A counter-intuitive approach to calculating non-exchangeable 2H isotopic composition of hair: treating the molar exchange fraction fE as a process-related rather than compound-specific variable

Hair is a keratinous tissue that incorporates hydrogen from material that an animal consumes but it is metabolically inert following synthesis. The stable hydrogen isotope composition of hair has been used in ecological studies to track migrations of mammals as well as for forensic and archaeological purposes to determine the provenance of human remains or the recent geographic life trajectory of living people. Measurement of the total hydrogen isotopic composition of a hair sample yields a composite value comprised of both metabolically informative, non-exchangeable hydrogen and exchangeable hydrogen, with the latter reflecting ambient or sample preparation conditions. Neither of these attributes is directly measurable, and the non-exchangeable hydrogen composition is obtained by estimation using a commonly applied mathematical expression incorporating sample measurements obtained from two distinct equilibration procedures. This commonly used approach treats the fraction of exchangeable hydrogen as a mixing ratio, with a minimal procedural fractionation factor assumed to be close or equal to 1. Instead, we propose to use full molar ratios to derive an expression for the non-exchangeable hydrogen composition explicitly as a function of both the procedural fractionation factor α and the molar hydrogen exchange fraction f(E). We apply these derivations in a longitudinal study of a hair sample and demonstrate that the molar hydrogen exchange fraction f(E) should, like the procedural fractionation factor α, be treated as a process-dependent parameter, i.e. a reaction-specific constant. This is a counter-intuitive notion given that maximum theoretical values for the molar hydrogen exchange fraction f(E) can be calculated that are arguably protein-type specific and, as such, f(E) could be regarded as a compound-specific constant. We also make some additional suggestions for future approaches to determine the non-exchangeable hydrogen composition of hair and the use of standards.