Sequence-Based Secondary Structure Prediction for Peptides

A secondary structure predictor assigns every residue in a submitted sequence to helix, strand or coil, and it does so for any string of amino acids — including one that has never been folded, never been solved, and has no relatives anywhere in a sequence database. A label always comes back. Whether that label carries information depends almost entirely on how much non-local context the method had access to, and a short designed peptide is the case in which that context is thinnest.

Local sequence does not fix local structure

Every propensity-based method rests on the premise that a residue's conformational state is largely set by its own identity and those of its immediate neighbours. That premise was tested directly and it failed. Searching 62 proteins of known structure comprising 10,000 residues, Kabsch and Sander found that the longest isolated sequence identities shared between unrelated proteins run to five residues, and that in 6 of 25 such cases the same five residues form part of an α-helix in one protein and part of a β-strand in another ^[1]. Pentapeptide structure within a protein is therefore strongly dependent on sequence context: considering the local sequence of five residues is not sufficient to predict the local conformation correctly, and cooperativity of length six or longer has to be taken into account ^[1].

The accuracy of the first generation of predictors reflects that limit. Benchmarked on 62 proteins of known structure, none of the three most widely used prediction algorithms of the period assigned better than 56% of residues correctly in a three-state helix/sheet/loop model ^[2].

What a propensity scale actually measures

The scales themselves are sound measurements answering a different question. Pace and Scholtz derived helix propensities for solvent-exposed residues in the middle positions of α-helices, pooling measurements from 11 systems covering both peptides and proteins: alanine is the most helix-favouring at 0 kcal/mol and glycine the least apart from proline at roughly 1 kcal/mol less favourable, with the remainder spread between (leucine and arginine 0.21, threonine 0.66, aspartate 0.69) ^[3]. For β-sheet, Minor and Kim substituted the twenty naturally occurring residues at a solvent-exposed guest site on the sheet of a small monomeric IgG-binding domain from protein G and derived a thermodynamic scale from the resulting thermal stabilities, spanning approximately 2 kcal mol^-1 excluding proline ^[4].

Two limits follow. Each number is a free-energy difference for one residue type at one position in one host — in the β-sheet case a folded protein domain, not a peptide — rather than a per-residue probability for your sequence. And the spread is small next to what context supplies: the same authors went on to design an 11-residue sequence that folds as an α-helix at one position in that protein G domain and as a β-sheet at another, both variants folding into structures similar to the native domain by several biophysical criteria, which demonstrates that non-local interactions can determine the secondary structure of peptide sequences of substantial length ^[5]. An eleven-residue stretch, longer than the neighbourhood a propensity rule integrates over, can carry no fixed answer at all.

The improvement evolutionary profiles bought

What took the field past the propensity ceiling was replacing the single sequence at the network input with a multiple sequence alignment. Rost and Sander trained a two-layered feed-forward network on 130 protein chains and found that including protein family information in this form increases prediction accuracy by six to eight percentage points, with a combination of three levels of networks reaching an overall three-state accuracy of 70.8% for globular proteins; a position-specific reliability index isolated half the residues, for which accuracy rose to better than 82% ^[6]. Jones replaced the alignment with position-specific scoring matrices generated by PSI-BLAST and reported an average Q3 of 76.5% to 78.3% on a test set of 187 unique folds, the range depending on the precise definition of observed secondary structure used ^[7]. Increasingly larger databases of protein sequences and structures for training, together with more powerful deep learning, have since raised the highest three-state accuracy achieved without relying on structure templates to 82–84%, against an estimated theoretical limit of 88–90% for three-state prediction ^[8].

Every one of those figures is an average over folded proteins for which homologues could be retrieved. That is exactly the resource a designed sequence does not have.

Designed and orphan sequences run in single-sequence mode

With no alignment to build, a profile-based predictor is running on one sequence whether or not it was built to. Methods trained for that condition exist and are the ones to use. SPOT-1D-Single, trained on 39,120 proteins deposited before 2016, gives three-state accuracies ranging from 72.12% to 74.28% across seven independent test sets; on the subset of SPOT-2018 proteins with no homologues at all (Neff = 1) it predicts three-state secondary structure 6.24% more accurately than the profile-based SPOT-1D from the same group ^[9]. Two things follow for a de novo peptide. Submit it to a single-sequence method rather than a profile method. And carry the single-sequence band, not the profile band, when deciding how much weight the prediction can bear — the benchmarks behind the two are different sets, so the gap is indicative rather than a subtraction you can apply to your own sequence.

Why short peptides are worse than any of those numbers

All the accuracies above are per-residue scores on residues embedded in folded domains: 130 chains, 187 folds, 39,120 proteins. A residue in the middle of such a chain is flanked on both sides by precisely the context that, per the pentapeptide result, determines its state. A 12-residue peptide has no such flanks; at both ends the model is being asked to read positions that its training data represented almost entirely as chain interiors.

The reference labels are unstable there too. Comparing DSSP, STRIDE and KAKSI on molecular dynamics conformations of deliberately irregular peptides, full-sequence segment overlap between assignment codes ranged from 70% for a 13-residue peptide with STRIDE as the reference down to 49% for an 18-residue polyasparagine with DSSP as the reference, the major differences falling in turns, in the distinction between α and 3₁₀ helices, and in short parallel-sheet segments ^[10]. A per-residue prediction cannot be scored more finely than the assignment it is scored against, and for a conformationally irregular peptide that assignment is itself a choice of algorithm.

The error also runs in the unhelpful direction. Sixteen-residue alanine-based peptides, solubilised by inserting three or more residues of a single charge type, show stable α-helix formation in water — a result the host-guest parameters then available did not predict, since those parameters implied a 16-residue peptide should show no measurable helix formation ^[11]. A short peptide can be more ordered than propensity arithmetic implies, not only less.

The helical wheel is a design tool, not a prediction

Schiffer and Edmundson introduced the wheel as a two-dimensional projection of an α-helix, observing that in most helical segments of myoglobin, haemoglobin and lysozyme the hydrophobic residues cluster at the n±3, n, n±4 positions of adjacent turns to give a distinctive hydrophobic arc, and that such arcs are not observed when non-helical segments are plotted the same way ^[12]. Eisenberg, Weiss and Terwilliger made this quantitative as the mean helical hydrophobic moment: the mean vector sum of the side-chain hydrophobicities, each vector's length the signed hydrophobicity of that side chain and its direction fixed by the orientation of the side chain about the helix axis. Plotting mean moment against mean hydrophobicity separates transmembrane helices, helices from globular proteins, and helices believed to seek surfaces between aqueous and non-polar phases into different regions of the plot ^[13].

Both constructions presuppose the helical geometry. The wheel advances each successive residue by the fixed angular increment an α-helix imposes, so it will draw a wheel for any sequence, helix-forming or not; and the original work demonstrated that contrast on segments whose conformation was already known from solved structures, then applied the wheels to six further sequences to divide them into helical and non-helical segments — an application of the method rather than a blind test of it ^[12]. Run forwards as a design tool the logic is sound: you have decided the segment should be helical and amphipathic, and the projection tells you which positions to load to build that face. Run backwards, as evidence that a designed peptide is helical, an amphipathic arc is a property of the plotting convention combined with the residues you chose, and it is a measurement rather than the wheel that establishes the helix.

What a disorder score does and does not assert

Disorder predictors ask whether a region has a well-defined structure at all rather than which of three states each residue occupies. IUPred estimates the total pairwise inter-residue interaction energy a sequence can form, on the assumption that intrinsically unstructured sequences do not fold because they are unable to form sufficient stabilising inter-residue interactions; separate built-in parameter sets are optimised for short disordered regions, long disordered regions and structured domains ^[14].

The Critical Assessment of protein Intrinsic Disorder evaluated 43 methods on 646 proteins from DisProt. The top disorder predictor reached F_max = 0.483 across the full dataset and F_max = 0.792 once bona fide structured regions were filtered out, while disordered binding regions remained hard to predict at F_max = 0.231; the best methods used deep learning and notably outperformed physicochemical ones ^[15]. Read those as three statements rather than one. The same predictor scores very differently depending on what the negatives are, so a disorder score is interpretable only against the reference definition it was scored on. A high score says the region is unlikely to hold a fixed fold under the conditions that reference describes. It does not say the region is conformationally featureless, and it does not tell you whether the region acquires structure on binding — those residues are the subset the assessment scored lowest.

Where a structure prediction sits relative to all this

A structure predictor answers a third question again, returning coordinates plus a per-residue confidence rather than a per-residue state. That confidence has been repurposed as a disorder score, and when compared against 20 disorder predictors on the same 646-protein benchmark, AlphaFold2-based disorder predictions reached an area under the ROC curve of 0.77 and were statistically outperformed by several modern disorder predictors securing around 0.80, at a median runtime of about 1200 s against about 20 s; for fully disordered proteins the AlphaFold2 call gave F1 = 0.59 against 0.91 for the best disorder predictor, and disorder content came back with a mean absolute error of 0.21 against 0.15 ^[16]. The same comparison found AlphaFold2 statistically more accurate for about 20% of proteins — relatively short sequences with a few disordered regions tending to sit at the sequence termini, and without disordered protein-binding regions ^[16].

The division of labour is worth stating as a rule. A structure predictor gives you a conformation and a confidence attached to coordinates, and what that confidence licenses is treated separately in this library's AlphaFold guide. A secondary structure predictor gives you a per-residue state with no coordinates behind it. A disorder predictor gives you a per-residue statement about whether any fixed state applies. You can of course run an assignment code over a predicted model to obtain per-residue states, but those states then inherit the model's fold error instead of being predicted independently, and they inherit the code-to-code variation described above as well.

Settling it: circular dichroism and NMR

A prediction is a statement about a sequence. The peptide in a tube has a solvent, a temperature, a concentration and an ionic strength, none of which the predictor saw. Two measurements close that gap, and they close different parts of it.

Far-UV CD returns fractional composition, not a residue-by-residue assignment, and the comparison is closer than it looks: Rost and Sander noted that the accuracy of their method in predicting the content of the three secondary structure types is comparable to that of circular dichroism spectroscopy ^[6]. Agreement on composition therefore does not validate the per-residue assignment. The standard deconvolution packages — CONTIN, SELCON3 and CDSSTR — fit a spectrum against reference sets of proteins whose secondary structure assignments came from DSSP; across five reference sets built from 29 to 48 proteins the three performed comparably in spite of their different algorithms, CDSSTR best with a smaller reference set and larger wavelength range, CONTIN/LL best with a larger reference set and smaller wavelength range, and the performances for individual secondary structures mixed ^[17]. The authors' own conclusion is that analysing a spectrum with all three should improve the reliability of the resulting fractions ^[17]. Note what the reference sets are made of: folded proteins carrying structure-derived DSSP assignments. A 14-residue peptide is not represented in that space, which is the reason to use a CD-derived helix fraction comparatively — the same peptide before and after a substitution, or across a temperature series — rather than as an absolute percentage to be scored against the predictor's output.

NMR chemical shifts give the readout that matches what a secondary structure predictor emits. The chemical shift index classifies each residue by the deviation of its backbone shifts from random-coil values; extending the index from ¹Hα to ¹³Cα, ¹³Cβ and carbonyl ¹³C supplies four independent chemical-shift measurements per residue, and combining the ¹H and ¹³C indices into a consensus estimate identifies and locates protein secondary structure with a predictive accuracy in excess of 92%, which the authors take to suggest that the secondary structure of peptides as well as proteins can be obtained accurately from ¹H and ¹³C shifts without recourse to NOE measurements ^[18].

That is the comparison to make. The predictor names a state per residue, the consensus index names a state per residue, and the two align position by position. Where they disagree the disagreement localises: a predicted helix read as coil over its first three residues is fraying, one of the deformations that also drives assignment codes apart ^[10], and it is exactly the failure mode the missing flanking context predicts.

None of this yields a structure. A propensity, a per-residue state assignment and a disorder score are three summaries of a sequence, each carrying a stated error rate on folded proteins and a wider, unquantified one on a 12-mer. Use the single-sequence prediction to place the hypothesis, use the wheel to build the face you intended, and let the spectrum or the shift index decide.