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A Shortcut to Structure in AlphaFold 3

Jonathan Feldman, Jeffrey Skolnick

arXiv:2610.08937v1q-bio.BMcs.AI

TL;DR

How AlphaFold 3 forms global protein geometry internally, and what structural information its MSA supplies, remain poorly understood. The study intervenes on representations and probes Pairformer blocks, finding that a different protein’s alignment can recover structure when its columns match the target’s structural correspondence.

  • Problem

    How AlphaFold 3 forms global structure internally and how much its predictions reflect protein-folding biophysics remain open questions.

    Source: §1 · p. 1

  • Method

    The study intervenes on MSA-enriched pair representations, probes fold emergence across Pairformer blocks, and transplants structurally corresponding alignment columns between proteins.

    Source: §2.2 · p. 3, §2.9 · p. 9, §3 · p. 11

  • Results

    Median TM-score against experiment rises from 0.442 to 0.717 for Sabmark pairs sharing 9% sequence identity when supplied structurally aligned columns from another protein’s alignment.

    Source: §3 · p. 11

  • Takeaways & Limitations

    The model can read a transferable description of structure from an alignment when it is supplied in the correct register, rather than requiring evolutionary relatedness to the query.

    Source: §3 · p. 11

    The authors conclude that structure prediction remains unsolved until models can recover protein structure confidently and accurately from sequence alone, without input that already encodes much of the fold.

    Source: §3 · p. 11

Abstract

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AlphaFold 3 predicts protein structures with remarkable accuracy, yet how structural information emerges within the model remains poorly understood. Here, through causal interventions on internal representations and direct probing of every Pairformer block, we trace the formation of global protein geometry and identify the multiple sequence alignment (MSA) as a structural shortcut to the fold. Removing the MSA largely preserves local secondary structure while disrupting the long-range relationships that define global topology. Restoring the MSA-enriched pair representation at only forty residues recovers most of this lost organization, including at pairs never directly modified. This contribution depends on the detailed direction of the MSA module's output rather than its magnitude. The Pairformer rapidly converts this signal into global geometry: the final fold becomes recoverable by approximately block 9 of 48 for a majority of proteins, roughly twenty-seven blocks before the model's decoder can render it, whereas without the MSA it remains inaccessible for most proteins throughout the pass. Which homologs are supplied shapes this trajectory more strongly than which query is supplied; it persists for a designed query that never evolved but collapses for a shuffled sequence. Most importantly, an alignment built for a different protein that shares the fold, supplied only at the structurally corresponding columns, raises the median TM-score against experiment from 0.44 to 0.72, while the same alignment shifted a few residues along the chain performs worse than supplying no alignment at all. What AlphaFold 3 reads from an alignment is therefore a description of the fold itself, transferable between proteins that share one, rather than the query's own evolutionary history. This explains both its accuracy and the limits of what it has solved.

1 Introduction

Although AlphaFold 3 predicts many structures with near-experimental accuracy, how its internal computations produce structure—and how closely they reflect protein-folding biophysics—remains an open question. This section frames the unanswered role of the MSA and outlines an investigation of how its information shapes global fold formation.

1 Introduction

  • The study asks how AlphaFold transforms amino-acid sequences into accurate structures and whether its predictions reflect protein-folding biophysics.AlphaFold 3 extends structure prediction to nucleic acids, small molecules, and biomolecular assemblies.Source: §1 · p. 1
  • Prior work found that removing the MSA substantially degrades AlphaFold 3’s representations, confidence, and predictions, while one to five diverse homologs can recover much of the benefit.The remaining questions concern which structural relationships depend on evolutionary information, how much MSA-enriched representation is needed, and how the Pairformer turns it into geometry.Source: §1 · pp. 1–2
  • The study examines MSA-dependent structural features, causally tests sparse restoration, probes fold emergence across Pairformer blocks, varies queries and alignments, and transplants structurally corresponding alignment columns.Its central question is whether the alignment contributes the query’s evolutionary history or a description of the fold in the correct correspondence.Source: §1 · p. 2

2 Results

These results examine how MSA-derived pair information shapes recovery of global fold organization, including its effects under removal, sparse restoration, and Pairformer processing. They also assess how homolog choice and structurally corresponding alignment columns relate to convergence toward shared folds and target-fold accuracy.

2.1 MSA information preferentially supports nonlocal structural organization

  • Without the MSA, novel proteins retained 84% of helices and 71% of strands, but long-range contact retention fell to 28%; median TM-score declined from 0.96 to 0.52.Exact β-bridge retention was 42%, and retained secondary structure did not guarantee correct placement in the global fold.Source: §2.1 · p. 3

2.2 Sparse restoration of MSA-enriched information recovers the global fold

  • Restoring pair information for 40 contact-selected anchors recovered 71% of the experimental TM-score gap and raised novel-cohort long-range contact retention from 28% to 73%.Recovery extended to pairs never directly modified, and four disjoint 40-residue sets produced comparable TM-scores, indicating distributed, partially redundant information.Source: §2.2 · pp. 3–4

2.3 The MSA module writes a distributed evolutionary representation that influences structural prediction

  • Native MSA-update direction, not magnitude, drove structural effects: native direction with shuffled magnitude yielded median TM-score 0.96 versus 0.70 for native magnitude with shuffled direction.The native direction recovered a median 1.000 of available structural difference, versus 0.011 for native magnitude; the module wrote essentially all of the difference between MSA conditions.Source: §2.3 · p. 4

2.4 The Pairformer transforms the MSA into structural geometry

  • The Pairformer progressively transformed the MSA-aligned signal: it retained about 54% of its initial value at block 20 and 8% at block 47, while the orthogonal residual dominated around block 25.Contact information was already decodable early; preference for native-only over shuffled-only contacts rose from 0.494 at checkpoint B to 0.714 at block 0, 0.782 at block 1, and nearly 1.0 by block 15.Source: §2.4 · pp. 4–5

2.5 Intermediate diffusion reveals an overcompact proto-fold

  • At block 14, diffusion produced an overcompact proto-fold with radius of gyration 48% of the final prediction and only 6% global structural agreement.Readouts recovered helices first, then strands, then exact β-bridge partnerships, with global architecture resolving only near block 44.Source: §2.5 · pp. 5–6

2.6 Probing the pair representation reveals an early, MSA-dependent global fold

  • By block 9, MSA-enriched representations yielded median TM-score 0.51 and 52% of proteins exceeded 0.5, while no-MSA representations reached only 0.29 by block 47.The decoded fold appeared roughly 27 blocks before diffusion could produce a structure of comparable accuracy; without the MSA, only 14% exceeded 0.5 by block 47.Source: §2.6 · p. 6

2.7 Intermediate representations reveal convergent MSA-dependent inference trajectories

  • At block 14, two MSA subsets of the same query agreed at TM-score 0.58, versus 0.69 for the same subset across different queries, showing MSA choice shaped trajectories more than query choice.Q, a natural homolog, and a ProteinMPNN design tracked within about 0.02 through block 24, whereas a shuffled query stayed at floor; five-sequence subsets reached comparable accuracy to the full MSA only near block 40.Source: §2.7 · pp. 7–8, Table 1 · p. 7

2.8 Sequence-divergent homologs converge on a shared fold dictated by the MSA

  • The study tested fold convergence by applying existing probes to 98 Sabmark proteins and comparing reconstructions for 542 same-group pairs with median sequence identity 9.4%.Partners’ reconstructed structures were compared on structurally aligned residues at each block, with and without the MSA; the supplied passages describe this test but do not report its outcome.Source: §2.8 · p. 8
  • With the MSA, homologs’ aligned-residue agreement reached 0.32 by block 9 and 0.45 by block 47, versus an unrelated-protein baseline of 0.15 at block 9.Without the MSA, fold TM-scores remained below threshold, partners showed at most 0.04 excess agreement over the unrelated baseline, and their final aligned TM-score was 0.28 versus 0.57 with the MSA; fractional convergence was similar across sequence-identity quartiles.Source: §2.8 · pp. 8–9

2.9 The MSA supplies structure rather than evolutionary relatedness to the query

  • 0.717 median TM-score against experiment came from a different protein’s structurally aligned MSA columns, versus 0.442 with no alignment, 0.836 with the target’s same columns, and 0.951 with its full alignment.The donor alignment shared no more than 19.5% sequence identity with the query (p = 7 × 10−9).Source: §2.9 · p. 9
  • Using same-depth donor alignments occupying the same number of columns, shifting the mapping three or seven residues along the target chain yielded 0.425 and 0.397; scrambling yielded 0.399, all at or below the no-alignment floor.Corrupting the target’s structurally aligned columns reduced its score from 0.836 to 0.519; gapping those same columns yielded 0.570.Source: §2.9 · pp. 9–10
  • On 38 novel targets, donor aligned columns raised median TM-score from 0.568 without alignment to 0.762, while the target’s own alignment over the same columns reached 0.884.Register-shifted, scrambled, and corrupted-column conditions scored 0.538, 0.456, and 0.479, respectively, at or below the no-alignment floor.Source: §2.9 · p. 10
  • Where donor coverage spanned most of the chain, transplanted and target alignments had similar TM-scores through block 24, while no null condition decoded a fold before block 27.Transplant accuracy rose from 0.567 in the least-covered quartile to 0.856 in the best-covered (Spearman ρ = +0.51, p = 1 × 10−7); probes under-read block-47 transplant representations, but the diffusion decoder recovered their folds.Source: §2.9 · p. 10
  • The results indicate that AlphaFold 3 extracts structural information from alignments: a different family’s alignment recovers much of the fold in the correct register, but performs worse than no alignment when displaced.Source: §2.9 · p. 10

3 Discussion

AlphaFold 3 uses alignments as a structural shortcut: correctly registered information can restore or transfer global fold information, while removing the MSA disrupts long-range organization. The Pairformer rapidly makes that fold recoverable, but this does not mean the model has solved sequence-only structure prediction.

3 Discussion

  • Restoring MSA-enriched pair representations at 40 residues recovered a median 71% of lost experimental accuracy, including global organization beyond the restored residues.The information is distributed, partially redundant, and does not depend on a privileged residue set or the complete MSA-enriched state.Source: §3 · p. 10
  • With the MSA, the global fold is decodable by block 9; without it, no proteins show emergence then and only 14% do by the first-pass end.The Pairformer rapidly transforms a compact evolutionary signal into an extractable global-fold representation.Source: §3 · p. 10
  • The pair representation encodes a near-native-sized fold roughly 27 blocks before diffusion renders it, while intermediate diffusion outputs progress from compact structures to helices, strands, and exact β-bridge partnerships.The compactness belongs to the diffusion model, not the pair representation.Source: §3 · pp. 10–11
  • Full MSAs yield the global fold within roughly ten blocks, versus about thirty-six for small diverse subsets; homolog choice shapes early trajectories more than query choice.A designed query retains emergence pace, whereas a shuffled query yields no emergence; the query and its alignment must be structurally compatible.Source: §3 · p. 11
  • Structurally registered columns from another protein’s alignment raised median TM-score against experiment from 0.442 to 0.717 in Sabmark pairs and 0.568 to 0.762 in post-cutoff proteins; shifted or scrambled columns performed worse than no alignment.The Sabmark pairs shared 9% sequence identity.Source: §3 · p. 11
  • The alignment acts as a transferable structural description when supplied in the correct register, rather than merely as evolutionary evidence from which the model infers a fold.Frontier models including ESMFold2 and OpenDDE still perform best with evolutionary information, so sequence-only recovery remains an open boundary.Source: §3 · p. 11
  • The authors suggest donor alignments could convey structural hypotheses or alternative conformations, but neither application was tested and both require care.The proposed alternative-conformation approach would supply columns from a protein adopting the alternative fold at regions expected to switch.Source: §3 · p. 11
  • Predictive accuracy alone does not reveal whether a model derives an answer or reads information already present in its inputs; interventions and intermediate readouts can distinguish these routes.The authors expect this approach to inform study of other biological models whose accuracy has outpaced understanding of how it is achieved.Source: §3 · p. 12

4 Methods

The methods compare AlphaFold 3 representations and predictions across proteins with different sequence-similarity histories, then intervene on the MSA-enriched pair representation to test its contribution. They track how that contribution is encoded and relate its magnitude and direction to structural information.

4.1 Protein cohorts

  • The study compares 200 novel proteins with no pre-cutoff PDB sequence match above 40% identity against 200 similar proteins exceeding that threshold.All proteins were deposited after the September 30, 2021 training cutoff.Source: §4.1 · p. 13

4.2 AlphaFold 3 predictions

  • Predictions used AlphaFold 3 with internal-representation hooks, full-MSA or query-only alignments, and no structural templates.Representations were saved before and after the MSA module and after Pairformer passes; selected blocks were also sampled for analyses.Source: §4.2 · p. 13

4.3 Structural comparison metrics

  • Structural metrics distinguish contact retention by sequence range, secondary-structure and β-bridge retention, pairwise-distance agreement, and compactness relative to the final full-MSA prediction.Contacts are defined using Cα distances; secondary-structure retention is per residue and does not require matching 3D positions.Source: §4.3 · pp. 13–14

4.4 Activation patching at checkpoint B

  • At checkpoint B, the study patches selected rows and columns of the no-MSA pair representation with full-MSA values before running the Pairformer and diffusion module.A selected anchor restores its pairwise relationships with every residue, not only its isolated local properties.Source: §4.4 · p. 14

4.5 Anchor selection strategies

  • Patch anchors are chosen by full-MSA long-range contact count, MSA column conservation, or random sampling.Contact and conservation strategies select the top k residues; the disjoint-set analysis partitions ranked lists into four sets of 40.Source: §4.5 · p. 14

4.6 MSA-module contribution

  • The MSA-specific module contribution is defined as the difference between full-MSA and no-MSA updates from checkpoint A to B, and its projection accounts for 99.5% of the checkpoint-B difference.The identity was numerically verified for every protein with residual below 10^-6.Source: §4.6 · pp. 14–15

4.7 Magnitude–direction decomposition

  • The study decomposes each pairwise MSA-specific contribution into magnitude and unit direction, then analyzes the spatial distribution of magnitudes using effective rank.The magnitude matrix is N × N and its singular-value spectrum is used for the effective-rank calculation.Source: §4.7 · p. 15

4.8 Within-column MSA shuffling

The methods perturb cross-column relationships in the MSA while preserving selected column properties, then recombine native and shuffled module updates. This separates the structural contribution of update direction from that of magnitude.

4.8 Within-column MSA shuffling

  • Within-column shuffling randomly permutes homolog amino acids in selected columns while keeping the query and gap positions fixed, preserving column frequencies but disrupting cross-column relationships.Predictions were generated at seven shuffle fractions from 10% to 99%.Source: §4.8 · pp. 15–16

4.9 Magnitude–direction swap experiments

  • The swap experiment decomposes native and 99%-shuffled module updates into magnitude and direction, then recombines components to form hybrid checkpoint-B representations.The hybrids replace the live checkpoint-B state before computation continues through the Pairformer and diffusion module.Source: §4.9 · p. 16
  • Direction and magnitude rescue are measured by TM-score against the full-MSA prediction; 43 of 200 novel proteins were excluded because their control score difference did not exceed 0.1.A rescue value of 1.0 matches recovery by the native contribution, while 0.0 indicates no recovery relative to the shuffled condition.Source: §4.9 · pp. 16–17

4.10 MSA-module persistence across Pairformer blocks

The methods track the MSA-specific contribution through Pairformer blocks and assess when contacts and structures can be read from intermediate representations. They also vary the supplied homologs and query sequence to compare their influence on the trajectory.

4.10 MSA-module persistence across Pairformer blocks

  • At each Pairformer block, the study projects the full-MSA versus no-MSA representation difference onto the original MSA-specific contribution and separates aligned and orthogonal components.Projection coefficients measure alignment with the original contribution; they are distinct from normalized component magnitudes.Source: §4.10 · p. 17

4.11 Contact probes across Pairformer blocks

  • Ridge-regression probes are evaluated across Pairformer blocks for long-range contact discrimination, including generic evaluation and frozen-probe comparisons of native-only versus shuffled-only contacts.Probe training uses similar-cohort proteins, while the novel cohort is reserved for shuffling and hybrid analyses.Source: §4.11 · pp. 17–18

4.12 Intermediate diffusion readouts

  • Intermediate pair and single representations are passed to the diffusion module for independent structural readouts, which are compared with experimental structures and the final full-MSA prediction.Because diffusion is trained on completed representations, intermediate readouts indicate accessible information rather than optimized predictions or physical folding intermediates.Source: §4.12 · p. 18

4.13 Disjoint-MSA subsets

  • For each qualifying protein, two disjoint five-sequence MSA subsets are folded with a fixed seed, and intermediate structures are generated at selected Pairformer blocks.One hundred of the 200 novel proteins met the subset-selection constraints.Source: §4.13 · pp. 18–19

4.14 Query substitution

  • Query-substitution experiments hold MSA subsets fixed while using the original query, a natural homolog, a ProteinMPNN-designed sequence, or a composition-preserving shuffled sequence.The shuffled sequence is intended to destroy the query's structural signal; the designed sequence has median 45% identity to the native query.Source: §4.14 · p. 19

4.15 Probing the pair representation

The methods probe pair representations for distances, reconstruct structures from decoded distances, and compare trajectories across queries and fold-sharing alignments. They also specify display procedures, recycling conditions, and statistical reporting.

4.15 Probing the pair representation

  • Layer-specific ridge probes decode final full-MSA Cα distances from pair representations, using similar-cohort proteins for training and novel-cohort proteins for evaluation.The target distances stay fixed across layers while the representation varies; probes are trained separately for full-MSA and no-MSA representations.Source: §4.15 · p. 19

4.16 Reconstruction and evaluation of decoded structures

  • Decoded distance matrices are converted to Cα coordinates by classical multidimensional scaling and evaluated against the final full-MSA prediction using TM-score and additional distance, contact, and compactness measures.Both mirror reconstructions are evaluated because classical multidimensional scaling determines coordinates only up to reflection.Source: §4.16 · p. 20

4.17 Trajectory comparison

  • Trajectory comparisons measure progress toward the original query's final full-MSA prediction and similarity between runs at the same layer.For homolog queries, residues are mapped to the original numbering and comparisons are restricted to mapped positions.Source: §4.17 · p. 20

4.18 Display of reconstructed structures

  • For displayed structures, decoded-distance reconstructions are refined for local geometry and rebuilt into full backbones, but reported measures use unrefined reconstructions.Residues in displayed structures are colored by reconstructed-versus-final Cα positional distance.Source: §4.18 · p. 20

4.19 MSA transplantation

  • MSA transplantation supplies a fold-sharing donor's alignment at structurally corresponding target columns while retaining the target query, with register-shift and other ablations testing correspondence and alignment content.Novel-cohort pairs are selected by structural similarity and sequence divergence; the transplant, controls, and ablations use matched alignment depth and controlled column placement.Source: §4.19 · p. 21

4.20 Sabmark trajectories

  • Sabmark trajectory analysis compares reconstructed structures for same-group protein pairs across Pairformer blocks, against final-structure ceilings and different-group baselines.The analysis also groups pairs by sequence-identity quartile and reports aligned-residue RMSD alongside TM-score.Source: §4.20 · p. 22

4.21 Recycling

  • Most analyses use one Pairformer pass without recycling; the novel-cohort no-MSA condition additionally samples structures from recycling iterations C1 through C10.Source: §4.21 · p. 22

4.22 Statistical reporting

  • Reported medians, fractions, and counts use the protein sets specified for each analysis, and paired conditions are tested with two-sided Wilcoxon signed-rank tests.Figure shading denotes interquartile ranges across proteins.Source: §4.22 · p. 22

S1 The structural deficit without the MSA

MSA removal disproportionately disrupts nonlocal structure relative to each protein’s own full-MSA prediction, with losses increasing by sequence separation.

S1 The structural deficit without the MSA

S2 Sparse restoration of the MSA-enriched representation

Sparse restoration of MSA-enriched pair representations improves long-range contact retention, including for pairs that were never directly modified.

S2.1 Dose response and selection strategy

S2.2 Recovery beyond the restored pairs

  • About 68% of long-range pairs were untouched UU pairs, yet 40 contact-selected anchors closed 34.9% of the available balanced contact-map accuracy gap in novel proteins and 49.4% in similar proteins.Recovery was greater for IU pairs (50.6% and 64.6%) and II pairs (62.9% and 81.0%) in novel and similar cohorts, respectively.Source: S2.2 Recovery beyond the restored pairs · pp. 32, 34, Table S2 · p. 34
  • The Pairformer and downstream structure-generation modules use restored information to reconstruct additional relationships throughout the protein, not merely transcribe injected pair representations.Source: S2.2 Recovery beyond the restored pairs · p. 34

S3 The MSA module’s contribution

The MSA module writes a spatially organized signal whose detailed direction, rather than magnitude, strongly shapes structural predictions.

S3.1 Spatial organization

  • MSA-derived update magnitude had median effective rank 1.15, with 95.1% of spatial spectral mass in the first ten components; larger updates tended to occur at more variable and better-covered residues.Source: S3.1 Spatial organization · p. 34

S3.2 Disrupting cross-column relationships

  • Shuffling homolog amino acids within columns preserved individual-column statistics, yet cosine similarity remained 0.938 while contact-map overlap fell to Jaccard 0.740, implicating cross-column relationships.Source: S3.2 Disrupting cross-column… · p. 34

S3.3 Magnitude and direction

S4 Structural progression of the diffusion readouts

Diffusion readouts recover structural features in stages, and the late improvement in global accuracy depends on MSA availability.

S4.1 The order in which features appear

  • Readouts recovered helices before strands, correct β-bridge partnerships, and global agreement; by block 40, helix recovery was 87%, strand recovery 36%, and exact β-bridge recovery 27%.The radius-of-gyration ratio rose from 0.48 at block 14 to 0.73 at block 40.Source: S4.1 The order in which features appear · p. 36

S4.2 The late transition depends on the MSA

S5 Probe controls

Three controls support interpreting probe reconstructions as residue-specific structural information in the pair representation, while the reconstructions remain imperfect interpolations of global arrangement.

S5 Probe controls

  • The generic-chain baseline reaches median TM-score 0.22 against final structures, setting a floor for reconstructions carrying no fold-specific information.Reconstructions near 0.22 carry no more structural information than generic chain-length statistics.Source: S5 Probe controls · p. 38
  • Permuting block-47 residue identities drives decoded-distance R2 below zero for every probe and representation combination.This supports the conclusion that probes read the identity and arrangement of specific residue pairs, not generic distance statistics.Source: S5 Probe controls · p. 38
  • A no-MSA-trained probe reaches median TM-score 0.62 at block 47 on with-MSA representations, versus 0.29 on its own no-MSA representations.The cross-arm result shows the learned features are decodable in principle but absent from the no-MSA representation.Source: S5 Probe controls · p. 38
  • Probe reconstructions interpolate global arrangement rather than diffusing structures, so their local geometry is imperfect and residues can deviate from final positions.Reported measures use unrefined classical reconstructions.Source: S5 Probe controls · p. 38

S6 Determinants of decoding order

The order in which residues become decodable is associated with burial and alignment quality, but measured features explain only part of that order. The earliest residues do not form a distinct folding nucleus after accounting for burial, and their order differs from diffusion placement.

S6 Determinants of decoding order

  • For each residue, earliness was defined as the first layer at which its long-range lDDT reached half of its final value and held; this score was related to residue burial, alignment gap fraction, column conservation, and covariation.Source: S6 Determinants of decoding order · p. 38
  • Burial and alignment gap fraction associate with decoding earliness, but conservation and covariation are the weakest correlates and all features together reach only 0.47.Buried residues in well-aligned columns tend to decode earliest; burial is positively associated in every protein and gap fraction negatively associated in 93%.Source: S6 Determinants of decoding order · p. 38, Table S5 · p. 38
  • The earliest-decoded residues cluster more than random sets, but not more than random sets matched for burial, providing no evidence for a distinct folding nucleus.Buried residues are necessarily near one another and the protein’s centre.Source: S6 Determinants of decoding order · p. 38
  • Decoding order is unrelated to the order in which diffusion places residues (Spearman ρ ≈0), indicating that the two readouts resolve structure in different sequences.The authors attribute the described compaction to the decoder rather than the representation.Source: S6 Determinants of decoding order · p. 38

S7 Diffusion readouts of the disjoint MSA subsets

Diffusion readouts can make two disjoint MSA subsets appear to follow similar early trajectories, even when their intermediate structures are poorly organized. Probe-based comparisons reveal a different early relationship and make the readout caveat consequential.

S7 Diffusion readouts of the disjoint MSA subsets

  • The subsets agree at TM-score 0.71 from block 14 through block 40, but this early agreement is an artifact of overcompact, poorly organized proto-folds.Compact masses of comparable size can resemble one another regardless of what produced them.Source: S7 Diffusion readouts of the disjoint… · p. 38
  • The diffusion readouts for two evolutionarily independent MSA subsets are compared with each other and against experimental structures for 100 novel proteins.Table S6 reports median TM-scores for both comparisons.Source: Table S6 · p. 39
  • Diffusion-readout agreement is interpretable only from block 40 onward, when both predictions have recognizable structures; final predictions differ at 0.81.This qualifies the apparent early similarity between subsets.Source: S7 Diffusion readouts of the disjoint… · pp. 38–39
  • Probe-based comparisons show only 0.58 agreement at block 14 and reverse the ordering with respect to query substitution, avoiding the decoder’s intermediate-state behavior.The probe reads the representation directly.Source: S7 Diffusion readouts of the disjoint… · p. 39

S8 Supplementary Methods

Supplementary analyses specify how anchor restoration, structural progression, decoding order, residual contact enrichment, and alignment transplantation were measured. They also describe the transplantation ablations and the scope of the associated comparisons.

S8 Supplementary Methods

  • Supplementary methods follow the main-text conventions unless stated otherwise and provide additional algorithms and analyses.The listed procedures cover anchor titration, pair categorization, structural progression, decoding order, residual enrichment, and transplant algorithms.Source: S8 Supplementary Methods · p. 39

S8.1 Anchor titration

  • Anchor titration varies restoration across 10, 20, or 40 residues and 5%, 10%, or 20% of sequence length under three selection strategies; fractional recovery excludes 72 proteins with an experimental TM-score gap at most 0.1.The exclusion avoids an unstable ratio when the no-MSA/full-MSA gap approaches zero; 328 of 400 proteins remain.Source: S8.1 Anchor titration · p. 39

S8.2 Touched and untouched pair categorization

  • Long-range pairs are grouped by whether both, one, or neither residue is an anchor, and recovery is measured against the full-MSA prediction using balanced contact-map agreement.Restoring an anchor modifies its complete pair-representation row and column; the categories only distinguish whether evaluated pairs were directly modified. Table S7 reports median TM-score and gap recovery, with subset conditions not directly comparable to pooled values.Source: S8.2 Touched and untouched pair… · p. 39, Table S7 · p. 40

S8.3 Structural element progression

  • Structural progression tracks helix, strand, exact β-bridge, global agreement, and radius-of-gyration measures across Pairformer readouts relative to the final recycled full-MSA prediction.The corresponding no-MSA readouts are compared block by block, excluding block 14.Source: S8.3 Structural element progression · p. 41

S8.4 Determinants of decoding order

  • Decoding earliness is the negative of the first layer where long-range lDDT reaches half its block-47 value and remains there; analyses relate it to four residue features and test clustering against burial-matched sets.Features are burial, alignment gap fraction, conservation, and covariation; the joint feature model uses five-fold cross-validation grouped by protein.Source: S8.4 Determinants of decoding order · p. 41

S8.5 Contact enrichment in the orthogonal residual

  • Contact enrichment in the orthogonal residual compares its median norm at long-range contact pairs with its median norm at non-contact pairs; enrichment rose between blocks 20 and 40.Values above one indicate that the residual is concentrated at pairs that end in contact, supporting its re-expression in a form increasingly aligned with the predicted contact map.Source: S8.5 Contact enrichment in the… · p. 41

S8.6 Transplant and ablation algorithms

  • Transplant algorithms place donor-alignment rows into target columns while retaining the target query; shift and scramble ablations keep donor depth and occupancy but alter column correspondence.The supplement reports transplant conditions and nulls for 38 novel targets, and reports that coverage correlates more strongly with transplant accuracy than sequence identity (+0.51 vs +0.35); Table S8 is restricted to 20 higher-coverage targets for the contiguous-block transplant.Source: Table S8 · p. 40, S8.6 Transplant and ablation algorithms · p. 41, Table S10 · p. 42
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