Isotopic fractionation in proteins as a measure of hydrogen bond length

TL;DR

This paper investigates how isotopic fractionation factors in proteins relate to hydrogen bond lengths, using a theoretical model to interpret experimental NMR data and support the existence of short low-barrier hydrogen bonds.

Contribution

It introduces a diabatic state model to calculate fractionation factors as a function of hydrogen bond length, linking vibrational energies to experimental measurements.

Findings

Correlation between fractionation factor and H-bond length established

Model successfully reproduces experimental NMR data

Supports presence of short low-barrier hydrogen bonds in enzymes

Abstract

If a deuterated molecule containing strong intramolecular hydrogen bonds is placed in a hydrogenated solvent it may preferentially exchange deuterium for hydrogen. This preference is due to the difference between the vibrational zero-point energy for hydrogen and deuterium. It is found that the associated fractionation factor $\Phi$ is correlated with the strength of the intramolecular hydrogen bonds. This correlation has been used to determine the length of the H-bonds (donor-acceptor separation) in a diverse range of enzymes and has been argued to support the existence of short low-barrier H-bonds. Starting with a potential energy surface based on a simple diabatic state model for H-bonds we calculate $\Phi$ as a function of the proton donor-acceptor distance $R$. For numerical results, we use a parameterization of the model for symmetric O-H.... O bonds. We consider the relative contributions of the O-H stretch vibration, O-H bend vibrations (both in plane and out of plane), tunnelling splitting effects at finite temperature, and the secondary geometric isotope effect. We compare our total $\Phi$ as a function of $R$ with NMR experimental results for enzymes, and in particular with an empirical parametrisation $\Phi(R)$, used previously to determine bond lengths.