PepTri: Tri-Guided All-Atom Diffusion for Peptide Design via Physics, Evolution, and Mutual Information
Authors: Ngoc-Quang Nguyen
Jaeyoon Jung
Seijung Kim
Sunkyu Kim
Jaewoo Kang
Venue: ICLR 2026 Poster (2026)
Keywords: sequence-structure peptide design
all-atom
guided latent diffusion
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
TL;DR: Designing peptides with tri-guidance diffusion model via physics, evolution, and mutual information

Abstract: Peptides, short chains of amino acids capable of high-specificity protein binding, represent a powerful class of therapeutics. While deep generative models have shown promise for peptide design, existing approaches are often structure-centric and therefore generate sequences and structures in a decoupled manner, failing to ensure that designs are simultaneously physically stable, evolutionarily plausible, and internally coherent. To overcome this limitation, we introduce \textbf{PepTri}, a novel diffusion framework that addresses this by jointly generating peptide sequences and 3D structures within a unified, SE(3)-equivariant latent space. Our proposed model integrates three complementary guidance signals during the generative process: (i) physics-informed guidance via differentiable molecular mechanics to ensure structural stability and realism; (ii) evolutionary guidance to bias sequences toward conserved, functional motifs; and (iii) mutual information guidance to explicitly maximize sequence-structure coherence. This tri-guided approach ensures the generative process is steered by biophysical laws, biological priors, and information-theoretic alignment in tandem. Extensive evaluations on challenging peptide-protein design benchmarks, cross-domain (PepBench, LNR) and in-domain (PepBDB), demonstrate that PepTri substantially outperforms strong baselines, achieving state-of-the-art results in binding affinity, structural accuracy, and design diversity. Our results establish that integrating these complementary signals directly into the denoising process is crucial for generating viable, high-quality peptide medicines. PepTri is available at: https://github.com/aigensciences/PepTri

Published as a conference paper at ICLR 2026
PEPTRI: TRI-GUIDED ALL-ATOM DIFFUSION FOR PEPTIDE DESIGN VIA PHYSICS, EVOLUTION, AND MUTUAL INFORMATION
Ngoc-Quang Nguyen*
Jacyoon Jung'
Seijung Kim
Sunkyu Kim
Jaewoo Kang
1 "AIGEN Sciences
Korea University
[quang.ggyenn, faeyoon.jung seijung. kim, sunkyu.kim, jaewoo. jangoo.kang) aigensciences.coo
ABSTRACT
Peptides, short chains of amino acids capable of high-specificity protein bind- ing, represent a powerful class therapeutics. While deep generative models have shown promise for peptide design, existing approaches centric and therefore generate sequences and structures in a decoupled manner, failing ensure that designs are simultaneously physically stable, evolutionar- ily plausible, and internally coherent. To overcome this limitation, we intro- duce Pep'Tri, novel diffusion framework that addresses this by jointly gener- ating peptide sequences and 3D structures within unified, SE(3)-equivariag tent space. Our proposed model integrates three complementary guidance signals during the generative process: (i) physics-informed guidance via differentiable molecular mechanics to ensure structural stability and realism; (ii) evolutionary guidance to bias sequences toward conserved, functional motifs; and (iii mu- tual information guidance to explicitly maximize scquence-structure coherence. This tri-guided approach ensures the generative process is steered by biophysical laws, biological priors, and information coimaattoo-thoorttic alignment tandem. Exten- sive evaluations challenging peptide-protein design benchmarks, cross-domain (PepBench, LNR) and in-domain (PepBDB), demonstrate that Pep'Tri substan- tially outperforms strong baselines, achieving state-of-the-art results in binding affinity, structural accuracy, and design diversity. Our results establish that inte- grating these complementary signals directly into the denoising process is cru- cial for generating viable, high-quality peptide medicines. Pep'Tri is available at: httpp:://itte com wwt.c//aigeeceencceeeeeeeee
often structure-
la-
INTRODUCTION
The therapeutic potential of peptides-shor chains of amino acids-is rapidly being realized, evi- denced by over 100 approved drugs and robust pipeline of hundreds more in development. (Kaygi- siz et al. 2025| Zhai al.) 2025). Their advantages over small molecules and biologics include high specificity. low toxicity, and the ability to target "undruggable" proteins (Craik et al. 2013 Lai et al.)
2.25). Yet rational design remains challenging: the sequence space astronomical (20 possibil-
ities), peptides are highly flexible and often lack stable tertiary structure, and candidate sequences must satisfy interdependent geometric, evolutionary, and physicochemical constraints (Muttenthaler al. 202T)
Deep generative models have advanced peptide and protein design but remain incomplete. Structure- aware generators produce plausible geometries yet neglect evolutionary constraints; evolutionary sequence models capture conservation but ignore 3D stability; and physics-based checks are usually applied post hoc rather than during generation (Ho al. 2020; Kong al.) 2024). No existing method ensures designs that are simultaneously physically stable, evolutionarily plausible, and se- quence-structure coherent.
"Corresponding authors.

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Published as a conference paper at ICLR 2026
We introduce PepTTr,, tri-guided diffusion framework integrating complementary signals during training and sampling: (i) physics guidance with SE(3) awareness to ensure molecular stability; (ii) evolutionary guidance via BLOSUM-derived embeddings and co-variation; and (iii) mutual- information maximization aligning sequence and structure representations. Our contributions in- clude parameter-efficient architecture with compact latents, dynamic guidance schedule bal- ancing stability and diversity, a unified diffusion objective combining physics, evolutionary, and information-theortti terms, and robust training pipeline with mixed-precision and EMA stabiliza- tion. Together, these enable PepTrr to generate diverse peptides with physically plausible, energeti- cally favorable structures.
RELATED WORK
Physics- and empirical design. Traditional ceselinns--uaaggnnneee phage display, and Rosetta- based modeling- have succeeded in narrow settings but face limited sampling and costly exploration of vast sequence spaces (Smith & Petrenko 1997 Leaver-Fay et al. 2011] Kuhlman & Bradley 2019).
Evolutionary sequence models. Potts/MSA--ra based models bias sequences toward biological plau- sibility (Marks et al. (2IIT) but depend homologs and do not enforce geometric energetic realism during generation.
Structure-aware generative modeling. Diffusion and flow-based models learn backbone scaf- fold distributions and generate diverse structures (rippe et al., 2022 Watson et al., 2023 Abdin
& Kim 2024). While accurate predictors (e.g., AlphaFold) aid evaluation (Abramson al. 2024).
they are not generative. For peptides, coupling sequence, structure, and domain constraints inside the generative loop remains unresolved.
Peptide-focused baselines. PepGLAD uses latent diffusion with auxiliary geometry losses but leaves energetics post hoc (Kong et al. 2024). PepFlow factorizes modalities via flow matching but checks stability only after generation (Li et al. 2024). UniMoMo unifies binders and pockets but relies heuristics (e.g., distance thresholds) that weaken fine-scale couplings (Kong et al.) 2025). Across these, physics and evolutionary priors remain auxiliary rather than shaping denoising dynamics.
Our position. Most existing models prioritize generating plausible 3D backbones but treat peptide sequences as secondary, often decoupled from structure or checked only post hoc. This imbalance leads to geometries that appear stable but in fact correspond to unrealistic or biologically implausible sequences. PepTrri addresses this by unifying sequence and structure an -Eu3ivequi latent space and applying tri- tri-guidance- p-gguuanneeppyiics..... -hyssics, evolution, and information -thooreticeccccc alignment during training and denoising, as illustrated in Figure [ By directly injecting physical guidance into gen- eration and explicitly aligning seruence-struccuue latents, Pep'Tri yields peptides that are not only geometrically sound but also evolutionarily plausible and sequence-structum coherent.
METHODOLOGY
We adopt a two-stage framework: first, a VAE that compresses sequence-structure inputs into a latent space while preserving full SE(3) geometry; second, a latent diffusion model augmented with tri-guidance (physics, evolution, and mutual information) to generate biologically plausible peptides.
3.1
VAE WITH SE(3)-EQUIVARIAS ENCODING
The PepTrri encoder employs
graph neural networks, which enforce rotational and translational symmetries while encoding both local residue-level interactions and global structural dependencies. This design enables accurate modeling of protein conformations within a symmetry- aware latent space, thereby facilitating downstream generative diffusion.
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Latent space
Diffusion with Tri-guidance
Z
1.Physics-b baseed guidance
E
3. Mututal information
Papstrer
Z
2. Evolutionary Guidance
Controlled corruption
Ei toe Kee Mosend
Recepace
M. (6A) n6, t9g.
Reverse diffusion
Figure 1: PepTri architecture. An SE(()) encoder E maps sequence-structure
structure inputs (S, X) latents (Zz, =h): decoder D reconstructs (Š, X). In latent space, sampling runs guided reverse diffusion from 2T (noise) to zy (sample), while training uses controlled corruption in the forward direction. At each step, tri-guidance term G, steers denoising: (1) physics-based guidance acts on 2e (bonds/angglesiclashes/vaa der Waals), (2) evolutionary guidance biases 2/, (BLOSUM- guidance aligns 2, and 24. The update follows 2t-1 Rs
like prior). and (3) mutual-informatt Ho (z f) Ge + ozS. Gray surface: receptor; green: generated peptide; orange: ligand (receptor shown for context; guidance is intra-peptide).
Graph construction. From sequence S E {O...., 19]4, coordinates X E R4xCx3 and mask M, form residue graph with (i) sequential edges (i, (. and (ii) spatial edges within radius Teut- Node features come from S, X; edge features are strictly SE(3)-invariant. The encoder outputs disentangled latents:
2n E Lxdd (sequence),
Z Lx (structure).
Ylaa E N is the number of structural latent anchors (channels) per residue; each anchor carries 3D coordinates.
-Eqiivauiar message passing. We developed an enhanced version of adaptive multi- channel EGNN (Kong et al. 2023). Invariant edge features include pairwise distances d, and averaged triplet angles Vig. Updates are:
x Σ
d(dig, his hy)) xz),
JEN(1)
h/ the his Σ
then (hi, dij.dij wirs)
jEN(()
All coefficients are invariant, and updates use only relative vectors, guaranteeing SE(3)- equivariance.
The VAE is trained to reconstruct both sequence and structure while enforcing geometric invariance:
Training objective.
LVAE = CF(S, + +|X - x11 + LKI. Ageom D(X) II
(1)
where D(X) is the pairwise distance matrix. This enforces SE(3)-invariant structural consistency.
Thus, all inputs, features, and updates respect equivariance, and the mcoder-decode is strictly eqqivvaann We use a VAE framework instead of a direct diffusion model to improve training stability and allow for compact, structured latent space.
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3.2 TRI-GUIDANCE DIFFUSION
As shown in Figure [ we augment latent diffusion with three complementary signals: (1) physics- informed structural guidance, (2) evolutionary sequence guidance, and (3) sequence-structure co- herence via mutual information. These guide denoising to respect physical laws, evolutionary con- straints, and sequence-structuue alignment.
3.2.1 PHYSICS-INFORMED STRUCTURAL GUIDANCE
When relying only on data, found that generated coordinates often exhibit broken bond lengths, unrealistic bond angles, or steric clashes that violate physical plausibility. To address this, we aug- ment diffusion with physics-informed regularization. Our goal is guide the model toward 31) structures that are both consistent with the data and stable under physical principles.
Inputs and scope. We represent peptides in all-atom format, X E RRCXX3 with C channels (backbone sidechain), together with binary design mask M E 1) indicating which residues to optimize. For numerical stability, physics-guidance terms are computed the Co trace, while the full atom tensor propagated and decoded.
Physics parameterization.
We use a composite energy over the designed region:
Ephys S: = Σ my S)
with active terms: bond-length, bond-angle, van der Waals, electrostatics, clash prevention, secondary-structure proxy, and diffusion smoothness. By averaging across all valid masked C, interactions (excluding self-pairs and, for non-bonded terms, immediate neighbors), we obtain a well-scaled and numerically stable energy landscape.
Gradient computation. Inspired by (Guo al. 2024), we treat Ephys as an additional training- time regularizer. At each training step, we:
1. Obtain predicted coordinates X for the designed region (Ca trace) from the en- coder/decoder stack.
2. Evaluate (p (X, S; M).
3. Backpropagate to obtain a masked gradient V Ephys. which propagated through the encoder and diffusion network update the model parameters.
This regularizes the denoiser toward physically plausible structures on designed residues. Because the energy depends only on internal coordinates (distances, angles, and masked pairwise interac- tions) rather than absolute positions, the resulting gradients naturally preserve SE(3)iinvariance.
OpenMM coupling.
We additionally add a differentiable force field term:
LOPenMM Fo (X, S; M),
computed via OpenMM. In our implementation. Pep'Tri is coupled to the Amber14 all-atom force field (ammmrr4-all.xm/// (Case et al. 2023 Eastman et al. (2233 to evaluate EO and its forces on C. atoms in the designed region, contributing an additional physics-based training loss that encourages realistic bond geometry, sterie stability, and electrostatics.
In addition, we provide an optional test-time energy-guided sampler that performs energy-guided denoising.
(4) where E, is the predicted noise at step t and the gradient is restricted designed residues. This gently nudges the diffusion trajectory toward lower-energy conformations and acts as a physics- aware correction during generation.
E, + E, - 7 V ExpenMM (Zt, S) M
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Physies loss.
phyys Aphys SX 20penMMM
(5)
This module therefore enforces bond geometry, non-bonded interactions, and steric constraints while remaining Sonssscon,, ensuring generated structures remain physically plausible.
Further details are provided in Appendix P.4
3.2.2 EVOLUTIONARY SEQUENCE GUIDANCE
Nature has already performed an enormous combinatorial search over protein space, leaving be- hind patterns of conservation and co-evolution that encode which residues "work". We inject this evolutionary signal so generated peptides remain biologically plausible.
Inputs and scope. We begin with residue-level embeddings Ho RLxd from the VAE encoder and a mask M. Evolutionary guidance contributes training losses on these clean embeddings; its effect sampling implicit via the learned denoiser.
BLOSUM-like embeddings.
We learn BLOSSUM-inspired matrix B E 20 residue features
= Ho + d F2 b2, Φ ReLU, E Ryo learnable.
(6)
Y represents the one-hot encoded amino acid type, Y L2220 and F projection.
Residue dependency attention via multi-head self-attention. PepTri captures inter-positional dependencies with residual multi-head self-attention. Let h denote the number of heads and d₁, d/h. For head m,
HFQ (T
head Softmax
HFM MHA(H)
head, ||
[head, FO,
(7)
ddn
and we set
Hevevo H + MHA((H), a>
Conservation and fitness heads. Because Softmax produces probability vector over K classes, the output lies on the (K 11--mmppee::
K
Softmax R
K-1
Pa 0,
Σ
Pa
1
With 20 amino acids (K = 20), the output lies on
20
A 19 {pe 20 Pa 2 0,
Pa = 1}.
(10)
a=1
Hence, position wise conservation preferences produced by small MLP. For each position i, and the self-supervised fitness score pools the designed region
Peons,t = Softmax V. ( Heoevo.)) E 19
(11)
F(Hroewo)) [o] (FFy Pool Henevv M))) E (0, 1).
(12)
Losses. In the current study, we do not use external MSA/PLM priors or MSA-depth gating. In- stead, we combine self-supervised evolutionary fitness target with entropy regularization of the learned conservation distribution:
Lat SmoothL1((P (F THE), Tie. 0.8,
(13)
Leut
1
Σ M Σ
Pcons,ia ia log Peons,i.
(14)
Σ, M,
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minimizing Cent maximizes the entropy of Pcons and encourages diversity. When decoder logits Spred,s are available, we additionally add a local alignment term
LKL-local
E. Σ (Irredd, Pcons,i):
(15)
The KI, divergence term encourages the latent space to remain compact and well-structured, pre- venting posterior drift and collapse. The total evolutionary objective is
Levo
AatCa + dent + XKLLoo-loc
(16)
Taken together, evolutionary guidance biases peptide design toward conserved motifs and globally fit sequences, narrowing the search space to biologically plausible candidates while still encouraging diversity.
Further details are provided in Appendix P.5
3.2.3 MUTUAL INFORMATION REGULARIZATION
functional peptide is not just plausible sequence or a plausible structure - the two must be aligned. Inspired by (Belghazi et al., 2018), to ensure coherence, we maximize the mutual infor- mation (MI) between sequence and structure embeddings. This encourages our model to generate sequences that "make sense" in the structural context.
MINE objective and physics validity. We pool embeddings from both sequence Henevo and structure embedding Astruct. then compute summaries ʃa (Pool [Poolll (oooooooooeo.... M)), fz (2stuctttt M)). We train a critic To:
I = ( =)] log (iggT((eo)))
C=I= -
(17)
Additionally, we include an auxiliary head Pphys that predicts whether structure is physically valid from its latent embedding z. This gives an extra push toward physically sensible outputs.
MI loss.
LMI-total AMI LMI + XMI--hhs (SE(Pphys: 1).
(18)
Thus, MI regularization aligns sequence semantics with structural intent, reducing incoherent de- signs and promoting functional alignment.
Further details are provided in Appendix P.6 and Appendix M
3.2.4 LATENT INPAINTING DIFFUSION
We represent the latent at step t as z = (z xx.), stacking sequence and structure components. Redesign is localized by a binary residue mask M E {0, 1):: noise and supervision are applied only where M 1. The denoiser conditions on positional encodings, atom features, and M, and predicts é; (É,,,, x
Forward noising (masked inpainting). We variance-preserving cosine schedule with a; 1 and ā. II'- 0a. The forward process
qzz, zu) Vāa Za + vI 04 Et.
E, ~ I),,I.
(19)
realized as latent inpainting by adding noise only where M =
2, M O (Vā, Zo + vI- ā. E:) + (1 M) o Za.
(20)
Masked diffusion loss. To supervise only redesigned residues, we broadcast M latent di- mensions:
Mx M 1,ax3 MH M & 1d. For t~U(1 ... T3 and e,~0 N,0, I), the masked noise-prediction loss is
(21)
1
(EH,, - εH,)) @ Mn l
+ Ax [[xxx - éx,,) & Mx
Cain (t) =
Aи
(22)
||M
||Mx||
where of 1-ae-1 3: for the cosine schedule. I-6r

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Training the denoiser. We learn parameters by minimizing the diffusion loss together with physics, evolutionary, and MI objectives.
8r arg min E, Be..o.e. (t) +
CpAys
Levo
CMI-total
]. (23)
structure quality
sequence viahility
sequence structure consistency
Here, Lait (1) depends explicitly on the sampled diffusion timestep I, whereas Pphyss Levor LoI-ttotll and are time-independent regularizers computed on decoded pooled representations for each sam- plc. At inference, parameters are frozen, and we write
é = co. (Ze, t) (=H,0- (Zz, t), 6x,0- (2,,t))
evolutionary and MI guidance act via 8* The À ablation can be found in Appendix
Reverse diffusion with explicit physics guidance. Starting from ²T ~ (N I), we iteratively
update to Zo. We apply physics correction only the structural component:
ÉH, EHH (Zz, t),
(24)
εx, Ex (Z,, vI
G
Gplys
-Aphys Vzx, Ephys S;
(25)
where X, is a partial decode of xx.t (coordinates only). Because pphys depends only on internal distances/angles. this guidance is consss-onsstt We anneal Aphys to strengthen physics late in the trajectory. The Gaussian reverse transition
2-11
1
2t
1 1
aq āt
+ +.
g {~N(0,1),
(26)
Var
VI
where & is an independent standard normal (resampled at each step) with the same shape as Zy.
Stochasticity and context control. To confine randomness redesigned residues, optionally
mask the noise:
& < Mog To keep the context fixed, we clamp unmasked entries after each step:
of E a (M @ E)
2 4-11 M 1 + (1 M) zo.
(27)
Running equation 26-equation 27 for T steps yields (Hy, Xu) while preserving the unmasked struc- tural context. Evolutionary and MI guidance influence sampling through 8", whereas the explicit physics term stabilizes local geometry and reduces clashes during generation.
Together, the proposed tri- tri-guidance objective integrates diffission with physical, evolutionary, and MI regularization, producing peptides that are physically stable, biologically grounded, and se- quence-structure coherent.
Further details are provided in Appendix P2
EXPERIMENTS
4.1 DATASETS
In our experiments, the dataset primarily consists of short peptides, with a substantial proportion shorter than 30 amino acids. This characteristic highlights the model's strength in generating such sequences (Wei et al. 2024). Following the recommendations of (Kong et al. 2024). we employed two experimental setups: Cross-domain: To assess the model's generalization capability, we trained on the PepBench dataset, which contains 105 non-redundant
ppretde complexes, and eval- uated on the non redundannd dataset (LNR) from Tsaban (Tsaban et al. 2022), comprising 93 pro- tein-peptide complexes with canonical amino acids curated by domain experts. In-domain: Using PepBDB (Wen et al. 2019), which includes 7,014 complexes. We ensured that no protein target was duplicated between the training and test sets, thereby preventing data leakage and enabling fair evaluation. To achieve this, we applied the MMseqs2 clustering technique.
Further details of the datasets are provided in Appendix O and Appendix 0.1

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4.2 EVALUATION METRICS
To rigorously assess the performance of the proposed methods against state-of-the-art (SOTA) mod- els, we employed a comprehensive set of evaluation metries capturing both structural quality and functional relevance. These include: Success Rate (fraction of generated peptides with thermody- namically stable binding, defined as AG < -5 REU from Rosetta (Alford et al. 2017)). Bind- ing Free Energy (AG), DockQ (interface quality), GDT TS (global structural similarity), Con- tact_F1 (local interaction accuracy), Local RMSD (local structural precision), Clash in (Ca in- ternal clashes), Clash out (Ca interface clashes), Bond-outlier rate (fraction of backbone bonds deviating from ideal geometry), Sequence Diversity (BLOSUM62 clustering). Sequence Validity (fraction of generated sequences passing biochemical criteria), Structure Diversity (RMSD clus- tering), and Consistency (Cramér's across multiple generations). To capture variability across targets, additionally report per-target standard deviations for six primary metrics.
Further details of evaluation metrics are provided in Appendix
4.3 SEQUENCE-STRUCTURE PEPTIDE CO-DESIGN TASK
During training and evaluation, peptide design was carried out in situ within the receptor's binding pocket. The receptor treated as rigid scaffold, and all diffusion steps for the peptide sequence and structure were conditioned on its local environment. This setup ensures that generated peptides evaluated in the same geometric and energetic context in which binding occurs. We report each metric for before relaxation and after relaxation (shown in italics). Geometry refinement was carried out using OpeNMM energy minimization with the Amber14 force field, applied consistently across our models and baseline models. To preserve backbone geometry, positional restraints with a stiffness constant of 10.0 were applied all non-hydrogen atoms. The minimizer was run with no iteration cap (maximum iterations = 0), allowing convergence to a local minimum.
4.3. BINDING QUALITY, INTERFACE ASSESSMENT, AND STRUCTURAL ACCURACY
Table 1: Binding quality metrics on PepBench and PepBDB. Higher success rate and DockQ, lower AG, are better. (without relaxation / with relaxation)
Dataset
Method
Success Rate (1)
AG (REU)
DockQ (?)
PepRench
PepGLAD
0.29 10.79
15.63
/4.48221144
0.60 00.59+0.14
PepFlow
0. 40.74
-17.05=2.2s
/ 1-35.08
0.33 00.42=0.00
Ungle
0.34
10.79...13
-19.04
/ 1.3.1919.55
0.57 23/ 00.4.20.11
PopTri(Ours)
0. 10.83 /0.83 10
-19.39 /-36.66=14.27
0.63 00.62
PepBDB
PepGLAD
0.15 /0.67 20.26
-14.48 /-31.22-13.22
0.43 20 20.43
PopFlow
0.30+a.15 / +0.01
-17.44=9.52 /-34.98 225.97
0.41 21 /0.37 +0.15
UniMoMo
0.30 / 0.74
-18.8921.598 / 1344.05 18..99
0.44 20 0.43
PopTri(Ourrs
0.31 23 0.74
-18.15
1.4.822118.00
0.49 10.49
Table I summarizes binding success, thermodynamic favorability, and interface quality across both cross-domain (PepBench) and in-domain (PepBDB) evaluations. Pep'Tri achieves the strongest overall performance, outperforming baselines in success rate and interface quality and maintain- ing highly competitive AG values in both pre- and post-relaxation settings. This indicates robust generalization and stable peptide-receee receptor interfaces even under relaxation. Relaxation improves force-field energy but does not guarantee increased nativeness, often shifting poses toward lower- energy basins with slightly reduced DockQ. PepTriis guided denoising produces interfaces that remain native-like after refinement, suggesting that its tri- tri-guidance mechanism shapes physically coherent structures rather than relying on post-hoc relaxation to correct them.
4.3.2 STRUCTURAL ACCURACY
Table 2 reports that PepTri consistently achieves the highest Contact. F1 and GDT.TS on both Pep- Bench and PepBDB in both pre- and post-relaxation regimes. For local RMSD. PepFlow is slightly better before relaxation, whereas PepTri attains the best post-relaxation RMSD on both datasets, indicating that its conformations refine particularly well. Since GDT TS > 0.5 indicates reasonable
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Table 2: Structural accuracy metries on PepBench and PepBDB (without relaxation with relax- ation).
Dataset
Method
Fontact.F (1)
Local RMSD (4)
GT)
PepBench
PepGLAD
0.80 0080
1.22.20.4 1.21 2:043
0.72
2073
PepFlow
0.8010.35 0.
1.07
/106600.0
0.74 20 1,774
UniMoMoaingte
20.30
=0.67
1.98 1.37
0.62 40.22
PepTri(Ours)
0. 23 0.84
1.8+0.42
1.10000.4
0.75 /0.76 19
PepBDB
PepGLAD
0.52 00,60=0.88
1.92#1.83
0.52+ 26 00.00
PepFlow
0:71 30 0.72
1.27 20.45
1.35 44
0.65 21 /0.63 22
UniMoMo,ingie
0.48
00.55
2.78
7,.22
D.48 0..56
PepTri(Ourr)
0.75 0.77
134+1.43 /.2990..4
0.66 0.67
Table 3: Clash and geometry quality metrics on PepBench and PepBDB (without relaxation with relaxation). Lower better for all metrics.
Dataset
Method
Clash (%)
Clush out (%)
Bond Outliers
PepBench
PepGLAD
7.99 28 5.60
12.56 /1.45
17.41 / 66.53+3.08
PepfFlow
7.64 2..70.2.36
7.82 /0.69
19.64 77 77 1..20
UniMoMoaxagie
5.99 114777
1..
1.55
10.891
14.95 32 2.79
Pep'Iri (Ours)
6.16+13.65 1..59
4.73=:1.06 3..54
15.60. :5.77
PepBDB
PepGiLAD
10.36 15.44
8.52_16.64 / 1.10
37.13 39 /7,28
PepFlow
19.43 22448+2.12
12.45+13.35
11.004.660
28.93+4..60 /5.17+1.00
UniMoMoavv.gie
15.07 /0.83
7.82=17.49 1145
32.13 2446
Pep'Iti (Ours)
16.72 4.25
6.22 1077
28.27 sal 4.70
structural similarity, these results confirm that our generated peptides remain globally faithful to native folds, with the largest gains PepBDB. Complementing these structural metries, Table 3 summarizes clash and eovalnntgeommety outlier rates (lower is better for all metrics). Energy mini- mization substantially reduces clashes and bond-length violations for all methods, showing that the predicted backbones lie close to valid local minima. After relaxation, PepTri attains the best or near-best Clash in, Clash out, and bond-outlier rates across both datasets, yielding peptide struc- tures that are not only accurate in terms of global fold but also highly clash-free and geometrically well-formed.
4.3.3 DIVERSITY ANALYSIS AND SEQUENCE VALIDITY RATE
Table 4: Design diversity metrics on PepBench and PepBDB (without relaxation with relaxation).
Dataset
Method
SeqDiv (t)
Sel
StrDiv(t)
Consistency(1)
PepBench
PepGLAD
0.92
0.27
0.54 / 0.60
0.81 10.4
PepFlow
0.83
0.25
0.44 / 0.58
0.67 0.80
UniMoMosingte
0.92
0.21
0.62 0.65
0.79 0.84
PepTri (Ours)
0.93
0.27
0.44 / 0.63
0.80 0.86
PepBDB
PepGLAD
0.92
0.24
0.81 / 0,82
0.94 0.96
PepFlow
0.67
0.20
0.58 / 0.71
0.74 0.82
UniMoMosingte
0.90
0.20
0.81 0.80
0.92 0.94
PepTri (Ours)
0.93
0.28
0.63 0.70
0.89 0.95
Table 4 reports sequence and structure diversity, sequence validity, and sequence-structuue consis- tency. Pep'Tri attains the strongest overall balance across these metrics, producing diverse yet bio- logically plausible sequences and coherent strucccr pairs. While its structural diversity is moderate, this reflects its tendency to generate low-energy, near-native conformational ensembles. PepTrri also achieves the highest near- highest consistency after relaxation, indicating that evolu- tionary guidance helps maintain coherence between sequence and fold while still supporting broad sequence exploration.
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Practical implications. Results show balanced, physics constricco exploration that preserves sequence diversity while converging to stable structural basins, benefiting peptide design and drug discovery; Cross-domain robustness: binding metrics, evidencing tri-guidance under distribution shift; Refinement-frennlly geometry: best post-relax RMSD both datasets indicates that SF(3)-aware latent modeling with physics guidance reaches physically consistent minima; Diverse yet coherent designs: highest sequence diversity alongside strong sequence-structure consistency validates sequence and structure latents.
PepTrr achieves state-of-the-an results PepBench
ABLATION STUDY ANALYSIS
Serup. We quantify the contributions of four components: physics guidance, evolutionary guidance, mutual information (MI) guidance, and all-atom modeling- single-component removals (Ta- 5) and single-guidance variants (Table 7 Unless stated otherwise, higher values are better; for MaaL_MMS_MMeee and Sliding-AAR, lower is better. Our ablation study evaluates the high-level contribution each guidance type (physics, evolutionary, and MI) because these components are designed to function integrated modules. The full model, PepTri, achieves the strongest overall performance, with leading scores mean success rate, AG, DockQ, Contact F1, GDT-TS, sequence validity, and consistency. Removing any component degrades at least underscoring the synergy between structural physics, evolutionary constraints, enformationnthhorede coupling, and atomistic detail.
dimension of quality,
Table 5:
Ablation study results comparing different settings when removing single components..
No phys
No evo
No mi
PepTripaccbone
PepTri
Physics guidance (phys)
Evolutionary guidance (evo)
Mutual information guidance (mi)
All atom
Mean success rate (AG 0)
0.401
0.443
0.545
0.397
0.583
AG (REU) 4
-15.485
-16.501
-18.949
-16.961
19.387
DockQ
0.621
0.618
0.633
0.578
0.633
Contact F1
0.750
0.769
0.804
0.760
0.829
Local RMSD (À) $
1,432
1.418
1.154
1.260
1.179
GDT TS
0.704
0.709
0.745
0.726
0.747
Sequence Diversity
0.917
0.915
0.920
0.917
0.926
Sequence Validity rate
0.256
0.250
0.259
0.260
0.273
Struet Diversity
0,465
0.427
0,431
0.499
0,436
Consistency
0.783
0.771
0.779
0.744
0.799
Sliding-AAR
0.352
0.361
0.354
0.347
0.342
TM-score
0.221
0.220
0.250
0.242
0.244
6 CONCLUSION
We introduced PepTri, a latent-diffusion framework for peptide co-design that operates in an SE(3)- aware latent space with separate sequence and structure representations. Joint denoising preserves geometric equivariance and enables efficient control over both modalities. Pep'Tri incorporates three complementary forms of guidance: physics-based gradients that enforce geometric plausibility, evo- lutionary priors that encourage realistic sequences, and mutual-information regularization that pro- motes coherent sequence-structure behavior and high-quality peptide candidates. Overall, PepTri provides principled way to inte- grate physical and evolutionary priors into equivariant generative models, with clear opportunities for extension broader conditioning and to more complex protein-peptide systems.
structure design. These components together produce stable sampling
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ACKNOWLEDGEMENTS
This research was supported by a grant of the Korea Machine Learning Ledger Orchestration for Drug Discovery (ojja((K-EELLODDY,,, funded by the Ministry of Health & Welfare and Min- istry of Science and ICT, Republic of Korea (grant number: RS-2024-004624471, This work was supported by the Technology Development Frogram(RS-2022-0052366 SMEs and Startups(MSS, Korea). This research was supported by grant from the Korea Health Technology R & Project through the Korea Health Industry Development Institute (KHIDI), funded by the Ministry of Health & Welfare, Republic of Korea (grant number: RS-2025-25462758) We also thank Soojung Lee 2 for her expertise, which significantly enhanced the quality of this work.
funded by the Ministry of
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USE OF LARGE LANGUAGE MODELS
We used large language model to (i) polish grammar and wording across drafts, (ii) assist with high- level ideation and code, and (iii) find related works, All technical claims, equations, experiments, and analyses were conceived, implemented, and verified by the authors. The model was not used to generate data or run experiments. All citations and numerical results were manually checked by the authors.
A NOTATION
Table 6: Summary of notations used throughout the paper.
Symbol
Meaning
8 {0, (0..... 19)
Amino acid sequence of length L (20 canonical residues)
X E RLxOx3
All-atom 3D coordinates (C 14 channels: backbone + sidechains)
M E 10
Binary mask for inpainting (M, = redesigned, M, = 0 context) Residue-level embeddings; H R Lxd
hi, H
2A E RLxds
Latent sequence features (invariant)
2x E R LLxnuxx
Latent structural anchors (equivariant)
2, = (#H,1) Ex,))
Latent variables at diffusion step Denoiser network parameterized by
Ea
Predicted noise at step t Guided noise with physics correction Diffusion schedule coefficients (cosine schedule) Variance term in reverse diffusion
on, Be, 0tt.
Gaussian noise sampled at each diffusion step Bond angle residue between atoms and k Physics energy (bond, angle, vdW, electrostatics, etc.)
Gizk
Ephys
Gh
Physics gradient guidance step t Position-specific conservation distribution at residue Global self-supervised evolutionary fitness score VAE training loss (reconstruction + KL + geometry) Diffusion noise prediction loss
Pronsi
F(Heoevo)
LVAE
Laif
pphys
Physics-informed loss
Lovo
Evolutionary guidance loss
LMI
Mutual- intuualiifformation loss
8*
Trained PepTri parameters
B THREE GUIDANCE DISCUSSIONS
B.1 PHYSICS GUIDANCE: ENFORCING ENERGETIC FEASIBILITY
Imposes molecular mechanics constraints sampled conformations are sterically and energetically plausible.
Ablation Impact (No phys). This ablation causes the largest degradation in binding strength: mean
success rate drops by 31.2% (0.583 - 0.401) and AG weakens (-19.387 - -15.485). Contact-
level accuracy also declines (Contact_Fi) FI: 0.829 - 0.750; DockQ: 0.633 0.621). Why indispensable. Physics guidance anchors generation to biophysical reality; without it, designs drift toward energetically unstable states that are unlikely bind.
B.2 EVOLUTIONARY GUIDANCE: MAINTAINING BIOLOGICAL PLAUSIBILITY
Uses conservation signals to steer designs toward foldable, functionally plausible sequence distribu- tions.
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Table 7: Comparison of models with single guidance across evaluation metries.
Noevo Nomi Nophys Nomi Noevo Nophys
PepTTi
Physics guidance (phys)
Evolutionary guidance (evo)
Mutual information guidance (mi)
All atom
Mean success rate (AG < 0)
0,534
0.363
0.369
0.583
AG (REU)
-185355
-14.912
-15.134
19.3887
DockQ
0.531
0.532
0.539
0.633
Contact
0.803
0.738
0.722
0.829
Local RMSD (A)
1,260
1.427
1,401
1.179
GDT TS
0.745
0.704
0.701
0.747
Sequence Diversity
0,925
0.918
0.912
0.926
Sequence Validity rate
0.256
0.262
0.247
0.273
Struct Diversity
0.423
0.402
0.409
0.436
Consistency
0.797
0.742
0.716
0.799
Sliding-AAR
0.346
0.347
0.343
0.342
TM-score
0.256
0.214
0.208
0.244
Ablation Impact _eoo) Removing evolutionary guidance harms interface and global fold met- rics: Contact_FI drops by 7.2% (0.829 0.7)9), GDT-TS by 5.1% (0.747 - 0.709), and consis- tency decreases (0.799) (0.799- - 0.771). Sequence validity decreases from 0.273 to 0.250.
Why indispensable. Evolutionary constraints curb exploration of physically permissible but bi- ologically irrelevant sequences, improving validity and the reliability of the sequence requence-ostructure >structure mapping.
B.3 MUTUAL INFORMATION (MI) GUIDANCE: COUPLING SEQUENCE AND STRUCTURE
Maximizes MI between sequence and structure representations to promote coherent long-range de- pendencies and stable folding.
Ablation Impact (No_mi). A nuanced trade-off: removing MI slightly improves Lo- cal WMMSDMccar (1.179 + 1.154) and TM-score (0.244 + 0.250), but reduces success rate (0.583 0.545), Contact F1 (0.829 + 0.804), and consistency (0.799 - 0.779).
Why indispensable. MI guidance strengthens global sssidue-residus coherence and contact fidelity. Even if local RMSD tightens marginally without MI, overall stability and reliability suffer.
B.4 ALL-ATOM REPRESENTATION SIDE-CHAIN RESOLUTION FOR PRECISION
Goes beyond backbone constraints capture side-chain packing that determines interface quality. Ablation Impact (PepTrinncktone:: The backbone-onle variant underperforms across contact- sensitive metries (DockQ: 0.633 - 0.578, Contact F1: 0.829 0.760) and consistency (0.799 0.744), highlighting the need for atomistic detail.
Why indispensable. Binding is dictated by side-chain chemistry; atom-level modeling required to evaluate and optimize interface specificity and packing.
B.5
VARIANTS: No SINGLE SIGNAL IS SUFFICIENT
Observation. Physics-only, Evo-only, and MI-only models (Table 7 trail PepTri on nearly all met- rics, especially DockQ, Contact F1, and consistency. For instance, the physics-only variant (No- evo_Nomí) attains Contact F1 0.803 and DockQ 0.531, below PepTrri (0.829 and 0.633). This confirms that no single guidance signal captures the multifaceted requirements of accurate, valid, and stable design.
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B.6 TAKEAWAY
Synergy is non-negotiable for high-performance peptide design. Our ablation study demonstrates that the integration of physical, evolutionary, and information-theorrtic principles paramount. For practitioners, this provides a clear hierarchy for model design:
1. Anchor designs in physical reality. Physics- bassid guidance is the most critical single component for predicting strong binding.
2. Model at atomic resolution. An all-atom representation essential for achieving precise interface quality.
3. Enforce global consistency. Mutual information guidance is key to ensuring sequences reliably fold into their intended structures.
4. Constrain for function. Evolutionary guidance ensures designs are biologically plausible and evolutionarily informed.
While the physics+atom foundation is essential, the full integration of all four components in Pep is required to simultaneously maximize binding affinity, structural accuracy, and biological validity.
C DISCUSSION
Our poysics-guided peptide design model demonstrates a compelling and biologically meaningful trade-off between structural quality and conformational diversity when compared to the state-of-the art PepGLAAD. While achieving substantial gains across most structural and binding quality metrics, approach shows moderate reduction in structural diversity- a result that offers valuable insight into how physics-based constraints influence generative peptide design. These improvements indi- cate that such constraints effectively guide the model toward energetically favorable and structurally realistic peptide conformations.
PepTrri currently models canonical residues and peptides predominantly shorter than 30 aa. The MI estimator (MINE) can be high variance; we mitigate this with EMA baselines and gradient clipping. Reported energies are computational proxies (Rosetta/OpenMMM) and may not perfectly correlate with experimental affinities.
C.1 QUALITY VS. DIVERSITY: A BENEFICIAL TRADE-OFF
The observed trade-off between structural quality and conformational diversity in our physics- guided peptide design model represents beneficial optimization for therapeutic applications. The substantial improvements in binding prediction, structural accuracy, and biological consistency sig- nificantly outweigh the reduction in structural diversity. This finding supports the hypothesis that physics-based constraints serve as valuable inductive biases for peptide design, guiding models to- ward biologically relevant and therapeutically promising conformational space. (Ferruz al., 2022 Dauparas et al. 2022).
Biological Perspective Natural peptides do explore the entirety of conformational space; instead, they preferentially adopt low-energy, functional conformations. Evolutionary pressures se- lect for sequences that fold into stable, functional structures rather than maximizing conformational diversity. For therapeutic peptides, specific binding conformations are often required, making struc- tural quality and binding accuracy more critical than maximizing diversity.
Computational Perspective Physics based constraints serve strong inductive biases, reducing the exploration of unrealistic conformational space. By concentrating sampling efforts on physically plausible structures, the model improves computational efficiency while preserving functional rele- vance. In practice, improvements in structural quality and binding prediction directly translate into better drug design outcomes.
C.2 ROLE OF EVOLUTIONARY GUIDANCE
Our ablation indicates that evolutionary guidance a principal contributor to reliability and realism in PepTri. In Table 5, removing it (No evo) reduces mean success rate (0.583 0.443, -24%
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rel.), weakens stability ( AG -99.887 - -16.001), and degrades contact accuracy and global fold quality (Contact_FI 0.829 + 0.769; GDT.TS 0.747 - 0.709), while slightly affecting diversity. In contrast, physics dominantly shapes stability and success, and MI adds modest but consistent gains in coherence; the full model combines these effects most effectively.
We hypothesize that three mechanisms underlie these gains. First, evolutionary embeddings blended via a learnable gate bias residue substitutions toward plausible regimes, reducing off-manifold pro- posals. Second, residue dependency attention captures residue-residue couplings that sharpen con- tact maps and local packing, improving Contact_Fi and GDT-TS. Third, a weak self-supervised evolutionary fitness regularizer calibrates broad biochemical profiles (e.g., charge, hydropathy), aid- ing foldability without collapsing diversity. A part of the Table I1 also indicates that maximizing evolutionary information benefits the model.
There are trade-offs and limits. No.evo shows slight improvement in Sliding-AAR, suggesting that evolutionary priors may occasionally down-weight rare but compatible chemistries. Benefits can diminish when homologous information is sparse (shallow MSAs), and BLOSUM-like priors may bias novelty if over-wei
C.3 LIMITATIONS AND FUTURE DIRECTIONS
C.3.1 LIMITATIONS
We highlight the main limitations of our current study:
Computational cost. The all-atom representation combined with SE(3) mes- sage passing is compute- and memory-intensive, mmyyics-guidee sampling further increases runtime relative to unguided diffusion.
Sampling assumes a fixed receptor. Induced-fit effects and explicit environment (solvent/water, ions, pH) not modeled, which can limit realism at the interface. The known binding pocket information is required, which limits applicability to discovering novel binding sites or cryptic pockets on target receptors.
Rigid receptor & missing environment.
Length & multi-chain generalization. Training focuses peptide-scale systems; scala- bility to longer proteins and multi-chain assemblies remains untested.
Evaluation coverage. Our docking/biophysies metrics (c.g., AG, DockQ) are computa- tional proxies for binding and fold quality. Prospective experimental validation of binding and function is outside the scope of this work.
C.3.2 OPTIMIZING THE QUALITY-DEE DIVERSITY BALANCE
Future research could investigate strategies to retain quality improvements while recovering some degree of structural diversity:
1. Adaptive Physies Weighting: Dynamically adjust the physics loss weights during training to balance quality and diversity.
2. Multi-Objective Optimization: Simultaneously optimize for both quality metrics and di- versity measures.
3. Ensemble Methods: Combine multiple physics-guided models with varying constraint strengths.
4. Temperature Scaling: Use lemperature--oontolleed sampling to fine-tune the explo- ration-exploitatiion balance.
The success of our tri- tri-guided approach highlights clear pathway for further enhancement, particu- larly in enhancing the biological realism and applicability of the evolutionary guidance component:
Adaptive Evolutionary Guidance: Implement dynamic guidance schedule that explic- itly manages the exploration-exploitaatee trade-off during denoising. By annealing the in- fluence of evolutionary priors, the sampler could initially explore diverse sequence land- scape before converging to evolutionarily fit and conserved regions, potentially increasing the hit rate of functional designs.
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Advanced Force Fields and Solvation Models: Enhance the physical realism of gener- ated structures by integrating more sophisticated force fields, polarizable charge models, and explicit solvation effects. This would provide particularly for designing peptides that function in specific cellular environments or require precise electrostatic interactions.
accurate energetic landscape,
Allosteric and Long-Range Constraints: Extend the physics-informet guidance to model allosteric mechanisms and long-range interactions explicitly. Incorporating constraints de- rived from molecular dynamics elastic network models could capture the dynamic formational changes essential for modulating protein function.
Integration of Experimental Data: Incorporate experimental constraints (e.g.. from NMR spectroscopy, X-ray crystallography, or cryo-EM densities) structural restraints during the diffusion process. This would enable a closed-loop design pipeline where experimental data directly refines and validates generative proposals.
Richer evolutionary priors: Explore integrating MSA- PLM-based conservation sig- nals to capture stronger position-specific constraints, while addressing their data availabil- ity and computational overhead. Developing lightweight cached evolutionary features that remain applicable to short peptides and novel targets is an important direction for future work.
D CORRELATIONS AMONG STRUCTURAL, ENERGETIC, AND SEQUENCE-LEVEL DESCRIPTORS
Metric Correlations (Spearman)
1.00
(MSDICA)
GOT T2 1.05
0.59
160.00
075
Cenac:
0.00 917
5,200
Dock)
0.26
050
Beckfjo-n..t 0.16 0.23
0:760
11
Dock
5.02 0:17
4:1
1..00
charge 0.02 000.28 02..0......00..0.00000000000
025
060.39 39
Instatelly__iiees 05:024
0.00
tHe, length 2.400 000.00
net chargegrgeooooo ok
033 5:166
6.18
0.033
0.
0.220.000
-025
Intti 020.3.00030.. 016.0003
asaay
GBT_1A
CDn 6.39 60550 460000
0.089.44 161
GB9T46-5333 00500.000..000
0.30.450
0.50
0.11
0.000.1880 0.000.20.00
0.07
GDT, (00_54..0 -::25 946 6410 K0..77
9.37
0.0233300
390
0.010
-072
Contact Overap 1507 014 6.10 286.20
0.070
1915 5350 saso 180.033
0.022.13 000
Local MMD Mux 2:23
9.40 0.07 Rapo 450 0..50.0... 15..22.00 0.8 8.25 2.07
3,15 bas 0...o.... 0.20 2.28 300
Contact a
uocal swnp Hean
detacio
Ded
Becign 40
ent dhagee
wet charpe
Ivesiuityy.o crable
graee
eay
Contact Ovenler
cay,
Contast Precisas
Costart Decal
Lecal sunso Mel
Louae AMGI Mar
Figure 2: The paired metric heat map of results from PepTri for relaxed cross-domain experiment.
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The pairwise correlation analysis shown in Fig. reveels distinct patterns among geometric accuracy metrics, energetic scores, and sequence-derived descriptors.
Structural quality metrics. DockQ emerges as the most reliable indicator of structural correct- ness. It exhibits nearly perfect inverse association with C. RMSD (p & -0.98), indicating that lower backbone deviations directly translate to higher DockQ scores. DockQ also correlates strongly with TM-score (p +0.61) and GDT (p +0.65), confirming that models with high DockQ not only achieve accurate local geometry but also preserve global topology. Local RMSD statistics (mean, min, max) show moderate associations with TM-score and GDT (p +0.64), but weaker alignment with DockQ, suggesting that localized backbone distortions contribute to global accuracy without directly determining interface quality. Contact- metrics (precision, recall, F1, overlap) show only weak correlations with DockQ and RMSD (p < 0.32), indicating that recovering the correct set of contacts is insufficient to capture either precise geometry or overall structural fidelity.
Energetics. Rosetta interface energy (AG) shows only a weak positive association with DockQ (p R2 +0.28). However, AG correlates moderately and negatively with RMSD (p ~ -0.24), TM- score (p = -0.33), and GDT (p ~ -0.35). Because more negative AG values represent more favorable binding energies, this pattern suggests that globally accurate structures tend to have some- what better energetic profiles. Nevertheless, the magnitude of these correlations is insufficient for AG to serve as primary ranking criterion.
Sequence-level descriptors. Most sequence-derived properties-includii including net charge, hydropa- thy (GRAVY), isoelectric point, and instability index-show negligible correlations with 3D accu- racy metrics (DockQ, TM-score, GDT, RMSD,, and contact F1). The one consistent exception is sequence length, which exhibits negative correlation with DockQ (p -0.68) and also with AG (p ~ -0.46), indicating that longer sequences tend to produce models with lower DockQ and less favorable interface energies. This effect likely arises because longer peptides form larger binding in- terfaces, which increase conformational flexibility and thereby pose greater sampling challenges. To avoid confounding effects, future analyses should explicitly control for sequence length, for example by computing partial correlations or by stratifying models into length-mater matched bins.
Summary. Together, these results establish DockQ as the most robust single metric for assessing structural quality, validated by its near-perfect correspondence with RMSD and strong agreement with TM-score and GDT TS. While Rosetta AG provides complementary information about ener- getic plausibility, its weak correlation with DockQ limits its utility to secondary ranking. Sequence- level properties generally fail to predict structural quality, with the important exception of sequence length, which systematically influences both DockQ and AG and should be considered as a potential confounder in downstream evaluations.
E PEPTRI POSITIONING VS PRRGLAD/PEEFLLOW//NNMOO
Compared to PepGLAD, which relies sequential decoding with auxiliary geometry losses, and PepFlow, which factorizes sequence and structure into separate flows and applies energy evaluation only after generation, PepTri integrates physics, evolutionary priors, and sequence structure -trruccc-ttruuture cou- pling term directly into the denoising process within joint SE(3)-equivariant latent space. While UniMoMo offers a domain-agnostic abstraction that facilitates cross-domain transfer, our approach instead targets peptide-scale interactions within protein pockets, where in-loop physics and mutual information bring clear benefits. On our benchmarks, under consistent relaxation and success cri- teria, these design choices correlate with lower binding energies and higher success/DockQ scores, though we also observe instances where baseline methods remain competitive on specific metrics.
F CASE STUDY
As shown in Fig. B and Fig. key outcome of our case study is that PepTri does more than reproduce training data it discovers energetically favorable conformations and outperforms base- line models. Because the diffusion process is guided by differentiable physics terms, the model
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Table 8: Design dimensions for peptide co-design (V native; O partial: explicit).
Dimension
GLAD Flow
UniMoMo
PepTri
Joint SF(3) latent
No11IO
In-loop guidance
1ol
Evolutionary prior
Seq struct coupling (MI)
Mask-aware inpainting
Binder-pocket conditioning
Ref Seq AVSAPAATIOKAAAA
Segie TRRST INNGEQILYS
SegICTROO TNIGIQELYS
See: SHONAMT AACWAO
Seat GKQ4S PAGKOKKK
Ennepe
Rosetta 53.813
Freegyy-
Fneege
Fowegy
e) UniiMoMM
Ground
Ref Seq:aPYCVVRSSES
SeG:VIMASYL RIGTO Roserta Energy 44t 455.158
Seq :KYARGVPVEGEE
Seq:ATL VVDAASEE
Seq LTGLL TOPUF Pit
Rosetta Energy: Energy--25.00 22.813
Rosetta Energy -22 700
Roserta Energy: 32 2500
Poosenta Enenge $85
Ref EREQAMETGAQU SHADO
See AAOGSOLBVASSRRY GVIRA Bosslll Energye -6t--------.00
PIVYST EKAMEFSLM ADEM Rosetha Eneegee -11L88
FIRKKNAWWAGE QIAR Rosslli Erergy -00.816
SeguGAvO GAVOO KENQEPL HEGEM Resetta Energy: 87 .944
Rocetta Enengy: 0,961
Figure 3: PepTrr case study. PepTri is able to generate peptide conformations with lower computed physical energies than the experimentally resolved ground-trun -trth structures. This suggests that Pep- Tri's mhysics-guider denoising does not merely replicate training data but discover novel, ener- getically favorable conformations that remain sequence-structue coherent. While energy functions approximations, this trend indicates that the model integrates physical principles in meaningful way. In this experiment, we picked the best AG structures for each target.
consistently generates peptide structures with more favorable (lower) computed energies than the corresponding experimentally resolved conformations.
This observation highlights two important points:
Physics-consistent learning - PepTrri's generated conformations are lower in energy vali- dates that our mhysics-guides denoising not simply curve-fitting observed structures. Instead, the model learns to navigate conformational space in a manner consistent with molecular mechanics, uncovering stable regions that even ground-truth datasets may not fully represent.
Potential functional benefit - From a therapeutic design perspective, lower-energy confor- mations are often correlated with increased in vivo stability. By biasing generation toward such energetically favorable structures, PepTri improves the likelihood that designed pep- tides will remain folded and functional under physiological conditions, which is critical property for drug-like candidates.
Taken together, these results indicate that PepTri embeds physical priors directly into its generative process, yielding designs that not only statistically plausible but also biophysically robust. This positions PepTri as practical framework for peptide drug discovery, where stability and functional relevance equally important.
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Potetred
Ref SER.AVKRRAA CCAGQA
FRUG NANITLLLYS DNTS Rosetta Energy: 53.813
Segu TVVTACCLPK LDKM Rosetta Energy 48.056
MRIPKGATA
KRAKL
VYDE Rosetta Energy 62.289
K516 Roseita Energy: 33,
Rosetta Energy -17.87 -1.688
Ref SeG::PPCC APYCWMRSSSS
Seg:ViHASYLKIGTO Energy:
Seg:Gi Energy
Sing: KGRENNPDWWW
Deg: RSRELDORSSLLFOD RSQUFYDTS
Rosetta Enertyy 613
Rosetta Energy: -33.16
SQQUEERQAREISAQU RMADO
ADOGSO RVVASSIV VIRW
SeQ:AKIVETTLPLPLSEN DPVR Rosetta Energy:
TTg:LLLLLLLL. RDLR
TSVQ. Rosetta Energy: 46.378
Rosetta Energy: 0.981
Rosetta Energy: 56.264
Rosetta Energy: 47.043
Figure 4: Comparative visualization of peptide-prone protein binding across ground truth and design methods. Three representative complexes (PDB IDs: lee5, 4w50, 6qg8) are shown with peptides bound to protein receptor surfaces (gray). (a) Native ground-truth peptides (pink). (b-e) Designed peptides from Pep'Tri (ours), PepGLAD, PepFlow, and UniMoMo, respectively (green). Sequences and Rosetta binding energies are listed beneath each structure. PepTTri consistently produces pep- tides with tighter binding poses and substantially lower (more favorable) Rosetta energies compared to baselines, demonstrating improved sequence-structur co-design and binding affinity.
G RESULTS FOR AG 0( REU) THRESHOLD
Table 9: Comparison of success rates (without/with relaxation) in two thresholds of AG.
Dataset
Method
AG < -E((EUU)
AG < 0( REU)
PepBench
PepGLAD
0.294 0.799
0.459 0.862
PepFlow
0.308 0.742
0.437 0.815
UniMoMosingle
0.339 0.79/
0.532 0.839
PepTTrinccktone
0.254 / 0.784
0.397 / 0,849
Pep'Tri (Ours)
0.404 0.825
0.583 0.885
PepBDB
PepGLAD
0.154 / 0.670
0,441 0.753
PepFlow
0,299 / 0.659
0,467 / 0.725
UniMoMo,ingle
0.302 / 0.737
0.512 0.782
PepTribocktone
0.245 0.724
0.407 0.793
Pep'Tri (Ours)
0.313 0.742
0.530 0.805
In Table PepTrri consistently outperforms all baselines across both datasets, with especially strong gains under the stricter binding threshold (AG < -5). While success rates are naturally higher at the looser threshold (AG < -0), report results AG < -5 as it reflects meaningful binding affinity, making improvements more scientifically relevant and demonstrating the robustness of Pep'Tri under stringent conditions.
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H EFFECT OF RANDOM SEEDS ON PERFORMANCE METRICS
To evaluate the robustness of our protocol, we performed three independent runs using different ran- dom seeds. The resulting performance metrics summarized in Table TO In general, most of the structural quality indicators, including RMSD(Ca), TM-score, GDT -TS, Contact_Fl, Local RMSD, and DockQ exhibited very small standard deviations across the three runs. This indicates that the structural models generated are consistent and largely independent of the random seed. Similarly, amino acid recovery (Sliding-AAR) AAR), sequence diversity, and structural diversity values remained stable across replicates, suggesting that the design tendencies of the protocol are reproducible.
In contrast, the mean success rate showed noticeably higher variability among the three seeds (0.583, 0.559, and 0.563 with standard deviation of ~ 0.013). This difference arises because the success rate defined as thresholded metric, where each model is categorized as either "success" or "failure" according to preset quality cutoffs. Small differences in sampling due to the stochastic nature of the Rosetta search process therefore lead to discrete changes the number of models meeting the success criterion. As a result, the success rate is inherently more sensitive random seeds than continuous measures such as RMSD or DockQ.
Overall, these results demonstrate that while most structural and energetic metrics robust to the choice of random seed, the success rate can fluctuate appreciably. This highlights the importance of (i) performing multiple independent replicates, (ii) reporting averages together with standard devi- ations, and (iii) relying on continuous metrics when possible. Increasing the number of trajectories per seed would further reduce variance and yield more reliable estimate of the true success proba- bility.
Table 10; Performance variance across 3 independent runs of PepTri with different random seeds.
Metrics
runl
run2
run3
std
Mean success rate (AG < 0)
0.583
0.559
0.563
0.012858201
AG (REU) 4
-19.387
-19.365
-19.803
0.246773851
DockQ
0.633
0.640
0.628
0.006027714
Contact_Fi
0.828
0.837
0.821
0.008020806
Local RMSD (Å) 4
1.179
1.176
1.157
0.01 1930353
GDT-TS
0.747
0.746
0.738
0.004932883
Sequence Diversity
0.926
0.918
0.920
0.004163332
Sequence Validity
0.273
0.269
0.262
0.005567764
Struct Diversity
0.436
0.407
0.459
0.026057628
Consistency
0.798
0.793
0.788
0.005000000
Sliding-AAe AAR
0.342
0.357
0.355
0.008144528
T'Mscore
0.224
0.258
0.247
0.017349352
I GUIDANCE SCALE ABLATION STUDY
Ablation on guidanee weights. Table 1T shows that up-weighting any single guidance to À degrades overall balance. Our default tri-guidance (PepTri) attains the strongest profile across bind- ing and structure (mean success 0.583, AG = - 19.39, Dock 0.633, Contact_Fl 0.829, GDT_TS 0. 0.747), while preserving diversity (seq 0.926; struct 0.436) and the highest consistency (0.799). Overweighting evolution 11 slightly raises success (0.587) and improves local RMSD (1.158), but lowers DockQ (0.530) and consistency (0.779); overweighting MI (Am=1) tightens energy ( AG - 19.822 yet reduces DockQ (0.530) and diversity. Overall, extreme single-term guidance (A=1) harms docking and coherence, whereas moderate tri-guidance delivers the best joint gains in binding (success, AG), docking (DockQ), contacts, and fold (GDT_TS) without sacrificing diversity.
J OUT-OF-DISTRIBUTION STRESS TEST
To further assess the robustness and generalization capability of our model, we conducted an out-of- distribution (OOD) stress test. For this experiment, we constructed OOD benchmark by combin-
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Table 11: Guidance-weigge weight ablations where single component is upweighted to 1.0. Higher is better for all metrics except Local JMMSD_Mear and Sliding-AAR (lower is better).
Aphys=1
Aevo=1
AMI=1
A0pmm=i
PepTri
Mean success rate (AG<0)
0.559
0.587
0.564
0.565
0.583
AG (REU)
-18.122
-19.363
119815
-18.238
-19.387
DockQ
0.525
0.530
0.530
0.535
0.633
Contact_Fi
0.801
0.836
0.829
0.819
0.829
Local RMSD (A) +
1,211
1.158
1.197
1.201
1.179
GDT TS
0.745
0.745
0.746
0.736
0.747
Sequence Diversity
0.919
0.924
0.916
0.921
0.926
Sequence Validity
0.256
0.278
0.274
0.276
0.273
Struct Diversity
0.427
0.418
0.401
0.434
0.436
Consistency
0.780
0.779
0.746
0.769
0.799
Sliding-AAR
0.347
0.353
0.344
0,346
0.342
TM-score
0.224
0.255
0.253
0.247
0.244
ing PepBench and PepBDB and removing duplicated receptors to ensure non-overlapping receptor contexts. From PepBDB, specifically selected complexes containing peptides longer than 45 amino acids. We additionally removed 15 complexes that overlapped with our training set, resulting an OOD test set of 114 complexes with substantially longer peptides (46-49 amino acids). The model was retrained using only complexes with peptides shorter than 30 amino acids, allowing us directly evaluate how well it extrapolates peptide lengths not observed during training.
Table 12 summarizes the peptide length statistics for the training and OOD test sets. As expected, the test set exhibits a markedly different length distribution, with a mean nearly four times larger than that of the training data and significantly reduced variance. This deliberate mismatch establishes stringent challenge for sequence and structure generation.
Statistic
Train set
Test set
Complex count
12,823
99
Minimum length
1
46
Maximum length
30
49
Mean length
12.68
46.93
Standard deviation
7.33
0.94
Table 12: Peptide length statistics for the training and out-of-distribution test sets.
We report generation and structural evaluation metrics for the OOD test set in Table [3 after relax- ation. Despite the substantial distribution shift, the model maintains reasonable performance across both sequence-level and structure-level metrics. Notably, the mean success rate (&G 0) remains above 0.6, indicating that majority of generated peptides still achieve favorable binding energies even when extrapolating to much longer sequences. Structural quality metrics (DockQ. Contact FI, GDT TS. and Local RMSD) decrease compared in-distribution performance, expected under this challenging regime, but remain within a meaningful predictive range. Diversity and consistency metrics remain high, suggesting that the model continues generate varied yet coherent peptide candidates under OOD conditions.
K COMPARISON WITH REDIFFUSION-GENERAN 3D PEPTIDE-BINDER STRUCTURES
PepTri is preferable when accuracy and energetics are the main priorities, whereas RFDiffusion offers major advantages in speed and global topology preservation. The two methods therefore complement one another: PepTri as a precision tool for accurate designs, and RFDiffusion as high-throughput generator suitable for broad screening.
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Metric
Pep'ri
Mean success rate (AG 0)
0.624 (#: 0.208)
AG (REU)
45.878 (1.97))
DockQ
0.152 (# 0.026)
Contact FI
0.296 (+ 0.048)
Local RMSD
1.938 (# 0.988)
GDT-TS
0.150 (# 0.037)
Sequence Diversity
0,999
Sequence Validity rate
0.128
Struet Diversity
1.0
Consistency Sliding-AAR
0,999
0.189
Table 13: Performance metrics of the model on the out-of-distribution test set of long peptide receptor complexes.
Table 14: Comparison of 3D peptide-binder structure generation performance metrics between
RFDiffusion and PepTrr (40 samples per target without relaxation). Metric
RFDiffusion
Pep
AG (REU)
-16.479
-19.387
DockQ
0.286
0.633
Contact F1
0.808
0,828
Local RMSD (Å))
0.482
1.179
GDT-TS
0.812
0.749
Struct Diversity
0.401
0,436
Running Time (seconds per complex). +
60.224
5,821
Failed targets (Success rate 0.0)
33
Notes on RFDiffusion usage. Because the RFDiffusion model cannot be retrained for our specific tasks, we directly applied its released checkpoints for inference on our LNR sets. In practice, the method failed on substantial fraction of targets, particularly when attempting to generate very short peptides. We found that RFDiffusion has difficulty producing peptides shorter than amino acids, which further restricts its applicability. For this reason, do not report success rates for RFDiffusion, as such values would be misleading; instead, we focus on metrics that provide a clearer intuition for its performance relative to PepTrr.
In Table 14 PepTri provides more accurate and energetically favorable models, while also being significantly faster. RFDiffusion, despite achieving better global fold preservation and lower local distortions, is slower, inference-only, and limited in handling short peptides. In practice, PepTrri is better suited for accuracy- and efficiency-driven applications, whereas RFDiffusion may remain useful for generating diverse scaffolds or when global topology is prioritized.
L OPENMM FORCE-FIELD SENSITIVITY
Table 15: Comparison of CHARMM36 and Amber14 force fields. Amber14 yields slightly more favorable interface energies and higher success rate, while DockQ, Contact_Fi F1, and RMSD remain nearly unchanged. This shows that performance is consistent across force fields.
Metric
CHARMM36
Amber14
Amb Cha
Mean success rate (AG < 0)
0.842
0.884
+0.042
AG (REU) 4
-35.019
-363644
-1.345
DockQ
0.618
0.610
-0.008
Contact F1
0.845
0.837
-0.008
Local RMSD (A)
1.047
1.101
+0.054
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We evaluated the effect of force-field choice by comparing CHARMM36 and Amber14 under identi- cal protocols (Table Switching from CHARMM36 to Amber14 produced more favorable inter- face energies: the mean success rate increased from 0.842 0.884, and the binding energy decreased from -35.0 to -36.4 REU. At the same time, structure- -ased measures of interface nativeness were essentially unchanged, with DockQ and Contact_Fi differing by only -0.008 each. Local back- bone accuracy also remained stable, with a modest RMSD increase of just 0,054 A. Taken together, these results demonstrate that our conclusions are robust across force fields: Amber14 14 tends to yield slightly stronger energetic scores, while geometry- saase metrics remain consistent, indicating that performance does hinge on the specific choice of force field. Amber14 yields slightly more fa- vorable binding energies because of differences in parameterization. In particular, its torsional and nonbonded terms were tuned to reproduce peptide-protein interaction energies more closely, and its solvation model tends to give stronger stabilization of side chains at interfaces. As result, Amber 4 generally reports more attractive ppptide-protein energies and a higher success rate, even though the underlying structural metrics (DockQ, Contact FI, RMSD) remain nearly unchanged.
M CHOOSING THE MUTUAL-INFFORMATIN OBJECTIVE
We compare a contrastive objective (InfoNCE; (Oord et al., 2018) with our mutual-informationn objective (MI/MINE) under identical training and evaluation settings. Table [6] reports aggregate metrics and their differences MI-InfoNCE. For RMSD and Sliding-AAR, lower is better, for all other metrics, higher is better. The MI objective directly strengthens global dependence between sequence and structure latents the factor that drives binding success, energetic stability, and pose quality in peptides. By contrast, InfoNCE's instance- distriiiddiiiiiniiionn with finite negatives tends to emphasize local contact patterns and is sensitive small batches and false negatives. In particular,
(() Z log.N N LNCE,
(28)
so the bound tightens only slowly as batch size N increases, while false negatives (biophysically related pairs) corrupt the gradients. In peptide space, "negatives" are often related (shared motifs, fold families, local geometry). causing InfoNCE to underestimate [(X; Y) and to over ver-penalize useful similarities. Interestingly, Pep'Tri trained with InfoNCE yields a slightly higher fraction of valid sequences. Overall, for peptide co-design-short flexible chains with tight sequence-structure coupling- the MI objective provides a more suitable inductive bias. By reinforcing cross-modal alignment, it consistently improves binding success, energetic favorability, and pose accuracy.
Table 16: Aggregate comparison of InfoNCE vs. MI (MINE) for cross-domain experiment.
Metric
InfoNCE
MI (MINE)
MI InfoNCCC
Mean success rate (AG < 0)
0.5634
0.5831
+0.0197
AG (REU) 1
-1889115
-19.387
+0.4958
DockQ
0.6171
0.6331
+0.0161
Contact_FI
0.8567
0,8287
-0.0280
Local RMSD (A)
1.1841
1.1798
+.0043
GDT.TS
0.7465
0.7474
+0.0009
Sequence Diversity
0.9199
0.9261
+0.0062
Sequence Validity
0.2891
0.2734
-0.0157
Struct Diversity
0.4651
0.4363
-0.0288
Consistency
0.7794
0.7988
+0.0194
Sliding-AAR
0.3483
0.3428
-0.0055
TM-score
0.2430
0.2446
+0.0015
well established that the Mutual Information Neural Estimator (MINE) exhibits substantial variance during optimization, frequently resulting in unstable conver- gence and performance deterioration in later stages of training. To address these challenges, we employed two complementary stabilization strategies:
Handling Variance MINE
Learning rate decay- progressively reducing the step size helped dampen oscillations and avoid divergence in later iterations.
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Overall/Los/Valldattion
$ta.5t:1.7550
PepTiL
Enc: 9.9820
PepTli_ MINE
Min-9-9810 (epech 639.0)
10.6
PepTri 30,742
Loss Value
End: 9 9.9883
Min. 9:9782
(epoch 062-0)
10.4
10.2
10.0
100
500
600
700
Epachs
Figure 5:
The smoothed validation comparison curve on the Cross-domain experiment between InfoNCE and MINE on validation epochs.
Exponential Moving Average (EMA) smoothing the parameter updates improved robust- ness against variance spikes.
Together, as shown Figure and Figure these techniques not only stabilized training but also accelerated convergence, allowing us reach the early minima observed in our curves and sustain better performance across sequence and structure losses.
N REPRODUCIBILITY
We trained the model using PyTorch 2.6 with CUDA 12.4 on 8 x A100 GPUs.
The code for data processing, model definition, training, testing, evaluation, and trained weights will be made available at: https:: /tt::://gtttt com/ wttp:/ccccaaaaeae..
To compute the interface energy of generated peptides, used PyRosetta. Please refer to the official installation instructions: https: /tw.pyyosetta..rrg/
For structural quality assessment,
we employed DockQ: https://github. com/
walinerlab DDockQ
N.1 HYPERPARAMETERS
Encoder-Decoder Hyperparameters. We trained the encoder-devoder with the AdamW opti- mizer (learning rate 1.0 x 10 10-4) and applied a Reducel.ROnPlaten. scheduler (factor 0.8, patience epochs, mode min, evaluated validation epochs, minimum learning rate 5.0 10-6, max epochs 100).
Model configuration: embedding size 128, hidden size 128, latent size 8, latent channels number of layers 3, channels 14. Regularization: hierarchical KL weight 0.3, latent KL weight 0.5. Loss weighting: coordinate loss ratio 0.5, with subcomponents:
Lx: 1.0,
Lca-xi 1.0
Lob-bond: 1.0,
Lyo-bond: 1.0
Lab-diherra: 0.0,
Lsc-chi: 0.5
Additional settings: relative position encoding disabled; anchor at Co enabled; masking ratio 0.25; additive noise scale 0.1. Stability controls: spectral normalization disabled; 1 residual block used; gradient clipping 1.0; exponential moving average enabled with decay 0.999.
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Overall/Loss/Train
30
InfONCE:
PepTiL PepTri, MINE
End: 10.3832
Min: 5.55 (step 14518)
25
Mean:
PupTi MINE:
Loss Value
20
Start 25
End: 19:6408
5.6070 (stap
12.9416 2.3804
5
Training Steps
Seq/Loss H/Train
PeptrLinfoNCe:
PepTH InfoNCE
End: 1.7637
P
25
Min: 1. 1404 (stap 22040)
Mcan: 2222228222 0.8914
20
StarE 26.2749
Loss Value
End: 2,0624
Min: 1.1433
(stop 15296)
15
5
0
5000
10000
15000
20000
Training Steps
Struct/Loss X/Train
PopTFL InfoNCE:
Start 1.0899
PopTri, InfoNCE
PepTri_
Min:
17634)
Mean: 1.0321 0.3064
2.5
MINE:
Loss Value
2.0
End: 0.8380
Min: 0.2226 (step 7734;
Mcan: 1.0523 0.3087
1.5
1.0
0.0
0
5000
10000
15000
20000
Training
Figure 6: The smoothed validation comparison curve on the Cross-domain experiment between InfoNCE and MINE on training steps.
N.2 DIFFUSION HYPERPARAMETERS
Optimization. We trained using AdamW (learning rate 10-1) with ReduceLRRoP1 P ateau scheduler (factor 0.6, patience 3 epochs, mode = mi n, monitored at validation epochs, minimum learning rate 5.0 x 10-6).
Model configuration. We used the LDMPepDesign backbone with hidden size 128, 3 layers, 100 denoising steps, 32 RBF kemnels (cutoff 3.0), and distance-based RBF encoding (32 channels, cutoff 7.0). Both sequence and positional transformations were modeled via diffusion.
Physics-guided loss. cluded:
Physics loss was enabled with weight 0.15. The physics configuration in-
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Bond constraints: bond length weight 1.2; ideal Ca- Ca distance 3.8Å with tolerance 0.25A.
Angles: bond angle weight 0.8; ideal 109.5 with tolerance 18"
Torsions: torsion weight 0.4; Ramachandran prior weight 0.6.
Non-bonded: van der Waals weight 0.6 (a 3.4A, 0.12 kcal/mol);; electrostatics weight 0.5 with dielectric constant 78.0 and cutoff 10.0A.
Hydrogen bonding:
weight 0.7, distance cutoff 3.4A, angle cutoff 25".
Secondary structure: total weight 0.4 (helix 0.3, sheet 0.3).
Steries: clash prevention weight 1.8, minimum distance 2.1Å, soft clash threshold 2.7A. Solventhydrophobicityy SASA weight 0.3, hydrophobic weight 0.4.
Diffusion regularizer::: smoothness weight 0.25, temporal consistency weight 0.3.
Evolutionarr guidance. Evolutionary priors were incorporated with fitness weight 0.05 and bias weight 0.02, with conservation bias and coevolution enabled.
Information-theoreti regularization. Mutual information (MI) guidance was applied with weight 0.1, and additional coupling to physics with weight 0.05.
OpenMM guidance. Force-field based corrections were included with loss weight 0.01, guidance scale 0.001, and force-guidance scale 0.0001.
aware diffusion. We enabled SE(3)- latent diffusion with enhanced latent dimension 17 (8 global + 9 local). Integration with base latent features was via concatenation. SE(3) regular- ization weights were: rotation 0. translation 0.1, geometric consistency 0.1, scale invariance 0.05, local frame consistency 0.08, invariant feature weight 0.05.
O DATA ANALYSIS
Short peptides-ttpicallly fewer than 30 amino acids-offer notable advantages in efficiency, producibility, and overall experimental success. In this study, we focus on short peptides due to their ease of synthesis, higher yields, and lower error rates compared to longer sequences. Their smaller size also contributes to superior solubility and compatibility with high-purity purification techniques such High-Performance Liquid Chromatography (HPL.C). Moreover, in mass spec- trometry workflows, short peptides exhibit more reliable fragmentation and ionization, leading to improved detection accuracy. These attributes make short peptides particularly well-suited for va- riety of applications, including MHC binding assays, epitope mapping, and peptide-based screening.
While long peptides may be necessary for certain complex immunological applications, their pro- duction and handling present significant technical challenges. Notably, review of FDA-approved peptide drugs shows that the vast majority fall within the short peptide range: drugs like leuprorelin (10 amino acids), ziconotide (25 aa), and difelikefalin (9 aa) are examples of clinically successful therapies with short sequences. Comprehensive databases such as THPdh2 and analyses published in peer-reviewed literature confirm that most approved peptide drugs fall well below the 30-amino- acid threshold Therefore, prioritizing short peptide generation aligns with both technical feasibility and biological relevance.
Following the suggestion from PepGLAD (Kong et al. 2024), we used MMseqs2 to cluster entire dataset, enabling us to split it into training, validation, and test sets. As shown in Figures and there is no duplication between the targets in the training and test sets. More specifically, to assess cross-target generalization,
adopt the large non-redundant (LNR) dataset introduced by Tsaban et al. (T'sbaan et al. 2022) as the test set. The LNR, curated by domain experts, originally comprised 96 protein-peptide complexes; after excluding entries with non-canonical amino acids, 93 complexes remained. These complexes were then clustered together with PDB data by receptor,
Data source: httpa://pepttidese:::/ com
httts:://ww..st sci encedi rect..comm
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using sequence identity threshold of 40%. In PepBDB experiment, applied MMseqs2 clustering and then randomly partitioned the data into training, validation, and test sets based on the resulting clusters. To construct the test set, one protein-peptics complex was randomly chosen from each cluster, ensuring non-redundancy across samples.
Table 17: Peptide statistics of PepBench by train/val/test split
Split Train
Count
Mean
Median
Max
Unique Proteins
Unique Peptides
4157
11.17
10.0
25
2783
3504
Validation
114
13.26
13.0
25
94
111
Test (LNR)
93
10.15
10.0
26
93
93
Table 18:
Peptide statistics PepBDB by train/val/test split
Split
Count
Mean
Median
Max
Unique Proteins
Unique Peptides
Train
7014
13.13
11
30
4394
4349
Validation
323
13.61
13
30
226
248
Test
142
12.58
10
30
142
142
Spill Siasa (Pez8encc))
Protein Lengtn Ditribution
Pestide Longtn Dat-ibution Spl..
Datasel Desmiottion
1206
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3550
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13.00
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400
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Comudeeiie Pepride Length
Lenoth Perreetilles Triin
Peptide AAl Compoed Spitt
bution
Toth
3.0
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Traa
58.
5-2b
Figure 7: The comprehensive analysis examines the PepBench dataset (train from PepBench + vali- dation from PepBench + test from LNR).
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Stoes iPep R030
Protein Lengro Disribution
Pesiide Lemoth stribuution
by Salt
by Selt
Datased Desituutnn
27.03
1236-
6030
1390
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Cumulaitve Popsile longth
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25%
14
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Figure& 8: The comprehensive analysis examines the PepBDB dataset
0.1 CLUSTERING TARGET ANALYSIS USING MMSEQS2
We performed clustering using MMseqs2 based on three types of feature representations: composition-bast based, physicochemical-basee and a combined representation.
The composition-baxtt based representation achieved consistent separation across both datasets, indicat- ing stable performance regardless of peptide length or source. In contrast, the physicochemical- based representation showed greater separation the PepBench dataset, likely due its shorter pep- tide sequences, which emphasize physicochemical diversity. The combined representation yielded the best overall clustering performance, effectively capturing both compositional and physicochem- ical characteristics.
The average separation scores for each dataset further support these findings. For PepBDB, the clustering achieved an average separation of 15.2 as shown in Figure [7] indicating good clustering quality. In Figure g For PepBench, the average separation was 22.8, reflecting excellent clustering quality.
As shown in Figure 9 these results confirm that both datasets exhibit well-separated train/test splits, demonstrating the effectiveness of our feature engineering and clustering strategy.
These results indicate that both datasets exhibit well-separated train/test splits, validating the effec- tiveness of our feature extraction and clustering approach.
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Protein Clustering
PapED8 MMseqs2 Parameters: 90% Identity, 95% Coverage
Peplench Compestion (426g protora)
Feplienes Phydoommmmia 8455
Pepllecc Combieed
prote rol
TEMI
-15
-13
-30
-00
-50
-56
-25
15
(2479 probers)
17479 probaral
(1415 prote
-20
-153
Figure 9: The Pepbench data experiment (up) and PepBDB data experiment (down) with MMseqs2 clustering for targets. Composition clustering: Catches sequences with similar AA recipes. Physic- ochemical clustering: Catches functionally similar sequences. Combined clustering: Catches both types of similarity. Our average separation scores 10.0) across multiple feature representations (composition, physicochemical, combined) show that our dataset splits are well well-separated and min- imize the risk of data leakage.
P TRI-GUIDANCE LATENT DIFFUSION DETAILS
P.1 VAE WITH EQUIVARNTN GRAPH ENCODING
Our autoeneoder constructs a latent representation that functions the interface for the diffusion process, ensuring preservation of geometric consistency via graph-based message passing, The PepTrri encoder employs SE(()-equivariant graph neural networks, which enforce rotational and translational symmetries while encoding both local residue-level interactions and global structural dependencies. This design enables accurate modeling of protein conformations within a symmetry- aware latent space, thereby facilitating downstream generative diffusion.
Graph representation.
first represent peptides as molecular graphs where:
Nodes: Each residue E 40 with features h4 Rd encoding amino acid type and positional information
Edges: Two types of connections:
Sequential edges: Connect adjacent residues (i, i + 1) along the backbone
Spatial edges: Connect residues within cutoff distance = 10Å
Edge features: Distance-based radial basis functions (RBF) encoding 3D geometry
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Inputs and outputs. Given sequence S E (O.....197 and coordinates X E R with mask M E (0, 13" we construct:
g = Evoq U Eqpatial),
(29)
h (0) Embed (S)) + PosEmbed(i),
(30)
= RBF([ X - x2)))2),
(31)
where Ca denotes a-carbon coordinates used for graph construction.
-quivaauivar message passing with enhancements. We employ an enhanced Adaptive Multi-channel EGNN (AMEGNN) that performs K layers of equivariant message passing. The enhancement includes explicit SEn3a-inariaat geometric features beyond basic distances:
Core equivariant operations (preserved from baseline):
m
(F) vin (hg
((-1) h3
(f-1)
(t-1)
eij),
(32)
h (E) h! (e-1) (2)
t/
h;
(t-1) Σ
mij
(9
(33)
jEN(
(C 4 = (t-1) +
(x
(t-1)
Ij
(1-1))
(2)
(m)) (0).
(34)
JEN()
where d, ||=; - -zyl and th IRd R ensures scalar outputs.
SE(3)-invariant enhancements (new in enhanced version):
Bond angles: For each triplet (i.
(I; 2;) (2x - xz)
Sijk = arccos
(35)
||, Iy 2k xz
Dihedral angles: Four-body torsion angles Tijki along the backbone
Global shape descriptors:
Rg
2 =12 (radius of gyration)
(36)
\1, 22, A3 eigenvalues(S) (principal moments)
(37)
A A1
2 (A2 + Xa) (asphericity)
(38)
where S the gyration tensor. These are all SE(3)-invariant.
The enhanced message function incorporates these invariants:
maj
(0) (1) (6-1) (6-1) (e-1) (t-1) (t-1) Sigk : Tight Rg. A, eij)
(39)
SE(3) guarantees.
The architecture maintains strict SE(ivvaquvaariance through:
1. Invariant node features: All h; updates use only SE(3)-invariant inputs (never raw coor- dinates)
2. Equivariant coordinate updates: Position changes use relative vectors (z; mr)) scaled by invariant coefficients
3. Invariant aggregation: Summation neighbors preserves equivariance
4. No global reference frame: All computations are relative or invariant
Theorem: For any rotation E SO(3) and translation R
R. + = n1)(()) (invariance)
(40)
i
RX + +t) R.,,0 (x) (equivariance)
(41)
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Multi-channel processing.
To handle all atoms just Ca), extend to multi-channel coordi-
nates:
Each node processes C' atom channels in parallel
Channel-specifie attention weights wi E [0, indicate atom presence
All operations maintain per-channel SE(3) properties
Latent encoding.
After K message passing layers, the encoder outputs disentangled latents:
(h E xd, (sequence features, invariant),
(42)
2x (x(K R M (structure anchors, equivariant),
(43)
where VAB, and VAE, include reparameterization for variational learning,
Graph-aware training objective. The VAE is trained with geometric consistency:
LVAE Creson + 3 Lxt. + Agoom Lecom + Agraph gerph
(44)
where all loss terms are SE(3)-invariant:
Lreson CE(S, + +|X -- 112
(45)
Cgoom [ ((X)
(46)
Cgraph
Σ (1 +zا12 || 22
(47)
(iEEE
Advantages of SE(3)-enhanced graph representation.
Theoretical guarantees: Provable equivariance under rotations and translations
Richer features: Explicit geometric deseriptors complement learned representations
Physical interpretability: Bond angles, dihedrals have direct structural meaning
Improved generalization: SE(3) symmetry reduces sample complexity
P.2 GAUSSIAN REVERSE TRANSITION
We follow the DDPM formulation with cosine variance schedule and apply explicit physics guidance during sampling on the structural latent only Suuberman-SSiigelggae al. [2024] Meng
et al. 2023). Let E {H,X, X} denote, respectively, the sequence and structure latents at step T}. We use cosine schedule with small offset s = 0.01:
fi cos" ((/T)+ 1t
ā
ft fo
B.
6
at 1 Be.
ā
Forward diffusion (noising). For either latent E (H,X), sample ~ NO, and form
q(p: Po) = W(Vā.Po (1 (1-ā) a))
Equivalently, Pt Vau Po -1- - In practice we apply noising only to positions to be generated using a binary mask M (M = for generated positions),
P: = M (Vor v1 v1 10- (1 (1- (0-M) @ P
and retain the supervision target for the denoiser.
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Noise-prediction training loss. Let éa (HH te.t) (x) be the predicted noises. We use masked mean-squared error losses:
[(ex (x) O Mx l1
Lx
|| 11
(((H - -(H) o M 11
Ln
| 1
where the mask restricts the reduction to generated entries. These losses are combined with evolu- tionary, mutual- nntuallifformation, and physics terms during training.
At sampling time, given a noise predictor Eg and letting
- 0z
co(
a()
va
v1 dr
the Gaussian reverse transition without guidance is
Pt-1 = co(pe c1 co(pi, t)) + 02
2 ~~
(48)
with variance
1 āc-1 1 αq
of
Br (cosine schedule).
Physies guidance on structure. During sampling we incorporate differentiable molecular me- chanics as an energy Ephys (X.). In code, the predicted noise for X is modified as
(H,, X,,t) = εx Ex + VI Vx, Ephyssss(X
(49)
which corresponds to using guidance = - Vx, Epbys inside the denoiser and the update rule equa- tion 48 The structural reverse step is therefore
X,-1 co (x, - e1 HH,, + 022.
An optional weight Aphys can scale the guidance term (set to in our implementation), and with the OpenMM (if enable).
Thus, three signals (physics, evolutionary, mutual information) shape the denoiser &g through the training loss, while the physics contributes explicit gradient term during sampling for the structure latent.
P.3 LATENT INPAINTING DIFFUSION
Strengths. Our latent inpainting diffusion brings several practical advantages:
Targeted controllability:
Noise and supervision are masked (equation 21), so only de- signed residues modified while structural context preserved via clamping (equa- 27). This yields precise, locality-aware edits.
SE(3) consistency: The explicit guidance uses energies over internal geometry (dis- tances/angles), ensuring the correction in equation 23 invariant to global rota- tions/translations and remains compatible with the equivariant backbone.
Physics-aware generation: The composite energy penalizes Ca bond-length/angle vio- lations, steric clashes, and poor non-bonded interactions, leading to fewer post-relaxation artifacts and improved local geometry at sample time.
Stable guidance design: Evolutionary/MI terms act only during training (shape E while sampling applies only physics gradients. This separation avoids double-counting objectives and keeps inference stable.
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Algorithm Latent Inpainting Diffusion
1: procedure LIDPG(S, 2o, M, se {ar
2: Broadcast Mx, Mr using Eq. equation 21
3: Initialize noise: + M @
- M) 3z. Zu. 5 ~~1(0)
4: for tort= T,T 1..... do
5:
Predict noise: & + Eo. (2+,
6: Decode structure: X, decode(zx.))
7:
Physics guidance: G + Aphys Vax Vxx. EXe
8:
Guided noise:
SHH + EH,, εx,, + εx,t v1 /1- Ch. G..
9:
Sample masked noise & ~ (O, 7), optionally & +- M & Reverse update - using Eq. equation 26
11:
Clamp context: 2 + M O 2 + M) о 20
12:
return (Ho, Xo) decode 2x,0)
Noise and context control:
Optional masking of the per-step noise confines stochasticity to redesigned sites, while context clamping guarantees exact preservation the unmasked scaffold over the whole trajectory.
Late-stage refinement: A simple annealing of (t) emphasizes physical validity convergence without over-constraining early exploration.
Efficiency: Guidance is computed on C. (lightweight, numerically stable), with optional OpenMM as gated add-on. Gradients are obtained by differentiating through partial decode, reducing overhead.
Compatibillty: The reverse update (equation 26) supports both stochastic DDPM sam- pling (a, > 0) and deterministic DDIM-style sampling (a, = 0) without changing the architecture.
Interpretabilitty and compositionality: The energy is a transparent sum of physically meaningful terms with tunable weights, allowing principled trade-offs and easy integration additional constraints (motifs, distance restraints).
Limitations.
Heuristic energies: Electrostatics (distance-dependent dielectric), LJ radii, and secondary-structure proxies are coarse; weights wy require tuning and can interact non-linearly.
Training-sampling: Only physics is applied at sampling: evolutionary and MI act implic- itly via 0*, which can drift under strong guidance (Ingraham al. (023).
Hyperparameter sensitivity: Performance depends on Xphys(t), schedule, masking of E, and decode quality; poor settings cause smoothit or instability (Ho et al.) 2020 Dhariwal & Nichol, (022).
Local minima/exploraaion:
Energy guidance can trap samples in local basins; masking or using deterministic sampling reduces diversity (Jumper et al. 2021).
Scalability: Long peptides increase pair/triplet costs (non-bonded terms), stressing mem- ory/time without sparse approximations (Shaw et al. 2021)
P.4 PRYSICS-INFORMEE STRUCTURAL GUIDANCE
Motivation and scope.
Physics guidance addresses specific structural defects observed in purely
data-driven generation:
Local geometry violations: Incorrect bond lengths (e.g., C-N distances 1.5A)
Angular distortions: Unrealistic bond angles (e.g., N-Ca-C deviating from 109")
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Sterie clashes: Atom overlaps violating van der Waals radii
Unphysical conformations: Structures with high internal strain energy
OpenMM: Plays late-stage and selective role, closely aligned with the reviewer's sug- gestion to "apply it only near the end of the trajectory.
We represent peptides in all-atom format, X TR. 4xx11x where L. is the sequence length. This fixed-size representation allocates channels 0-3 for backbone atoms (N, Ca, C, O) and channels 4-13 for sidechain atoms following standard PDB atom ordering for each amino acid type. Residues with fewer than 14 heavy atoms have unused channels padded with the mean position of that residue's existing atoms. An atom validity mask Matom E {0, 1} fx114 tracks real atoms (1) versus padding (0), while separate design mask M E (0, indicates which residues to optimize. This uniform tensor representation enables efficient batched processing across
standard amino acids from glycine (4 atoms, channels 4-1 4-13 padded) to tryptophan (14 atoms, fully populated)-whing preserv- ing complete atomic detail for physics-basee based calculations.
Comprehensive physics energy function. multiple aspects molecular physics:
We define composite energy function that captures
7
Eptys X S;
(50)
where each term addresses specific physical constraints.
1. Bond length constraints. Maintains ideal covalent bond distances:
Frond Σ Kb (1|=
(51)
(K,))
where B is the set of covalent bonds, d' is the ideal bond length for atom types (i,j), and Kg 100
kcal/mol / 2
Typical values:
N-Ca: do 1.46 Á
Ca-C: do 1.53 Å
C-N: d 1.33 A(peptide bond)
C=O: d = 1.23 A(carbonyl)
Bond angle constraints.
Enforces ideal bond angles for triplets of bonded atoms:
Eangle
Σ ka (Sijk
(52)
(E.j,A)EA
where Cizk arccos
[in (M) 21) [2 z, F4 zjj
and Ka 50 kcal/mol/rrad"
Key angles:
N-Ca-C: ç0 111.0 (tetrahedral)
. Ca-C-N: 5 = 116.2
C-N-Ca: Ç" = 121.7 (peptide plane)
3. van der Waals interactions. potential:
Models non-bonded atomic interactions using the Lennard-Jones
12
Eyaw
Σ
4Gzj
Oij
Oij
(53)
rij
rij
1 where Tij = ||: xz (1. eij = Veres (well depth), and oij = (a; + +ay)/2 (collision diameter).
Parameters by atom type:
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Atom
a (A)
(kcal/mol)
1.70
0.110
N
1.55
0.170
1.52
0.210
S
1.80
0.250
4. Electrostatic interactions.
Coulombic interactions between charged residues:
Eelec
Σ
ke
(54)
11-11>1
where 332.0 kcal-A//mol-e, Ey 80 (water dielectric), and charges qi are:
Asp, Glu: q -1
Lys, Arg: q +1
His: +0.5 (at 7)
5. Clash prevention. Hard sphere repulsion to prevent atomic overlaps:
Eelash
Σ
kelash (Felash riz)
(55)
Tay SCrasa
where Telash 0.8 (a; + 02)/2 and hillash = 1000 kcal/mol A
Secondary structure preferences.
Encourages formation of regular secondary structures:
Es = Σ Σ P.(S.) fo(o., v/:)
(56)
(E(o,8)
where (S,) is the propensity of residue S for structure s, and f ab) is Gaussian centered at ideal Ramachandran angles:
o-helix: (d), tb) = (-60, -45)
S-sheet: (Ø, v/) (-120, 120)
7. Hydrogen bonding.
Promotes backbone hydrogen bonds:
Enbond
Σ
-ch (angte(n) fam((r))
(57)
(1.))
where:
(- (r (r-)))
faial (r) exp
Th 2.8A
(58)
20
Sungle cos*(n),
11 (N-H....0
(59)
with G = 2.0 kcal/mol for backbone H-bonds.
invarriiee of physics energy. All energy terms are constructed to be SE(3)-invariant:
Distances:
|| æاyl invariant under rotation and translation
Angles: arccos(vi v2/ ///lvvlll)) invariant
Dihedrals: Four-body angles invariant
No absolute positions: All computations use relative coordinates
Therefore: Fpphys (R.X (RXX t)
Fyphys (X) for any R SO(3), R33
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Gradient computation and application.
During diffusion sampling timestep t:
1. Partial decoding:
at decoder, 8 RLxxxx
(60)
2x
2. Energy evaluation:
Ea
( ( Σ AE S:M
(61)
3. Gradient computation:
0E 0x
V Ephys
(62)
0x 02t
4. Guidance application:
(2)1 /1 āz Aphys
Ephys
(63)
Adaptive weighting and scheduling. The physics guidance weight A can be:
Time-dependent: Aphys (t) Ao (1 t/T) (stronger near end)
Energy-dependent: Aphyx(E) = Xo tanh(E/ (a/E)) Eo) (adaptive to quality)
Component-specifi:: Different weights for each energy term
Computational optimizations. To make physics guidance tractable:
Cutoff distances: Only compute interactions within Feur 10A
Neighbor lists: Pre-compute interaction pairs
Approximations: Use smooth approximations for discontinuous potentials
Gradient clipping: / S T to prevent instabilities
Role and feasibility of using OpenMM with Co-level coordinates. In our implementation, OpenMM is used in a restricted and coarse-grained way: Backbone-only topology and Co coor- dinates. At the (clean) end of each training step, our Amber14 OpenMM wrapper constructs minimal peptide model containing only backbone atoms (N-Ca-C-O per residue, no side chains) from the sequence and assigns standard Amber14 parameters those backbone atoms. The posi- tions we supply come from the model's Ca outputs; for simplicity and efficiency we (i) evaluate the Amber energy/forces on this backhone-only system and (ii) project the resulting forces back onto the Co channel used by the diffusion model.
Single, weak, clamped loss on clean structures. This OpenMM term evaluated once per batch on the clean structure, not at every diffusion timestep, and it is down-weighted by small energy/force scales and an overall loss weight. We also explicitly clamp both energies and force magnitudes to fixed bounds before using them in the loss.
As result, the OpenMM contribution acts as a coarse, low-weight backhone regularizer rather than full high-fidelity all-atom simulation. We do not claim to obtain exact physical forces for detailed side-chain conformations; instead, we use OpenMM only to inject a modest, physically motivated signal that is numerically stable and compatible with Ca-level training setup.
P.5 EVOLUTIONARY SEQUENCE GUIDANCE
Evolutionary guidance leverages billions of years of natural selection encoded in protein sequences to guide peptide generation toward biologically viable designs. This component addresses critical limitation of purely physics- based approaches: while physics ensures structural validity, it doesn't t guarantee biological function evolutionary plausibility.
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Biological motivation. Natural proteins have been optimized through evolution for stability, func- tion, and interaction specificity. By incorporating evolutionary signals, we bias generation toward sequence patterns that have proven successful in nature. This is particularly important for:
Functional motifs: Conserved patterns essential for biological activity
Fold stability: Amino acid preferences that promote proper folding
Interaction interfaces: Residue combinations favorable for binding
BLOSUM- M-baeed evolutionary embeddings. We initialize amino acid representations using the BLOSUM62 substitution matrix, which captures evolutionary relationships between amino acids:
c BL.OSUM BLOSSM, E R220 E (O..... 19}
(64)
where each row represents substitution scores for amino acid These embeddings encode:
Physicochemical similarity (e.g.. hydrophobic: I-L-V)
Functional equivalence (e.g., charged: D-F, K-R)
Conservation patterns (high self-scores for C)
The BLOSUM embeddings are projected into the latent space:
hevo h a MLP (e (L.SSU((s))
(65)
where a is learnable weight balancing evolutionary and structural information.
Self-supervised evolutionary fitness scoring. We predict sequence viability using a self- supervised evolutionary fitness network:
fimess = a (M (Pool()ew))) E [0,
(66)
where a is sigmoid activation. The fitness score estimates the probability that a sequence is evolu- tionarily viable, trained on:
Natural sequences: furget 23 0.8 1.0
Mutated sequences: furget stability
Position-specifie conservation. conservation predictor:
model position-specifee amino acid preferences through
Peens (S.li, h) softmax W cons h, + (pos(t)
(67)
This captures:
Structural constraints: Proline in turns, glycine in tight loops
Hydrophobic core: Preference for L, buried positions
Surface preferences: K, R. D, E in exposed regions
Residue dependency attention modeling. Correlated mutations reveal functional coupling be- tween positions. We capture this through multi-head attention:
heve Wo:
K= K WK,
V hev Wy
(68)
QKT
softmax
(69)
Vdg.
hcoevo hev AV
(70)
The attention weights Aij identify co-evolving position pairs, such as:
Salt bridges: (D/E)~(K/R) pairs
Disulfide bonds: C-C pairs
Hydrophobic clusters: coordinated I/I/V patterns
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Evolutionary energy function. The total evolutionary guidance combines multiple terms:
Frevo (e = W1 fimess + (Peom))) W3 log Penevo
(71)
where:
Jimes:: Overall sequence viability (maximize)
(p Conservation entropy (balance diversity)
Pcoevo: Residue dependency attention consistency score
Gradient computation. During diffusion sampling at timestep t:
Vz. Bev -1 Vx,, + W2 Vz, H Wi Vz, 2n.
log Penevo
(72)
This gradient is computed by:
1. Partially decode zi, St (sequence probabilities)
2. Evaluate evolutionary scores
3. Backpropagate through the self-supervised evolutionary fitness and conservation networks
Ad Advantages of evolutionary guidance.
Biological relevance: Generated sequences resemble natural proteins
Functional bias: Promotes sequences likely to fold and function
Diversity: Conservation entropy prevents convergence single solutions
Interpretability: Attention weights reveal important interactions
P.6 MUTUAL INFORMATION FOR
CONSISTENCY
Theoretical motivation. In natural proteins, sequence fully determines structure (Anfinsen's prin- ciple). This deterministic relationship implies maximal mutual information: T(S;X) (X)
where (X) is the structure entropy. During generation, we must maintain this tight coupling to ensure:
Foldability: Sequence can actually fold into the generated structure
Uniqueness: Structure is the native fold for the sequence
Stability: Sequence-structure pair is thermodynamically favorable
Information-theorrtte foundation. Mutual information quantifies the reduction in uncertainty about one variable given knowledge of another:
X) H(S) H(X) - (S,
(73)
For peptide co-design, we decompose this into latent space:
p(zz, Zo
I [(z z.,) Ep(ny log
(74)
p ((zz)p(
where Zn and z are sequence and structure latents respectively.
MINE estimator. Since direct computation of MI is intractable for continuous high- figh-dimensional variables, we employ the Mutual Information Neural Estimator (MINE):
1 2x) 2 E Eppcn....) (Zo 2. log (og(Ep(en)pca.) (oTen
(75)
where Ta between:
Rd dd IR neural network (statistics network) that learns to distinguish
Joint samples: (Zn, 2x)) ~ p(2 uh. 2x) (matched pairs)
Product samples: 24, p p(zn), ) 2x p(z..) (independent)
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Statistics network architecture.
The MINE statistics network processes sequence-structtue pairs:
(z Zz) = MLP nima (concat on (z.), (z) (Zn @ z=)l)
(76)
where:
Ok: Sequence feature extractor (captures motifs, conservation)
p Structure feature extractor (captures geometry, contacts)
v Cross-modal interaction network
Element-wise product for capturing correlations
Training the MINE estimator.
The statistics network is trained maximize the lower bound:
CMINE
Bx 2i )-Pr (To Z/, zw)]
(77)
Ta -pa, R up [og(( + [T(()n
(78)
where a structure samples shuffled across the batch break sequence-strructuee correspon- dence.
Q DETAILED METRICS CALCULATION
The pipeline calculates five critical metrics for evaluating peptide design quality. Each metric ad- dresses different aspects of structural and functional prediction accuracy. This document provides detailed mathematical formulations and biological significance for each metric.
Q.1
BINDING FREE ENERGY SUCCESS RATE
Q.1.1 DEFNITIOO
The Binding Free Energy Success Rate measures the percentage of predicted peptides that exhibit favorable binding thermodynamics. To evaluate the best performance of the model. We calculate the
Q.1.2
MATHEMATICAL. FORMULATION
N
1
Success Rate
Σ
I(AG, <0)
(79)
N i=1
x is
where T(x:)
(80)
otherwise
The binding free energy AG is calculated using PyRosetta interface energy:
AG Ecomplex
Execeptor
Epuptide
(81)
Q.1.3 CALCULATION PROCESS
1. For each predicted peptide structure, perform energy minimization using PyRosetta Fas- tRelax
2. Calculate interface energy between receptor and peptide chains
3. Determine AG < or AG < -5 (favorable binding following criteria)
4. Compute success across all predictions
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Q.1.4 SIGNIFICANCE IN PEPTIDE DESIGN
Thermodynamic Viability: Ensures predicted peptides can actually bind to target proteins
Drug Development: Critical for therapeutic peptide design
Functional Validation: Confirms structural predictions have biological relevance
Design Optimization: Guides model training toward energetically favorable conforma- tions
To evaluate the best performance of the model, report the median of the minimum AG value for each target, as the median is more robust to outliers than the mean. To capture variability across all test targets, report the standard deviation. In practice, some failed complexes may yield extreme values of REU.
Report:
Q.2 DOCKQ SCORE
Q.2.1 DEFINITION
DockQ is a continuous, bounded measure of docking model quality that combines three CAPRI- style criteria fraction of native contacts (Fna)), interface RMSD (iRMSD), and ligand RMSD criteria-fraction
(LRMSD)-into single score in [0, 1]. Higher is better.
Q.2.2
MATHEMATICAL FORMULATION
DockQ normalizes iRMSD and LRMSD with saturating transforms and averages them with Foat:
1 Fuat 3
DockQ
(82)
1
IRMSD
+
LRMSD
1.5
The constants 1.5 Å (for iRMSD) and 8.5 Á (for LRMSD) follow the original DockQ calibration to CAPRI categories.
Components.
Fnat native contacts recovered]
(83)
# (native contacts]
iRMSD RMSD over interface C., atoms (CAPRI definition),
(84)
LRMSD RMSD of ligand (peptide) C. atoms after superposition on the receptor.
(85)
For each target, we report the mean DockQ value. To capture variability across all test tar- gets, we report the standard deviation. Complexes that failed were assigned score of 0. Backbone models were calculated using Ca settings.
Report:
Q.2.3 CONTACT AND INTERFACE DEFINITIONS
Native contacts (for Fuat) residue pairs (one from each partner) that have any heavy-atom distance < 5.0 in the reference complex. We count a contact as "recovered" if the same residue pair is within 5.0 Á in the prediction.
Interface residues (for iRMSD) follow CAPRI practice: residues whose any heavy atom in the reference complex lies within chosen cutoff (typically 10 A) of any atom in the binding partner. iRMSD is then computed as the RMSD over the interface C₂ atoms after the standard superposition (as in CAPRI).
Q.2.4 S1GNIFICANCE IN PEPTIDE DESIGN
Interface nativeness:
DockQ summarizes how well predicted peptide-protein protein interface matches the reference geometry (contacts and pose).
Comparability: The bounded transforms make iRMSD/LRMSD
commensurate with
Funt. enabling single score.
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Community alignment: DockQ correlates with CAPRI quality classes and is widely used to compare docking methods.
Quality thresholds (commonly used):
DockQ 2 0.80: High quality (near-native)
DockQ 2 0.49: Medium quality
DockQ 2 0.23: Acceptable quality
DockQ < 0.23: Incorrect
Q.3 GLOBAL DISTANCE TEST TOTAL SCORE (GDT-TS)
Q.3.1
DEFINITION
GDT_TS measures the percentage of residues that can be superimposed within multiple distance
thresholds after optimal structural alignment. It is superior to TM-score for short peptides.
Q.3.2
MATHEMATICAL FORMULATION
1 GDT.TS 4
(GDT, + GDT2 + GDT, + GDTs)
(86)
N
GDT N 1=
11r2 T(r,rrr)))) d)
(87)
where:
d 2, are distance thresholds in Angstroms
T represents optimal superposition transformation (Kabsch algorithm)
rel rreeed are reference and predicted coordinates for residue N is the number of residues
Q.3.3 INDIVIDUAL. THRESHOLD INTERPRETATION
GDT; Ultra-high precision (crystallographic quality)
(88)
GDT, High precision (functional accuracy)
(89)
GDT, Good structure (correct fold)
(90)
GDT; Acceptable structure (gross topology)
(91)
Q.3.4
SIGNIFICANCE IN PEPTIDE DESIGN
Length Independence: No normalization bias for short peptides (unlike TM-score)
Multi-scale Assessment: Captures both precision and overall fold quality
Better Discrimination: More sensitive quality assessment for peptides < 50 residues
Functional Relevance: Higher GDT-TS correlates with binding site accuracy
Q.3.5 QUALITY BENCHMARKS FOR PEPTIDES
GDT TS > 0.7: Excellent model (publication-worthy)
GDT TS > 0.5: Good model (functionally relevant)
GDT TS 0.3: Acceptable model (some utility)
GDT TS 0.3: Poor model (requires improvement)
Report: For each target, report the mean of the maximum GDT TS value.
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Q.4
CONTACT FI SCORE
Q.4.1 DEFINITION
Contact_Fi measures the accuracy of predicting inter-residue contacts using the harmonic mean of precision and recall.
Q.5 MATHEMATICAL FORMULATION
2 Precision Recall
Contact_
(92)
Precision + Recall
TP
Precision TP + FP TP
(93)
Recall
(94)
TP FN
where:
TP [(i,j): Oj. 1 Cped
1H
(95)
ij
FP [((,)): Cf 0 Cpre
1H
(96)
FN ((i,5) Of 1 A Cpreed
0H
(97)
Q.5.1
CONTACT MAP DEFINITION
Contacts are defined with sequence separation constraint:
C₁ -I r,ll2 8.0 AA i- 2
(98)
Q.5.2
SIGNIFICANCE IN PEPTIDE DESIGN
Local Interaction Accuracy: Mcasures spatial relationship prediction quality
Functional Prediction: Contacts determine binding specificity and affinity
Binding Site Assessment: Critical for peptide-protels interaction prediction
Design Validation: High Contact_Fi F1 indicates reliable interaction patterns
Q.5.3
PERFORMANCE INTERPRETATION:
Contact Fl 0.6: Excellent contact prediction (highly reliable)
Contact_F1 > 0.5: Good contact accuracy (useful for drug design)
Contact F1 > 0.4: Acceptable prediction (some functional value)
Contact_F] < 0.4: Poor contact accuracy (unreliable for design)
We report the mean with standard deviation of the maximum GDTTS value for each target.
Report:
Q.6
LOCAL RMSD
Q.6.1 DEFINITION
Local RMSD measures regional structural accuracy using sliding window analysis, providing more detailed assessment than global RMSD.
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Q.6.2 MATHEMATICAL FORMULATION
Local_Rae _RMSD
Teu
(+tt))11
(99)
w
N N-w++1
Local_MMSD -ean
Local RMS...MM
(100)
0
where:
w is the window size (5 consecutive residues)
Tw is an optimal superposition transformation for window w
is total number of residues
Window spans residues [i, i + 1]
Q.6.3
ADDITIONAL. STATISTICS
N N-w+1
Hii__MMD_MMM. = min 1=1
Local_Ran R.MSD
(101)
Local_RMSD Max
w++1 max
Local_RMSI
(102)
N N-w+11
Local_RMSD
(LocaL_RMSD,. (i)
Mean)
(103)
N
+1
Q.6.4
SIGNIFICANCE IN PEPTIDE DESIGN
Regional Quality Assessment: Identifies well-predicted vs poorly-predicted regions
Functional Region Analysis: Key binding regions may be accurate despite poor global
structure
Design Optimization: Guides focused improvement of specifie peptide regions
Flexibility Analysis: Shows structural variation along peptide sequence
Q.6.5 QUALITY INTERPRETATION
Local RMSD < 2.0 A: Excellent regional precision
Local _MMDD 3.0 Á: Good regional structure
Local_RMST RMSD < 5.0 Á: Acceptable regional quality
Local RMSD 5.0 Á: Poor regional structure
Report: we report the mean and the standard deviation of the Local RMSD(Meen)) value for each target.
Q.7
Ca CLASH METRICS (PRIMARY GEOMETRY METRIC)
Q.7.1 DEFINITION
We CA Clash in and CA Clash out primary geometry metrics, following the UniMoMo definition. They quantify steric crowding at the Ca level:
CA Clash in: fraction of ligand residues whose Ca atom is too close to another ligand Ca (internal clashes).
CA Clash out: fraction of ligand residues whose Co atom is too close any receptor Co (interface clashes).
A clash is defined by Ca-Ca distance below fixed threshold detsh 3.6574 A.
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Q.7.2 MATHEMATICAL FORMULATION
lig Nig Let {x; Ji=1
be ligand Ca coordinates (in sequence order), and {y)e) ym receptor Ca coordinates.
Internal clashes AAAACllsh_in
We ignore self-pairs and immediate sequence neighbors (i, +
1). A ligand residue is in clash if
k & {i 1, ||x,
lif 112
< detush.
Then
# [clashing ligand residues} x 100 (%).
CA CA.Clash in
Mig
Interface clashes (CA Clash_ooutt
A ligand residue is in clash with the receptor if
fj:
|
lig
1
<
delash-
Then
# (ligand residues clashing with receptor) 100 (%).
CA-Clash_out
Nig iig
Q.7.3 SIGNIFICANCE IN PEPTIDE DESIGN
CA Clash in: detects over-packed or self-colliding peptide backbones.
CA Clash out: measures whether the peptide backbone fits into the binding pocket with- out penetrating the receptor.
Model comparison: these two percentages directly comparable across methods (e.g., UniMoMo vs ours).
Report: we report the mean and standard deviation of CA.Clash.in and CA.Clash.ou across all designs for each target.
Q.8 BACKBONE BOND LENGTH OUTLIERS
Q.8.1 DEFINITION
BondLeegthh Outlier fractions measure how often backbone bonds (N-CA, CA-C, C-O, C-N) deviate from ideal lengths by more than a threshold T.
For each bond k:
4 >
A
ldk
iddall Ck
0,
otherwise
Outlier.Frac (T)
Σ
(T)
Te {0.10, 0.20, 0.50) Á.
k
M
We report these fractions globally and for the ligand backbone only, as mean # std across designs.
Q.9 SEQUENCE DIVERSITY
Q.9.1 MATHEMATICAL FORMULATION
BLOSUM62(S; S,)
Similarity,; BI. (BLOSUM62(S, BLOSUM62(SJ, ST) S,)
(104)
Distance;j = Similarity,;
(105)
Unique Clusters
Sequence Diversity =
(threshold 00.4)
(106)
N
where, N is the number of generated complexes.
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Q.9.2 SIGNIFICANCE
Measures amino acid sequence space exploration. Higher diversity indicates better functional ex- ploration and prevents mode collapse.
Q.9.3 INTERPRETATION
0.6 Excellent exploration
(107)
0.4 Good diversity
(108)
< 0.3 Mode collapse concern
(109)
Q.10
SEQUENCE VALIDITY RATE
Given N generated sequences and assay pH (default pf 7.4),
Valid count
[eiCCaageeK, A GRAVY_OK, A Instability.KK, A PL.OK.]
Valid count
Valid rate
N
The four criteria are
NetChargeOK,
> netecarge, (plt) [-2, 4,, GRAVY > GRAVY, E [-1.0, 0.5).
Instability OKK; = ciuubblity_indess < 40,
pl OK, = |PL, - -pHH 0.5.
Q.11 STRUCTURAL DIVERSITY
Q.11.1 MATHEMATICAL FORMULATION
RMSD
(8)
(110)
L
Unique Structure Clusters
Structural Diversity
(threshold 4.0 Å)
(111)
N
(e)
where x
are Ca coordinates of residue & in structure i.
Q.11.2 SIGNIFICANCE
Quantifies conformational space coverage. Critical for binding versatility and allosteric mecha- nisms.
Q.11.3 INTERPRETATION
0.5 Excellent conformational exploration
(112)
0.3 Good struetural variation
(113)
0.2 Limited conformational coverage
(114)
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Q.12 CONSISTENCY
Q.12.1
MATHEMATICAL FORMULATION
Given sequence clusters Csey and structural clusters Cstmat:
T
[ : Sog [k] i Stnucr [k] = )}
(115)
T
Eny)
(116)
Eij
X²
Consistency
(117)
N x (min(Nesg) Tlstract)
where Fij are expected frequencies under independence assumption.
Q.12.2 SIGNIFICANCE
Measures correlation between sequence and structural clustering using Cramér's V. Tests biological constraint preservation (similar sequences - similar structures).
Q.13 TM-SCORE
TM-score max A
(118)
Leef (i.))E.A 1 ||| [1(pp-r)())) 2
do do(Lrot))
do(Trer) = max(0.5, 1.24 (Ireet - 15) 1.8)
(119)
where:
ref predd are C. coordinates of the reference and predicted peptides. :
A is residue-residue alignment (index pairs (i.j)): we choose the alignment that maxi- mizes TM-score.
T is the optimal rigid transform via Kabsch on aligned C. pairs.
Lief is the reference sequence length; do (oree) is the length-dependent scale (with 0.5 floor for very short peptides).
Q.13.1 DISCUSSION: TM-SCORE IN PEPTIDE DESIGN CONTEXT
TM-score is a global fold-similarity metric for full proteins, and breaks down for short, flexible peptides and interface design. It doesn't reflect what actually matters in peptide design (pose at the binding site, contacts, and energeties). TM-score isn' 't great for ranking peptide binders, but we still squeeze value out of it in a few very specific, low-stakes roles.
Q.14 SLIDING-AAR (AMINO ACID RECOVERY)
Q.14.1 DEFINITION
Sliding-AAR measures the maximum sequence identity between generated and reference peptides across all possible alignments, accounting for potential positional shifts in the generated sequence.
Q.15
MATHEMATICAL FORMULATION
Sliding-AAR maxk k E K (Sliding-AAAe AARe ((()) cand: Spot)
(120)
Sliding-AAR (1, Sz)
1
Σ
[(S Sz(i))
(121)
1=1
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where:
K = {-(Lrer - 1),..,, O,... Land 1}
(122)
((kk) cand
pad
if h or 1: 2 Leand
(123)
Seand k: otherwise
Q.15.1
ALIGNMENT PROCESS
The algorithm evaluates all possible alignments:
Alignments {S (k: + [aar] 0 Leant + Lvef - 2}
(124)
where the candidate sequence is padded with (Irer 1) special tokens each side.
Q.15.2 DISCUSSION: SLIDING-AAR IN PEPTIDE DESIGN CONTEXT
Sliding-AAR poorly suits peptide design because peptides require exact positioning for function. Their short length (5-30 residues) means alignment flexibility counterproductive. The metric's fundamental flaw is the sequence-structuue disconnect: high Sliding-AAR doesn't ensure functional similarity. Two peptides with 80% sliding similarity may have entirely different structures and no binding activity. This creates dangerous false positives where designed peptides score well but fail functionally. Structure-based metrics (Contact F1, Local RMSD, binding energy) directly assess molccular recognition requirements and better predict function. Sliding-AAr -AR should remain supplementary, useful only for motif identification or initial diversity screening, never as primary validation metric for functional peptide design.
shifts often destroy binding activity, making
49


Reviews:
[{"review_id": "LjNiQriCGZ", "reviewer": "Reviewer_4LzT", "summary": "The paper introduces PepTri, a framework for peptide co-design that can generate both the sequence and the full-atom 3D structure at the same time. It works in an SE(3)-equivariant latent space and adds three kinds of guidance during the denoising process. The first is physics-based, using differentiable terms like bond lengths, angles, clashes, and van der Waals forces to keep the structure realistic. The second is evolutionary, adding BLOSUM-style priors and co-variation patterns to make the sequences biologically reasonable. The third is mutual-information guidance, which helps align the sequence and structure representations using a MINE-style objective. On peptide–protein benchmarks such as PepBench, LNR, and PepBDB, PepTri achieves state-of-the-art performance. The ablation studies show that each type of guidance clearly helps, for example increasing the success rate (Delta G < 0) to 0.583 and improving stability scores. Overall, the paper focuses on combining physical, evolutionary, and statistical signals directly in the denoising process rather than adding them after generation.", "questions": "Receptor awareness in physics guidance:\n In Fig. 1 you mention that the guidance is intra-peptide. Do you also include receptor–peptide vdW or clash terms during sampling? If not, could you try adding an interface-aware term, even a simple one, and see if DockQ or Contact-F1 improve without reducing diversity?\n\n\nAblation on evolutionary priors:\n Besides the BLOSUM-like embedding, how would performance change if you added conservation information from MSA or PLM-based scores? A small controlled comparison could help show where the improvements are actually coming from.\n\n\nOOD stress tests:\n Could you include some harder out-of-distribution cases, like longer peptides, flexible or induced-fit receptors, and low-homology targets? Showing success rates by interface size or flexibility would make the generalization results more convincing.\n\n\nEnergy function design:\n How is the energy function defined, and why was it designed that way? Could leaving out other physical terms (like electrostatics or solvation) be affecting the final performance?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper presents a fresh and well-motivated idea by combining three kinds of guidance to jointly control both the structure and sequence during diffusion. This tri-guidance setup goes beyond traditional structure-focused pipelines and post-generation checks, offering a more integrated way to ensure the generated peptides are physically and biologically consistent. The use of mutual information to explicitly link sequence and structure is conceptually clear and feels natural for this type of task. Overall, the framework is well designed: it uses an SE(3)-equivariant encoder–decoder with latent diffusion, and the guidance is smoothly applied at every denoising step. The experiments are thorough, with detailed ablations showing how each component contributes to improvements across metrics like Delta G, DockQ, and Contact-F1. The paper is also clearly written, with figures that make the flow of the three guidance types easy to understand. Results on benchmarks such as PepBench, LNR, and PepBDB show consistent and meaningful gains—for example, the success rate with Delta G < 0 rises from about 0.37–0.55 in simpler versions to 0.58 in the full model—demonstrating strong potential for real-world peptide design where both physical realism and biological relevance matter.", "weaknesses": "Physics term scope and calibration:\nThe paper combines bond, angle, clash, and van der Waals terms into a differentiable physical energy on the peptide side, but it’s not clear how receptor interactions are handled during guidance. The figure suggests the guidance might only cover intra-peptide terms. This could mean the model under-penalizes interface clashes when sampling. It would help to show how sensitive the method is to receptor proximity and whether adding receptor-aware terms changes the results.\n\nMI estimator stability:\nMINE-based objectives can be unstable and depend a lot on the critic’s capacity. The paper doesn’t explain how the MI head is regularized or early-stopped, and it doesn’t mention any failure cases like MI collapse. It would be useful to include some diagnostics—like critic loss curves or MI estimates over training—and maybe test an alternative objective such as InfoNCE to check stability.\n\nGeneralization claims:\nThe paper claims the method generalizes across datasets like PepBench and LNR, but it doesn’t really test out-of-distribution cases such as unseen folds, receptors with low homology, or longer peptides. A breakdown by interface size or flexibility would make the generalization story more convincing.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "W5R52EVbVO", "reviewer": "Reviewer_55wn", "summary": "This paper proposes PepTri, a latent diffusion framework based on a VAE backbone for peptide generation guided by multiple co-design-related priors. Specifically, the model introduces three types of guidance, including physics, evolutionary, and mutual-information-based guidance, to improve sample validity and diversity. Experimental results on peptide datasets demonstrate promising performance, suggesting that the model can generate structures with better physical plausibility compared to prior works.", "questions": "1. The term $L_{phys}$ is used both as a training objective and as a guidance signal at inference time. Why is only this loss term used in both phases? How about the other loss terms?\n\n2. How strong is the reconstruction capability of the VAE itself? Does it constrain the generation quality?\n\n3. Generally, why are the loss terms in Section 3.2 incorporated into the latent diffusion training rather than during the VAE training phase? What is the design motivation for this choice?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "1. This paper focuses on an important problem, namely the integration of multiple guidance or prior knowledge into a latent diffusion framework, which is essential for improving controllability and enhancing domain-specific generation quality.\n2. Experimental results indicate that the proposed model achieves reasonable improvements in generation quality over baseline methods.", "weaknesses": "1. The overall method remains somewhat vague. Beyond the VAE backbone, the backbone model design of the latent diffusion model is not sufficiently described. Besides, Section 3.2 suffers from inconsistent notation, where the superscript $t$ for time is retained in Section 3.2.1 but omitted in Sections 3.2.2 and 3.2.3. It is unclear which loss terms are time-dependent.\n2. The ablation study is insufficient. The paper considers three types of guidance, and the current ablation only evaluates the overall contribution of each type. However, each guidance term itself contains multiple components, and the paper does not analyze how the weights among these internal components are balanced or influence performance.\n3. The motivation is not clearly discussed. The introduction, methodology section, and the main figure (Figure 1) do not clearly explain why choose these three specific types of guidance. The rationale behind this combination should be better justified.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "t1YPhsE08J", "reviewer": "Reviewer_eX3Z", "summary": "This paper proposed PepTri, a latent diffusion model for peptide sequence-structure codesign. This model has two decoupled autoencoders, one for sequence and one for structure. Physical guidence based on OpenMM force field is used to constrain structure sampling by backpropagating the energy to the latent space through 3D coordinates. BLOSUM-like constraints are applied to sequence sampling as the evolutionary constraint. Since the model has two autoencoders, a mutual information regularization is added to align sequence and structure representations. The model shows good performance on benchmarks.", "questions": "- Why did the authors use two separate auto-encoders for sequences and structures instead of a unified auto-encoder? What is the reason for not using a unified auto-encoder?\n- What data are the global fitness predictor trained on? How did the author define \"global fitness\"?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The structural and evolutionary guidances are well-motivated. Since the size of peptide training set is small, it's important to use physical and evolutionary knowledge to constrain the sampling. In addition, previous works applied constraints directly in 3D space, whereas this work formulated a latent space guidance, which is novel.\n- The model is evaluated across diverse datasets on metrics such as binding score and demonstrates performance gains consistently.\n- Ablation study supports justified the three main components of this model.", "weaknesses": "- The main novelty of this work is more in putting the components together rather than core algorithm contribution. Specifically, both physical and structural constraints have been explored in previous diffusion models for proteins/peptides.\n- Evaluation metrics are outdated. Only Rosetta scores are computed which is however noisy and sensitive to minor perturbation. A more reliable evaluation method that has  been used more recently is using AlphaFold to predict the complex structure and compare the RMSD between generation and AlphaFold prediction.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "BvnEkBr9PY", "reviewer": "Reviewer_wyh8", "summary": "This paper introduces PepTri, a novel diffusion-based framework for joint sequence-structure peptide design. The core innovation is the integration of three complementary guidance signals during the latent diffusion process: (1) physics-informed guidance via differentiable molecular mechanics (OpenMM/Amber14) to ensure structural stability; (2) evolutionary guidance using BLOSUM-inspired embeddings and co-evolution attention to bias sequences toward biologically plausible motifs; and (3) mutual information (MI) guidance to explicitly maximize sequence-structure coherence. The model operates in a compact, SE(3)-equivariant latent space, enabling efficient and geometrically consistent generation. Extensive evaluations on cross-domain (PepBench→LNR) and in-domain (PepBDB) benchmarks demonstrate that PepTri achieves state-of-the-art performance in binding affinity, structural accuracy, and design diversity, outperforming strong baselines like PepGLAD, PepFlow, and UniMoMo.", "questions": "1. SE(3)-GNN Architecture: Is the SE(3)-equivariant GNN a novel architecture or an adaptation of existing work? Please provide citations and architectural details in the main text.\n\n2. Physics Guidance Mechanics: How are bond lengths and angles enforced during generation when the peptide sequence (and thus 2D topology) is evolving?\n\n3. Energy Function Redundancy: Why are both a composite energy function and OpenMM force field used? What does each contribute that the other doesn't? They looks very similar to me.\n\n4. Evolutionary Training Details: What data is used to train the evolutionary fitness scorer? How is \"stability\" defined for mutated peptides? How is the conservation predictor trained?\n\n5. Co-evolution MHA: How does the co-evolution multi-head attention differ from standard MHA? What specific evolutionary signals does it capture?\n\n6. Evaluation Metrics: Why are direct structural validity metrics (bond lengths, angles, clashes) not reported?\n\n7. Ablation Study Placement: Why are the critical ablation studies only in the appendix rather than the main text?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "Originality: The tri-guidance mechanism represents a novel and creative integration of physical, evolutionary, and information-theoretic principles within a unified diffusion framework.\n\nComprehensive Evaluation: Extensive benchmarking across multiple datasets (PepBench, LNR, PepBDB) using established metrics (DockQ, ΔG, Contact_F1, GDT_TS) demonstrates clear superiority over strong baselines.\n\nSignificant Contribution: Addresses a critical gap in peptide design by ensuring simultaneous physical stability, evolutionary plausibility, and sequence-structure coherence, with clear implications for therapeutic development.", "weaknesses": "Unclear Implementation Details: The technical details supporting a full understanding of this paper are not enough in the main text. Key components like the SE(3)-GNN architecture and all-atom representation are mentioned but not properly described in the main text, with no citations to established architectures. Also, how bond energies are calculated when 2D molecular topology changes during generation, and the relationship between composite energy and OpenMM force field appears redundant without justification. The evolutionary guidance components lack details on training data sources, stability definitions for mutated peptides, and the distinction between co-evolution MHA and standard MHA.\n\nEvaluation Gaps: Despite physics guidance aiming to improve structural validity, no direct evaluation of bond lengths, angles, or clashes is provided to validate these specific improvements. The sequence-structure consistency results show worse performance compared to baselines, which cannot support that the mutual information guidance explicitly maximizes sequence-structure coherence\n\nSuboptimal Organization: Critical ablation studies are relegated to the appendix rather than being in the main text, where they would better support the claims.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)