Wednesday, April 16, 2014

A definitive experimental signature of short hydrogen bonds in proteins: isotopic fractionation

I have written several posts about the controversial issue of low-barrier hydrogen bonds in proteins and whether they play any functional role, particularly in enzyme catalysis.

A basic issue is to first identify short hydrogen bonds, i.e., finding a reliable method to measure bond lengths.
I recently worked through and a nice article,
NMR studies of strong hydrogen bonds in enzymes and in a model compound
T.K. Harris, Q. Zhao, A.S. Mildvan

Surely, these bond lengths just be identified with x-ray crystallography? No.
the standard errors in distances determined by protein X-ray crystallography are 0.1–0.3 times the resolution. For a typical 2.0 Å X-ray structure of a protein, the standard errors in the distances are ±0.2–0.6 Å, precluding the distinction between short, strong and normal, weak hydrogen bonds. 
[Aside: I also wonder whether the fact that X-ray crystal structures are refined with classical molecular dynamics using force fields that are parametrised for weak bonds is also a problem. Such refinements will naturally bias towards weak bonds, i.e., the longer bond lengths that are common in proteins. I welcome comment on this.]

The authors then discuss how NMR can be used for bond length determinations. One of these NMR "rulers" involves isotopic fractionation, where one measures how much the relevant protons exchange with deuterium in a solvent,

Essentially, the relative fraction [ratio of concentrations] in thermodynamic equilibrium,

is determined by the relative zero-point energy (ZPE) of a D relative to an H in the enzyme. As described in a key JACS article the ratio is given by a formula such as
where T is the temperature.

If Planck's constant was zero, this ratio would always be one. It would also be one if there was no change in the vibrational frequencies of the H/D when they move from the solvent to the enzyme. Generally, as the H-bond strengthens [R gets shorter] the frequency change gets larger and so the difference between H/D gets larger [see this preprint for an extensive discussion], and phi gets smaller. However, for very short bonds the frequencies harden and phi will get larger, i.e. there will be a non-monotonic dependence on R, the distance between the donor and acceptor. This was highlighted in an extensive review which contains the following sketch.

Harris, Zhao, and Mildvan consider a particular parametrisation of the H-bond potential to connect the observed fractionation ratio with bond lengths in a range of proteins. They generally find reasonable agreement with other methods of determining the length [e.g., NMR chemical shift]. In particular the resolution is much better than from X-rays.


  1. Measuring the hydrogen bonds is very important, these days I am writing a manuscript about high sensitivity of Raman spectroscopy to determined the hydrogen bonds in crystal methanol and ethanol. I read lots of paper that employed X-ray diffraction or NMR technology to measure the hydrogen bonds, the reported error was 0.01 or 0.001 Å, but you say in this blog the error should be 0.2-0.6 Å, which is much larger than previous reported errors. Actually recently I find the Raman spectra is very sensitive to the change of hydrogen bond, the difference of 0.0001Å could be easily be observed in Raman spectra.

    1. Hi LIn Ke

      Thanks for the comment. For small molecules X-rays can measure the bond lengths to less than 0.01 A, but for proteins, the error is at least 0.2 A.

      Please give a reference for how Raman is so sensitive to bond length. It sounds impressive.

  2. The earliest paper I know is JCP, 1965, 46:2079-2087, the authors use Raman spectra to discuss the hydrogen bond distribution in liquid water. Maybe after our recent manuscript is submitted to a journal, I can something in my blog about how use the Raman spectra to determine the hydrogen bond in crystal.