SupraTITO: Transferable Generative Molecular Dynamics for Supramolecular Systems

Weilong Chen; Nuno Costa; Julija Zavadlav

Figure 1 : SupraTITO architecture and generation of peptide assembly trajectories. Peptide sequences are represented through learned amino-acid and terminal-role embeddings, illustrated for DF. The condition encoder combines these features with the current configuration

\mathbf{x}_{t}

and physical lag

\tau

to produce per-residue context for the velocity network. Both networks use pair representations that combine nonuniform minimum-image distance bins with directed intramolecular bond categories, providing learned attention biases for interactions within and between molecules. The condition encoder uses the observed geometry, whereas the velocity network recomputes pair distances from the intermediate configuration implied by

\mathbf{x}_{t}+\mathbf{z}_{u}

at each ODE evaluation. Integrating the velocity field from Gaussian noise produces a displacement; adding it to the current configuration and wrapping into the periodic box gives the next state. Repeated application with fresh noise generates an assembly trajectory. The DF snapshots illustrate assembly over multiple learned transitions. Green and coral distinguish residue positions, and sticks connect intramolecular pairs. Colored embedding blocks are schematic; molecular snapshots are centered for display.

Figure 2 : Transfer to held-out dipeptide sequences. Markers show means across five independent SupraTITO rollouts, and vertical error bars show one standard deviation of their late-window means. MD values are averaged over the final

125\,\mathrm{ns}

. Each point represents one ordered sequence and is colored by its MD largest-cluster fraction, providing a common measure of aggregation across peptide chemistries. Dashed lines indicate exact agreement. Panel annotations report Pearson correlation (

r

) and mean absolute error (MAE).

Figure 3 : Dynamical fidelity on held-out sequences. a–c , largest-cluster fraction for representative dispersed, intermediate, and assembled sequences. Green curves show MD and blue curves show SupraTITO. Faint green curves show raw MD values, faint blue curves show framewise means across rollouts, solid curves show 21-frame moving averages, and blue bands show one standard deviation across smoothed SupraTITO rollouts. Insets show the final MD configurations, with teal and orange denoting the first and second residue sites of each peptide. d , baseline-corrected contact-persistence area under the curve over

0

–

25\,\mathrm{ns}

. Markers and vertical error bars show the mean and one standard deviation across SupraTITO rollouts and are colored by the MD late-window largest-cluster fraction.

Figure 4 : Transfer improves with training-sequence coverage. SupraTITO is trained on nested subsets of 40, 80, 160, and 320 ordered sequences and evaluated on a common held-out set. Percentages denote the fraction of the complete sequence corpus used for training. a , mean absolute error for each observable, normalized by the range of its MD late-window means. b , Pearson correlation between generated and MD late-window means. Gray markers show the individual SupraTITO observables and blue markers show their arithmetic mean. The orange dashed lines and diamonds show the full-data DEP benchmark described in section 5.2 ; orange and blue bands are 95% bootstrap confidence intervals. The horizontal DEP references do not represent a coverage sweep.

Figure 5 : Finite-lag learning versus direct ensemble prediction. Both methods use the same training sequences and are evaluated on the same held-out set. a , sequence-resolved late-window SASA, ordered by the MD mean. Green, blue, and orange curves show MD, SupraTITO, and DEP, respectively. Generated curves show means across five independently sampled ensembles, and shaded bands show one standard deviation. b , mean absolute error and Pearson correlation for six structural observables, followed by the one-dimensional Wasserstein distance

W_{1}

and Kolmogorov–Smirnov distance between generated and MD SASA distributions. Values in parentheses give the standard deviation across five stochastic generations in the final reported digits. SASA is reported in

\mathrm{nm}^{2}

, contact counts are dimensionless, and radius of gyration (

R_{g}

) is reported in nm.

Figure 6 : Transfer beyond the training concentration. Late largest-cluster fraction as a function of peptide concentration for six representative sequences at fixed peptide number. Dashed green curves show MD, solid blue curves show SupraTITO, and shaded regions show one standard deviation across generated rollouts. Complete SASA trajectories for each condition are provided in section 12.1 .

Held-out pair groups
AC	AE	AI	AT
CH	CR	CT	DG
DH	DN	DY	EQ
ER	ES	FI	FL
FV	FW	GK	GS
GT	HK	HN	IQ

Table 1: Held-out unordered dipeptide pairs. Both ordered versions of every listed pair are included in the evaluation set.

Peptides	Condition IDs	Comparison	Conditions
FF, QI	C050 , C075 , C100 , C125 , C150	Concentration	$M=100$ , concentrations of $50$ , $75$ , $100$ , $125$ , and $150\,\mathrm{mM}$ obtained with $L_{0}=14.917$ , $13.032$ , $11.840$ , $10.991$ , and $10.343\,\mathrm{nm}$ , respectively.
FF, QI	S050 , C100 , S200	Finite size	$M=50$ , $100$ , and $200$ at $100\,\mathrm{mM}$ , with $L_{0}=9.397$ , $11.840$ , and $14.917\,\mathrm{nm}$ , respectively.
FF	R050 , R150	Fixed-box route	$M=50$ and $150$ in the fixed $L_{0}=11.840\,\mathrm{nm}$ box, corresponding to $50$ and $150\,\mathrm{mM}$ .
FH, IK, AG, KR	C050 , C100 , C150	Concentration	$M=100$ at $50$ , $100$ , and $150\,\mathrm{mM}$ , with $L_{0}=14.917$ , $11.840$ , and $10.343\,\mathrm{nm}$ , respectively.

Table 2: Concentration and finite-size transfer panel.

M

denotes the number of peptides and

L_{0}

the initial cubic box length. The C100 conditions are the corresponding baseline trajectories reused from the exhaustive corpus.

Component	Condition network	Velocity network
Transformer layers	4	6
Site-representation width	64	128
Conditioning width	64	128
Pair width	32	64
Attention heads	8	8
Distance categories	64	64

Table 3 : Architecture of the reported translation-invariant, molecule-consistent nonuniform-64 model.

Task	Hardware	Computational cost
MD production, $1.25\,\mu\mathrm{s}$	Intel Xeon Platinum 8480+ and GPU Max 1550	$\approx 2\,\mathrm{h/system}$
SupraTITO training	32 NVIDIA H100 GPUs	$\approx 1{,}300$ GPU-hours
Lag-1000 transition, one system	One NVIDIA H100 GPU	$\approx 0.25\,\mathrm{s}$
Lag-1000 transition, 80 systems	One NVIDIA H100 GPU	$\approx 6.4\,\mathrm{s}$

Table 4 : Computational cost of reference simulation and SupraTITO. Inference timings exclude compilation, file output, and post-processing.

Quantity	Symbol	Default	Role
SASA bead radius	$r_{b}$	$0.29\,\mathrm{nm}$	Effective radius of one residue bead
Probe radius	$r_{p}$	$0.14\,\mathrm{nm}$	Solvent-probe contribution
Sphere directions	$P$	20	Surface quadrature
Contact cutoff	$r_{c}$	$0.875\,\mathrm{nm}$	Peptide-center contact graph
Late interval	$T_{\mathrm{late}}$	$125\,\mathrm{ns}$	Physical-time averaging window
Contact-memory interval	$T_{\mathrm{pers}}$	$25\,\mathrm{ns}$	Corrected persistence AUC

Table 5 : Numerical parameters used for trajectory analysis unless stated otherwise in the corresponding figure caption.

Figure 7 : Final-frame transfer to held-out dipeptide sequences. SupraTITO is compared with MD using the instantaneous final configuration of each held-out trajectory. Each point is one ordered sequence, vertical bars show the rollout standard deviation, and color denotes the MD final-frame largest-cluster fraction. Dashed lines indicate exact agreement. Relative to the late-window averages in figure 2 , the final-frame values retain the principal sequence trends but exhibit greater dispersion because no temporal averaging suppresses structural fluctuations or differences between metastable realizations.

Figure 8 : SASA trajectories for all held-out sequences. Each panel compares MD (green) and SupraTITO (blue) for one ordered sequence. Faint green curves show raw MD values, faint blue curves show framewise means across rollouts, solid curves show 21-frame moving averages, and blue bands show one standard deviation across rollouts. Each panel retains its own SASA scale.

Figure 9 : Largest-cluster-fraction trajectories for all held-out sequences. Green curves show MD and blue curves show SupraTITO. Faint curves show raw MD values and framewise SupraTITO means, solid curves show 21-frame moving averages, and blue bands show one standard deviation across rollouts. The observable is computed from the PBC-aware peptide-center contact graph.

Figure 10 : Baseline-corrected contact persistence for all held-out sequences. Each panel compares peptide-pair contact memory from MD and SupraTITO over the final

250\,\mathrm{ns}

, with MD in green and SupraTITO in blue. The sequence- and trajectory-specific contact-occupancy baseline is removed before averaging the generated curves. The blue band shows one standard deviation across rollouts. Persistence is evaluated for lags up to

25\,\mathrm{ns}

using the peptide-center contact definition in equation 34 .

Figure 11 : Largest-cluster-fraction autocorrelation for all held-out sequences. Each panel compares MD (green) and SupraTITO (blue) autocorrelations computed over the final

250\,\mathrm{ns}

, using offsets up to

50\,\mathrm{ns}

. The blue band shows one standard deviation across independently evaluated rollouts. These curves complement the contact-memory comparison in figure 3 d.

Figure 12 : Matched assembly snapshots for the representative dispersed sequence AT. MD configurations are shown above the corresponding SupraTITO configurations at five physical times. Both trajectories retain a predominantly dispersed peptide population throughout the rollout. The first and second sequence positions are colored blue and coral, respectively.

Figure 13 : Matched assembly snapshots for the representative intermediate sequence LQ. MD and SupraTITO both form a substantial cluster while retaining a population of unassociated peptides, consistent with the partial and fluctuating assembly dynamics in figure 3 b.

Figure 14 : Matched assembly snapshots for the representative held-out assembled sequence YP. The two stochastic trajectories follow different microscopic pathways but both rapidly form a compact aggregate, consistent with figure 3 c.

Figure 15 : Final configurations for all held-out sequences. Muted blue points show the MD reference. TUM blue and orange points show the first and second residue positions in SupraTITO, respectively, and black lines connect the indexed sites of each peptide using minimum-image geometry. Generated coordinates are from one representative rollout. The XY projection supports visual comparison of morphology and molecular connectivity but can hide separation along the third coordinate.

Figure 16 : Intramolecular bond-distance distributions for all held-out sequences. Distances are computed for fixed indexed residue pairs with the full three-dimensional minimum-image convention and pooled over analyzed frames and peptides within each rollout. Each panel compares the MD distribution with the SupraTITO mean and one standard deviation across rollouts.

Figure 17 : Sequence-wise SASA errors for DEP and SupraTITO. Each point is the mean for one held-out sequence, with horizontal and vertical bars showing one standard deviation across five DEP generation seeds and five SupraTITO rollout seeds, respectively. Points below the equal-error diagonal favor SupraTITO. Color denotes the MD late-window largest-cluster fraction, and logarithmic axes retain both low-error systems and outliers.

Figure 18 : Complete sequence-resolved SASA distributions for the DEP comparison. Each panel contains 50 MD samples, 250 independent DEP predictions, and 250 SupraTITO late-window configurations. Per-panel axes retain the sequence-specific SASA range and probability-density scale.

Figure 19 : Concentration-resolved SASA for AG. Each panel is one 100-peptide system at the indicated concentration. The green lines show the raw MD values and their 31-frame moving average. Faint blue lines show the individual rollouts; the solid blue line and shaded band show the mean and one standard deviation of their 31-frame moving averages.

Figure 20 : Concentration-resolved SASA for FF. Plotting conventions follow figure 19 .

Figure 21 : Concentration-resolved SASA for FH. Plotting conventions follow figure 19 .

Figure 22 : Concentration-resolved SASA for IK. Plotting conventions follow figure 19 .

Figure 23 : Concentration-resolved SASA for KR. Plotting conventions follow figure 19 .

Figure 24 : Concentration-resolved SASA for QI. Plotting conventions follow figure 19 .

Figure 25 : Late structural response at new system sizes. a , late largest-cluster fraction when peptide count and box size are changed to keep concentration near

100\,\mathrm{mM}

. b , FF peptide-count sweep at fixed box size. Dashed green lines show MD; solid blue lines and bands show the SupraTITO mean and one standard deviation across five independent rollouts.

Figure 26 : Condition-specific SASA trajectories at new system sizes. The top and middle rows vary peptide count and box size together at approximately

100\,\mathrm{mM}

for FF and QI. The bottom row varies FF peptide count in a fixed

11.84\,\mathrm{nm}

box. Every panel is one physical system. Line and uncertainty conventions follow figure 19 .

SupraTITO: Transferable Generative Molecular Dynamics for Supramolecular Systems

Abstract

Figures & tables

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