X-Ray Crystallography of Peptide-Protein Complexes

A crystal structure of a peptide bound to a protein is not a photograph of the complex. It is a model — atomic coordinates, displacement parameters and occupancies — adjusted until the diffraction pattern it predicts resembles the one measured. The measurement is a set of reflection intensities. The electron density is a map computed from those intensities together with phases that, in almost every modern structure, come largely from the model itself. The coordinates are an interpretation of that map. Reading such a structure well means keeping those three apart, and watching the part of the model that contributed least to the data: the peptide.

What the resolution number is, and what it permits

The resolution quoted for a structure is the smallest interplanar spacing among the reflections included in refinement. It is a property of the data set as truncated by the crystallographer, and that decision is less settled than one number suggests. Karplus and Diederichs argued that merging R values are poorly suited to determining the high-resolution limit and that standard protocols built on them discard much useful data; they introduced CC*, a statistic estimating the correlation of an observed data set with the underlying true signal, which also puts model and data quality on the same scale and so reveals when data quality is what limits model improvement ^[1]. Evans and Murshudov reached a compatible conclusion from refinement trials against observed and simulated data, automated model building, and maps computed to different limits: adding weak high-resolution data beyond the commonly used cutoffs may give some improvement and does no harm ^[2].

What a given resolution permits is a separate question from where the cutoff sits. It is ordinary bench practice, not a literature finding, that at around 2.5 to 3.0 Å a backbone can be traced and side chains placed approximately while individual atoms are not separately resolved. At the top end, reviewing enzyme structures determined at sub-Ångström resolution, Vrielink and Sampson discussed the visualization of hydrogen atoms, multiple side-chain conformations, anisotropy and substrate strain — features not previously visible in lower-resolution maps ^[3]. So claims about hydrogen-bond geometry, protonation, or a specific rotamer carry very different weight at 1.0 Å than at 2.8 Å, even though both structures are drawn with the same sticks.

Global statistics do not police a small ligand

The R value measures agreement between observed and calculated structure-factor amplitudes across the whole data set. Brünger introduced the free R value as a cross-validation analogue, computed on a test set of reflections omitted from modeling and refinement, on the grounds that stereochemical restraints do not prevent overfitting or misfitting and an incorrect model can be refined to a fairly good R value; he reported a high correlation between free R and the accuracy of the model phases ^[4].

Both are global, and that is the problem for a bound peptide. Weichenberger, Pozharski and Rupp put it directly: every atom contributes to every structure factor, and a ligand's scattering mass — several hundred daltons for a small molecule, up to a few thousand for a complete peptide — is small against a target of tens to hundreds of kilodaltons, so the ligand contribution to total scattering is often two to four orders of magnitude less than the protein's ^[5]. A complex can therefore carry a respectable free R value while the peptide in the binding site is wrong, misplaced, or absent.

Density before model

Because model phases enter the map calculation, the maps routinely used during structure solution are almost always model-biased — anything added to the model tends to appear in the map, which hinders validation. Liebschner and colleagues set out the standard remedy: omit the atoms in question, update the structure factors, and compute a residual map, in which real atoms should reappear as positive features. They note that the flat bulk-solvent model used in most modern refinement programs assigns constant density to unoccupied volume and can obscure weak omitted density further, and describe polder maps, which keep bulk solvent out of the omit region and are particularly useful for weak density from ligands, solvent, side chains, alternative conformations, and residues in loops and terminal regions ^[6].

A difference map carries information only under conditions worth stating. Weichenberger and colleagues point out that difference density analysis is meaningful only when the model contributes to the calculated structure factors, or the observed data contain an actual ligand contribution, or both; if a peptide has been refined with extreme B factors or very low occupancy so that it barely contributes, and the data hold no real ligand signal, the difference synthesis reduces to noise subtraction ^[5]. Contour level and map type therefore have to be declared for a density figure to mean anything, and the usual convention — 2mFo−DFc at 1σ with mFo−DFc at ±3σ — is a presentation choice, not a result.

Local fit is assessed in real space, most often by the real-space R value or the real-space correlation coefficient, evaluated residue by residue or atom by atom. The correlation coefficient appears directly in wwPDB validation reports and the real-space R value enters them as a Z-score of its distribution (RSRZ), and both, as the same authors note, share the flaw of not distinguishing model accuracy from model precision — a model can correlate poorly because it is misplaced, or because the density is genuinely smeared ^[5].

B-factors: one number carrying several different things

The atomic displacement parameter, usually called the B-factor, scales how sharply an atom's electron density is smeared. It reflects structural heterogeneity, which Carugo's review names as what atomic displacement parameters depend on ^[7]; the single refined number does not, as a matter of ordinary refinement practice rather than any published finding, separate thermal motion from static disorder across unit cells or from model error. Carugo's review emphasizes that B-factors are differently affected by several factors, from crystallographic resolution to refinement protocol, so standardization is essential before comparing two or more structures, and notes a modern tendency to allow them to inflate to extremely large values with little physico-chemical meaning ^[7].

That inflation has a specific mechanism. Refinement is routinely run without any restraint on the upper limit of B, so atoms undetected in the electron density are allowed to inflate to extremely large values, even above 100 Ų; the positions of such undetected atoms are, in Carugo's phrasing, purely speculative rather than based on experimental evidence ^[8]. Against that he proposed a ceiling on a structure's average B-factor rather than on any single atom, obtained by regressing average B-factor against percentage of crystal volume occupied by solvent across Protein Data Bank structures deposited before 2008, separately within eight resolution ranges, and extrapolating each fit out to the absurd limit of 100% solvent. The output is a table, not one number: with all atom types pooled, the limit is 25 Ų for data better than 1.5 Å, rising to 83 Ų in the 3.0–3.3 Å range and 80 Ų in the 3.3–4.0 Å range. A structure is judged against the value for its own resolution range, and where the average exceeds it, Carugo's reading is that some of its atoms have likely been refined with B-factors too large to count as visible. He names the limitation himself: the extrapolation runs to 100% solvent while observed solvent contents are always below 80%, so the figures may be inaccurate ^[8].

For a bound peptide the same behavior is diagnostic. When a peptide is fitted poorly or lacks supporting density, refinement reduces its scattering contribution by raising its B factors, producing a distinctive rise relative to neighboring protein atoms; Weichenberger and colleagues scored this, subtracting the average B factor of atoms within 6 Å of a peptide chain from the average B factor of the chain itself ^[5].

Occupancy, and why it trades against B

Occupancy is the fraction of unit cells in which an atom is present at the modeled position. For protein atoms it is conventionally fixed at 1.0 unless there is reason to do otherwise; for a bound ligand that convention is often wrong. Weichenberger and colleagues note that ligand occupancies can only approach 100% asymptotically, in the best cases of tight binding, so the already small ligand contribution to scattering falls further ^[5].

Occupancy and B are not independent, because lowering occupancy and raising B both reduce the same thing — an atom's contribution to the calculated structure factors. Carugo found an empirical relationship between occupancy and the displacement parameter of water molecules by comparing a set of well-refined sperm whale myoglobin structures, and reported it to be independent of protein fold ^[9]; that result is about ordered waters and should not be transferred wholesale to peptide atoms. The related observation on ligands comes from Caldararu and colleagues, who found in six protein-ligand complexes that groups flagged as flexible by ensemble refinement coincided with those giving high displacement parameters or non-unity occupancy when optimized in standard refinement ^[10]. Refining occupancy and B together at moderate resolution is poorly determined, and whether a deposited occupancy was refined or simply left at 1.0 is worth checking, not assuming.

How a bound peptide comes to be partly ordered

Partial order is the normal condition for a bound peptide, not an exception. Conformational freedom in a ligand frequently increases with distance from the specifically bound parts, which Weichenberger and colleagues identify as particularly problematic for extended peptide chains ^[5]. Unmodeled regions are ordinary in structures generally: analyzing 16,370 X-ray structures representing 18,101 PDB chains and 5,434 proteins, Le Gall and colleagues found only about 25% of the data set had more than 95% of its sequence length observed, about 10% of the proteins contained consecutive missing or ambiguous stretches longer than 30 residues, and about 40% shorter such regions of at least 10 and fewer than 30 residues ^[11].

The clearest picture for peptides comes from the Twilight survey. Its authors scored peptide-ligand chains using real-space correlation coefficients from wwPDB validation reports — 112,565 residue values across 9,747 chains — then inspected the density for the hundred worst-scoring protein-peptide complexes and classified what they found ^[5]. The percentages below are proportions of that examined hundred, chosen because it scored worst; they are not proportions of the Protein Data Bank.

• 23% showed no continuous electron density supporting the hypothesis that a peptide molecule is present at all.
• 40% contained significant disorder, in two flavors: density showing only a backbone-like tube with little side-chain evidence, so that sequence register cannot be inferred; or clear density for a well-ordered portion that degrades toward the termini, where, in the survey authors' reading, a longer peptide stretch appears to have been modeled than the evidence can reasonably support.
• 17% had peptide placed into density the survey judged likely to originate from partially ordered mother-liquor components.
• 11% involved peptides extended using noncrystallographic symmetry.
• 2% had density resembling the proposed peptide, with the peptide not correctly placed in it.
• 6% were scoring errors — false positives and false negatives of the survey's own measure.

Those six figures sum to 99%: nearly every case examined fell into one. The second class is the one to hold onto. A peptide can be genuinely present and genuinely bound while the crystallographic data support only part of the modeled chain; the authors note there is no consensus on how such partly supported regions should be included in a model, and that the unmodeled part must lie near the modeled part, which excludes that space for other moieties and is itself of some value ^[5].

Ensembles, cooling, and the single-conformer habit

A single set of coordinates with one B-factor per atom compresses a distribution. Fraser and colleagues analyzed available data for 30 different proteins and reported that cryocooling remodels the conformational distributions of more than 35% of side chains and eliminates packing defects, exposing a bias in structural databases toward smaller, overpacked and unrealistically unique models ^[12]. Since modern structures are based nearly exclusively on cryogenic data ^[12], most deposited peptide complexes inherit it.

Modeling more than one conformer is possible but not free. Caldararu and colleagues applied ensemble refinement to six protein-ligand complexes and found it sometimes indicated flexibility in parts of the ligand and some side chains beyond what a single conformer plus displacement parameters can describe; molecular dynamics and automatic generation of alternative conformations agreed. But the electron-density maps were comparable and free R values slightly increased, so by that statistical criterion the original single-conformer structure remained the better model, and the authors caution that ensemble diversity is often exaggerated and should not be trusted in detail ^[10]. They present it as a diagnostic for which parts of a structure are poorly described by one conformer, not a replacement for standard refinement.

What the data cost, and what they do not establish

Diffraction data are collected at a dose. Owen, Rudiño-Piñera and Garman measured, on four holoferritin and three apoferritin crystals at a third-generation synchrotron, a dose of 43 (±3) MGy for the diffracted intensity of cryocooled crystals to fall by half, and recommended 30 MGy — a ceiling below that half-intensity dose — for typical macromolecular crystallography once other data-quality indicators are considered; they also observed a 10% decrease in crystal lifetime for a tenfold increase in dose rate ^[13].

Several things a peptide complex structure does not deliver are worth naming, none needing a citation. It gives no affinity and no association or dissociation rate constant, and no population weighting for the conformations present in solution. It reports one crystal form, in which lattice contacts are part of the peptide's environment. And where density supports only part of the chain, the remaining coordinates are a hypothesis stored in the same format as the evidence.

Reading a deposited peptide complex

• Check whether structure factors were deposited; without them nobody can re-examine the model against density.
• Read the peptide's real-space correlation values residue by residue in the validation report, not the global R and free R.
• Compare the peptide's mean B factor against the protein atoms surrounding it, not the structure-wide average.
• Check whether occupancies were refined or fixed, and read low occupancy together with the B factors.
• Ask for an omit or polder map before accepting a binding pose, and for the map type and contour level of any density figure.
• Note which residues were modeled and which were not, and treat conclusions about the unmodeled part as inference.

None of this makes crystallography unreliable. It makes explicit that a deposited peptide complex is a claim of a particular strength, readable from the same file as the coordinates. The recurring failure is not fabrication; it is a well-refined protein with a peptide drawn into density that could not carry it.