Solution NMR does not measure a structure. It measures resonance frequencies, scalar couplings, and cross-peak intensities. Coordinates are inferred from those numbers under assumptions you supply — about how intensity maps to distance, about how fast the molecule moves, and about what counts as a satisfactory model. For a folded protein those assumptions are usually harmless. For a short, flexible peptide they are the whole problem, because the peptide spends its time in many conformations and every observable you record is an average over them.

What the experiment actually records

Four families of observable carry conformational information. Chemical shifts report the local magnetic environment of each nucleus. Three-bond scalar couplings report torsion angles through the intervening bonds. Nuclear Overhauser effects report through-space proximity between protons. Relaxation rates report motion. Nothing in that list is a coordinate.

Before any of it means anything, resonances must be assigned to specific atoms in a specific residue. For a synthetic peptide at natural isotopic abundance this is usually done from homonuclear spectra — a through-bond experiment such as TOCSY to group protons by spin system, then a through-space experiment such as NOESY or ROESY to walk sequentially along the chain — with carbon shifts, if needed, taken from natural-abundance heteronuclear correlation rather than from labeled material. Shifts are quoted against an internal reference compound at a stated temperature and pH. These are conventions of practice rather than findings, and they are stated here without citation. They matter anyway: an assignment error propagates into every restraint that uses that resonance, and a referencing error shifts an entire index.

Sample heterogeneity shows up here too. Chemically distinct species — a deamidated fraction, an oxidized fraction, a residual protecting group — give their own resonances, so extra peaks are as likely to mean the sample is impure as to mean the peptide is populating a second conformation. Distinguishing the two is the analyst's job before the structure calculation starts.

NOE intensities and the distances drawn from them

The NOE between two protons depends steeply on the distance between them, in the simplest treatment as the inverse sixth power, and on the correlation time of the vector joining them. In practice an intensity is converted to a distance by calibration against a proton pair whose separation is fixed by covalent geometry, under the initial-rate approximation — read the build-up early enough that magnetization has not had time to relay through third spins.

Two things break that. The first is relay itself. Magnetization does travel through intervening spins, and the effect is not symmetric in its consequences: when multiple-spin effects are significant, calculated distances are often underestimated — biased short — and one analysis showed that this bias persists even under a complete relaxation matrix treatment, because random errors in the measured NOE intensities push the result that way; the same work showed that usable upper and lower bounds can be recovered if the intensity errors are propagated explicitly rather than ignored [1]. The second is that correcting for relay requires a structure. In one published implementation, built for extracting exact NOEs, a full relaxation matrix analysis calculates the spin-diffusion contribution to the cross peak of each individual spin pair of interest, and the program requires a three-dimensional structure as input — either a crystal structure or an NMR structure determined by the conventional approach [2]. The correction you apply therefore depends on the answer you are trying to get, which is tolerable when the molecule is rigid and circular when it is not.

Because of all this, NOE-derived restraints are almost always applied as bounds rather than as distances, and the upper bound is the load-bearing one. An observed NOE is evidence that two protons come close at least some of the time; a missing NOE is weak evidence of anything, since it can also reflect overlap, exchange broadening, or an unfavorable correlation time. Treating absence as a lower distance bound is not sound, and it is not standard practice.

Chemical shift indexing

Chemical shifts are the cheapest conformational data available, because you already have them from the assignment. The chemical shift index exploits a systematic observation: the alpha-CH proton shift of all twenty naturally occurring amino acids moves upfield of its random-coil value in a helical configuration and a comparable amount downfield in an extended, beta configuration. The original method turned this into a simple digital filter over the assigned alpha-proton shifts to locate secondary structure elements along the chain, and its authors described it as nearly as accurate as NOE-based secondary structure determination and proposed it as a complement to, not a substitute for, those methods [3]. Extending the index to backbone carbon-13 shifts — alpha carbon, beta carbon and carbonyl — gives four independent chemical shift measurements, and the authors of that extension reported that combining the proton and carbon-13 indices into a consensus estimate achieved predictive accuracy in excess of 92% [4].

Later work is less flattering about the original. The authors of a machine-learning successor describe the classic index as only about 75–80% accurate and report for their version an average identification accuracy, Q3, of 90.56% under repeated tenfold cross-validation on a training set of 181 proteins and 89.35% on a test set of 59 proteins [5]. Those two accuracy figures are not measured against the same benchmark as the 92% claim, and the discrepancy is best read as a caution about comparing accuracy numbers across evaluation sets rather than as a refutation.

Two limits deserve emphasis. Shift indexing returns secondary structure, not coordinates — it tells you a stretch is helical, not where the helix sits relative to anything else. And every index is defined as a deviation from a random-coil reference, so the reference set, and its temperature, pH and neighboring-residue corrections, is part of the measurement. For a peptide with no tertiary structure, that limitation may be a feature: one study comparing two helical peptides in water and bound to detergent micelles concluded that NMR structure ensembles generated from their NOE data do not fully reflect the conformational averaging present in those systems, and suggested that secondary structure definition from chemical shift deviations may be the most appropriate treatment for peptides that lack tertiary structure [6]. That hedge is the authors' own: a suggestion, not a rule.

Conformational averaging in flexible peptides

Whether averaging is visible depends on how fast conformations interconvert relative to the frequency difference between the resonances they produce. Slow interconversion gives separate sets of peaks, which is why cis and trans proline isomers can often be counted directly; fast interconversion gives one population-weighted peak, and the populations are hidden inside it. This is standard exchange-regime lineshape behavior and is stated here without citation.

The steepness of the NOE distance dependence makes that weighting badly non-linear. Consider two conformations of a peptide interconverting fast, with a given proton pair at 2.5 Å in one and 5.0 Å in the other. At equal populations — the denominator is the total time, split 50/50 — the inverse-sixth-power-averaged effective distance is about 2.80 Å, not the 3.75 Å arithmetic mean. Make the compact state a minority, populated 10% of the time against 90% for the open state, and the effective distance is still about 3.59 Å, against a population-weighted mean distance of 4.75 Å. A conformation occupied a tenth of the time can dominate the restraint. This is arithmetic, stated here without citation, and it holds only under the assumptions that let the NOE be written as an inverse-sixth-power average in the first place — initial-rate conditions, and internal motion fast compared with overall tumbling.

Short peptides in water are the regime where this bites hardest. A systematic proton NMR study of short linear peptides found that in the unfolded state they adopt predominantly extended chain conformations in water, while certain sequences show substantial populations of reverse-turn conformers, with rotating-frame NOE spectroscopy providing the evidence for the turn populations; in that work the temperature coefficient of the position-4 amide proton was used as a measure of beta-turn population, for the specific series Tyr-Pro-X-Asp-Val where X was every L-amino acid except tryptophan and proline [7]. Note the scope: a criterion calibrated on that series is not a general calibration.

When the conventional readouts mislead

Amide proton temperature coefficients are widely used as a hydrogen-bonding indicator, and they are solvent-conditional. In a study of two 18-residue alpha-helical peptides in 50% trifluoroethanol, where both were maximally helical, temperature coefficients of −10 to −6 ppb/K were observed even for hydrophobic residues in the middle of the helices — a range the authors describe as usually indicative of the lack of intramolecular hydrogen bonds — while slow hydrogen isotope exchange for residues 4 to 16 in both peptides indicated that intramolecular hydrogen bonds were in fact intact. Their proposed explanation was that the amide shift pattern in these solvents is dominated by bifurcated intermolecular hydrogen bonding between backbone carbonyls and the fluoroalcohol [8]. The lesson is not that temperature coefficients are useless; it is that a threshold validated in one solvent does not transfer to another.

Cosolvents and detergents change the answer in a more basic way as well. A helix induced by trifluoroethanol or by a detergent micelle is a real observation about the peptide in that medium, and says nothing on its own about the peptide in buffer.

Restraints that average differently

Because different observables average with different weightings, disagreement between them is informative. Three-bond couplings average roughly linearly in the coupling constant rather than as an inverse sixth power of distance, so a conformer distribution that satisfies the NOEs need not satisfy the couplings. Residual dipolar couplings, measured under weak alignment, add orientational information that is not distance-based at all; short peptides do give measurable values, with peptides of 2 to 15 residues of arbitrary sequence reported to exhibit a modest range of residual dipolar couplings when aligned in strained polyacrylamide gels or in alkyl-PEG bicelles, though line broadening in bicelles for a subset of residues indicated that some peptides bind weakly to the lipid disks — the alignment medium is not always a passive spectator [9].

A worked case makes the disagreement concrete. A 16-residue peptide spanning a coiled-coil trigger sequence had been refined by a standard single-structure protocol using 172 NOE distance restraints together with 14 hydrogen-bond and 11 phi torsion-angle restraints, giving 20 regularly alpha-helical models. Those models slightly violated some measured NOE bounds and did not reproduce all 15 measured three-bond amide-proton to alpha-proton couplings. Only ensembles generated with simultaneous time-averaged NOE distance and coupling-constant restraining reproduced all the experimental data, and the authors concluded that the conformational variability admitted by the 187 measured NMR data is larger than the model set represents. That total is what remains once the hydrogen-bond and torsion-angle restraints are set aside: the 172 NOEs plus the 15 couplings. They attributed the inconsistency to the neglect of averaging effects and to the inclusion of hydrogen-bond and torsion-angle restraints that have little basis in the primary measured data [10].

Why an ensemble is not a structure

A deposited NMR entry is typically a bundle of models. That bundle is a sample of the conformations consistent with one restraint set under one calculation protocol. Its spread is a statement about how tightly the data plus the protocol determine coordinates — precision — and it is not a measurement of accuracy, and not a measurement of the amplitude of motion. Two peptides with identical true flexibility can produce bundles of very different tightness if one was given more restraints than the other.

The literature on flexible peptides is explicit about the sources of trouble. One analysis of two beta-heptapeptides in methanol, comparing sixteen molecular dynamics simulations against the primary NMR data and against a set of single-structure-refined NMR model structures, identified three distinct problems with conformational interpretation of NOE and coupling data: conformational and time averaging, an insufficient number of experimental data, and insufficient accuracy of those data [11]. They are separate failures and they need separate remedies; more restraints do not fix averaging.

There is also a failure mode specific to forcing one model to carry an average. If two restraints are each satisfied only in different conformations, a single structure driven to satisfy both simultaneously can correspond to a conformation the molecule never populates. That is a consequence of averaging rather than a finding, and it is stated here without citation, but it is the reason a tight bundle around a physically odd geometry should raise suspicion rather than confidence.

Two practical consequences follow. First, apparent disorder in a bundle can arise either from genuine conformational sampling or from a mixture of species; work on flexible transmembrane peptides showing well-converged regions separated by flexible break points set out protocols intended, among other things, to differentiate oligomerization from ensemble-averaged observation of multiple peptide conformations [12]. Second, how you score a candidate ensemble changes what you conclude. In a modeling study of lanthipeptides, ensembles generated with Rosetta showed similar experimental agreement, lower Rosetta energy scores, and greater flexibility than the ensembles of lanthipeptides with NMR-determined structures in the PDB; the authors identified their use of ensemble-averaged NOE distances, instead of requiring each individual structure to satisfy every NOE restraint, as key to revealing that flexibility [13].

What to report, and what stays unknown

A useful methods section states the reference compound, temperature, pH and buffer, the cosolvent or detergent if any, the NOESY mixing times and whether build-up was measured, how distance calibration was performed, whether spin diffusion was assessed, the number of experimental restraints separated by type, how many of those are genuinely independent measurements rather than inferred hydrogen bonds, and the violation statistics. Restraint counts per residue and violation tables are what let a reader judge a bundle; the bundle alone does not.

What generally stays unknown for a flexible peptide is the population of each conformational state and the rate at which the states interconvert. A handful of averaged observables cannot resolve many states, and a structure calculation does not itself measure exchange rates. Ensemble methods make the averaging explicit, which is an improvement, but they trade an unstated assumption for a stated one — the force field, the number of replicas, the restraint weighting — and the answer depends on all three. The honest summary of a solution NMR study of a flexible peptide is usually a statement about which local conformations are populated and roughly how much, not a set of coordinates.