Predicting protein structures at any folding stage from sequence

Lisheng Zhang; Qingsong Li; Zinan Xie; Yanting Yang; Qikui Yang; Peng Lu; Zhican Fu; Wentao Cui

q-bio.BMNov 3, 2026

Predicting protein structures at any folding stage from sequence

Authors: Lisheng Zhang, Qingsong Li, Zinan Xie, Yanting Yang, Qikui Yang, Peng Lu, Zhican Fu, Wentao Cui,

Organizations: Peking University International Cancer Institute, Peking University–Yunnan Baiyao International Medical Research Center, School of Basic Medical Sciences, Peking University Health Science Center, Peking University, 38 Xueyuan Road, Haidian District, Beijing 100191, China · Yuanpei College, Peking University, 5 Yiheyuan Road, Haidian District, Beijing 100871, China · The Hong Kong University of Science and Technology (Guangzhou), Nansha, Guangzhou, Guangdong, China · Tsinghua University, Beijing 100084, China · Shenzhen Medical Academy of Research and Translation, Shenzhen, Guangdong 518107, China · Shenzhen Bay Laboratory, Shenzhen, Guangdong 518132, China · School of Pharmaceutical Sciences, Peking University Health Science Center, 38 Xueyuan Road, Haidian District, Beijing 100191, China · Beijing Life Science Academy, Beijing 102209, China · China Tobacco Gene Research Center, Zhengzhou Tobacco Research Institute of CNTC, Zhengzhou 450001, China · State Key Laboratory of Natural and Biomimetic Drugs, Department of Molecular and Cellular Pharmacology, School of Pharmaceutical Sciences, Peking University Health Science Center, 38 Xueyuan Road, Haidian District, Beijing 100191, China · Department of Prosthodontics, Peking University School and Hospital of Stomatology, Beijing 100081, China · Beijing Key Laboratory of Intelligent Drug Discovery, Beijing Gigaceuticals Tech. Co. Ltd., Beijing 102206, China

Abstract

Protein structure prediction has largely focused on native conformations, leaving the continuum of unfolded states, folding intermediates, and native structures difficult to access. We present FoldScape, a sequence-conditioned deep learning framework for generating protein conformational ensembles at specified folding fractions $Q$ . Trained on approximately one million conformations from 10,000 protein sequences, FoldScape combines coarse-grained folding and all-atom mechanical-unfolding trajectories. It reconstructs three-dimensional $C_α$ chains through hierarchical sliding-window regressions of inter-residue distances, chain-level assembly, and a rectified-flow decoder. By conditioning on folding progress, FoldScape generates conformations from unfolded states through intermediates to native-state structures without protein-specific molecular dynamics at inference. In matched-sample comparisons, FoldScape achieves median conformational-space coverage of 0.989, 0.722, and 0.877 along radius of gyration, fraction of native contacts $Q$ , and secondary-structure fraction, respectively, versus 0.05, 0.05, and 0.10 for seed-varied AlphaFold 3 ensembles. Coverage advantages are consistent across the evaluated proteins and robust to binning choices. Reconstruction accuracy remains approximately stable across the evaluated stages of a folding trajectory, and stride-one crop-and-superpose inference extends predictions to chains several times longer than the single-pass limit. Analyses of mechanical-unfolding trajectories show residue-resolved pathways, reproducible extension-conditioned observables across pulling velocities, and geometrically coherent segments in partially unfolded chains. FoldScape extends sequence-based structure prediction beyond a single folded endpoint to controllable conformational-ensemble generation across protein folding.

Figures & tables

Class	Method	Proteins	Direction	Primary output
A (equil.)	GoCa at $T_{f}$	4	Folding	$F(Q)$ , $Q_{\mathrm{TSE}}$ , $\varphi_{\mathrm{sim}}$
A (equil.)	Go-kit at $T_{f}$	4	Folding	$F(Q)$ , $Q_{\mathrm{TSE}}$ , $\varphi_{\mathrm{sim}}$
B (path)	GoCa production	4	Folding	Contact formation order
B (path)	Go-kit production	4	Folding	Contact formation order
C (SMD)	GoCa	4	Stretching	Contact rupture order
C (SMD)	Go-kit	4	Stretching	Contact rupture order, $F(x)$

Table 1: Validation simulation matrix. All simulations are performed for the four validation proteins (ubiquitin, titin I27, protein L, protein G) unless otherwise noted.

F(Q)

and

F(x)

denote free-energy profiles computed from the simulations themselves, used here only to locate the transition-state ensemble and to compare force fields; FoldScape makes no free-energy prediction anywhere in this work.

Study	Design	What it supports
$\varphi$ -value comparison	All-atom, 4 velocities, 4 proteins with experimental $\varphi$	The residue-level unfolding order sampled at the force peak corresponds to the mechanical transition state, ordinally. Not a quantitative $\varphi$ prediction; not informative away from the force peak.
Velocity robustness	All-atom, 4 velocities, 4 proteins, extension-binned	$Q$ and $R_{g}$ at matched extension are reproducible to 2.9–7.0% of their dynamic range; the per-residue contact-survival and domain-assignment profiles are reproducible in shape. Not absolute contact probabilities; not threshold- or rank-derived discrete labels; not collapse position.
Cross-force-field	4 force fields, fixed velocity, 4 proteins	Rupture order is consistent across a hierarchy of physical detail. Descriptive; no significance gate.
CG rate stability	AWSEM, 6 velocities to $4.0\text{\,}\mathrm{nm}\text{/}\mathrm{ns}$	The extension-conditioned contact-survival curves remain within the all-atom band above the production velocity.
Segment geometry	500 proteins, 11 species, 557,550 segments	Unfolded segments are well defined under a fixed-hyperparameter operator, and their end-to-end extension is determined by segment length to $\sim$ $3.9\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ . Velocity-invariance of the segment definition is not established.

Table 3: Scope of each validation study. Claims beyond the right-hand column are not supported by the corresponding study.

Figure 1: At matched sample size, FoldScape ensembles show consistently higher conformational coverage than AlphaFold 3 baselines across three order parameters. a, Coverage summary for twenty human proteins (36–857 residues) on three order parameters. Each row is one order parameter; small dots are per-protein point estimates (vertically jittered to avoid overplotting), thick horizontal bars are the across-protein interquartile ranges, the large circle and square are the across-protein medians, and the grey line joins the two medians. The annotated

\Delta C

is the median of the per-protein difference

C_{\mathrm{AF3}}-C_{\mathrm{FoldScape}}

, and the asterisks come from a two-sided Wilcoxon signed-rank test with the protein as the pairing unit, Holm-corrected across the three order parameters. b–d, Paired slope plots for each order parameter: radius of gyration

\hat{R}_{\text{g}}

( b ), fraction of native contacts

Q

( c ) and stable secondary-structure fraction

f_{\text{SS}}

( d ). Each grey line is one protein, joining its coverage point estimates under the two methods, and the heavy black line joins the two medians. The split is 20 to 0 on all three axes, with every protein pointing the same way. All coverage values are evaluated with

K=20

bins at matched sample size

n=100

, and point estimates are means over 2,000 subsamples drawn without replacement.

P

values are Holm-corrected two-sided Wilcoxon signed-rank tests; **** denotes

P<10^{-4}

Protein	Residues	$n$ (AF3)	$n$ (FoldScape)	$C$ , $\hat{R}_{\text{g}}$	$C$ , $Q$	$C$ , $f_{\text{SS}}$
E9PIP6	36	100	300	0.35 / 0.89	0.10 / 0.59	0.15 / 0.81
A0A2R8YF12	61	100	300	0.05 / 0.98	0.05 / 0.77	0.20 / 0.44
H3BM92	66	100	300	0.05 / 0.96	0.10 / 0.68	0.05 / 0.83
E5RK64	71	100	300	0.05 / 0.95	0.05 / 0.75	0.05 / 0.38
C9JYH9	96	100	300	0.15 / 0.99	0.05 / 0.61	0.05 / 0.89
A0A804HJL3	101	100	300	0.05 / 0.95	0.10 / 0.73	0.20 / 0.39

Table 4: Per-protein conformational coverage at

K=20

bins and matched sample size

n=100

. In each order-parameter column the value before the slash is the AlphaFold 3 coverage and the value after the slash is the FoldScape coverage. All 60 per-protein permutation tests are significant (Section 3.1 ).

Figure 2: FoldScape reconstructs C $\alpha$ structures across the entire folding coordinate. a , Superposition of C $\alpha$ traces for six proteins sampled at conditioning values $Q_{\mathrm{cond}}=0.6$ – $1.0$ (equation ( 2 )). Green, molecular dynamics reference; cyan, FoldScape prediction, taken as the chain-level trace exported by Stage 1 of the trained cascade and shown here as an intermediate of the cascade rather than as the output of the pipeline; the two are optimally superposed by the Kabsch algorithm. The overall topology, the order of secondary-structure elements and the relative orientation of domains are reproduced in all six cases; residual deviations are confined to helix-packing register within helical bundles (for example a(ii)) and to solvent-exposed long loops (for example a(v)). b , Six representative conformations along the complete folding trajectory of a single chain ( Arabidopsis thaliana AF-A0A7G2EJF6-F1, $N=706$ ). Blue, molecular dynamics reference; orange, FoldScape prediction from the complete trained pipeline including the flow-matching decoder, assembled from 507 overlapping 200-residue crops by the stride-one crop-and-superpose scheme of Section 2.13 and superposed onto the reference; the “window-merged and Kabsch-aligned” label inside the panel refers to that crop merge, not to the sliding-window consensus internal to R1 and R2. Panels are ordered by increasing $Q$ ; the indices annotated in the figure identify frames within the stored trajectory and do not follow the $Q$ order. Annotations give the global C $\alpha$ RMSD of each conformation. From the fully extended state in b(i) to the compact state in b(vi) the axis range contracts from approximately $2\times 10^{3}$ Å to approximately $10^{2}$ Å; b(iii) and b(iv) reveal a multi-domain route in which two domains collapse independently before the connecting segment contracts and brings them together. The 125.8 Å value in b(i) arises from the ill-conditioning of global superposition on a nearly one-dimensional extended chain rather than from a loss of local geometric accuracy (see Discussion). Axis ranges differ between panels; coordinate values are simulation-box coordinates and carry no absolute meaning.

Figure 3: Architecture of the FoldScape cascade. a , Data input and conditioning. Residue-level ESM-C embeddings [ 49 , 7 ] $e_{i}\in\mathbb{R}^{N\times 1152}$ and their sequence mean $\bar{e}\in\mathbb{R}^{1152}$ —the latter entering the cascade through the frozen conformational latent $\mathbf{v}$ of Section 2.8 —are combined with order parameters ( $Q$ , $\tilde{R}_{g}$ , $f_{ss}$ ) computed from the trajectory frames of the training corpus, namely Gō-C $\alpha$ coarse-grained MD on the 848 proteins drawn from AF-Sub1K and constant-velocity SMD, and are encoded by CondEncoder. AF-NR68K (67,605 sequences) is the non-redundant pool from which those subsets are drawn; the external MD repositories shown in the panel are held out for cross-validation and do not enter training. b , Round 1: sliding windows of $W=15$ residues with stride 1 pass through a 6-layer Transformer trunk ( $c_{s}=384$ , 16 heads) and a shared pair stream $z$ ; seven scale-specific PairFormer blocks (triangle update, triangle attention and pair-bias attention) predict the C $\alpha$ –C $\alpha$ distances $\hat{d}^{(k)}$ at sequence separations $k=|i-j|=1$ –7, which a multi-scale aggregation module and a 2-layer coordinate Transformer decode into the windowed trace $\hat{X}_{R1}$ . Conditioning $c$ (384) is re-injected by feature-wise linear modulation [ 24 ] ; $h^{(7)}$ , $z^{(7)}$ and $g^{(k)}$ are cached for Round 2. c , Round 2: the cached pair stream initialises $z^{(0)}\leftarrow\mathrm{Linear}(z^{(7)}_{R1})$ , and a second seven-scale cascade with a 4-layer coordinate Transformer predicts only the residual update $\hat{X}_{R2}=\hat{X}_{R1}+\delta X$ on the same 15-residue windows. d , Stage 1: cross-window attention pooling (short $k\leq 7$ , long $8\leq k<W$ , and residue-level $h$ ) lifts window-local features to the chain index; a 6-layer chain-level PairFormer trunk ( $c_{s}=384$ , $c_{z}=128$ ) with CondFiLM re-injection at every layer produces the single representation $s\in\mathbb{R}^{N\times 384}$ and, through an auxiliary head, the full-chain coarse trace $\hat{X}_{S1}=\hat{X}_{cons}+\delta X$ . e , Flow matching: a 5-layer AlphaFold3-style decoder [ 5 ] ( $c_{s}=384$ , 8 heads, AdaLN) with 32 register tokens, AdaLN modulation from $s$ , Fourier time features and self-conditioning learns the conditional velocity field $\hat{v}(X_{t},t,s)$ along a rectified-flow trajectory [ 28 , 27 ] ; 100-step Euler integration from noise $X_{0}$ yields the C $\alpha$ ensemble $\{\hat{X}_{1}^{(s)}\}_{s=1..S}$ . Bottom, training order: R1 $\rightarrow$ R2 $\rightarrow$ Stage 1 $\rightarrow$ flow matching, each stage trained with its upstream frozen.

Figure 4: Training convergence of the FoldScape cascade. a , Window-level coordinate error of Round 1: root-mean-square deviation between predicted and reference C

\alpha

traces within a 15-residue sliding window after optimal Kabsch superposition, for the training (blue) and validation (orange) sets over 80 epochs; the best validation value is 2.96 Å at epoch 75. b , Mean absolute deviation of C

\alpha

–C

\alpha

virtual bond lengths,

\bigl|\,\lVert\mathrm{C\alpha}_{i}-\mathrm{C\alpha}_{i+1}\rVert-3.80\,\text{\AA}\,\bigr|

, computed from the decoded coordinates of the same run; the curves reach their minima at epoch 10 (validation, 0.18 Å) and epoch 15 (training, 0.21 Å) and rise steadily thereafter to 0.30 Å and 0.32 Å at the final epoch, the validation curve fluctuating from epoch to epoch about that rise. c , Window-level coordinate error of Round 2 over 56 epochs; the dotted vertical line marks a cosine learning-rate restart at epoch 31, and the best validation value is 1.59 Å at epoch 54. d , Chain-level Kabsch-aligned RMSD of the Stage 1 auxiliary coordinate head at the end of the first epoch (training 7.11 Å, validation 6.70 Å; chains of at most 200 residues); the training value is a running average over the epoch and the validation value a single evaluation at its end. e , Training-set coordinate loss of the flow-matching decoder against optimisation step; the dark line is the exponential moving average and the pale band spans the range of the per-step raw loss, with spikes exceeding the axis limit truncated at 110. f , Validation-set coordinate loss of the same run, evaluated every 1,000 steps (47 evaluations); the pale line shows the individual evaluations and the dark line their exponential moving average (smoothing factor 0.6). Evaluations before step 3,000 exceed the axis range and are not shown. Vertical axes in a – d are in ångström; the coordinate loss in e and f is the weighted translation term of the flow-matching objective and is dimensionless. All curves come from a single training run per stage; no repeated seeds were performed, and no error bars are therefore shown.

Figure 5: Simulation–experiment agreement at residue resolution is robust across two decades of pulling speed. Pearson $r$ (left) and Spearman $\rho$ (right) between $\Phi_{\text{sim}}$ at the force peak and experimental $\varphi$ -values, plotted against pulling velocity (0.01, 0.05, 0.1, 1.0 nm ns -1 per end). Warm solid lines: mechanical $\varphi$ -values (main evidence) — GB1 ( $1-\varphi_{\text{M2+U}}$ , $n=8$ ), I27 ( $\varphi_{\text{mech}}$ , $n=7$ ), protein L ( $\varphi_{\text{mech}}$ , $n=5$ ). Cold dashed lines: comparisons with chemical $\varphi$ -values — ubiquitin ( $\varphi_{\text{chem}}$ , $n=8$ ), which is the specificity control, and I27 ( $\varphi_{\text{chem}}$ , $n=7$ ), shown for completeness but not a control, because its $\varphi_{\text{chem}}$ and $\varphi_{\text{mech}}$ are collinear at the seven measured sites ( $r=0.989$ ). Filled symbols, $P<0.05$ ; open symbols, not significant. Pink shading: positive half-plane (agreement with pulling experiments); blue shading: negative half-plane (agreement with chemical denaturation). All 12 mechanical combinations fall above zero; all 4 ubiquitin combinations fall below zero. Bootstrap 95% CIs (10,000 replicates) omitted for clarity.

Figure 6: Global conformational observables agree across two decades of pulling speed when plotted against extension. Each row shows one protein: a–c ubiquitin (1UBQ); d–f titin I27 (1TIT); g–i protein L (2PTL); j–l protein G B1 (1PGB). Columns: C $\alpha$ -RMSD relative to the native state after Kabsch superposition [ 58 ] ( a,d,g,j ); native-contact fraction $Q$ ( b,e,h,k ); radius of gyration $R_{\text{g}}$ ( c,f,i,l ). Horizontal axis is end-to-end distance; four colours correspond to four pulling velocities.

Figure 7: Per-residue contact-survival maps at four pulling velocities. a ubiquitin; b titin I27; c protein L; d protein G B1. Within each panel, columns correspond to $v=0.01$ , 0.05, 0.1, 1.0 nm ns -1 . Colour: fraction of native contacts retained (C $\alpha$ –C $\alpha$ $<8.0$ Å, $|i-j|>3$ , as in equation ( 2 )). Segments that disrupt early and those that persist occupy the same sequence positions at all speeds; disruption boundaries appear as sharp colour steps rather than gradual gradients.

Figure 8: Per-residue cross-speed consistency: shape is preserved, absolute distributions are not. a ubiquitin; b titin I27; c protein L; d protein G B1. Top sub-panel: mean Pearson $r$ across six speed pairs. Middle: Spearman $\rho$ . Bottom: fraction of speed pairs with KS $p>0.05$ . Reference lines: $r=0.9$ (green dashed) and $r=0.7$ (orange dashed); KS panel 0.5 (grey dashed). High $r$ / $\rho$ with low KS fraction confirms that contact-survival trends are speed-invariant but absolute values at a fixed extension are not.

Figure 9: Domain-organisation topology is speed-invariant; complete disruption is speed-delayed. a ubiquitin; b titin I27; c protein L; d protein G B1. Upper sub-panel: structural domain count versus extension (four speeds overlaid). Lower sub-panel: per-residue domain-membership profile (dark: residue belongs to a sequentially contiguous, locally native domain). Domain profiles are significantly correlated across all 24 speed combinations (

r=0.720

–

0.967

, mean 0.845, max

P=3.0\times 10^{-33}

). The extension at which the domain count first reaches zero shifts systematically to larger values at higher speed (most pronounced for I27, panel b upper).

Figure 10: The linear extension law $\mathrm{ETE}=\alpha\times 3.8\,(N_{\text{seg}}{-}1)$ holds across 11 species, 500 proteins, and 557,550 unfolded segments. a, ETE versus $3.8\,(N_{\text{seg}}{-}1)$ for all segments ( $10^{5}$ randomly drawn for display). Black dashed line: $\alpha=1$ (full extension); red line: origin-constrained fit ( $\alpha_{\text{global}}=0.947$ , $R^{2}=0.980$ ). b, Two-piece fit: $N_{\text{seg}}\leq 30$ (coral, $\alpha=0.872$ ) and $N_{\text{seg}}>30$ (steel-blue, $\alpha=0.957$ ). c, Residuals of the two-piece model; MAE $=3.9$ Å. d, Per-segment $\alpha_{k}$ distribution ( $n=427{,}139$ ; $N_{\text{seg}}\geq 5$ , $L_{\text{max}}>1$ Å): mean 0.851, SD 0.146, CV 17.2%, median 0.900 (orange dotted). e, $\alpha$ versus segment length (log-spaced bins); error bars: $\pm$ 1 SD; grey numerals: per-bin counts. f, Per-protein $\alpha$ across 500 proteins: mean 0.906, SD 0.032, CV 3.5%.

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Abstract

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