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Communications ChemistryBiophysicsPeer-reviewed journal article

Deep generative modeling of temperature-dependent structural ensembles of proteins

Giacomo JansoniD, Alexander JussupowiD, Michael FeigiD

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Abstract

Deep learning has revolutionized protein structure prediction, but capturing conformational ensembles and structural variability remains an open challenge. While molecular dynamics (MD) is the foundation method for simulating biomolecular dynamics, it is computationally expensive. Recently, deep learning models trained on MD have made progress in generating structural ensembles at reduced cost. However, they remain limited in modeling atomistic details and, crucially, incorporating the effect of environmental factors. Here, we present aSAM (atomistic structural autoencoder model), a latent diffusion model trained on MD to generate heavy atom protein ensembles. Unlike most methods, aSAM models atoms in a latent space, greatly facilitating accurate sampling of side chain and backbone torsion angle distributions. Additionally, we extended aSAM into the first reported transferable generator conditioned on temperature, named aSAMt. Trained on the large and open mdCATH dataset, aSAMt captures temperature-dependent ensemble properties and demonstrates generalization beyond training temperatures. By comparing aSAMt ensembles to long MD simulations of fast folding proteins, we find that high-temperature training enhances the ability of deep generators to explore energy landscapes. Finally, we also show that our MD-based aSAMt can already capture experimentally observed thermal behavior of proteins. Our work is a step towards generalizable ensemble generation to complement physics- based approaches.

In-depth summary

Claude Opus 5.5 · xhigh effort · 8 Nov 2026 · from the full text of version 1 (13 Mar 2025) · CC BY 4.0

aSAM, a latent diffusion model trained on molecular dynamics, generates heavy-atom protein ensembles; its temperature-conditioned variant aSAMt reproduces mdCATH thermal unfolding and extrapolates beyond training temperatures.

Earlier ensemble generators trained on molecular dynamics (MD) model atomistic detail poorly and ignore environmental conditions: AlphaFlow's generative training uses only Cβ positions, while BioEmu needs post-processing to add side chains and works only at 300 K. aSAM encodes every heavy atom in a latent space to learn torsion-angle distributions, and aSAMt adds temperature as a continuous input, trained on the open multi-temperature mdCATH data.

Key results

  1. ShownOn the ATLAS benchmark, the constant-temperature aSAMc roughly matches AlphaFlow on residue fluctuations and Cβ positional distributions. It reproduces backbone and side-chain torsion distributions more faithfully and samples faster on a GPU.

    82 test proteins: Cα RMSF Pearson r 0.886 (aSAMc) vs 0.904 (AlphaFlow), significant by Wilcoxon signed-rank test; AlphaFlow slightly better on WASCO-global; aSAMc better on WASCO-local and chiJSD; MolProbity worse by 0.63; sampling 17.4× to 28.0× faster than AlphaFlow (51 to 554 residues, V100 GPUs). · Benchmarking aSAM on ATLAS; ATLAS dataset; Evaluation of ATLAS ensembles; Timing

  2. ShownTrained on mdCATH, aSAMt reproduces temperature trends in initRMSD (RMSD to the initial structure), radius of gyration, secondary-structure preservation and folded fraction on 90 held-out domains. It samples more broadly than aSAMc, but folded-fraction accuracy drops at high temperature.

    Average initRMSD MAE 0.051 nm (aSAMt, 320 K) vs 0.108 nm (aSAMc, ATLAS); underestimated in 67.8% vs 91.4% of cases; folded state fraction (FSF) MAE 0.016 at 320 K rising to 0.141 at 450 K; 53 of 90 domains within 0.1 at 450 K and 23 within 0.1 at all five temperatures. · Using aSAMt to learn temperature-dependent…; mdCATH dataset; Figure legends

  3. SuggestedTemperature is a continuous input, so aSAMt interpolates smoothly between training temperatures. Outside the 320 to 450 K training range it produces sigmoid unfolding profiles that resemble melting curves.

    Ensembles generated from 250 to 670 K in steps of 20 K for 8 test domains; FSF and secondary structure element preservation (SSEP) lie near MD values at mdCATH temperatures, stay near 1 below 320 K for most systems and approach 0 at high temperature; apparent Tm values fitted from FSF and from SSEP are typically similar. · Interpolation and extrapolation across…; Figure legends

  4. ShownAgainst long ANTON MD of 12 fast-folding proteins, aSAMt places free-energy minima at the native state in every case and samples non-native basins for most systems; at 450 K, unfolded-state exploration grows for several systems. Relative free energies are inaccurate, and kinetically distant states are missed.

    12 D.E. Shaw proteins; 500,000 aSAMt conformations each at the MD temperature (290-370 K) and at 450 K, projected onto TICA landscapes; states not reached for WW-domain, NTL9, BBL, protein B, alpha3D and λ-repressor; generated conformations occupy regions absent from the mdCATH training snapshots. · Energy landscapes of fast-folding proteins; Long MD trajectories of fast folding proteins; Figure legends

  5. SuggestedWithout any experimental training data, aSAMt-derived apparent melting temperatures correlate moderately with measured Tm and recover the sign of stability differences between homologs. They also place RFdiffusion-designed thermostable proteins above structurally matched natural controls.

    62 monomeric proteins: Pearson r=0.510 vs experimental Tm, but apparent Tm is systematically 130 K higher; ribosomal L30E mesophile/hyperthermophile pair: apparent ΔTm 32.6 K vs experimental 48.1 K; 7 of 9 RFdiffusion designs exceed every natural protein, and the 9 AlphaFold DB controls were always lower. · Estimation of thermostability and comparison…; Proteins with experimentally observed thermal…; Figure legends

Methods, data and reproducibility

Two-stage latent diffusion. A transformer encoder maps heavy-atom coordinates to SE(3)-invariant per-residue latents (c = 32), which an AlphaFold2 Structure Module decodes. A DDPM with a Diffusion Transformer-style denoiser, conditioned on sequence, initial MD structure and optionally temperature, samples these latents; restrained minimization then removes clashes.

  • ATLAS explicit-solvent MD of PDB protein chains, three 100 ns runs per chain; AlphaFlow splits, with train/validation chains capped at 500 residues · n = 1,390 chains; 1,174 train and 38 validation after filtering, 82 test
  • mdCATH explicit-solvent MD of CATH domains at 320, 348, 379, 413 and 450 K, five trajectories of up to 500 ns each; length cutoff of 320 for training · n = 5,398 domains (5,268 train, 40 validation, 90 test)
  • Long unbiased ANTON MD of fast-folding proteins from D.E. Shaw Research (CHARMM22* force field), 290-370 K · n = 12 proteins
  • Adaptive-sampling MD of fast-folding proteins (Majewski et al.), used to compare state coverage
  • S[Temp] experimental Tm set (Pucci et al.; DSC or circular dichroism), filtered to monomers without disulfides or cofactors · n = 62 of 222 proteins
  • Homologous protein pairs with differing experimental Tm, including a mesophile/hyperthermophile ribosomal L30E pair · n = five pairs · PDB 1CN7; PDB 1H7M
  • RFdiffusion-designed thermostable monomers (AF2 models, 200 and 300 residues) plus AlphaFold Database Swiss-Prot controls matched for length and shape · n = 9 designs and 9 controls
Methods & tools
AlphaFlow-MD+Templates, ESMFlow-MD+Templates, COCOMO2 Cα force field in OpenMM 8.0.0 (elastic network baseline), cg2all, AlphaFold2 Structure Module (OpenFold implementation), DDPM with Diffusion Transformer-style denoiser, WASCO (global and local scores), MolProbity, MDTraj, PyEMMA (TICA), DSSP, MODELLER
Software & environment
PyTorch 1.31.1 (version as printed), OpenFold-derived Structure Module and FAPE losses, PyTorch Lightning; OpenMM 8.0.0 for COCOMO2 baselines; MDTraj, PyEMMA, SciPy, MODELLER, PyMOL.
Assay conditions & compute
Sampling timed on NVIDIA V100 32GB GPUs; multi-GPU training via PyTorch Lightning; aSAMt 2,317× and 1,000× faster than OpenMM MD for 4qbuA03 and 4a57A02 (2,500 ns of MD vs a 500-snapshot ensemble).
Reproducibility gaps
D.E. Shaw Research supplied the long fast-folder trajectories directly (no public link given); training hardware and wall-clock time are not stated; the BioEmu comparison relies on published figures because its ensembles are unavailable.
Limitations (6)
  • aSAMt covers broad conformational space but misestimates the relative probabilities (free energies) of states, likely because mdCATH trajectories last at most 500 ns with few transitions. Kinetically distant states are missed even at 450 K. · stated by the authors
  • Raw aSAM outputs contain side-chain clashes that require restrained energy minimization. Soft clashes remain, giving MolProbity scores 0.63 units worse than AlphaFlow, and heavy clashes increase with temperature. · stated by the authors
  • Folded-fraction accuracy degrades at high temperature (MAE 0.141 at 450 K), with 17 domains overestimated and 20 underestimated by more than 0.1. Both ATLAS-trained aSAMc and AlphaFlow fail to sample states far from the input structure. · stated by the authors
  • Apparent Tm runs systematically 130 K above experiment (force field not parametrized for thermal stability; short runs started from folded structures). Oligomers, disulfides and cofactors are unsupported, and homolog pairs above 50% identity give small apparent ΔTm. · stated by the authors
  • The fast-folder evaluation is not fully held out: six of the 12 proteins have mdCATH training homologs (NTL9 at 100% and λ-repressor at 96% identity over aligned regions). Parity with BioEmu is judged only from its published figures. · noted in this summary
  • Behavior outside the training range (250 to 670 K) is assessed on only 8 domains, by physical plausibility and without reference simulations. A single Q threshold of 0.6 defines foldedness for every system, which may bias FSF-based apparent Tm. · noted in this summary

Read this if you develop MD-trained protein ensemble generators and need atomistic side-chain torsion modeling or temperature-conditioned sampling, or want deep-learning estimates of thermal unfolding and melting trends.

Citations
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