## Sunday, June 3, 2012

### Interpreting Protein Structural Dynamics from NMR Chemical Shifts

The effect of dynamical averaging on chemical shift predictions
In this work snapshots from MD simulations of are used as input to chemical shift predictors Sparta+, ShiftX+, Camshift, and ShiftS to compute average chemical shifts for two homologous ribonuclease H enzymes from Escherichia coli (ecRNH) and Thermus thermophilus (ttRNH).  What I especially liked about this article is not only the thoroughness: all the most popular chemical shift predictors were compared and the averaging is based on 100 ns MD simulations, one of which was tested against a 1000 ns MD simulation, but also how clearly the results were analyzed and presented.

Does averaging improve overall accuracy?
In the case of ecRNH, RMSDs from experiment computed from averaged chemical shifts are always more accurate than those computed from the x-ray structure for all nuclei and methods tested - on average by 23%, while for ttRNH the improvement is much less and for methods like ShiftX+ averaging consistently leads to slightly worse results. The resolution of the x-ray structures of ecRNH and ttRNH are 2.8 Å and 1.5 Å, respectively, so some of the improvement for ecRNH presumably derives from errors in the low resolution x-ray structure that gets fixed by the MD, and the authors describe one concrete example of this.

Identifying and analyzing interesting residues
However, as the authors point out RMSDs only tell part of the story.  One interesting analysis tool employed in the study is a plot of $|\delta_{x-ray}-\delta_{Exp}|-|\delta_{MD}-\delta_{Exp}|$ as a function of residue number to identify where averaging significantly improves the prediction and where it makes it significantly worse compared to using the x-ray structure.  Some of these cases are then chosen for further analysis to highlight the different underlying structural causes.  Here the authors use another powerful tool: a plot of the probability distribution of chemical shifts [$P(\delta)$], which in many of these cases is bi-modal, i.e. it clearly shows that the average chemical shift is not the most likely chemical shift and that it represents at least two distinct conformations.

The size of the ensemble: dynamical vs conformational averaging
Most of the averages presented in the paper are computed using 22,200 protein structures, but looking at the data makes me wonder how many conformations it really represents.  For example, in the case of Sparta+ C$_\alpha$ chemical shift predictions for ttRNH, averaging leads to significant improvements over x-ray for only about 3-4 residues out of about 145 (and worse predictions for three other residues!).

Furthermore, the peak or peaks in the $P(\delta)$-plots appear quite symmetric in the examples shown, which means that the most probable chemical shift from that peak is a good approximation to the average value computed using that peak.  I wouldn't be surprised if one could identify 10-20 ttRNH structures that would lead to equally accurate average chemical shift values.

Empirical vs QM-based chemical shift predictors
Finally, the authors note an interesting case (Phe27 C') where ShiftS, which is parameterized based on QM-data, gives a completely different $P(\delta)$-plot compared to the other methods (although an equally accurate average chemical shift value for that particular residue!).  I would love to see a detailed analysis of this issue before completely ruling out the ShiftS results.