Joint Design of Protein Surface and Backbone Using a Diffusion Bridge Model
Authors: Guanlue Li
Xufeng Zhao
Fang Wu
Sören Laue
Venue: NeurIPS 2025 poster ()
Keywords: Diffusion Bridge model
Molecular Surfaces
Protein Design
Primary area: machine_learning_for_sciences

Abstract: Protein-protein interactions (PPIs) are governed by surface complementarity and hydrophobic interactions at protein interfaces. However, designing diverse and physically realistic protein structure and surfaces that precisely complement target receptors remains a significant challenge in computational protein design. In this work, we introduce PepBridge, a novel framework for the joint design of protein surface and structure that seamlessly integrates receptor surface geometry and biochemical properties. Starting with a receptor surface represented as a 3D point cloud, PepBridge generates complete protein structures through a multi-step process. First, it employs denoising diffusion bridge models (DDBMs) to map receptor surfaces to ligand surfaces. Next, a multi-model diffusion model predicts the corresponding structure, while Shape-Frame Matching Networks ensure alignment between surface geometry and backbone architecture. This integrated approach facilitates surface complementarity, conformational stability, and chemical feasibility. Extensive validation across diverse protein design scenarios demonstrates PepBridge's efficacy in generating structurally viable proteins, representing a significant advancement in the joint design of top-down protein structure.

Joint Design of Protein Surface and Structure Using a Diffusion Bridge Model
Guanlue Li University of Hamburg
Xufeng Zhao University of Hamburg
Hamburg. Germany guanlue.. li Liiuni--ie ceani-hammurg.com
Hamburg, Germany
xufeng. manolunnihambbuggg.o com
Fang Wu* Stanford University Stanford, CA, USA fangvu97@stanf edu
Sören Laue
University of Hamburg
Hamburg, Germany
soeren. laue@uni caamburammuug...o de
Abstract
Protein Protein-protein interactions (PPIs) are governed by surface complementarity and hydrophobic interactions at protein interfaces. However, designing diverse and physically realistic protein structure and surfaces that precisely complement tar- get receptors remains significant challenge in computational protein design. In this work, we introduce PepBridge, novel framework for the joint design of protein surface and structure that seamlessly integrates receptor surface geometry and biochemical properties. Starting with receptor surface represented as 3D point cloud, PepBridge generates complete protein structures through multi-step process. First, it employs denoising diffusion bridge models (DDBMs) to map ceptor surfaces to ligand surfaces. Next, a multi-mode. diffusion model predicts the corresponding structure, while Shape-Framt Frame Matching Networks ensure alignment between surface geometry and backbone architecture. This integrated approach facilitates surface complementarity. conformational stability, and chemical feasi- bility. Extensive validation across diverse protein design scenarios demonstrates PepBridge's 's efficacy in generating structurally viable proteins, representing a sig- nificant advancement in the joint design of top-down protein structure. The code can be found at http:://tthbbb.ommgaaaaeel///ppp
Introduction
Proteins are fundamental biological macromolecules that perform their functions through intricate interactions with other biomolecules, particularly through protein-protein protein interactions (PPIs) (22). PPIs are primarily determined by surface complementarity and hydrophobic interactions at the interface regions, which facilitate specific and stable binding [36]. Understanding and designing PPIs is central challenge in computational protein design, which seeks predict sequences, generate structures, and design proteins with tailored properties while adhering to biochemical and geometric constraints [9]. These constraints are crucial for engineering proteins with desired binding characteristics and functional properties. Recent studies underscore that a protein's 's surface features, such as geometry and biochemical properties, have a more direct influence on its biological function This insight is particularly relevant PPIs, where interacting protein complexes exhibit geometric complementarity in the 3D space.
than its sequence or backbone structure alone (20 53
Corresponniig authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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The interacting surfaces conform to their ligands' shapes and chemical properties, highlighting the importance of surface characteristics in protein design.
Protein design methods can generally be categorized into three approaches: sequence-based meth- ods
55 58 and sequence-structure co-design ap- methods focus on isolated aspects, which simplifies modeling but limits their ability explore interactions interface regions. Co-design approaches aim to holistically model both sequence and structure to capture their interdependence. yet they still struggle to accurately represent interface interactions. Providing the crucial role of protein surface analysis in predicting interaction sites and inferring PPIs [35 46 47]. more efforts have considered comprising surface geometry and biochemical properties for protein discovery in parallel. For instance, Gainza et al. [14] built a surface-centric de novo design framework to capture the physical and chemical determinants of molecular recognition for new protein binders. Subsequent works [3 extract surface fingerprints from protein-ligand complexes for innovative incorporates surface point clouds augmented with biochemical properties for protein engineering. Despite these advancements, existing methodologies face several limitations: (i) Limited ability to generate diverse yet receptor-compatible surface configurations. (ii) Lack of explicit modeling to establish robust correspondences between molecular shapes and backbone structures. (iii) Absence of a comprehensive strategy for top-down protein design, where coherent protein structures are generated based on receptor surface features.
15
30
49
structure-based methods (50
proaches 21 25
Sequence-based and structure-
drug-controlled cell-based therapies. Another line of works 44
48
To address these challenges, we introduce PepBridge. a novel framework for top-down protein design based on a multi-modal diffusion approach [7 4144 As shown in Figure [ given receptor represented as a surface point cloud and structure annotated with geometric and biochemical properties, PepBridge generates complete protein structure, including both the upper surface and the underlying residue structure. Notably, PepBridge leverages denoising diffusion bridge models (DDBMs) 62 633, which interpolate between paired distributions, enabling the direct mapping of receptor surfaces to ligand surfaces while preserving physical and biochemical relevance. For structure generation, PepBridge employs an SEE(3 diffusion model for backbone prediction, torus diffusion model for torsion angle generation, and a logit-normal diffusion model for residue identity prediction. To ensure alignment and consistency, introduce Shape-Fram Frame Matching Network that learns correspondences between generated ligand surfaces and backbone structures.
Our main contributions are as follows:
Unified Protein Design Framework: We present PepBridge, a novel framework that jointly designs protein surfaces and structures by integrating receptor surface geometry and bio- chemical cooperties-tackling core challenges in top-down protein design.
Methodological Advances:
PepBridge incorporates DDBMs generate receptor-come compatible ligand surfaces and multi- modal diffusion model for peptide structure prediction. Addi- tionally, a Shape-Framt Matching Network introduced to align generated surfaces and backhone structures, improving geometric and biochemical consistency.
We demonstrate the efficacy of Pep- Bridge through extensive validation on peptide design tasks, showcasing its ability to generate diverse, structurally viable proteins with receptor-specific binding characteristics.
Effective Validation:
Figure 1: Top-down view of the excettr--epticee complex.
2 Preliminaries and Background
Diffusion Models. Let go (2n) be a d-dimensional data distribution. The forward diffusion pro- cess [17 40 (2) is defined by the following stochastic differential equation (SDE) with initial condition 2g ~ qu:
da; f())x,dl g({)dw,,
(1)
where t [0. f(t) and g(t) are scalar-valus valued drift and diffusion coefficients. respectively. Wi 2d is standard Wiener process. go usually conforms random Gaussian noise. The

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(8)
(b)
(C)
Peptióe surface distriition
datritrion
Surface-Framee Matching
Forward SDE
Networks
receptar
peptide
Cr
Frame
Surface
Time-reversed SDE
Figure 2: Illustration of the PepBridge architecture for joint surface- peptide generation. (a) The model processes receptor-ligan pairs through a top-down structure comprising molccular surface and frame components. (b) Two specialized diffusion models employed simultancously. A diffusion bridge model leverages the receptor surface as the starting point to generate peptide surfaces. An SE(3) diffusion model shoulders the responsibility of frame construction, which incorporates translation and torsion angles. (c) surface-frame matching network facilitates the interaction between creased structures, while multi-me modal diffusion reconstructs the complete peptide structure.
corresponding reverse-time SDE for sampling from go (xo) is: dæ, [f(t) V log qu (x::))dtt + g(t)
(2)
where W, denotes the reverse-time Wiener process and Va, a, log q (x:) is the score function of the marginal density Qt-
Diffusion Bridge Models. Traditional diffusion models assume a Gaussian prior as the starting point for the generative process. However, in many practical scenarios, including protein design, the initial state may not follow a random Gaussian distribution. requiring a more flexible approach. To address this limitation, diffusion bridge models 7
33 provide a framework for modeling structured data distributions by matching the conditional score of tractable bridge distribution. These models enable transport between distributions through either a reverse SDE or a probability flow ordinary differential equation (ODE). For diffusion bridges with initial condition 2g go Pdata and terminal condition æт y. the forward process is:
dæ, f() (t)) + g (t) log q y| + g(t)dwr,
(3)
where y is drawn from a prior distribution rather than Gaussian noise. The corresponding reverse SDE is:
dæ, = [f(()); - (() log g æτ = y) Va. log (2T = ylæ:))), + g(t)d&,
(4)
where Va, logg(x:(ETT y) represents the bridge score function and @ is the reverse-time Wiener process.
Method
3.1 Problem Statement
The protein-peptide complex pair can be represented C PUP. where P and R denote the peptide and receptor, respectively. For both the peptide and the receptor, we build the top-down structural representation 2/ U B, where Ut = {u,NN, N,, denotes the spatial surface point cloud and B [b; Ne denotes the residue-level structure. The bottom structure B is composed of amino acid residues, where each residue b, characterized by its backbone frame, residue type, and side-chain dihedral angles [12], as illustrated in Figure [ The goal of target-aware peptide generation to learn probabilistic model that captures the distribution over peptide top-down structures, RP)) conditioned on the receptor structural and biochemical reference.

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3.2 Surface Diffusion Bridge
Peptides typically fold into complementary shapes when binding to their receptors 29 The geo- metric and biochemical properties of the receptor's s binding site impose natural constraints on the conformational space compatible peptide structures. For the sake of leveraging this relationship. we develop tailored diffusion bridge model 63 that treats the receptor surface UR as prior distribution to generate energetically favorable peptide conformations with complementary binding surfaces Up.
Surface Representation. Firstly, we devise pipeline for molecular surface processing and point cloud extraction. Starting with protein structure in PDB format, we use PyMol [10] to generate solvent-accessible surface representations. The probe molecular surface approximates both the Dolvent-Accessibee Surface Area (SASA) and Solvent Excluded Surface (SES). The resulting point cloud consists of surface points uy each annotated with 3D spatial coordinates and physicochemical
features, including hydrophobicity and hydrogen bonding potential [3 31
Diffusion Bridge via h-traasform. The surfaces of receptor and peptide exhibit close interactions, with their distributions pp and pR naturally forming pairs. We model their surface fit by reconstructing stochastic trajectory between observed positions. Specifically; let (Mo,Ur) denote pair of surface datasets with empirical marginal distributions po and at times = 0 and t = T' respectively. Given these endpoint distributions, our objective is reconstruct the continuous-time stochastic process Pt over & E [0, T" that interpolates between po and pr. Using Doob's 's h-transform [8)) we define a surface diffusion process that transitions from the peptide surface Ug the receptor surface Ur. The forward SDE is given by:
did f(u, t)dt + g(t)) t, + g(t)dw
(5)
where h(44, t, tR, T) = Vu, log p(uy (4))uu=llp My, =1e represents the gradient of the logarithmic transition kernel. The corresponding reversee SDE constructed
dud [f(4,, + t.
t,uR, T) - huU, t, TT)]dt + g(t)d(;;
(6)
As shown in Figure 2 we use the receptor surface as an informative prior in place of Gaussian noise, enabling more efficient generation of complementary peptide surfaces tailored to the binding site. Accordingly, we define the forward transition kernel as q(44 Ltr) = N NMe,, I) where f = du. SNR=UT + anyoo(1 - SNRT and oā = of SNRr). a is a fixed signal scaling factor ar ENR,
SNR,
and normally takes the value of 1.0. or defines the noise schedule, and SNR, =a//o denotes the signal-to-noise ratio at time t. During the sampling process, we start from pr Pit and approximate the score via s(4,, (,,R,, T) Vu, log q((4:((1) (t =lyp where ((4,)(4))
Je, q(44 UT gama (14 ( )dld-
Surface Generation Loss. We employ denoising score-matching 422 with neural network approxi- mation of the true score Vu, log q(.), leading to the surface generation loss Lee as:
Lu = E, (ff 24n) (4n [w(t) || so (4,, Ur, t) Vu, log 944, (4, ( 1121,
where (244 24r) is the previously defined forward transition kernel and wn(t) is the time-dependent weighting function. spp (-) represents the parameterized geometric network, with detailed information provided in Appendix D.
3.3 Bottom Structure Diffusion Generation
Bottom Structure Parameterization. Following AlphaFold2 and recent works 226
57 58), we
parameterize the peptide backbone using four key atoms N C* C*, O", which form rigid body frame. The rigid frame centered C. atom, i.e., C+ (0, 0, 0). Applying an SE(3) transformation T, to the local backbone frame of residue n yields the global atomic coordinates:
NN, Cn, (Ca)al = Tn [N', C", C. O, = Tn Tpaa (vh)) O",
where T, = (Fn, mn) consists of rotation matrix Tn E SO(3) and a translation vector m, E R-3 The transformation?. psi (v/,.) (r(r))), mpsi) encodes rotation of O* around the C, C bond by torsion angle vn. The amino acid type of the i-th residue a; E {1..20) is determined by the side-chain R group. The side-chain conformation is governed by torsion angles between side-chain

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atoms, represented as E [0, 20, A detailed description is provided in Appendices A and B. Our approach bottom structure prediction integrates three components: a multi-modal diffusion process on SE(3) for backbone prediction, torus diffusion model for torsion angle generation, and logit-normal diffusion model for residue identity prediction.
Frame Structure Generation. Given sequence of N rigid transformations T
[T Tvl E The forward
SE(3), we model their distribution using Riemannian diffusion on SE(3) 8 diffusion process on the SE(3)-invariant measure is:
dT. [0, - - m. + [d S0(3) ,dB.")
where B, (B [Br S0(3) B represent Brownian motion SO(3) and R and P E RaNx3N is a projection matrix removing the center of mass N Σ> Mn. In Appendix C, we show the choice of metric on SE(3), which allows decomposing the process into independent translational and rotational components. The backward process given by
Vr, Vr ( + dB, (0(3) Vm, = P1 m. + Vm ( PdB, (O(s)
where Tp denotes the final time step. We show more details about the training and sampling in Appendix C.
Structure Generation Loss. Backbone generation is supervised by denoising score matching loss LT, combining rotation and translation components. The loss function for the rotation component is expressed mathematically as:
(0) E.
Err (ra | |I V Pogopri((re/oo)) se(t. re) [|3],
(8)
where the rotation weighting schedule formulated as X; = 1/E[1l V Vlog ro) Mcanwhile, the translation loss component is written as:
[|
Lm (0) E, my Em, mo so (t, m:) [|2].
We observe that directly regressing Ca coordinates improves stability over using score matching for my This operation ensures that the generated backbone structures remain physically consistent with the receptor-ligand complex. The translation weight schedule is defined as A," = (1 - ///e-///)
Residue Type Prediction. Residue types a' are modeled as categorical variables embedded in logit if = a², otherwise - K, with K 0 a fixed constant. Applying softmax transformation e yields a distribution over the 20- simplex, sharply peaked at the index corresponding to a². This effectively embeds the discrete residue type as a concentrated categorical distribution on the simplex. We define forward diffusion process <
space via a sharp one-hot encoding: v E TR:20, where [']
in logit space: q(v: \v-n)) ))- -V(v/: | /a, v/ (1 (1-oo K²)) with the prior p( (++)) NN K22, I).
corresponding to logit-normal distribution [3. The reverse process recover the categorical residue types by sampling from the softmax output:
Varag + vie E~N(0,
(10)
with final prediction ad ~ softmax vo)). The model is trained to predict using the following loss function:
Clype v.g. ll 6% (v?,
(11)
Torsion Angle Prediction. The torsion vector X; E 2 consists of four side-chain angles and one backbone torsion angle s. To model angular diffusion, we apply the DDPM framework on the torus, using wrap function to maintain values within -,, w): wrap(x) (x (2(m)) т. The forward process perturbs the angles with Gaussian noise: X = wrap(y -
v1 dtE), 6 (0, I), where āg = IT'=1 (1 - Ba) and Br E [0, 1] is the noise schedule,The reverse pro- cess approximates the posterior distribution: p(x" Ix') = wrapnormal [Ho(x', t), of1], where
(t) t) = wrap Var (x+ 1-a, ang (xx: ()) is the model-predicted mean. The network pre- 5g
dicts the noise vector Eg and the training loss is defined as:
Lang Ex,x.. wrap(e, ang (Xi,t) E) =12
(12)
5

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3.4 Shape-Frame Matching Network
Our co-design network implements iterative updates to the top-down structure through a Shape- Frame Matching Network. We denote its I-th layer as SFMNet(( (1) (1)) ((2 =i ), {hg #. }). Here, zu E (1)))
(1) RNNux3 BB E N are transformed coordinates of surface and frame, while h E Nuxd
and hg E RRNxxx are feature embeddings. This architecture jointly transforms both features and coordinates to perform interaction between surface points and backbone frames. By stacking layers of SFMNet, ensure equivariant updates to the protein's 's top-down structure. The single (-th
layer is formulated as a variant the 3D equivariant graph neural network (EGNN) [39, 54]. First of
all, we get the attention score att (!) Jar (h:;
(h)) (Q) Wx + 9:5), where Wq E RRdxxdu and
WK E Rdux are learnable matrices. A geometric structural embedding fiş E Rdu is incorporated into the attention computation. It is obtained by feeding the geodesic distance into multi-layer perceptron (MLP) as Dij = MLP(I Th Tu I])- Then we aggregate the message from both
backbone frames and surface points, and update the backbone node features hg as
(1) hy att L, ab; Tuz II), Vb. 2u b.
((+1) -b (h) (1) E JEN(b.)
Mbyag)
where On and on (.) are two additional MLPs to accumulate the adjacent messages and features. (bb) is the neighborhood set of frame node b, that contains all surface points {uyl Ts. -Eb, || 7 that interact with this residue, where y is the distance threshold. After that, we calculate the shift of translation Am' and rotation Ar', adding them to the original values:
(++1 m
(1) m, Φm (hp (++t))))
Th,
((+1)
(1) Tb (1
(13)
3.5 Overall Training Loss
The complete loss function combines the surface and bottom structure loss functions:
Leotal μ [Lu, Lr, Lms Lypes Langl,
(14)
where μi denotes the set of weighting hyperparameters balancing each loss term. This formulation enables joint optimization over both surface geometry and residue structure for comprehensive protein structure prediction.
Experiments
This section presents comprehensive experimental evaluations to demonstrate the efficacy of our proposed method. Our investigation addresses three fundamental questions: Q1: How do the generated samples perform in terms of quality? Q2: Does the method generate physically valid samples? Q3: What is the impact of key architectural decisions on model performance? We evaluate PepBridge and baseline methods on two tasks: (1) Surface-Structuu Joint-design. Generation of peptide structure and surface conditional on specified receptor binding site. This task involves the simultancous generation of peptide surface characteristics and structural conformations, conditional on a specified receptor binding site. (2) Side-chain Packing. Prediction of optimal side-chain angles for peptides when they are bound specified receptor site.
4.1 Experimental Setup
Dataset. The evaluation utilized the PepMerge dataset [25]. a collection derived from the integration of PepBDB [2) and Q-BioLip (5T) databases. Following the protocol established in (25).
implemented rigorous filtering criteria: eliminating redundant entries, excluding structural data with resolution exceeding 4 Å, and selecting peptides with sequence lengths between 3 and 25 residues. We evaluate the generation model's performance using multiple criteria to ensure candidates exhibit high diversity and novelty while maintaining validity and desired distributional properties. For each receptor, generate 40 candidates. Additional dataset details are provided in Appendix E.
Baselines. We compare our approach against two distinct categories of state-of-the-art protein design methods. The first category consists of backbone-centric approaches that do not explicitly model

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Table 1: Evaluation surface-struee structure joint-design. On each target, 40 candidates are generated for evaluation, Div., Aff. and Stab. are abbreviations for diversity, affinity and stability, respectively.
Div (1)
Aff. % (t)
Stab, % (1)
RMSD Á(
BSR (1)
ProteinGencrator RFDiffusion
0.54
13.47
23.48
4.35
24.62
0.38
16.53
26.82
4.17
26.71
Chroma (RIA)
0.59
17.96
16.69
3.97
74.12
PPFLOW
0.53
17.62
17.25
2.94
78.72
PepGLAD
0.32
10.47
20.39
3.83
19.34
PepFlow w/Bb
0.64
18.10
14.04
2.30
82.17
PepFlow w/Bb+Seq
0.50
19.39
19.20
2.21
85.19
PepFlow w/Bbb+Se+AAng
0.42
21.37
18.15
2.07
86.89
PepBridge w/Bb+surf
0.60
20.07
21.75
2.04
84.62
PepBridge SeB
0.62
22.07
20.71
2.18
84.91
PepBridge w/Bb+ScqAAng+sur
0.59
19.16
25.02
2.19
83.90
side-chain conformations, such as REDiffusion [50]
ProteinGenerator and PPFLOW 26 RFD-
iffusion generates backbones via diffusion, followed by sequence prediction with ProteinMPNN [
while ProteinGenerator jointly models sequence and backbone. PPFLOW (26) conditions on the get receptor and uses conditional flow matching on torus manifolds to generate peptide backbones by modeling torsional geometry. The second category comprises full-atom models like PepGLAD [1], Chroma [1]], and PepFlow 25 which explicitly generate side-chain conformations. To evaluate Chroma, we used its conditional generation with receptor interaction area (RIA) as the conditioning input. Further details are provided in Appendix E.2.
4.2 Surface-Structure Joint-Design
Metrics. We evaluate the validity of the generated backbone structures using the following metrics. (I) Diversity: The average one minus the pairwise TM-score [59] between generated peptides. higher diversity score indicates higher dissimilarity and greater structural variety among the generated peptides. (2) Affinity: Binding affinity is evaluated using Rosetta's energy function (2), measured in kcal/mol. We report that the proportion of generated peptides with binding energies is lower than that of the native peptide. (3) Stability: The percentage of generated peptide-proted prodein complexes with total energy lower than the native complex. (4) RMSD The root mean square deviation of C atom coordinates between the generated and reference peptide structures, measured in Ångströms (Å). (5) BSR: The binding site ratio, which measures the overlap between the binding sites of the generated and native peptides on the target protein.
Results. As shown in Table T PepBridge consistently benefits from explicit surface conditioning. Among our variants, PepBridge w/Bb+Seqtsuuf attains the highest affinity. and PepBridge w/Bb+surf yields the lowest RMSD across all methods, indicating strong geometric fidelity to native-like docked poses. PepBridge wBb++Seq+Ang+surr ranks second in stability at 25.02% and maintains competitive structural diversity. Surface-aware generation consistently outperforms backbone-only counterparts. Relative to PepFlow w/Bb, PepBridge w/Bb+surf increases affinity and markedly reduces RMSD. PepBridge w/Bb++Se+suurf continues this trend, further reducing RMSD while raising affinity. PepBridge variants deliver strong RMSD, affinity, and stability, translating into competitive enrichment (BSR). Modeling interface geometry through joint surface-backbone conditioning proves especially effective for enhancing conformational accuracy and binding complementarity.
4.3 Ablation Study
To comprehensively assess the contribution of each component in our proposed model, we conduct an ablation study by systematically removing or modifying key elements. (1) vanill//vanilla diffussoo:: The denoising diffusion bridge model is replaced with a standard diffusion model, which diminishes the incorporation of receptor surface geometry as prior information. (2) -bridge/+ CFG diffusion: The denoising diffusion bridge model is replaced with classifier-free guidance diffusion model [16), which enables receptor-guided conditional generation. However, this approach still maintains Gaussian prior distribution, rather than incorporating explicit geometric priors. (3)

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Table 2: Ablations on different components of PepBridge, where the best model is in bold.
Ablations
Divara
Div.ut (1)
Aff.
Stab. %
RMSD (())
BSR (1)
Con. (1)
PepBridge
0.59
19.16
25.02
0.43
vaidge/ ditfusion
0.42
0.39
15.97
17.72
3.18
46.21
0.31
+ridge/+CFG diffusion
0.39
0.41
16.38
19.32
3.46
57.39
0.36
-surface context
0.51
16.17
15.37
4.21
31.37
&frrfcee&rrmme matching
0.42
0.35
14.82
22.41
3.71
54.71
0.25
PDB:SDJA
PDB:1UJ0
PDB:2R02
PDB:3AVC
Figure 3: Visualization of generated peptides by our PepBridge. Top: Generated peptides (in orange) for receptors (in purple). The PDB ID of the receptors 5DJA, 1UJ0, 2R02, and 3AVC. Bottom: The generated backbone structure and surface. The ground truth surface structure (in black) and generated surface (in orange) are shown to compare the ability of the interface caption.
-surface context: Surface context information is removed, leaving only the backbone generation component. (4) -surface&frame matching: The surface-frame matching mechanism is excluded during the training of the denoising model. We also evaluate additional metries to analyze model performance: (1) Consistency: Surface-structure consistency is quantified using Cramér (5), which measures the association between surface and structure clustering labels. Higher consistency values indicate that candidates with similar structures tend to have similar surfaces, suggesting that the model effectively captures the interdependence between backbone structures and surface features. (2) Surface Diversity: Div is computed based surface alignment similarities. Detailed information about the metrics can be found in Appendix E.3.
Table records the ablation results. It shows that during surface generation, the basic diffusion model struggles capture the correct distribution compared to the diffusion bridge model, resulting in instability and low consistency in the generated structures. Replacing the denoising diffusion bridge model with the classifier- free guidance diffusion model still fails to capture the surface distribution accurately. When eliminating the surface context and only generating the backbone, the performance on affinity, RMSD, and BSR drops dramatically, since can not get enough binding set information. Without surface guidance, the model will generate unrealistic and unstable peptides. As for the component the surface-frre frame matching mechanism, through the result, we can know that the network helps to achieve high stability and enhance consistency between the surface and backbone. also helps to reduce RMSD by providing effective structural patterns.
4.4 Visualization
We further present four examples generated peptides in Figure 4.3 We observe that PepBridge produces peptides with proper geometries and positions. The generated surface exhibits similar

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Table 3: Evaluation of different methods in the side-chain packing task, where the best and the suboptimal approaches are bolded and underlined, respectively.
Angle MAE "(J)
Angle Accuracy %(1)
X1
X2
X3
X4
All residues
Core residues
Surface residues
SCWRL4
29.79
30.12
52.38
62.03
45.93
66.25
34.59
DLPacker
28.35
32.62
54.69
59.60
49.00
68.03
39.56
AttnPacker
29.61
28.83
47.66
53.64
47.53
71.65
38.90
DiffPack
26.29
29.57
47.64
56.85
55.86
79.62
41.31
PepFlow A/Bb+Seg+Ang
27.61
25.60
48.20
54.02
54.29
70.47
44.06
PepBridge (ours)
25.96
26.76
46.81
52.95
56.71
73.79
46.17
conformation with the ground-truth surface, which show the ability interact with the target binding sites and capture the right shape. We provide additional experiments Appendix F.
4.5 Side-chain Packing
The backbone prior state is initialized using a native peptide structure and subsequently generate the surface and side-chain angles. We compare our approach against established methods including SCWRL4 (23). DLPacker [44,, AttnPacker [32], DiffPack [60], and PepFlow (25] The evaluation metrics include: (1) Angle MAE, which quantifies the mean absolute error between predicted and ground-truth angles, and (2) Angle Accuracy, which considers torsion angles correct when their deviation falls within 20" Following the methodology of [60], we present results for core residues, surface residues, and all residues. For each peptide, we generate ensemble of 64 conformations.
Table presents the comparative results. Our model demonstrates superior performance predicting X1. Xs. and X4 angles. Particularly, PepBridge reduces the prediction error by 2% to 52.95 for the most challenging angle X4- This suggests that the integration of surface-lveel information enhances side-chain angle prediction accuracy. Furthermore, the model exhibits particularly strong performance in surface residue prediction with high accuracy of 46. 17%, indicating that PepBridge effectively captures spatial relationships in interface regions. It also attains the best overall accuracy of 56.71 1% which significantly improves the prior statc-of-thee PepFlow by 4.45%
5 Related Works
Computational Protein Design Sequence-based and structure-based approaches two main trajectories in computational protein design. The former models amino acid chains by language models [15] 30 49 whereas the latter models the 3D geometry. Notable structure-based methods include Folding Diff (55), which represents protein backbones through sequential angles, and RFD- iffusion (50). which employs varied diffusion schemes for backbone generation. FrameDiff (58) advanced this field by developing -Evaaiann diffusion models for protein modeling. Flow models have also shown promise in backbone design, as demonstrated by FOLDFLOW
and PPFLOW 226. Recently, sequence-structte structure co-design has gained attention, with models such as PepGLAD 21 and PepFlow 225. PepHAR (24] further targets peptide binders via hotspot sam- pling and multifragment autoregressive extension, enforcing geometric validity. Surface-conditionel protein modeling represents the latest frontier in this field. Surface-VQV VQMAE (53 introduced a Transformer-baset architecture that integrates surface geometry and captures patch-level relations. Despite those achievements, the joint design of the surface and structure remains an unexplored area, and we position our study pioneering effort in this direction.
Surface Context in design ligands Classical methods explicitly model geometric and physicochem- ical complementarity (e.g., shape matching, lock-and-key). Mesh-based learning like MaSIF [33 encodes surfaces with handcrafted geometric/ccemiial descriptors, while dMaSIF [47 accelerates
this via point-cloud surfaces with atom-level features. Recent generative methods like ShEPhERD II] and DSR (46) incorporate surface features into diffusion frameworks, and SurfPro 44 generates sequences conditioned on known surfaces. However, these approaches typically assume strict com- plementarity, require hand-crafted features, or depend on ground-truth surfaces. PepBridge instead uses denoising diffusion bridge models to learn data-driven mappings between receptor and ligand

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interfaces, capturing flexible, non-complementary interactions crucial for peptide binding where induced fit dominates.
Diffusion Models Diffusion models have emerged as powerful probabilistic generative models 17
41.43
Recent advances have extended these models to handle data with inherent invariances [ 56
as well as to discrete domains (28 33 In parallel, manifold-awan diffusion models have been introduced, including the Riemannian Score-Based Generative Model (RSGM) and the Riemannian Diffusion Model (RD A significant variant, diffusion bridge models [ 62 63], enables interpolation between paired endpoint distributions. this work, we employ diffusion bridge model to construct a stochastic bridge between receptor and ligand distributions, enabling the generation of complementary. high-quality samples.
Conclusion
This work presents PepBridge, novel framework conditioned receptor structures for joint protein surface-backbone design. We employ a stochastic bridge process between receptor and ligand surfaces with tractable marginal distributions, where the model learns by matching conditional scores of the bridge distribution. For backbone generation, an SE(3) diffusion model is used to predict frame geometry. The Surface-Frame Matching Network enables bidirectional information flow between surface and backbone levels, facilitating coherent structural development. The superior performance of PepBridge highlighs the advantages of shape-drih driven generation target protein design.
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A Backbone Representation
As introduced in 3.3 section, every frame is composed by four atomic group N C. C* O*, which idealized atom coordinates that assumes chemically idealized bond angles and lengths.
We use the tuple T' (r,m) to denote the Euclidean transformations corresponding frames, where r S3(3) for the rotation and m E IR's for the translation components. We use the dot product operator (-) to denote application of transformation to the position of frame b R²:
b T
(r, m)
rb + m.
The composition of Euclidean transformations denoted as:
T Ti T2
(r, m) = (T1, m1) (T2, m2)
(ri72, mi m1).
The group inverse of the transform T' is denoted as:
T (r, m,)
(r-1, m)
The tuple transforms position local coordinates blocal E Rd to a position in global coordinates Dglobal E R as
bylobal
T biucal
rbacaall + m.
In local position of frame, the bond angles and lengths values differ slightly per amino acid type. Follow (58 and [57] we set the local coordinates as:
N (-0 --0.255, 1.363, 0.0)
C+ (0.0, 0.0, 0.0)
(15)
C* (1.526, 0.0, 0.0)
O* (0.627, 1.062,
where C is central in protein backbones, connecting N* and C* groups Using the transformation Tn, we manipulate idealized coordinates to construct global coordinates of backbone atoms for residue n via:
[N,, Cu, (Ca)a, On] = Tn, No, Tn C", T, C T, (V,( -O*].
(16)
Given the coordinates of three atoms [Nn, Cn, (Co).)s we construct local rigid frame using Gram-Schmidt process:
w1 C, - (C.).:
W2 = N, - -Caa)
e1 w1/ |w/ll
Ug w2 - ei(ef w2),
e2 uy |eel
E3 E2
(17)
Ta = (E1, E2, E3),
m. (Ca)n:
T, = Mn).
21

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In this construction, two directional vectors are first defined: from Co to C and C. to N. We normalize the first direction w define the local x-axis e, and orthogonalize and normalize w2 to define the y-axis 62. The 7-axis 63 is computed as the cross product of and forming right-hander orthonormal basis. The resulting frame Tn placing the local frame at the C. of residue n. To define the local frame for placing the oxygen atom, we begin with the residue's central frame T..
then apply secondary transformation: T (10n (rx((e (#n), mpsi), where thn represents a rotation angle along x-axis. The transformation funtions are defined
0 cos 2b sin eb (+))
Mapii (1.526, 0.0, 0.0).
(18)
sin 1b cos
This transformation represents a rotation around the x-axis (aligned with the bond from C. to C) by an angle vh,, followed by translation to the position of the carbon atom C* in the idealized frame centered at C% The combined transformation T, T (p,, thus defines the final frame in which the idealized oxygen O is placed obtain its global coordinate.
B Diffusion on the Toric Manifold
torsion vector E [0, 2m)² naturally resides on a flat d-dimensional torus, which can be represented as the quotient space R where L (2m2²) denotes a discrete lattice subgroup I& isomorphic zd. This space models periodic angular data, and inherits a flat metric from its covering Euclidean space. The tangent space of the torus at any point is identified with Rá, and all operations are performed modulo 2T.
C Diffusion on SE(3)
Following previous work [58]. we treat the group SE(3) as the product space SO(3) x R2 and endow with a product Riemannian metric. Specifically, for tangent vectors (a, b), (a', 8/) E T, SO the metric is defined as:
(aa b), (d', (2)))s())) (a, a ssos)))))))))))))))))))3) (b, ()))))...
This structure allows for natural decomposition of differential geometric objects on SE(() into rotational and translational components. In particular, the gradient of a function f :SF(3) R at T = (r, x)) is given by:
VTf(T) [V.f(r, m), fmf(r, m)]]
and the Laplace Laplace-Beltrami operator decomposes as:
ASB(3) Aro m) + Age f(r, m..
We define Brownian motion on SE(3) as the product of independent Brownian motions on SO(3) and R3.
B
SE(3)
B 80(3)
where the rotational and translational components evolve independently. This product metric allows us to treat the rotational and translational components of the forward diffusion process independently. leading to the following decomposition of the conditional score:
T. log (T. r.. (ogoerj(rr (mo), Vm, logPejo(mm /mo)]
The forward process SE(3) is thus described by independent SDEs. Let M be compact Lie group (e.g., (3)))) and let X denote the character of the l-th irreducible unitary representation of dimension d,. Then, the heat kernel (transition density of Brownian motion) on M is given by:
P))o(re/zo) = Eter dee 2
where A is the eigenvalue of the Laplace- Beltrami operator associated with Xe- Specializing to SO(3), the heat kernel becomes the isotropic Gaussian on SO(3):
fww, 1) (2e + 1)e- (((+))))) ((n((11))))
(19)
sin(w/2)
22

---

where w is the angle of the relative rotation. The corresponding score function is:
(w)(
V log (T ro) = log(ro T&) f(wl),t)
(20)
where wa is the angle of the relative rotation To and the matrix logarithm term maps to the tangent space Tt-
For the translational component, we model the forward process using a Variance Preserving SDE (VP-SDE). The transition density is given by: Ptj(mmlmmm) = Naaae 1/2 1/2mm, (1-c-()1))
(21)
Then we can get the score as:
Moggoommmmmm - -- (e 1/2 my - mm))
(22)
We use learned denoising network to approximate the conditional score of the full SE(3) transfor- mation. The score is decomposed into rotational and translational components as follows:
VT, log Prjo To) = (t, Te), $ (t. Te)):
(t, Tτ) = r, Pojo Po),
(23)
m 9 (t, Tt) = Vm, Pr (m)
D Architecture
Here we provide mathematical detail of PepBridge presented in method section. Let h [Kf..... Ny] E RNND2 denote the node embeddings at layer É, where hy, represents the embedding for residue Similarly, let z E NxNNND represent the edge embeddings, where oi encodes the interaction between residues and
Node embeddings are initialized using residue indices, atom coordinates, backbone dihedral angles, side-chain angles hus and the diffusion timestep l. For edge (residue-pair) embeddings, incorporate a combination of residue-type pairs, relative sequence positions, pairwise distances, and relative orientations. Each of these features is individually encoded using dedicated multi-layer perceptron (MLP). The resulting feature vectors are concatenated and passed through another MLP to produce the final embeddings.
The initial layer-O embeddings for residues i and residue pairs (i,j) are computed using MLPs applied to sinusoidal encodings <(-) of the input features:
h MLP((o(he.),, o(t)) RD 3j MLP((o(hs,)) ((h,)) d(i j), ((dis(i, (((diis(i.)).orrr((..)))))) o(t)) E RDD,
(24)
where Da, D2 denote the dimensions of the node and edge embeddings, respectively. The functions óf (ddisii.j) and Φ(ori(t, j)) represent sinusoidal encodings of the distance and relative orientation between residues/ i and j.
To encode the surface of the receptor protein, extract node-level features from the surface points and apply an MLP to obtain embeddings. Each surface node represented by its 3D position (surf,), hydrogen bonding potential (surfatond)) and hydrophobieity score (surfup). These features concatenated and passed through an MLP to produce the surface node embeddings:
h
MMLP([surf, surfabond. surfig))
(25)
For the peptide surface representation, we encode only the 3D positional coordinates using an MLP, omitting auxiliary features such as hydrogen bonding and hydrophobicity. At each diffusion timestep the model takes input the receptor's node and edge embeddings, the noised peptide descriptors, and a sinusoidal embedding of the timestep. It predicts denoising score that guides the reverse diffusion process toward the clean peptide descriptors at O. The model architecture is based attention to capture interactions
on Invariant Point Attention (IPA), which employs between the receptor and the peptide. The output of the IPA module is passed through separate MLP decoders to reconstruct various ground-truth peptide descriptors, such as atom coordinates, dihedral angles, and residue types. Notably, certain residue types may be partially inferred from the number of side-chain dihedral angles, due to structural constraints.
23

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E Experimental Details
The experiments were conducted on computing cluster with 2 NVIDIA RTX A6000, each with 48 GB of memory. The total computation time for training was approximately 21 hours. We trained for 900000 steps with batch size We used the Adam optimizer with a start learning 5e-4. We also schedule decay the learning rate exponentially with factor of 0.6 and minimum learning rate of le-6. The learning rate is decayed if there is no improvement for the validation loss consecutive evaluations.
E.1 Dataset
The filtered dataset underwent sequence-based clustering using MMseqs2 [45, resulting in 9,816 protein-peptide complexes organized into 292 distinct clusters. For systematic evaluation, we designated 10 clusters encompassing 158 complexes as the test set, with the remaining complexes allocated to training and validation cohorts.
E.2 Baselines
We briefly summarize the baselines and tools used in our study, including generative approaches for protein and peptide design, well as side-chain packing methods.
ProteinGenerator 27 is Rose based diffusion model that jointly generates
protein sequences and structures, with flexible conditioning on target sequence and structural attributes.
RFDiffusion [50]
generative model fine-tuned structure denoising tasks, enabling high-accuracy design monomers, binders, and symmetric protein assemblies.
PPFLOW [66] target-aware peptide designer that performs conditional flow matching torus manifolds to model peptide torsion-angle geometry.
PepFlow 25 is multimodal flow-matching model for full-atom peptide design targeting
specific protein receptors. jointly models backbone geometry, side-chain conformations, and residue identities over appropriate geometric manifolds.
PepGLAD 21 combines geometric latent diffusion with receptor-specific transformations to generate full-atom peptides. The model operates in learned latent space and adapts to diverse binding geometries for improved generalization.
Chroma [9 is unified generative framework for proteins and protein complexes that inte- grates a polymer-aware diffusion process with a scalable architecture, supporting constraint- driven design across sequence, structure, and function.
SCWRL4 23 is a widely used side-chain packing tool employing a backbone-dependent rotamer library and statistical energy function.
DLPacker 34 is 3D CNN-based model for residue side-chain conformation prediction.
We utilize the official implementation along with the model weights.
AttnPacker 32 utilizes equivariant attention mechanisms on backbone 3D geometry to predict all side-chain coordinates simultaneously.
DiffPack 61 is diffusion-- based generative model that autoregressively samples side-chain angles on a toric manifold.
E.3 Training Metrics Details
RMSD. Root-Mean- Root-Mean-Square Deviation is widely used metric for assessing structural similarity between proteins. In our evaluation, we align the generated peptide to the native peptide within the complex using the Kabsch algorithm. considering only the peptide portion for superposition. We then compute the RMSD based on normalized C, atom distances between the generated and native peptides. Lower RMSD values indicate greater structural similarity.
BSR. Binding Site Recovery measures the similarity of interaction patterns between the generated and native peptide-protein complexes. Specifically, it evaluates whether the generated peptide

---

engages target protein residues in a manner similar to the native peptide, potentially reflecting similar biological functions. A residue in the protein is considered part of the binding site if its Cş atom lies within of any residue the peptide. BSR defined as the ratio of overlapping binding site residues between the generated and native complexes. Higher BSR values indicate greater similarity in binding interactions.
Consistency represents the statistical association between the clustering results of surface and structures. This metric quantifies how well model captures the fundamental consistency between surfaces and their corresponding structures. A model that accurately represents the joint distribution should achieve high score, while a low score indicates the model generates inconsistent surface- structure pairs. The evaluation process involves clustering both surfaces and structures, assigning discrete labels to each. These clustering labels can be interpreted as nominal variables. Given that similar surfaces should correspond to similar structures. We employ Cramér's V association [5] to measure this correlation, where a value of 1.0 indicates perfect association and 0.0 indicates no association. For surface representation, we first obtain molecular fingerprints using the methodology described in [44]. These fingerprints serve as input for the clustering algorithm, which assigns labels to the generated peptide surfaces.
Diversity. To assess diversity, we compute pairwise TM-scores among the generated peptides for a given target using the original TM-align program. TM-scores quantify structural similarity between peptide pairs. We define diversity as minus the average TM-score, where higher values indicate greater structural variability among the generated peptides. This metric reflects the breadth of structural exploration achieved during the design process.
E.4 Hyperparameters
Our proposed method incorporates several hyperparameters, including sample step, learning rate, batch size and feature dimensions. To validate these hyperparameters, we conducted a random search. The search space are presented in Table 4
Table 4: Search space for all PepBridge. The parameters used in validation marked in bold
Parameter
Search Space
Learning rate
0.0009, 0.0007, 0.0005, 0.00001
Hidden dimension of residue feature
64, 128, 256
Hidden dimension of edge feature
64, 128, 256
Hidden dimension of surface feature
16, 24, 32
Number of attention heads
8, 16, 24
Loss weight of surface
0.1, 0.5,
Loss weight of backbone position
0.1, 0.5,
Loss weight of backbone rotation
0.1, 0.5,
Sampling steps
500, 1000. 1500
Training steps
500, 1000, 1500
Batch size
4, 8, 16
E.5 Computational Complexity
We compared PepBridge with several baseline methods in terms of training time, inference time per sample, GPU usage, and model size. The time cost is reported as the total time spent divided by the number of designed candidates. As summarized in Table multi-modal processing does introduce additional complexity relative to uni-modal approaches, our analysis shows that PepBridge achieves good balance between computational efficiency and performance.
25

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Table 5: Computational cost and resource footprint across methods. Training and inference times normalized per designed sample.
Method
Training time
Inference time (s/sample)
GPU(s) used
Params (M)
RFdiffusion
days
80-180
8xA 100
~20
ProteinGenerator
4 weeks
152
64xV100
~20
PepFlow
20 hours
14-24
2xA6000
~
Chroma
10 weeks
185-226
8xV 100
~0
PepGLAD
29 hours
3
1x24 GB GPU
225
PepBridge
21 hours
16-37
2xA6000
~0
Additional Experiments
Visualization
Figure 1 provides additional examples of peptides generated by PepBridge. These visualizations include both surface and backbone structures of the generated peptides a top-down view, further illustrating the model's ability to produce geometrically coherent and interface-aware designs.
PDB:4CC2
PDB:3AV9
PDB:1607
PDB:2XS1
Figure 4: Visualization of generated peptides by PepBridge. Top: Generated peptides (in orange) for receptors (in purple). The PDB ID of the receptors are 4CC2, 3AV9, 1B07, and 2XS1. Bottom: The generated backbone structure and surface. The ground-truth surface structure (in black) and generated surface (in orange) shown to compare the ability of interface caption.
F.2 Training and Sampling Time Steps
We ablated the number of diffusion steps used during training while fixing the sampling procedure at 1000 steps. The results are summarized in Table Increasing the number of steps consistently improved all quality metrics. The largest gains occurred up 1000 steps, with smaller but still measurable improvements between 1000 and 1500 steps. Given these trends, we adopt 1000 training steps as favorable trade-off between overall accuracy and computational cost.
We further conducted experiments assess how different inference time steps affect the final performance metrics using the model trained with 1000 steps. As shown in Table 7 the results indicate that longer sampling chains (e.g., 1000 steps) improve quality of the generated structures. However, performance gains begin to plateau beyond 800 steps, and observe slight decrease in structural diversity, suggesting trade-off between generation determinism and diversity. Based on this analysis, selected 1000 steps the default setting to achieve the best overall balance.
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Table 6: Effect of training steps on performance (sampling fixed at 1000).
Higher is better (1) except
RMSD ()).
Divatm (1)
Aff. % (1)
Stab. % (1)
RMSD A(L)
BSR (t)
PepBridge (time step =500)
0.57
18.96
24.79
2.96
82.84
PepBridge (time step =800)
0.61
19.07
26.31
2.36
85.57
PepBridge (time step =1000)
0.59
19.16
25.02
2.19
83.90
PepBridge (time step =1500)
0.62
23.28
26.68
2.11
86.92
Table Effect of sampling steps on performance (model trained with 1000 steps). Higher is better (1) except RMSD ()).
Divam (1)
Aff. % (1)
Stab. % (1)
RMSD Á(L)
BSR (t)
PepBridge (time step =500)
0.61
17.42
23.97
2.85
80.05
PepBridge (time step =800)
0.62
18.77
24.58
2.69
82.33
PepBridge (time step =1000)
0.59
19.16
25.02
2.19
83.90
PepBridge (time step =1500)
0.56
18.46
24.71
2.74
83.78
G Limitations and Future Work
While PepBridge presents structured approach to joint protein surface and backbone design, several limitations remain that can addressed future work. One key limitation lies in the simplification of surface representations. The current model relies on solvent-accessible point clouds with biochemical annotations, which, while effective, may not fully capture finer molecular interactions such electrostatic potential fields and solvent dynamics. These factors play crucial roles in protein-protein interactions and could enhance the accuracy of designed peptides if incorporated. Another limitation is the model's reliance receptor geometry. PepBridge assumes that receptor surface features sufficiently dictate the constraints on peptide binding. However, this does not account for receptor flexibility or conformational changes upon ligand binding, which are common in many biological systems. Addressing this aspect could make the model more applicable to highly dynamic binding sites. Computational efficiency also poses challenge. The diffusion bridge model and SE(3) diffusion backbone generation require computationally intensive sampling. While the hierarchical generation process improves efficiency, generating high-quality peptides remains expensive, particularly for longer sequences. Further optimization is necessary to reduce the computational cost while maintaining or improving accuracy. Additionally, the current evaluation primarily focuses on geometric complementarity and binding affinity predictions. While these provide useful insights, they do fully capture the functional stability of designed peptides. Wet-lab experiments and molecular dynamics simulations are necessary to assess real-world applicability, ensuring that the generated structures remain stable under physiological conditions.
Future work can address these limitations in several ways. Enhancing surface representations by incorporating higher-order biochemical features such electrostatic potential fields, solvent effects, or graph-based molecular embeddings could improve the precision of curface-conditioned peptide generation. Furthermore, integrating receptor flexibility into the model by leveraging conformational ensembles or reinforcement learning-basee refinement strategies would allow for more realistic modeling of dynamic binding sites. To improve computational efficiency, future research could explore accelerated sampling techniques, such as adaptive noise schedules, score distillation sampling (SDS), or wow-mhhhiing approaches. These methods could significantly reduce inference time while preserving or enhancing model accuracy. Finally, validating PepBridge through real-world applications, particularly in therapeutic peptide design, remains crucial next step. Incorporating experimental validation through biochemical assays and integrating co-evolutionary signals into the design process could further enhance the biological relevance of the generated structures. By addressing these challenges, PepBridge can be refined to enable more accurate, efficient, and versatile protein design.
27


Reviews:
[{"review_id": "J2cpXjSCtJ", "reviewer": "Reviewer_Qs9a", "summary": "The authors propose a joint framework to jointly design peptide sequence and structure while ensuring the surface complementarity in peptide design task. The proposed method is first use a diffusion bridge model to predict the ligand surfaces with receptor surfaces, and then jointly predict the residue type and frame structure with a multi-modal diffusion model. The authors provide a good illustration of their method and extensive experiments to show its superiority.", "questions": "1.There has been a long history to use surface complementarity to design ligands in traditional protein or small molecule design previous to deep learning era. I think authors should include this part of related works, and provide a discussion whether PepBridge can perform better than these methods.\n\n2.Following the previous context, there are two questions for surface-based design:\n1)How is the robustness of surface complementary methods against imperfect structure? The error of crystal structure is not significant in whole protein structure, but can be harmful when describing very local surface. If we use AlphaFold-like models to predict the receptor  structure, the error could be even larger.\n2)Another problem is that the surface complementarity condition can be misleading sometimes. I think this could probably be a major advantage for learning-based methods, because they don't need to assume a very strict complementarity but can learn from data. Could authors help me understand how is PepBridge designed to address this issue?\n\n3.I think there should be more ablation study contributed to understand the performance of separate components. For example, how is the DDBM surface diffusion part and structure design part influence each other? I notice that the authors already provide some ablation study on the change of joint performance, but I wonder if it is possible to decompose the model totally.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "The paper is well written and easy to understand. The experiments are extensive with sufficient ablations and benchmarks. The result seems promising and proves the authors' point that the bidirectional information flow between surface and designed structure can help this task. I think a major concern is that such joint models with multiple losses and components could introduce potential problems for efficiency and robustness. However, considering the task formulation and authors' intention to jointly design surface and peptide structure, the proposed method is a reasonably sophisticated method. More ablation studies by further decomposing the model could be helpful to address this issue.", "was_revised": true, "final_justification": "My concerns are well addressed and I think I have no further major concerns. Thus I will keep my scores unchanged as 4.", "rebuttal": "We sincerely appreciate your valuable feedback and provide point-wise responses below.\n\n---------------------------------------- \n> Q1. There has been a long history to use surface complementarity to design ligands in traditional protein or small molecule design previous to deep learning era. I think authors should include this part of related works, and provide a discussion whether PepBridge can perform better than these methods.\n\nYou are absolutely correct that surface complementarity has been a fundamental principle in protein and small molecule design well before the deep learning era. We will add a section discussing classical approaches including:\n\n\nClassical methods often relied on explicit modeling of geometric and physicochemical surface complementarity, such as shape matching or lock-and-key models. More recently, methods like MaSIF [1] represented protein surfaces as meshes and used predefined geometric and chemical descriptors to fingerprint surface patches. To reduce the high computational cost of mesh-based methods, dMaSIF [2] modeled molecular surfaces as point clouds, demonstrating competitive performance by assigning atom types and computing features directly from atomic positions.\n\nIn molecular generation, ShEPhERD [3] incorporates multiple surface-level features (e.g., shape, electrostatics, and pharmacophores) into a joint diffusion-denoising framework for 3D molecular graphs. DSR [4] models protein surfaces using implicit neural representations to capture dynamic structural features over time. Similarly, SurfPro [5] generates functional protein sequences conditioned on ground-truth surfaces and their biochemical properties. However, this reliance on known target surfaces limits its applicability in scenarios where accurate surface reconstruction is difficult or unavailable.\n\nThese methods demonstrate the power of surface-based design. However, they typically assume strict geometric complementarity or require hand-crafted features and ground-truth surfaces. In contrast, PepBridge leverages denoising diffusion bridge models (DDBMs) to learn a data-driven mapping between receptor and ligand interfaces. This allows PepBridge to capture non-obvious, flexible, and non-complementary interactions that classical methods might miss—especially important in peptide binding, where induced fit and flexible recognition often play a key role.\n\nWe will update the manuscript to reflect this broader context and provide a more detailed comparison highlighting the strengths and limitations of surface-based methods relative to PepBridge.\n\n[1] Deciphering interaction fingerprints from protein molecular surfaces using geometric deep learning. Nature Methods. \n\n[2] Fast end-to-end learning on protein surfaces. dMaSIF CVPR 2021.\n\n[3] ShEPhERD: Diffusing shape, electrostatics, and pharmacophores for bioisosteric drug design. ICLR 2025.\n\n[4] DSR: Dynamical Surface Representation as Implicit Neural Networks for Protein. NeurIPS 2023.\n\n[5] SurfPro: Functional Protein Design Based on Continuous Surface. ICML 2024.\n\n> Q2.1 How is the robustness of surface complementary methods against imperfect structure? The error of crystal structure is not significant in whole protein structure, but can be harmful when describing very local surface. If we use AlphaFold-like models to predict the receptor structure, the error could be even larger.\n\nThis is a very good question regarding the sensitivity of surface-based methods to structural inaccuracies. ! We agree that while global structural deviations may be minor (e.g., 0.5–2.0 Å RMSD), even small atomic-level perturbations can significantly affect local surface features such as curvature, pocket geometry, accessible surface area, and electrostatic potential. This challenge is especially relevant when using predicted structures from models like AlphaFold, where the overall fold is typically reliable, but side-chain placements and flexible loop regions may be less accurate.\n\nTo address this issue and improve the robustness of PepBridge, we are considering the following strategies:\n\n `1. Learned Error Tolerance:`\n\nThe model could be trained on a diverse set of protein structures—including high-resolution crystal structures, NMR ensembles, and computational models—covering a broad range of structural qualities. This heterogeneity allows the model to learn representations that are inherently more tolerant to local inaccuracies and noise, improving its generalizability across different structure sources.\n\n `2. Ensemble-Based Modeling: ` \n\nTo mitigate the reliance on a single static structure, especially for predicted or low-resolution inputs, PepBridge can be extended to incorporate ensemble-based inputs. Using multiple conformations or perturbed variants (e.g., from molecular dynamics simulations or AlphaFold confidence-based sampling) can help account for uncertainty and enhance prediction stability.\n\n `3. Empirical Robustness Evaluation: `\n\nWe are actively investigating robustness by evaluating PepBridge on (i) structures with synthetic coordinate perturbations, (ii) comparisons between AlphaFold-predicted structures and corresponding crystal structures; and (iii) NMR ensembles that capture native conformational variability. These experiments help quantify how sensitive predictions are to structural imperfections.\n\nAdditionally, we acknowledge that proteins are not rigid entities; they undergo constant fluctuations in physiological conditions. Capturing the dynamic nature of the surface—rather than relying solely on static snapshots—could further enhance modeling accuracy for protein–protein interactions. Future work will explore integrating dynamic surface representations derived from conformational ensembles or time-averaged properties.\n\n> Q2.2 Another problem is that the surface complementarity condition can be misleading sometimes. I think this could probably be a major advantage for learning-based methods, because they don't need to assume a very strict complementarity but can learn from data. Could authors help me understand how is PepBridge designed to address this issue?\n\nThank you for this insightful question about surface complementarity limitations. We fully agree that strict surface complementarity assumptions can be misleading and that learning-based methods offer significant advantages in this regard.\n\nHowever, it is worth noting that several key innovations are specifically designed in PepBridge to address the limitations of rigid surface complementarity:\n\n `1. Learning-based Surface Relationship Modeling: `\n\nRather than assuming strict geometric complementarity, PepBridge employs denoising diffusion bridge models (DDBMs) to learn the complex relationship between receptor and ligand surfaces from data. This allows the model to capture subtle, non-complementary interactions that are crucial for binding but would be missed by purely geometric approaches.\n\n `2. Integration of Biochemical Properties: `\n\nPepBridge goes beyond surface geometry by incorporating biochemical properties alongside geometric features. This enables the model to learn that effective binding often involves electrostatic interactions, hydrophobic patches, and other physicochemical factors that don't necessarily require perfect shape complementarity.\n\n `3. Flexible Surface-Structure Coupling: `\n\n Our joint design framework enables dynamic adjustment between surface geometry and backbone structure through Shape-Frame Matching Networks (SFMN). This flexibility encourages the generation of binding interfaces that may not exhibit perfect complementarity but are biologically relevant and energetically favorable.\n\n `4. Multi-Step Refinement Process: `\n\n The multi-model diffusion approach allows for iterative refinement where initial surface predictions can be adjusted based on structural constraints and vice versa, leading to more realistic binding interfaces that balance complementarity with other binding determinants.\n\nAll above designs make PepBridge generate peptides that engage targets through diverse binding modes, including those involving conformational flexibility and partial complementarity - scenarios where traditional geometric complementarity assumptions would fail.\n\n> Q3. I think there should be more ablation study contributed to understand the performance of separate components. For example, how is the DDBM surface diffusion part and structure design part influence each other? I notice that the authors already provide some ablation study on the change of joint performance, but I wonder if it is possible to decompose the model totally.\n\nWe thank the reviewer for this insightful question. To better understand the contributions of individual components in our model, we performed ablation studies using several PepBridge variants with and without surface diffusion information. As shown in the table below, incorporating surface features improves performance across the evaluation metrics.\n\n| | Div\\_stru (↑) | Aff. % (↑) | Stab. % (↑) | RMSD Å (↓) | BSR (↑)|\n|:--|:-:|:----:|:---:|:---:|:----:|\n|PepBridge w/Bb+Seq         |0.56 |17.12  |16.41|2.87|79.79|\n|PepBridge w/Bb+Seq+surf    |0.62 |22.07  |20.71|2.18|84.91|\n|PepBridge w/Bb+Seq+Ang     |0.53 |18.46  |19.73|3.21|76.53|\n|PepBridge w/Bb+Seq+Ang+surf|0.59 |19.16  |25.02|2.19|83.90|\n\n----------------------------- \n\nWe would like to thank you again for your valuable comment and suggestions, which significantly improve our paper quality."}, {"review_id": "tCkSLXnpoY", "reviewer": "Reviewer_HJCF", "summary": "This paper introduces **PepBridge**, a diffusion-based framework for joint peptide surface and structure generation conditioned on a receptor. It uses a **Surface Diffusion Bridge** to map receptor surface point clouds to complementary peptide surfaces, followed by multi-modal diffusion for backbone and side-chain modeling. A shape-frame matching module aligns surface and structure. The method shows solid performance on peptide design tasks, with the key contribution being the integration of surface geometry as a generative prior.", "questions": "**Questions**\n\n1. As I understand, the model does not use receptor backbone or sequence information. Would adding these information further help?\n\n2. Could PepFlow benefit from adding surface context similarly? Also, can you elaborate on why the performance gain is modest compared to PepFlow despite richer modeling\n\n3. Could you also discuss the cost of surface computation, which could affect real-world applicability.", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n- Clarity/Quality: The paper is well-written and easy to follow. Figures and illustrations clearly convey the architecture and main ideas. The paper includes thorough ablation studies, multiple baselines, and clear evidence that each component contributes to the final performance.\n\n- Originality: The proposed **Surface Diffusion Bridge** is a novel and elegant approach to modeling receptor-conditioned surface generation.\n\n- Significance: The task of receptor-aware peptide generation is important and underexplored. The method highlighs the advantages of shape-driven generation in target protein design.\n\n**Weaknesses**\n\n- Quality: The performance improvement over strong baselines like PepFlow is relatively modest. While statistically sound, the gain may not fully justify the increased model complexity\n\n- Significance: When surface context is removed, performance drops sharply. This raises the question that could other peptide design models, such as PepFlow, also benefit from adding surface? The core contribution may be this **surface + bridge** formulation.", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thoughtful questions and for engaging deeply with our work. We respond to these suggestions point-by-point below:\n\n---------------------------\n\n> Q1. As I understand, the model does not use receptor backbone or sequence information. Would adding these information further help?\n\nThank you for this important question. Our model does indeed incorporate both receptor backbone and sequence information.\nSpecifically, for both receptor and ligand residues, we initialize node embeddings using multiple structural and sequence features: residue indices, atom coordinates, backbone dihedral angles, side-chain angles, and the diffusion timestep $t$. For edge embeddings between residue pairs, we incorporate residue-type pairs, relative sequence positions, pairwise distances, and relative orientations (details can be found in Appendix D).\n\nOur denoising network architecture is built on Invariant Point Attention (IPA), which uses SE(3)-invariant attention mechanisms to effectively model interactions between the receptor and peptide while preserving the geometric relationships encoded in the backbone structure.\n\nOur experimental results demonstrate that receptor backbone and sequence information are crucial contributors to model performance. We believe this comprehensive incorporation of structural and sequence features contributes significantly to the model's performance.\n\n> Q2. Could PepFlow benefit from adding surface context similarly? Also, can you elaborate on why the performance gain is modest compared to PepFlow despite richer modeling\n\nThank you for this insightful question regarding both the potential for surface context in PepFlow and our performance comparison.\n\n**Surface Context in PepFlow:**\n\nPepFlow could potentially benefit from incorporating surface context similar to our approach. Surface complementarity is fundamental to protein-peptide binding, and adding explicit surface representations could enhance PepFlow's ability to model binding site compatibility and geometric constraints.\n\n**Performance Comparison and Methodological Differences:**\n\nThe key differences lie in the underlying mathematical frameworks:\nPepFlow uses flow matching with deterministic ordinary differential equations (ODEs) that learn direct velocity fields between distributions. In contrast, our diffusion bridge approach employs stochastic differential equations (SDEs) that incorporate controlled noise during generation. This stochasticity offers several advantages for peptide-receptor binding:\n\n `1. Exploration of binding diversity:`\n\nThe stochastic process naturally explores multiple viable binding modes, which is crucial given that peptides often exhibit conformational flexibility at binding sites.\n\n`2. Surface complementarity modeling:`\n\nThe noise inherent in SDEs helps model the probabilistic nature of surface-surface interactions, where slight variations in positioning can lead to different binding modes.\n\n`3. Sampling flexibility:`\n\nOur SDE framework allows switching between stochastic (DDPM) and deterministic (DDIM) sampling strategies, providing controllable trade-offs between diversity and binding mode exploration.\n\n**Future Directions:**\nWe plan to investigate combining surface context with flow matching formulations to explore the benefits of both approaches.\n\n> Q3. Computational complexity analysis, runtime comparison with baselines, and the impact of computational efficiency on practical applicability.\n\nWe appreciate the reviewer’s concern regarding the potential computational overhead introduced by our multi-modal diffusion framework. To address this, we compared PepBridge with several baseline methods in terms of training time, inference time per sample, GPU usage, and model size. The time cost is reported as the total time spent divided by the number of designed candidates.\n\nWhile multi-modal processing does introduce additional complexity relative to uni-modal approaches, our analysis shows that PepBridge achieves a strong balance between computational efficiency and performance. The modest increase in resource usage is well-justified by the substantial gains in structural precision and interface quality, especially in biologically critical tasks such as therapeutic protein design.\n\n### Table: Comparison of Computation Time and Resources\n\n| Method   | Training Time  | Inference Time (s/sample) | GPU(s) Used |  Params (M) |\n|-------------------------------|---------------------|----------------------------|-------------------|------------|\n| RFdiffusion | 3 days | 80–180  | 8 A100 | ~ 120 |\n| ProteinGenerator | 4 weeks | 152 | 64 V100 | ~ 120 |\n| PepFlow | 20 hours | 14-24 | 2 A6000 | ~ 7 |\n| Chroma  | 10 weeks | 185-226 | 8 V100  | ~ 20 |\n| PepGLAD  | 29 hours | 3 | 24G GPU| ~ 2.5 |\n| PepBridge | 21 hours | 16-37 | 2 A6000  | ~ 10 |\n\n------------------------------ \nWe appreciate your thorough review and advice to make our study more readable."}, {"review_id": "cIcse6wSzc", "reviewer": "Reviewer_WAQ2", "summary": "The authors introduce an approach that uses an annotated 3D surface of a receptor (with amino acid and atom position information) and generate a compatible ligand surface as well as the backbone in the form of frame geometry. They use diffusion bridge models starting from the receptor surface instead of Gaussian noise, which they demonstrate to be beneficial. As for the backbone generation, they use a surface frame matching network which is jointly trained. With their approach, they generate high quality samples and also demonstrate superior side-chain packing performance.", "questions": "1. I would be interested in seeing how consistent the results are, as the authors did not provide any standard deviation. In the caption of table 1 they state that they draw 40 candidates, but it is hard so say if this is enough for the results to be consistent. Also, did the authors run the inference with multiple different seeds?\n\n2. How does the runtime of the different methods compare, and how does it scale with size? How many inference steps did have been used for the diffusion model and how does the number of steps impact the sample quality?\n\n3. Although I am aware that diffusion bridges can be seen as a generalization of flow matching, I am curious to hear why the authors decided opted to use diffusion bridges instead of flow matching? \n\n4. It is not entirely clear to me how the authors encoded the surface structure. As I understood it, they use a point cloud for the surface, but I am not sure how many points do they use (one for each atom?) and if it could benefit from a more precise parameterization (i.e., more points).", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The paper is well written, clearly structured and easy to follow. The authors have presented (to my knowledge) novel ideas and new models; especially the idea of incorporating the surface structure seems promising. This idea could potentially transfer to other applications and be used in a variety of different models and settings. \n\nThe authors show improved results in some metrics (such as the RMSD), but do not improve the results in all benchmarks. Due to the lack of error bars and/or standard deviations, it is hard to judge how consistent the improvements are. Especially because most models are intrinsically stochastic during inference. \n\nHowever, the authors mitigate this by comparing their approach with multiple different methods and also perform ablation studies how the different parts of their approach impact the main results. Compared to other approaches, their model support side-chain packing, making it more versatile.", "was_revised": true, "final_justification": "The authors present a novel framework in a well-prepared manuscript. PepBridge shows strong empirical results, with clear visualizations and a comprehensive set of experiments demonstrating its practical usefulness.\n\nDuring the rebuttal phase, the authors addressed my main concerns, including the consistency of results by providing standard deviations and clarifying the number of inference samples. They also elaborated on architectural choices (e.g., diffusion bridges vs. flow matching vs. stochastic interpolants) and provided further implementation details. Looking at the other reviews, the updated manuscript will include new ablation studies that clarify the contribution of individual components. \n\nOverall, I believe that the paper is well-motivated, the approach original, and the experiments support the claims.", "rebuttal": "We appreciate the reviewer’s thoughtful feedback and suggestions, which have helped us improve the clarity and completeness of our work. Below, we address each of the concerns raised.\n\n> Q1. I would be interested in seeing how consistent the results are, as the authors did not provide any standard deviation. In the caption of table 1 they state that they draw 40 candidates, but it is hard so say if this is enough for the results to be consistent. Also, did the authors run the inference with multiple different seeds?\n\nThank you for this insightful question. We indeed conducted inference using 5 different random seeds, generating 40 candidates per seed. The table below reports the standard deviation across all runs. These results demonstrate that the performance of our method is consistent across different random seeds.\n\n| | Div\\_stru (↑) | Aff. % (↑) | Stab. % (↑) | RMSD Å (↓) | BSR (↑)|\n|:--|:-:|:----:|:---:|:---:|:----:|\n|PepBridge |0.59 $\\pm$ 0.12|19.16 $\\pm$ 0.87 |25.02 $\\pm$ 1.36|2.19 $\\pm$ 0.16|83.90 $\\pm$ 1.61|\n\n> Q2. How does the runtime of the different methods compare, and how does it scale with size? How many inference steps did have been used for the diffusion model and how does the number of steps impact the sample quality?\n\nWe appreciate the reviewer’s concern regarding the potential computational overhead introduced by our multi-modal diffusion framework. To address this, we compared PepBridge with several baseline methods in terms of training time, inference time per sample, GPU usage, and model size. The time cost is reported as the total time spent divided by the number of designed candidates.\n\nWhile multi-modal processing does introduce additional complexity relative to uni-modal approaches, our analysis shows that PepBridge achieves a strong balance between computational efficiency and performance. The modest increase in resource usage is well-justified by the substantial gains in structural precision and interface quality, especially in biologically critical tasks such as therapeutic protein design.\n\n## Table: Comparison of Computation Time and Resources\n\n| Method   | Training Time  | Inference Time (s/sample) | GPU(s) Used |  Params (M) |\n|-------------------------------|---------------------|----------------------------|-------------------|------------|\n| RFdiffusion | 3 days | 80–180  | 8 A100 | ~ 120 |\n| ProteinGenerator | 4 weeks | 152 | 64 V100 | ~ 120 |\n| PepFlow | 20 hours | 14-24 | 2 A6000 | ~ 7 |\n| Chroma  | 10 weeks | 185-226 | 8 V100  | ~ 20 |\n| PepGLAD  | 29 hours | 3 | 24G GPU| ~ 2.5 |\n| PepBridge | 21 hours | 16-37 | 2 A6000  | ~ 10 |\n\n> Q3. Although I am aware that diffusion bridges can be seen as a generalization of flow matching, I am curious to hear why the authors decided opted to use diffusion bridges instead of flow matching?\n\nThank you for this excellent question about our choice of diffusion bridges over flow matching. While both approaches can model transport between distributions, several factors made diffusion bridges more suitable for our protein surface generation task:\n\n` 1. Stochastic exploration: ` \n\nProtein-protein interactions inherently involve stochastic processes at the molecular level, including thermal fluctuations and conformational sampling. Diffusion bridges use stochastic differential equations (SDEs) that naturally incorporate noise during the generation process. This stochasticity is beneficial for exploring diverse protein surface configurations, as it allows the model to discover multiple viable binding modes rather than converging to deterministic solutions. Whereas the deterministic ordinary differential equations (ODEs) of flow matching may oversimplify the complex, probabilistic nature of surface complementarity between receptor and ligand.\n\n` 2. Superior performance on structured biological data:`  \n\nWhile flow matching has shown promise for image generation, diffusion models have demonstrated superior empirical performance on highly structured data like protein structures and molecular surfaces. Given that our 3D point cloud representations of protein surfaces exhibit complex geometric and biochemical constraints, the proven effectiveness of diffusion approaches on structured biological data was a decisive factor.\n\n` 3. Flexibility in sampling: ` \n\nThe SDE framework allows us to easily switch between stochastic (DDPM) and deterministic (DDIM) sampling strategies, providing controllable trade-offs between diversity and quality.\n\n> Q4. It is not entirely clear to me how the authors encoded the surface structure. As I understood it, they use a point cloud for the surface, but I am not sure how many points do they use (one for each atom?) and if it could benefit from a more precise parameterization (i.e., more points).\n\nWe thank the reviewer for pointing out the need for clarification. We generate solvent-accessible surface representations using PyMol, which provides a triangulated molecular surface based on a probe radius that approximates both the Solvent-Accessible Surface Area (SASA) and Solvent-Excluded Surface (SES). From this surface, we sample a point cloud in which each point is annotated with 3D spatial coordinates and relevant physicochemical features, such as hydrophobicity and hydrogen bonding potential. To encode the surface of the receptor protein, we extract node-level features from the surface points and apply an MLP to obtain embeddings. Each surface node is represented by its 3D position ($surf_t$), hydrogen bonding potential ($surf_{hbond}$), and hydrophobicity score (${surf}_{hp}$). These features are concatenated and passed through an MLP to produce the surface node embeddings.\n\nOn average, we sample approximately three surface points per residue. This density was selected to balance surface resolution and computational efficiency. We also implement a subsampling strategy to avoid excessive surface points, which would significantly increase computational cost without substantial performance gains. While increasing the number of surface points could provide a finer geometric representation, our experiments showed diminishing returns in predictive performance beyond a certain point density. Exploring more adaptive or finer-grained surface parameterization remains an interesting direction for future work.\n\n-------------\nWe sincerely thank you for your insightful comments, which have greatly enhanced the clarity and quality of our manuscript."}, {"review_id": "Ukq11qR4I3", "reviewer": "Reviewer_Q8ka", "summary": "This paper proposes a top-down joint design framework for protein surface and structure based on a multi-modal diffusion approach. The key innovation lies in employing a denoising diffusion bridge model to directly map the receptor surface to the ligand surface, rather than relying on a traditional Gaussian noise prior.", "questions": "1. How do different hyperparameters affect the final performance?\n\n2. Although diversity metrics have been reported, there is a lack of in-depth analysis on how to find the optimal balance between diversity and quality.\n\n3. Although visual results are provided, I cannot see if they meet the practical significance. Can it be used for practical applications? Does the author plan to conduct wet experiments for validation? How to prove the reliability of computational predictions without experimental verification?\n\n4. The multi-modal diffusion process requires simultaneous processing of surfaces, torsion angles, and residue types, which inevitably leads to computational overhead. Is the additional computational cost reasonable compared to existing uni-modal methods? Can you provide a detailed analysis of computation time and resource consumption?\n\n5. Is it applicable to receptors without obvious binding pockets?\n\n6. There is another small but important point: the introduction of surface modeling is an innovative aspect of the paper, but how can it be proven to be effective?", "limitations": "yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. Using the receptor surface as an informative prior instead of Gaussian noise is a promising approach.\n\n2. The methodological design is well-founded, decomposing the complex protein design problem into two interrelated sub-tasks: surface generation and structure prediction. \n\n3. The topic is very innovative, although the method has certain shortcomings compared to existing methods.\n\nWeaknesses:\n1. In the introduction, the author mentions \"(i) Limited ability to generate diverse ...\" However, according to the experimental results in Table 1, it seems that the \"Div\" metric has not improved compared to \"PepFlow w/Bb\", but rather decreased.\n\n2. In the original paper of \"PepFlow w/Bb\", the effect of \"PepFlow w/Bb+Seq+Ang\" seems to be the best, why not compare it with \"PepFlow w/Bb+Seq+Ang\"? Although there have been improvements in some metrics, they do not show a breakthrough compared to \"PepFlow w/Bb\".\n\n3. The paper did not provide a detailed analysis of computational complexity and comparison of running time. The multi-modal diffusion process may bring significant computational overhead.\n\n4. The figures in the paper are beautifully drawn, but it would be clearer to see if there were more textual descriptions.\n\n5. It seems that the author may need to further compare with [1].\n\n6. The PPFLOW [2] method has been mentioned in the related work section, but why hasn't it been compared in Table 1? Can you explain it?\n\n[1] Hotspot-Driven Peptide Design via Multi-Fragment Autoregressive Extension. ICLR 2025\n\n[2] PPFLOW: Target-Aware Peptide Design with Torsional Flow Matching. ICML 2024", "was_revised": true, "final_justification": "I have read the feedback from other reviewers. I hope the author can respond to my additional questions before I consider maintaining my score. In addition, after further discussion, I found that the author's experimental results showed that performance actually declined as the timestamp increased. This is a counterintuitive result. As the timestamp increases, the model's performance tends to saturate and stabilise. Performance will continue to improve, even if the improvement is limited, but I do not believe that it will decline. I am concerned about the author's experimental setup. Based on this, I decided to lower my score.\n\nLatest update (AOE 8.8): The authors further clarify that the model was trained at 1000 timestamps and tested at other numbers of timestamps. I think this contradicts the author's previous response. (The author claimed in the previous rebuttal that \"Based on this analysis, we selected 1000 steps as the default setting to achieve the best overall balance\". Therefore, I am not sure that the reason why the author is able to make such a judgment is that he has trained on all timestamps.) If the results provided by the author are accurate, then the experimental setup is incorrect. So I am very uncertain whether the experiment provided by the author is accurate. If my judgment is incorrect, I am willing to increase my score to 4. Please AC confirm further.", "rebuttal": "We appreciate the constructive feedback which helps us enhance the readability and quality of our paper. Below are our point-wise responses to the reviewer's concerns:\n\n---------------------------------------- \n> W1. The claim in the introduction that method addresses \"Limited ability to generate diverse ...\" while Table 1 shows their \"Div\" (diversity) metric decreased compared to baseline \"PepFlow w/Bb\" method.\n\nThank you for your insightful comment. Our claim: \"Limited ability to generate diverse yet receptor-compatible surface configurations\" . This refers to the diversity of 3D molecular surface geometries at the protein-protein interface. Table 1 metric: The \"Div\" metric measures structural diversity using TM-score between generated peptide backbones, which captures overall fold similarity rather than surface-specific diversity. Our method generates peptide surfaces de novo, enabling exploration of novel surface configurations that may not be captured by backbone TM-score diversity. A peptide can have similar overall fold (high TM-score) but present very different surface properties for receptor binding. In addition, since structures with TM-scores >0.5 maintain recognizable folds while allowing local surface variations, this constrained diversity may actually be more biologically relevant than purely maximizing structural dissimilarity.\n\n> W2. Compare against “PepFlow w/Bb+Seq+Ang.\n\nThank you for pointing this out. We include additional experiments comparing PepBridge variants directly against this method across all core metrics. Preliminary results show that “PepBridge w/Bb+Seq+Ang+Surf” achieves comparable or better performance in terms of stability, while \"PepBridge w/Bb+Seq+surf\" demonstrates better performance on affinity and diversity. We will include these results in Table 1 and expand the discussion accordingly.\n\n| | Div\\_stru (↑) | Aff. % (↑) | Stab. % (↑) | RMSD Å (↓) | BSR (↑)|\n|:--|:-:|:----:|:---:|:---:|:----:|\n|PepFlow w/Bb                   |**0.64**   |18.10      |14.04      |2.30|82.17|\n|PepFlow w/Bb+Seq               |0.50       |19.39      |19.20      |2.21|_85.19_|\n|PepFlow w/Bb+Seq+Ang           |0.42       |_21.37_|18.15      |_2.07_|**86.89**|\n|PepBridge w/Bb+surf            |0.60       |20.07      |_21.75_|**2.04**|84.62|\n|PepBridge w/Bb+Seq+surf        |_0.62_ |**22.07**  |20.71      |2.18|84.91|\n|PepBridge w/Bb+Seq+Ang+surf    |0.59       |19.16      |**25.02**|2.19|83.90|\n\n> W4. Add more textual descriptions to figures for clarity.\n\nWe appreciate this suggestion and have added more detailed textual explanations alongside key figures. The updated description for Figure 1 is: “In the top-down representation of a protein, the molecular surface plays a central role in mediating interactions between the peptide and its target receptor. Each residue is defined by its backbone and side-chain atoms, whose spatial positions are governed by a rotation $r$, a translation $m$, and torsional angles $\\psi$ and ${\\chi}$.”\n\n> w5 w6. Compare with recent methods PepHAR and PPFLOW in the main experiments.\n\nThank you for raising this point. We conducted additional experiments to benchmark our PepBridge variants against both methods. We will update Table 1 accordingly and expand the discussion.\n\n| | Div\\_stru (↑) | Aff. % (↑) | Stab. % (↑) | RMSD Å (↓) | BSR (↑)|\n|:--|:-:|:----:|:---:|:---:|:----:|\n|PepHAR (K=1)                   |0.58      |18.56      |15.69|3.73|84.17|\n|PepHAR (K=2)                   |0.61      |19.82      |15.91|3.19|84.57|\n|PepHAR (K=3)                   |**0.65**  |_20.53_|16.62|2.68|**86.74**|\n|PPFLOW                         |0.53      |17.62      | 17,25|2.94 | 78.72\n|PepBridge w/Bb+surf            |0.60      |20.07      |_21.75_|**2.04**|84.62|\n|PepBridge w/Bb+Seq+surf        |_0.62_|**22.07**  |20.71      |_2.18_|_84.91_|\n|PepBridge w/Bb+Seq+Ang+surf    |0.59      |19.16      |**25.02**|2.19|83.90|\n\n> Q1. How do different hyperparameters affect the final performance?\n\nThank you for this important question. We conducted experiments to assess how different sampling time steps affect the final performance metrics. The results indicate that longer sampling chains (e.g., 1000 steps) improve the quality of the generated structures. However, performance gains begin to plateau beyond 800 steps, and we observe a slight decrease in structural diversity, suggesting a trade-off between generation determinism and diversity. Based on this analysis, we selected 1000 steps as the default setting to achieve the best overall balance.\n\n| | Div\\_stru (↑) | Aff. % (↑) | Stab. % (↑) | RMSD Å (↓) | BSR (↑)|\n|:--|:-:|:----:|:---:|:---:|:----:|\n|PepBridge (time step =500) |0.61  |17.42 |23.97|2.85|80.05|\n|PepBridge  (time step =800)  |0.62 |18.77 |24.58|2.69|82.33|\n|PepBridge  (time step =1000) |0.59 |19.16 |25.02|2.19|83.90|\n\n> Q2. Although diversity metrics have been reported, there is a lack of in-depth analysis on how to find the optimal balance between diversity and quality.\n\nPepBridge addresses the diversity-quality trade-off through flexible sampling strategies. We explored different sampling approaches to tune this balance: DDPM sampling: Incorporates Gaussian noise at each denoising step, yielding higher diversity but potentially lower structural quality. DDIM sampling: Uses deterministic denoising trajectories, producing higher-quality structures with reduced diversity. This flexibility allows us to prioritize either exploration (diversity) or optimization (quality) based on specific design objectives. Future work could develop adaptive sampling strategies that dynamically adjust noise levels based on intermediate quality metrics, potentially achieving both high diversity and quality simultaneously.\n\n> Q3. The method’s practical applicability, plans for experimental validation, and the reliability of its computational predictions.\n\nThank you for your insightful comment. While computational results show promising agreement with known structural and energetic metrics, experimental validation remains essential. We acknowledge these results represent necessary but not sufficient conditions for biological activity.\n\nWe are planning to develop a multi-tiered validation approach:\n\n`1. In silico validation:` \n\nMolecular dynamics (MD) simulations and free energy perturbation (FEP) calculations on top-ranked candidates to assess binding stability and thermodynamics under physiologically relevant conditions.\n\n`2. Biochemical assays:` \n\nWet-lab binding assays (e.g., surface plasmon resonance, isothermal titration calorimetry) to measure actual binding affinities and kinetics.\n\n`3. Enhancing Computational Reliability:` \n\nTo improve prediction reliability, we plan to develop PepBridge-derived scoring functions for virtual screening applications.\n\n> W3 Q4. Computational complexity and comparison of running time.\n\nWe appreciate the reviewer’s concern regarding the potential computational overhead introduced by our multi-modal diffusion framework. To address this, we compared PepBridge with several baseline methods in terms of training time, inference time per sample, GPU usage, and model size. The time cost is reported as the total time spent divided by the number of designed candidates. While multi-modal processing does introduce additional complexity relative to uni-modal approaches, our analysis shows that PepBridge achieves a good balance between computational efficiency and performance. \n\n### Table: Comparison of Computation Time and Resources\n\n| Method   | Training Time  | Inference Time (s/sample) | GPU(s) Used |  Params (M) |\n|-------------------------------|---------------------|----------------------------|-------------------|------------|\n| RFdiffusion | 3 days | 80–180  | 8 A100 | ~ 120 |\n| ProteinGenerator | 4 weeks | 152 | 64 V100 | ~ 120 |\n| PepFlow | 20 hours | 14-24 | 2 A6000 | ~ 7 |\n| Chroma  | 10 weeks | 185-226 | 8 V100  | ~ 20 |\n| PepGLAD  | 29 hours | 3 | 24G GPU| ~ 2.5 |\n| PepBridge | 21 hours | 16-37 | 2 A6000  | ~ 10 |\n\n> Q5. The generation of peptides targeting receptors without obvious binding pockets.\n\nThank you for this important question about PepBridge's applicability to receptors lacking well-defined binding pockets. We conducted experiments using randomly sampled surface patches to quantify this effect. \n\n| | Div\\_stru (↑) | Aff. % (↑) | Stab. % (↑) | BSR (↑)|\n|:--|:-:|:----:|:---:|:---:|\n|PepBridge (random pockets) |0.61 |18.95 |25.17|84.12|\n\nThese results demonstrate that PepBridge remains effective even when applied to less constrained or uncertain surface regions, maintaining high structural and biochemical performance.\n\nFor receptors without obvious binding pockets, we recommend a two-step approach:\n\nBinding site prediction preprocessing: Users can integrate established binding site prediction tools to identify potential interaction regions before peptide generation\n\nMulti-site exploration: When binding sites are uncertain, PepBridge can be applied to multiple predicted or suspected interaction regions, allowing exploration of different binding hypotheses.\n\n> Q6. The effectiveness of incorporating surface modeling.\n\nWe appreciate the reviewer’s question. We conducted ablation studies using PepBridge variants with and without surface representations. The results, shown in the table below, demonstrate that incorporating surface information leads to substantial improvements across multiple performance metrics.\n\n| | Div\\_stru (↑) | Aff. % (↑) | Stab. % (↑) | RMSD Å (↓) | BSR (↑)|\n|:--|:-:|:----:|:---:|:---:|:----:|\n|PepBridge w/Bb+Seq         |0.56 |17.12  |16.41|2.87|79.79|\n|PepBridge w/Bb+Seq+surf    |0.62 |22.07  |20.71|2.18|84.91|\n|PepBridge w/Bb+Seq+Ang     |0.53 |18.46  |19.73|3.21|76.53|\n|PepBridge w/Bb+Seq+Ang+surf|0.59 |19.16  |25.02|2.19|83.90|\n\n------------------------------ \nWe are grateful for your constructive feedback and thoughtful suggestions that helped us refine our work."}]

Author rebuttal:

Meta-review: This submission introduces a joint framework for designing peptide sequences and structures while explicitly ensuring surface complementarity. The proposed surface diffusion bridge for receptor-conditioned surface generation is considered both novel and elegant. By adding baseline models, improving computational efficiency, and expanding the discussion, the authors have strengthened the robustness and readability of the paper. Reviewer Q8ka raised concerns about hyperparameters—particularly the time step—and aspects of the experimental setup. These points should be addressed in future revisions in order to further improve evaluation rigor. Overall, I recommend acceptance of this paper.
Decision: Accept (poster)