Ligand-observed NMR – quantitatively

Ligand-observed NMR is one of the most popular fragment-finding methods. Among its strengths is the ability to find extraordinarily weak fragments that most other techniques would miss. However, common ligand-observed NMR methods such as STD are not quantitative: they can tell you that a fragment binds, but not how tightly. In a new open-access J. Med. Chem. paper Manjuan Liu and colleagues at the Institute of Cancer Research provide an easy solution.

 

The approach is based on an NMR phenomenon called transverse relaxation (see here), which describes how atomic nuclei return to their ground state after being excited by a radiofrequency pulse in a magnetic field. The transverse relaxation rate R₂ for a given nucleus depends on the tumbling speed of the molecule in which it is contained: small molecules tumble rapidly and have small R₂ values, while larger molecules tumble slowly and have larger R₂ values. When a small molecule binds to a protein its tumbling speed slows and its R₂ increases. The R₂ values can be measured experimentally using a Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence.

 

This is all fairly standard for NMR spectroscopists, and in fact CPMG is widely used to find fragments. Liu and colleagues proposed that, by measuring the change in R₂ with changing concentrations of small molecule, they would be able to extract the dissociation constant (K_d). The theory gets a little hairy (14 equations), and the analysis depends on non-linear regression curve fitting, but this is easily done using modern analytical software. The technique is called R2KD.

 

The experiment itself is straightforward. The ligand alone is prepared at two different concentrations; these are used to determine the R₂ values of the free ligand. Another eight samples contain protein and various concentrations of ligand. The R₂ values are measured and fit to an equation to extract the dissociation constant. An initial test case with a known 50 µM ligand for the protein BCL6 was encouraging, giving a K_d of 53 to 78 µM for four different protons on the ligand. The accuracy could be further improved by using a “global fit” with all the data rather than analyzing each NMR peak in isolation.

 

Next, seven ligands against three proteins were analyzed using R2KD and compared with their literature values. Here too the results were in agreement, mostly within a factor of two. The lower limit for sensitivity is dependent on the NMR signal for the ligand; below concentrations of about 20 µM the experiments become impractically long. The upper limit is dictated by the solubility of the ligand. The researchers could reliably measure dissociation constants around 1 mM and suggested that with a sufficiently soluble ligand even weaker ligands could be measured.

 

The R2KD experiment requires that the protein concentration be less than about 20% of the lowest ligand concentration. (That said, protein concentrations up to 35 µM gave reasonable results.) Preserving protein is usually a goal, so lower concentrations (single-digit micromolar) are desirable from both a practical and theoretical standpoint.

 

Finally, the researchers demonstrated the application of R2KD to assess 10 fragment hits from a 1000-compound screen against the E3 ligase complex CRBN/DDB1, one of the most popular targets for PROTACs. The hits had dissociation constants ranging from 70 to 1200 µM, and the R2KD values were similar to those found in a fluorescence polarization (FP) assay, though for the most part the affinities from R2KD were higher. In particular, two compounds with essentially no activity in the biochemical assay came in at sub-millimolar by R2KD, which may speak to the insensitivity of the FP assay.

 

Overall this is a lovely and, as befits this blog, practical paper, and I hope R2KD becomes widely adopted. With a sweet spot for K_d values of 10-1000 µM the technique fills an important niche: biochemical assays are well-suited for tighter binders but less reliable at millimolar ligand concentrations. As crystallography becomes increasingly popular as a primary screen, I could imagine R2KD being used to rank the resulting fragment hits.