and α: (8) This equation can be used to determine α by plotting ln(R/R0) versus ln{f/[(1 + R)/(1 + R0)]}. Applying this approach to the data of the experiment with Desulfobacterium cetonicum (as given in Fig. 1 in reference 3), an α value of approximately 2.7 is obtained instead of −5.09. The value of 2.7 is only an approximation, since the data for the calculation were estimated from Fig. 1 in reference 3. The calculated value is in the typical range for primary hydrogen isotope effects. Using the correct equation, the introduction of an uncommon parameter to characterize isotope fractionation becomes unnecessary and the data can be discussed in a framework consistent with a large number of studies on isotope fractionation during enzymatic reactions.