The Rayleigh equation is frequently used to describe isotope fractionation as a function of conversion. In this article we propose to draw a parallel between isotope and enantiomeric enrichments and derive a set of conditions that allow the use of the Rayleigh approach to describe the enantiomeric enrichment-conversion dependencies. We demonstrate an implementation of the Rayleigh equation for the enantioselective enzymatic hydrolysis of Mecoprop-methyl, Dichlorprop-methyl, and dimethyl-methylsuccinate by lipases from Pseudomonas fluorescens, Pseudomonas cepacia, and Candida rugosa. The data obtained for all the studied reactions gave good fits to the Rayleigh equation, with a linear regression R(2) > 0.96. In addition to that, our analysis of four microcosm studies on the hydrolysis of the individual enantiomers of Dichloroprop methyl, Lactofen, Fenoxaprop-ethyl, and Metalaxyl reported in the literature by other research groups revealed a suitability of the Rayleigh dependence. Two dimensional plots describing the isotope fractionation versus enantiomeric enrichment are demonstrated for all studied cases. Processes not accompanied by enantiomeric enrichment (acid and base hydrolysis) and by isotope enrichment (transesterification) are demonstrated, their 2-D plots are either horizontal or vertical which can illuminate concealed degradation pathways.

In this study we propose a new approach for analyzing the enantioselective biodegradation of some antidepressant drugs mediated by human and rat liver microsomes by using the Rayleigh equation to describe the enantiomeric enrichment−conversion dependencies. Analysis of reported degradation data of additional six pesticides, an alpha blocker and a flame retardant by microsomes or hepatocytes in vitro reaffirmed the universality of the approach. In all the in vitro studied cases that involved enantioselective degradation, a Rayleigh dependence of the enantiomeric enrichment was observed. Published data regarding in vivo retention of myclobutanil in liver, kidney, muscle and brain tissues of rabbits following injection of the racemate were remodeled showing prevalence of the Rayleigh law for the chiral enrichment of the fungicide in the various tissues. This approach will revolutionize data organization in metabolic pathway research of target xenobiotics by either liver microsomes, hepatocytes or their organ-specific in vivo retention. The fact that the enantiomeric enrichment as a function of the conversion can be described by a single quantifier, will pave the road for the use of structure activity predictors of the enantiomeric enrichment and for mechanistic discrimination based on parametric dependence of the quantifier.

It was recently demonstrated that under environmentally relevant conditions the Rayleigh equation is valid to describe the enantiomeric enrichment - conversion relationship, yielding a proportional constant called the enantiomeric enrichment factor, εER. In the present study we demonstrate a quantitative structure-activity relationship model (QSAR) that describes well the dependence of εER on molecular structure. The enantiomeric enrichment factor can be predicted by the linear Hansch model, which correlates biological activity with physicochemical properties. Enantioselective hydrolysis of sixteen derivatives of 2-(phenoxy)propionate (PPMs) have been analyzed during enzymatic degradation by lipases from Pseudomonas fluorescens (PFL), Pseudomonas cepacia (PCL), and Candida rugosa (CRL). In all cases the QSAR relationships were significant with R(2) values of 0.90-0.93, and showed high predictive abilities with internal and external validations providing QLOO(2) values of 0.85-0.87 and QExt(2) values of 0.8-0.91. Moreover, it is demonstrated that this model enables differentiation between enzymes with different binding site shapes. The enantioselectivity of PFL and PCL was dictated by electronic properties, whereas the enantioselectivity of CRL was determined by lipophilicity and steric factors. The predictive ability of the QSAR model demonstrated in the present study may serve as a helpful tool in environmental studies, assisting in source tracking of unstudied chiral compounds belonging to a well-studied homologous series.