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SupraTITO: Transferable Generative Molecular Dynamics for Supramolecular Systems

Weilong Chen, Nuno Costa, Julija Zavadlav

arXiv:2610.01381v1physics.chem-phcond-mat.softcs.LGphysics.bio-ph

TL;DR

Peptide assembly prediction must address slow collective dynamics across a large sequence and condition space. SupraTITO learns transferable finite-lag transitions for peptide systems, reproducing assembly structures and dynamics across sequences and concentrations, including dilute conditions outside training.

  • Problem

    Predicting how sequence and physical conditions shape supramolecular structures and their assembly dynamics is difficult because collective processes are slow and sequence-condition space is broad.

    Source: §1 · pp. 1–2

  • Method

    SupraTITO learns transferable implicit transfer operators conditioned on peptide sequence, molecular topology, and periodic geometry.

    Source: §1 · p. 2, §4.1 · p. 5, §4.2 · p. 6

  • Results

    SupraTITO reproduces assembly structures and dynamics for held-out sequences while preserving molecular integrity over long rollouts, outperforming direct ensemble prediction on late assembly structures and transferring across concentrations.

    Source: §6 · p. 12

  • Takeaways & Limitations

    The results support a shared generative description of molecular integrity and collective assembly dynamics across peptide sequences and concentrations, with potential application to other periodic supramolecular systems.

    Source: §6 · p. 12

    The study covers homogeneous dipeptide systems trained at a single concentration and system size, and does not establish transfer to longer peptides, co-assembly, or arbitrary system sizes.

    Source: §6 · p. 12

Abstract

from arXiv · show

Peptide sequence governs both the structures formed through supramolecular assembly and the dynamics by which they emerge, but predicting either requires resolving slow collective processes among many interacting molecules. Molecular dynamics (MD) provides microscopic insight into these processes, yet the long timescales of assembly and the vast peptide sequence space make systematic exploration computationally demanding. We introduce SupraTITO, a transferable generative molecular dynamics (GenMD) framework for supramolecular systems, demonstrated through peptide self-assembly. SupraTITO learns transferable implicit transfer operators (TITO) conditioned on peptide sequence, molecular topology, and periodic geometry, allowing configurations to be propagated over physical intervals much longer than an MD integration step. On a comprehensive dipeptide benchmark, SupraTITO generalizes to held-out sequences and reproduces sequence-dependent structures and dynamics while maintaining molecular integrity over long rollouts. Compared with direct ensemble prediction trained on the same trajectory data, SupraTITO more accurately reproduces assembly structures while also resolving their temporal evolution. The learned dynamics generalize across peptide concentrations, including dilute conditions not represented during training. These results extend transferable GenMD to collective dynamics in periodic supramolecular systems and provide a foundation for modeling related processes beyond peptide assembly.

1 Introduction

Predicting supramolecular assembly requires modeling how sequence and environment shape collective structures and their dynamics, but slow processes and broad sequence-condition space make simulation costly. SupraTITO learns transferable finite-lag transitions for periodic peptide systems and reproduces assembly behavior across sequences and concentrations.

1 Introduction

  • Slow collective processes among many interacting molecules require long trajectories and often multiple replicates, while each sequence-condition combination generally requires a separate simulation.Coarse-graining reduces computational cost but does not remove the burden of broad exploration.Source: §1 · pp. 1–2
  • Existing dynamical GenMD methods primarily address individual-molecule conformational dynamics, whereas supramolecular prediction must capture collective organization and dynamics.The challenge includes changing intermolecular contacts, topology and periodic-domain consistency, and stability during recursive rollouts.Source: §1 · pp. 1–2
  • SupraTITO learns finite-lag transition densities conditioned on peptide sequence, molecular topology, and periodic geometry, using conditional flow matching.Its shared molecular representation supports application to peptide sequences excluded from training.Source: §1 · pp. 2–3
  • SupraTITO reproduces sequence-dependent assembly structures and dynamics on a dipeptide benchmark, preserves molecular integrity over long rollouts, and transfers across peptide concentrations.It also more accurately reproduces the late-time structural ensemble than direct ensemble prediction trained on the same trajectory data.Source: §1 · p. 3
  • The framework extends GenMD to collective supramolecular processes and is proposed as applicable in principle to systems such as micelles, bilayers, viral capsids, and DNA origami.The evaluation assesses transfer across sequences and physical conditions using structural and dynamical observables, molecular fidelity, and direct ensemble prediction.Source: §1 · p. 3
  • The periodic-system extension uses molecule-consistent minimum-image displacement targets, wrapped trajectory generation, and relative periodic geometry.The architecture combines sequence embeddings and current configuration with physical lag to generate successive states.Source: Figure 1 · p. 2, §1 · p. 3

2 Background and Preliminaries

The background defines molecular dynamics and transfer operators as descriptions of configuration evolution and ensemble propagation. It then introduces conditional flow matching as a way to learn finite-lag transition samplers and generate trajectories by repeated application.

2.1 Molecular Dynamics and Transfer Operators

  • A transition density gives the distribution of configurations reached after physical lag τ from a current configuration, while its transfer operator propagates a configuration density forward.The density determines both configurational statistics and temporal correlations of molecular observables.Source: §2.1 · p. 3

2.2 Conditional Flow Matching

  • Conditional flow matching trains a continuous normalizing flow using a regression objective built from probability paths conditioned on target samples.At inference, a sample from the reference distribution is integrated along the learned flow to generate a target sample.Source: §2.2 · p. 4

2.3 Implicit Transfer Operator Learning

  • Implicit transfer operator learning represents finite-lag molecular transitions with a conditional generative sampler, trained on current configurations, future configurations, and lag values.Repeated sampling advances physical time by τ; whether the retained state captures enough memory at that lag must be evaluated empirically.Source: §2.3 · p. 4

3 Related Work

Prior generative molecular dynamics methods learn equilibrium distributions, trajectory dynamics, or transitions, with much work focused on individual molecules. SupraTITO instead generates trajectories of peptide assembly, complementing methods that predict sequences or assembly outcomes.

Generative molecular dynamics

  • Generative molecular dynamics includes equilibrium samplers, latent-space simulators, autoregressive approaches, and methods that learn transitions or trajectory segments.Examples include Timewarp, EquiJump, MDGen, TITO, and PLaTITO.Source: §3 · pp. 4–5
  • Transferable implicit transfer operator methods extend finite-lag generation across molecular systems, while SupraTITO extends this approach to peptide assembly in periodic many-molecule systems.Earlier dynamical GenMD work primarily addressed single-molecule conformational dynamics.Source: §3 · p. 5

Machine learning for peptide assembly

  • Peptide-assembly machine-learning methods predict assembly propensity, guide sequence exploration, or design sequences and desired morphologies; SupraTITO instead generates assembly trajectories.The trajectory output provides complementary structural and dynamical information.Source: §3 · p. 5

4 SupraTITO: Generative Dynamics for Supramolecular Systems

SupraTITO models finite-interval molecular displacements conditioned on peptide sequence, topology, lag, and periodic geometry, with a shared parameterization across sequences and lag times.

4.1 Implicit Transfer Operators under Periodic Boundary Conditions

  • Molecule-consistent displacements combine a common molecular translation with internal change, reconstructing wrapped target configurations exactly.Source: §4.1 · pp. 5–6
  • A shared parameterization models finite-lag transfer operators across peptide sequences and lag times.Source: §4.1 · p. 6

4.2 Molecular Representation and Neural Architecture

  • Separate condition and velocity transformer networks integrate molecular features with periodic geometry to predict a displacement-generating vector field.Source: §4.2 · p. 6
  • Site identities, residue roles, directed bonds, and minimum-image pair geometry encode molecular identity and periodic neighborhoods.Source: §4.2 · p. 6

4.3 Training and Trajectory Generation

  • Training uses no assembly labels, force targets, or auxiliary bond-length losses.Source: §4.3 · p. 7
  • At inference, the model holds site contexts fixed during flow integration, then repeatedly samples finite-lag transitions with fresh Gaussian noise to generate stochastic trajectories.Source: §4.3 · p. 7

4.2 Molecular Representation and Neural Architecture

  • The architecture is permutation equivariant and translation invariant, but not exactly rotation equivariant because it uses Cartesian directions directly.Source: §4.3 · p. 7

5 Results

Across held-out peptide sequences, SupraTITO reproduces sequence-dependent assembly structures and dynamics, and it outperforms direct ensemble prediction on structural fidelity. It also tracks concentration responses, including dilute conditions and a held-out sequence.

5.1 SupraTITO transfers assembly dynamics across peptide sequences

  • Generated late-window averages match MD across six observables and dispersed, compact, and intermediate systems, while peptide bonds and intramolecular connections remain intact.Molecular fidelity persists through long recursive rollouts.Source: §5.1 · p. 8
  • SupraTITO reproduces cluster-growth evolution and temporal fluctuations for dispersed, intermediate, and assembled held-out sequences.Representative traces are shown in Figure 3a–c.Source: §5.1 · p. 8, Figure 3 · p. 10
  • SupraTITO reproduces sequence-dependent contact-persistence variation, with modest underestimation for some of the longest-lived contacts.The metric integrates baseline-corrected contact persistence over the first 25 ns; wrapped coordinates preclude an unambiguous estimate of long-time diffusion.Source: §5.1 · p. 8
  • As training-sequence coverage grows, errors decrease and MD correlations increase across all six observables, even after every amino-acid type is represented.Transfer also depends on exposure to diverse residue combinations and intermolecular environments.Source: §5.1 · p. 8, Figure 4 · p. 11

5.2 Finite-lag learning outperforms direct ensemble prediction

  • SupraTITO has lower errors and higher MD correlations than DEP for all six structural observables, with closer SASA distributions and sequence-resolved SASA.Full-data DEP performs only slightly better than SupraTITO trained on half as many sequences, while full-data SupraTITO clearly outperforms DEP.Source: §5.2 · p. 9, Figure 5 · p. 11
  • Unlike DEP’s independent configurations, SupraTITO learns changes from overlapping trajectory pairs and repeatedly applies them to generate temporally ordered trajectories.The current configuration provides information about the assembly state.Source: §5.2 · pp. 9–10

5.3 SupraTITO transfers across peptide concentrations

  • SupraTITO tracks MD concentration responses, including dilute conditions and held-out QI; SASA trajectories also reproduce exposure progression across tested concentrations.Concentration is varied through periodic box volume at fixed peptide number, with changed pair geometry supplied to the model.Source: §5.3 · pp. 10–11, Figure 6 · p. 12
  • For variable peptide counts, SupraTITO reproduces some MD trends less consistently than in concentration tests; training across sizes may be needed to learn collective effects.Variable-size architectural support alone does not establish transfer across finite system sizes.Source: §5.3 · p. 12

6 Conclusion

SupraTITO reproduces assembly structures and dynamics for held-out dipeptides while preserving molecular integrity, and its formulation offers a foundation for other periodic supramolecular systems. The study’s conclusions are bounded by its coarse-grained, single-trajectory dipeptide benchmark and current model scaling.

6 Conclusion

  • On the comprehensive dipeptide benchmark, SupraTITO reproduces structures and dynamics for held-out sequences, preserves molecular integrity over long rollouts, and outperforms direct ensemble prediction on late-time structures.Predictions improve with more diverse training sequences and transfer across concentrations, including dilute conditions outside training.Source: §6 · p. 12
  • The study uses homogeneous dipeptide systems, with training at one concentration and system size; transfer to longer peptides, co-assembly, and arbitrary system sizes remains unestablished.The authors identify training across peptide lengths, compositions, concentrations, and box sizes as a next step.Source: §6 · p. 12
  • Each of the 400 ordered dipeptides has one independently initialized coarse-grained trajectory, so benchmarks do not capture independent assembly pathways or polymorphic outcomes.The authors recommend independent initializations and comparisons of assembly-time, morphology, and physical-observable distributions.Source: §6 · pp. 12–13
  • SupraTITO uses a residue-level representation and reproduces Martini 2.1 dynamics, limiting accuracy when atomistic interactions such as hydrogen bonding or side-chain packing determine assembly.The authors propose adding atomistic detail or backmapping and validating against experimental structural and kinetic observables.Source: §6 · p. 13
  • Global self-attention scales quadratically with retained sites, potentially restricting application to longer peptides and larger supramolecular systems.A proposed extension combines local geometric message passing with an efficient periodic long-range mechanism.Source: §6 · p. 13

A.1 Dipeptide MD Dataset

  • The benchmark contains 400 ordered dipeptide sequences, each simulated for 1.25 µs with 100 peptides at approximately 100 mM using the Martini 2.1 force field.Configurations are stored every 2.5 ps; the retained representation keeps each residue’s backbone bead, giving 200 sites per system.Source: §A.1 · p. 17

A.2 Training and Held-Out Sequences

The evaluation holds out paired reverse-order dipeptide sequences and uses nested training subsets to test how sequence coverage affects transfer.

A.2 Training and Held-Out Sequences

  • The evaluation set contains both orderings of 40 held-out unordered dipeptide pairs, while all 20 homodipeptides remain in training.Reverse orderings are assigned together to prevent a held-out composition from appearing reversed in training.Source: §A.2 · p. 17, Table 1 · p. 17
  • The held-out pairs are selected to balance amino-acid coverage and the distributions of late-time MD SASA and relative SASA change.Both ordered versions of each listed pair form the evaluation set.Source: §A.2 · p. 17, Table 1 · p. 17

A.3 Sequence-Coverage Subsets

  • Nested training subsets contain 40, 80, and 160 ordered sequences from the 320-sequence training partition, with reverse orderings grouped at every coverage.All four models share the same architecture, optimization schedule, rollout protocol, and 80 held-out evaluation sequences.Source: §A.3 · p. 17

A.4 Condition and System-Size Evaluation Sets

A 28-system panel tests transfer across peptide concentrations and system sizes beyond the baseline training conditions.

A.4 Condition and System-Size Evaluation Sets

  • The transfer panel contains 22 concentration conditions at fixed peptide count and six evaluations at new system sizes.C conditions change concentration at fixed peptide count; S changes system size at baseline concentration; R changes concentration by varying peptide number at fixed box size.Source: §A.4 · p. 18, Table 2 · p. 18
  • Additional systems follow the exhaustive-corpus simulation protocol and differ only in peptide count, initial box size, and random insertion seed.The panel’s C100 conditions reuse the corresponding baseline trajectories from the exhaustive corpus.Source: §A.4 · p. 18, Table 2 · p. 18

B.1 Architecture and Hyperparameters

The reported model combines topology-aware molecular features with periodic geometry and molecule-consistent displacement targets. It generates long trajectories through finite-lag transitions, with reported training and inference costs.

B.1 Architecture and Hyperparameters

  • The approximately 3-million-parameter model uses amino-acid, chain-role, physical-lag, and flow-time embeddings, with pair representations fixed across transformer layers.Its molecule-consistent target assigns the two sites of a peptide a shared minimum-image center displacement and describes internal motion through their periodic bond-vector change.Source: §B.1 · p. 18, Table 3 · p. 19
  • Training samples physical lags uniformly from 1 to 1,000 saved frames and uses 500,000 transition pairs per epoch, with AdamW, a 10^-4 learning rate, and gradient clipping at 0.1.Training runs for 1,000 epochs with global batch size 768; the reported checkpoint is saved at optimization step 651,000.Source: §B.1 · p. 18

B.2 Trajectory Generation

  • A lag of 1,000 saved frames corresponds to 2.5 ns per generated transition; 500 transitions produce a 1.25 µs trajectory with 501 stored configurations.Each transition’s flow ODE uses 100 explicit Euler steps, and five trajectories are generated from each MD starting frame using independent flow noise.Source: §B.2 · p. 19

B.3 Computational Cost

  • Final-model training required approximately 1,300 H100 GPU-hours, while a complete 1.25 µs single-system trajectory is estimated to require about 2 minutes of inference compute.After compilation warm-up, one lag-1,000 transition takes approximately 0.25 seconds for one system or 6.4 seconds for a batch of 80 on one H100 GPU.Source: §B.3 · p. 19, Table 4 · p. 19

C Metric Definitions

The section defines coordinate-based observables and a sequence-level evaluation hierarchy for comparing MD with generated trajectories. It also specifies how periodic geometry, temporal dependence, and across-sequence agreement are handled.

C.1 Evaluation Hierarchy and Notation

  • Framewise observables are summarized within each trajectory before sequence-level comparisons, avoiding treatment of correlated frames or peptides as independent replicates.Generated estimates use the mean and sample standard deviation across five rollout trajectories unless otherwise stated.Source: C Metric Definitions · p. 19, §C.1 · p. 20

C.2 Coarse-Grained Solvent Exposure

  • SASA is a periodic-boundary-aware, coarse-grained exposure estimate from representative residue beads, not an atomistic SASA measure.The effective bead radius is 0.29 nm, and generated and MD coordinates use identical radii, sampling directions, and periodic handling.Source: §C.2 · p. 20

C.3 Peptide Centers and Contact Graph

  • Peptide contacts are defined from periodic-aware peptide centers, with one graph edge per contacting pair and a cutoff calibrated on training MD.Raw contact counts suit the fixed-peptide-count benchmark; comparisons across system sizes require normalized contact density.Source: §C.3 · pp. 20–21

C.4 Contact Memory

  • Baseline-corrected intermittent contact persistence characterizes relative molecular dynamics by tracking whether the same peptide pairs remain associated over time; larger eAc indicates longer retention of peptide-pair identity, not more contacts.Because it is intermittent and generated configurations are separated by 2.5 ns, it is a contact-memory diagnostic, not an uninterrupted contact lifetime or a rate estimate below the output resolution.Source: §C.4 · p. 21

C.5 Largest-Cluster Size and Morphology

  • The largest-cluster fraction measures the share of peptides in the largest connected component, while cluster shape is evaluated from unwrapped peptide centers.Anchor-based unwrapping can be ambiguous when a cluster spans more than half the box, so shape metrics for such frames warrant caution.Source: §C.5 · p. 22

C.6 Cluster Nematic Order

  • Nematic order measures shared orientation of peptides in the largest cluster and is independent of their spatial compactness.Values approach one for common alignment and zero when no orientation dominates; the metric is undefined for a singleton cluster.Source: §C.6 · p. 22

C.7 Intramolecular Bond Fidelity

  • Intramolecular bond fidelity is assessed from minimum-image distances between each peptide’s two indexed residue beads, pooled over frames and peptides.Distances are grouped within each sequence and rollout.Source: §C.7 · p. 22

C.8 Temporal Summaries and Autocorrelation; C.9 Across-Sequence Agreement

  • Temporal summaries include trajectory means, final values, and fixed-physical-window means, while autocorrelations descriptively compare persistence rather than estimate kinetic rates.Across-sequence agreement uses MAE and Pearson correlation; distributional comparisons use Wasserstein and Kolmogorov–Smirnov distances.Source: §C.8 · p. 23, §C.9 · p. 23

D Complete Results for Held-Out Sequences

The held-out-sequence results present final-frame and time-resolved comparisons, structural visualizations, bond-distance checks, and a direct ensemble prediction baseline. Concentration-resolved trajectories preserve distinct exposure responses, including for held-out QI at dilute conditions.

D Complete Results for Held-Out Sequences

  • The held-out-sequence appendix reports all sequences using the lag-1000 protocol, with five-rollout means and standard deviations for generated curves and markers.Static configurations come from one representative rollout because coordinate averaging across trajectories does not yield a physical configuration.Source: D Complete Results for Held-Out… · p. 24

D.1 Final-Frame Agreement Across Sequences

  • Final-frame comparisons retain the principal sequence trends seen in late-window averages but show greater dispersion without temporal averaging.Each point represents one ordered sequence; the figure compares held-out MD and SupraTITO final configurations.Source: Figure 7 · p. 24

D.2 Temporal Trajectories

  • Held-out temporal plots compare SASA and largest-cluster trajectories, contact memory, and largest-cluster-fraction autocorrelation between MD and SupraTITO.The contact-persistence figure removes sequence- and trajectory-specific contact-occupancy baselines before averaging generated curves.Source: Figure 8 · p. 25, Figure 9 · p. 26, Figure 10 · p. 27
  • Matched snapshots show both trajectories remain predominantly dispersed for AT, partially assemble for LQ, and rapidly form compact aggregates for YP.The YP trajectories follow different microscopic pathways despite reaching compact aggregates.Source: Figure 12 · p. 29, Figure 13 · p. 29, Figure 14 · p. 30

D.3 Final Configurations and Molecular Connectivity

  • Final-configuration views compare held-out MD and generated morphologies and display indexed molecular connectivity using minimum-image geometry.The XY projection can conceal separation along the third coordinate.Source: §D.3 · p. 30, Figure 15 · p. 31

D.4 Intramolecular Bond Fidelity

  • Bond-distance distributions test whether collective-assembly agreement is accompanied by physically consistent intramolecular separations across held-out sequences.The comparison shows MD distributions alongside SupraTITO means and rollout standard deviations.Source: §D.4 · p. 32, Figure 16 · p. 32

E Direct Ensemble Prediction Baseline

  • The DEP baseline generates independent late-ensemble configurations, whereas SupraTITO rollouts define trajectories; sequence-resolved SASA views compare their structural distributions with MD.DEP and SupraTITO use the same MD trajectory collection, but DEP is trained on the late ensemble and SupraTITO on finite-lag transitions.Source: E Direct Ensemble Prediction Baseline · p. 33, Figure 17 · p. 33, Figure 18 · p. 34

F.1 Concentration-Resolved Exposure Dynamics

  • Across 22 fixed-peptide-count conditions, SupraTITO preserves distinct exposure responses, including the concentration response of held-out QI at the most dilute conditions.The concentration-resolved SASA trajectories support the reported late largest-cluster-fraction trends.Source: §F.1 · p. 35, Figure 19 · p. 35, Figure 24 · p. 37

F.2 Evaluation at New System Sizes

SupraTITO can be evaluated on variable numbers of retained sites despite training at one system size, but its structural transfer is less consistent across sizes than across concentrations. The reported FF and QI outcomes show finite-size responses are not uniformly recovered.

F.2 Evaluation at New System Sizes

  • The evaluation varies peptide count and box size together near 100 mM and separately sweeps FF peptide count at fixed box size.SupraTITO is trained at one system size but accepts the resulting variable number of retained sites.Source: §F.2 · p. 37
  • At smaller size, SupraTITO reproduces QI partial assembly but leaves FF too dispersed; at larger size, it nearly completes FF aggregation but misses QI partial assembly.The fixed-box FF peptide-count sweep shows similar sensitivity to peptide number.Source: §F.2 · p. 37, Figure 25 · p. 37
  • Architectural compatibility with variable site counts does not determine finite-size effects on collective assembly when training uses only one system size.Transfer across system size is less consistent than transfer across concentration at fixed peptide number.Source: §F.2 · p. 38

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