How planar are planar peptide bonds?

One of the best‐known blunders in the history of molecular biology was the assumption of Bragg, Kendrew, and Perutz that peptide bonds are non‐planar, leading to their incorrect predictions for helical structures in proteins. Conversely, Pauling's knowledge that peptide bonds are planar was key to his seminal predictions of the α‐helix and β‐sheets.

But the question has remained: how planar is planar?

In the third edition of his classic, “Nature of the Chemical Bond,” published in 1960, Pauling himself estimated that a 3° rotation of the peptide group away from planarity would incur only a very modest strain energy of 0.1 kcal/mol. Therefore, deviations from strict planarity would not be surprising.

Consistent with this, in 1996 MacArthur and Thornton1 showed for small molecule crystal structures (which can typically be determined more accurately than proteins) that peptides deviate from planarity by 6°, on average. They also quoted specific examples, based on both crystallography and NMR, where the deviation from planarity ranged up to 20° or thereabouts.

Also in 1998, a consortium of structural biologists2 took eight of the highest‐resolution (1.2 Å or better) structures that were available, and carefully refined or re‐refined them. In these atomic‐resolution structures there were multiple cases where there were deviations from peptide planarity of 10° or more.

Based on a more recent survey that included only ultra‐high resolution (> 1 Å) protein structures, Berkholz et al.3 found that the root‐mean‐square deviation from planarity for trans peptides was ±6.3°. About 0.5% of the peptides departed from planarity by more than 20°. These deviations from planarity were not, in general, associated with functional requirements. Rather, they reflected features that are characteristic of protein structures in general.

Notwithstanding the clear evidence that modest (± 6°) departures from peptide planarity are commonplace in protein structures, Chellapa and Rose4 recently argued that protein models with near‐planar peptide bonds fit the X‐ray data as well as models that allow significant departures from planarity. This claim is puzzling on its face because a model allowing non‐planarity has more degrees of freedom than one in which planarity is enforced. All else being equal, a model with more degrees of freedom should allow a better fit to the observed data. In the crystallographic context, a relaxed model should give an R‐factor lower than a constrained model. But Chellapa and Rose4 claim that this is not the case. In their words “tightening default restrictions on the (peptide planarity angle ω) can significantly reduce apparent deviations from peptide unit planarity without consequent (increase) in…R‐factors”. How can this be?

In this context, it is instructive to review the procedure used by Chellapa and Rose.4 First they selected a dozen high‐resolution structures from the PDB that had been refined by a selection of refinement procedures. These were defined as “native” and their R‐factors, as determined with Phenix, were taken to be those for structures with “standard” restraints on peptide planarity.

To obtain R‐factors following “tight” restraints, the “native” coordinates from the PDB were first subjected to five cycles of refinement with Phenix with no restraints on peptide unit planarity, followed by five further cycles with tight ω restraints. Because some of the resultant “tight‐ω‐restraint” R‐factors were less than the “standard” ones, Chellapa and Rose concluded that the models with constrained planar peptide geometry agreed with the experimental data as well as the models with looser peptide planarity. The problem, however, is that the “tight‐ω‐restraint” and “standard‐ω‐restraint” R‐factors quoted by Chellapa and Rose cannot be compared because they do not come from equivalent, parallel, calculations. Indeed, Chellapa and Rose did not carry out any control refinements at all to obtain appropriate values of standard‐ω‐restraint R‐factors to compare with their tight‐ω‐restraint values. Rather than determining standard‐ω‐restraint and loose‐ω‐restraint R‐factors based on parallel refinements starting from identical coordinates, the R‐factors quoted by Chellapa and Rose were based on sequential refinements, with different starting coordinates, and in some cases using different refinement programs.

In this issue of Protein Science, Brereton and Karplus5 provide the missing data. Using the same set of 12 structures analyzed by Chellapa and Rose they carry out strictly parallel refinements to evaluate the consequences of applying standard ω restraints and tight ω restraints on peptide planarity. In every case both R and R _free are higher when the peptide bonds are kept close to planar.

At this point it might be appropriate to make a brief digression regarding R‐factors. In comparing structures with standard and tight ω‐restraints, Chellapa and Rose4 quote R‐factors using full data sets for each crystal, and also R‐factors based on the highest‐resolution shell of X‐ray data. Brereton and Karplus5 quote the former in their report and have made the latter available (personal communication).

It can be asked whether one type of R‐factor is superior to the other. On the one hand, the “highest‐resolution” R‐factor could be more appropriate because the highest‐resolution reflections should be most sensitive to the relatively small differences in atomic positions that differentiate planar and somewhat non‐planar peptide bonds. On the other hand, R‐factors based on the outer shell of data are determined from a limited set of X‐ray intensities which also tend to be measured less accurately than the lower‐resolution data. For both reasons, the “highest‐resolution” R‐factors will be more subject to statistical fluctuations.

Based on the parallel refinement calculations of Brereton and Karplus, the full‐data‐set R‐factors following standard‐ω‐restraint refinement of the 12 test structures are less than those following tight‐ω‐restraint by 0.5° ± 0.3°. If calculated just for the highest‐resolution shell of data, the reduction is 0.7° ± 0.5°. For R _free, the corresponding reductions are 0.6° ± 0.3° for all the data and 0.9° ± 0.9° for the highest‐resolution data. Perhaps as might be expected, based on just the highest‐resolution data, the average change in R‐factor is greater, but so is the standard deviation.

Although the consistent increase in R‐factor for tight‐ω‐restraint versus standard‐ω‐restraint is striking, this does not of itself prove that the models with “standard” deviations from peptide planarity are superior to models in which peptide planarity is strongly enforced. As noted above, models with more relaxed stereochemistry have more degrees of freedom and are expected to have lower R‐values (although this should not apply to R _free).

The quality of a refined model of a protein needs to be assessed not just from its R‐factors but, in particular, from so‐called “F _o – F _c” difference maps which show the difference between the actual electron density in the crystal and that corresponding to the model. Figure 1(B) of Brereton and Karplus5 provides an example. With the refined model in which the peptide bond is kept close to planar, there are strong positive and negative density peaks, respectively, to the “right” and “left” of the peptide nitrogen. This clearly indicates that the nitrogen atom in the model needs to be moved to the right (as occurs when the structure is refined with standard ω‐restraints).

Electron density maps such as shown by Brereton and Karplus in their Figure 1 and on the cover of the journal, as well as in the crystallographic literature (e.g., Wilson et al.2), provide compelling evidence that peptide bonds in proteins can depart substantially from planar. From a body of evidence the root‐mean‐square departure from planarity is about ± 6° and can exceed 20° in some instances. High‐resolution structures cannot be adequately represented using models with strictly planar peptide bonds. Also, as emphasized by Brereton and Karplus,5 ultra‐high resolution protein crystals, when evaluated appropriately, can provide reliable information about the fine details of protein structures.