Hotspot-Driven Peptide Design via Multi-Fragment Autoregressive Extension
Authors: Jiahan Li
Tong Chen
Shitong Luo
Chaoran Cheng
Jiaqi Guan
Ruihan Guo
Sheng Wang
Ge Liu
Jian Peng
Jianzhu Ma
Venue: ICLR 2025 Poster (2025)
Keywords: AI for Science; Protein Design; Generative Models;
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
TL;DR: Designing peptides based on hot-spot estimation and autoregressive fragment extension.

Abstract: Peptides, short chains of amino acids, interact with target proteins, making them a unique class of protein-based therapeutics for treating human diseases. Recently, deep generative models have shown great promise in peptide generation. However, several challenges remain in designing effective peptide binders. First, not all residues contribute equally to peptide-target interactions. Second, the generated peptides must adopt valid geometries due to the constraints of peptide bonds. Third, realistic tasks for peptide drug development are still lacking.
To address these challenges, we introduce PepHAR, a hot-spot-driven autoregressive generative model for designing peptides targeting specific proteins. Building on the observation that certain hot spot residues have higher interaction potentials, we first use an energy-based density model to fit and sample these key residues. Next, to ensure proper peptide geometry, we autoregressively extend peptide fragments by estimating dihedral angles between residue frames. Finally, we apply an optimization process to iteratively refine fragment assembly, ensuring correct peptide structures.
By combining hot spot sampling with fragment-based extension, our approach enables \textit{de novo} peptide design tailored to a target protein and allows the incorporation of key hot spot residues into peptide scaffolds. Extensive experiments, including peptide design and peptide scaffold generation, demonstrate the strong potential of PepHAR in computational peptide binder design. The source code will be available at https://github.com/Ced3-han/PepHAR.

Published as a conference paper at ICLR 2025
HOTsPOT-DRIVEN PEPTIDE DESIGN VIA MULTI- FRAGMENT AUTOREGRESSIVE EXTENSION
Jiahan Li Tong Chen²*, Shitong Luo², Chaoran Cheng', Jiaqi Guan Ruihan Guo Sheng Wang', Ge Liu', Jian Peng", Jianzhu Ma
'Tsinghua University, 2 ?University of Washington, Massachusetts Institute of Technology, 'University of Illinois Jrbana-Champala BytteDance Inc., "eelion Inc. ced31 jhypee gmail com ma sriannhu@tsinghhn edu. en
ABSTRACT
Peptides, short chains of amino acids, interact with target proteins, making them a unique class of protein-based therapeutics for treating human diseases. Recently, deep generative models have shown great promise in peptide generation. How- ever, several challenges remain in designing effective peptide binders. First, not all residues contribute equally peptide-target interactions. Second, the gener- ated peptides must adopt valid geometries due to the constraints of peptide bonds. Third, realistic tasks for peptide drug development are still lacking. To address these challenges, we introduce PepHAR, hot-spot-driven autoregressive gen- erative model for designing peptides targeting specific proteins. Building on the observation that certain hot spot residues have higher interaction potentials, we first use an energy-based density model to fit and sample these key residues. Next, ensure proper peptide geometry, autoregressively extend peptide fragments by estimating dihedral angles between residue frames. Finally, we apply an opti- mization process to iteratively refine fragment assembly, ensuring correct peptide structures. By combining hot spot sampling with fragment-based extension, our approach enables de novo peptide design tailored target protein and allows the incorporation of key hot spot residues into peptide scaffolds. Extensive exper- iments, including peptide design and peptide scaffold generation, demonstrate the strong potential of PepHAR in computational peptide binder design. The source code will be available at https//ggthub.comm/Ccaaaaaaaa
INTRODUCTION
Peptides, typically composed of 3 to 20 amino acid residues, are short single-chain proteins inter- acting with target proteins. (Bodanszky 1988). Peptides play essential roles in various biological processes, including cellular signaling and immune responses (Petsalaki & Russell 2008). They emerging as a promising class of therapeutic drugs for complex diseases such as diabetes, obesity, hepatitis, and cancer (Kaspar& & Reichert (013).. Currently, there approximately 80 peptide drugs on the global market, 150 in clinical development, and 400 - 600 undergoing preclinical evaluation (Craik al. 2013 Fosgerau & Hoffmann, 2015 Muttenthaler et al. [022 Wang et al., 2022). Tra- ditional peptide discovery methods rely on labor-intensive techniques like phage/yeast display for screening mutagenesis libraries (Boder & Wittrup 1997] Wu et al. 2016), or energy-basee -base compu- tational tools to score candidate peptides (Raveh et al. 1; Lee et al. 2018 Cao et al. 20022). both
of which face limitations due to the immense combinatorial design space.
Recently, deep generative models, particularly diffusion and flow-based methods, have shown sub- stantial promise in de novo protein design (Huang al., 2016 Luo et al.) 2022 Watson al. 2022. Yim et al. 2023a; [ose et al., 2023). Given the compact relationship between the structure and
sequence of peptides and their target proteins (Grathwohl & Wüthrich) 1976, Vanhee et al. 201
few methods have successfully designed peptides conditioned on target information (Xie et al.
2023
Li et al. 2024a: Lin et al. 2024). These approaches typically represent peptide residues as rigid frames in the SE manifold, angles in torus manifold, and types in statistical manifold
(Cheng et al. 2024; Davis et al. 2024). Encoder-decode architectures, particularly fow-matching
methods Lipman et (022),, are then used to generate all residues simultaneously.

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Postide
CB
Pipeciae
Ca
Bond
CB
CB
Ca
Ca
Hot Spot Residues
Left
Right
Figure I: Leftt: Hot spot residues are small number of critical residues in the peptide-target binding interface, while the remaining residues act as scaffolds. peptide design, we first sample the hot spots and then use scaffold residues to link them. Right: Each residue in the protein consists of backbone heavy atoms and side-chain groups. Adjacent residues are connected by peptide bonds, which establish a planar conformation around neighboring atoms. The backbone structure of adja- cent residues can be reconstructed using dihedral angles through the operations Left and Right.
Although these methods have initially succeeded in generating peptide binders with native-like struc- tures and high affinities, several challenges remain. First, not all peptide residues contribute equally to binding. As shown in Figure some residues establish key functional interactions with the target, possessing high stability and affinity. These are referred as hot spot residues and are critical in drug discovery (Bogan & Thorn 1998; Keskin et al. 2005 Moreira et al., 2007). Other residues, known as scaffolds. help position the hot spots the binding region and stabilize the peptide (Mat-) son & Stupp/ 2012: Hosseinzadeh et al. (22TT). Considering the different roles of these residues, generating all them one step may inefficient. Second, the generated peptides must respect the non-rotatable constraints imposed by peptide bonds, which enforce fixed bond lengths and planar structures (Fisher 200I). As illustrated in Figure [], adjacent residues must maintain specific rela- tive positions to form proper peptide bonds. A model that represents peptide backbone structures independently as local frames (Jumper et al. 2021) may neglect these geometric constraints. Third, peptides are not always designed from scratch in practical drug discovery. Initial peptide candidates are often optimized, or key hot spot residues are linked via scaffold residues (Zhang et al. [209 Yu al. 2023). Thus, more realistic in-silico benchmarks needed simulate these scenarios.
To tackle these challenges, we propose PepHAR, a hot-spot-driven autoregressive generative model. By distinguishing between hot spot and scaffold residues, we break down the generation process into three stages. First, we use an energy-based density model to capture the residue distribution around the target and apply Langevin dynamics sample statistically favorable and feasible hot spots. Next, instead of generating all residues simultaneously, we autoregressively extend fragments step by step. modeling dihedral angles parameterized by von Mises distribution to maintain peptide bond geometry. Finally, since the generated fragments may not align perfectly, optimization function to assemble the fragments into a complete peptide. To simulate practical peptide drug discovery scenarios, we evaluate our method not only in de nove peptide design but also in scaffold generation, where the model scaffolds known hot spot residues into functional peptide, akin to peptide design based prior knowledge.
apply hybrid
In summary, our key contributions are:
We introduce PepHAR, an autoregressive generative model based on hot spot residues for peptide binder design;
We address current challenges in peptide design by using an energy-based model for hot spot identification, autoregressive fragment extension for maintaining peptide geometry, and an optimization step for fragment assembly;
We propose new experimental setting, scaffold generation, mimic practical scenarios and demonstrate the competitive performance of our method in both peptide binder design and scaffold generation tasks.
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2
RELATED WORK
Generative Models for Protein Design Generative models have shown significant promise in de-
signing functional proteins Yeh et al., 2023 Dauparas et al. 2023 Zhang et al. 2023c Wang al.
2021 Trippe et al. 2022 Yim et al. [2024]. Some approaches focus on generating protein sequences
using protein language models (Madani al. 2020 Verkuil et al. 2022
Nijkamp et al. 2023) or
through methods like directed evolution (Jain et al.
2022 Ren et al. [0022] Khan et [ Stan-
lon et al. 2022). Others aim to design sequences based on backbone structures (Ingraham el al.
2019
Jing et al. 2020 Hsu et al. [0222] Li et al. 2022 Gao et al. 2022; Dauparas et al. (022)) 2) For
protein structures, which are crucial for determining protein function, diffusion-basse based (Luo al.
2022
Watson et al. [2022] Yim et al. 2023b) and flow-based models (Yim et al. 2023a Bose et al.,
2023
Li et al. 2024a Cheng et al. 2024) have been successfully applied to both unconditional
(Campbell et al. (2024) and conditional protein design (Yim et al. (024). However, these generative
models typically treat all residues as equal, generating them simultaneously and overlooking the
distinct roles of residues, such those involved in catalytic sites (Giessel et al. 2022) or binding
regions (Li ct al. 2024a).
Computational Peptide Design The earliest methods for peptide design rely on protein or peptide templates for design (Bhardwaj et al.) 2016] Hosseinzadeh et al. [202]] Swanson et al. 2022). These
approaches use heuristic rules to search for similar sequences structures in the PDB database as
seeds for peptide design. A more prevalent class of models focuses on optimizing hand-crafted or
statistical energy functions for peptide design (Cao et al. 2022 Bryant & Elofsson|
[023). While
effective, these methods are computationally expensive and tend to get stuck in local minima (Raveh
al. [001]] Alford et al. 2017). Recently, deep generative models, such as GANs (Xie et al. 2023).
diffusion models 12 et al. Wang et al.] 2024), and flow models (Li et al. 2024a Lin et al.,
2024]. have been applied to design peptide structures and sequences, conditioned on target protein information, offering more flexibility and efficiency in the design process.
3 PRELIMINARY
Protein Composition A protein or peptide is composed of multiple amino acid residues, each char- acterized by its type and backbone structure, which includes both position and orientation (Jumper) et al. 2222)_ y. For the i-th residue, denoted as R, (ca, R2 O₂) ). its type G E (1...20} refers to the class of its side-chain R group. The backbone position m, E R represents the coordinates of the central Ca atom, while the backbone orientation O, E SO(3) is defined by the spatial configuration of the heavy backbone atoms (N-Ca-C). In this way, a protein can be represented as a sequence of N residues: [R,...., Rx].
The goal of this work to generate a peptide D = [RI.... Rv]. consisting of N residues, based target protein T = [R...... Ray] of length M. We also define fragments, where the k-th fragment is denoted as F(R.i..t.) = [ -11, a contiguous subset of residues. Fragments are sequentially connected within the protein, where indicates the N-terminal residue's index of the fragment in the original peptide, and l represents the fragment's length. Multiple fragments can be assembled into a complete protein based on their residue indices.
Problem Formation
The sequential ordering from the N-terminal to the C-terminal residue, along with the covalent bonds between adjacent residues, is fundamental in our approach. As illustrated in Fig [ residues are linked via covalent peptide bonds (CO-NH), with each residue Rd connecting to its neighboring residues R;-1 and R,41- These peptide bonds are partially double bonds, limiting their rotational freedom and resulting in planar configuration for atoms between adjacent residues (Ca. Cg. O, and H atoms). The backbone structure of protein can thus be described using dihedral angles, which define the spatial relations between these planes in 3D space. Each residue has three associated dihedrals: tha di, and w; The first two angles determine the geometric relationship between adjacent residues, while the third controls the position of the O atom. Given protein's 's backbone structure, we can calculate the dihedral angles for each residue. Conversely, the backbone structure of neighboring residues can also be derived from the dihedral angles, which serve as the building blocks in our model. Specifically, given the backbone position I; and orientation O, we can approximate the backbone structures of neighboring residues RT-1 and R using coordinate
Directional Relations
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Founding Stage
Extension Stage
Correction Stage
Generate Hot Spots
Extend
Correct Geometries
Fragments
d=R
Co
Targer prosein
9 x, 0 T
P( Φ d, Rig E)
V Vo.oJ
Spoc
Residue
Uncorrected Bond Corrected Bond
New Residue
Environment
Figure 2: Overview of our three-stage approach: In the first foudning stage, k hot-spot residues are generated (k 2 in this example) from learned residue distribution around the target. New residues are extended the fragments' left right in the second stage based on dihedral angle distributions. Finally, in the correction stage, gradients from the objective functions are applied to refine the complete peptide.
transformations. Details are included in the Appendix
B
(0;-1,, 0:-1)
-eeft x; 14-1, Φz),
(1)
(1:+11 O++1) =Right Oi v/, (1+1)-
METHODS
To tackle the challenges in peptide design, propose three-stage approach to generate peptides D based on their target protein T. Our method generates hot-spot residues, extends fragments, and corrects peptide structures. As shown in Figure [ and Algorithm [ the first stage, the Founding Stage, independently generates a small number k of hot-spot residues Ri....., R;, from the learned residue distribution P(R T"). In the second stage, the Extension Stage, these hot-spot residues are used as starting points to progressively extend & fragments Fi..... F& by adding new residues the Left or Right in an autoregressive manner, until the total peptide reaches the desired length L. Finally. since each fragment is extended independently. the third stage, the Correction Stage, adjusts the sequences and structures of the fragments, refining them based on the gradients of the objective function to ensure valid geometries and meaningful peptide sequences.
4.1 FOUNDING STAGE
The founding stage first generates hot-spot residues based on the target protein T. By introduc- ing the residue distribution P(R T), hot-spot residues represent those with higher probabilities (i.e., lower energies) of appearing near the binding pocket compared to other backbone structures and residue types. The generation of hot-spot residues focuses on finding regions with high prob- abilities, where residues are more likely to interact directly with the target. Conversely, regions with low probabilities (i.e., high energies) will have fewer peptide residues. For example, peptide residues should neither occur far from nor close to the pocket (Cao et al. [022 Li et al. 2024a). as such regions may have near-zero probabilities (high energies) of residue occurrence. We parame- terize P(R T)) using an energy-based model, which is conditional joint distribution of backbone position æ, orientation O, and residue type
Pa(c, œ O O
T) 7 exp (go.c(x, T))
(3)
here ge a scoring function parameterized by an equivariant network, which quantifies the score of residue type occurring at given backbone structure with position and orientation O In other words, g is the unnormalized probability of type c. And the normalizing constant associated with sequence and structure information, which do not explicitly estimate.
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Algorithm 1: Peptide Sampling Outline
Data: Target protein T, peptide length N. hot-spot residue count k. and indices [i.....,
Founding Stage
for < to do
Sample hot-spot residue Ri, Po(c, a,, ()) based on Eq. 6 Initialize fragment Fu. f- :
and
Extension Stage
while + +
< No do
Randomly choose a fragment index E I,..., k and direction E []; Set the starting residue as either the N-terminal Ri or the C-terminal Ri 11
Sample new residue on the left R, or on the right Riys2, based on Eq. 15 and 16
10 Add the new residue to fragment Fy;
11 Merge fragments into the peptide D + Fi +... FF
12
Correction Stage
13 for t f 1, do
14 Calculate the objective I based on the current peptide using Eq Update the peptide using gradients from Eq 23 and 24
15
16
return D = [R..... ER......Ny Ry]
Network Implementation The density model go is parameterized by the Invariant Point Attention backbone network (Jumper al., 2021 Luo al. 2022 Yim et al. 2023b), which is SE(3) invari- ant. It takes positive residues (peptide residues) and negative residues (perturbed residues) along with the target protein as input, encoding them into hidden representations. A shallow Multi-Layer Perceptron (MLP) is then used to classify residue types for likelihood evaluation.
Training We use the Noise Contrastive Estimation (NCE) train this parameterized energy-based model Gutmann & Hyvärinen, 2010). NCE distinguishes between samples from the true data distribution (positive points) and samples from a noise distribution (negative points). The posi- tive distribution corresponds to the ground truth residue distribution of the peptide over the tar- get (c, x. 0) ~ p(R T), while the negative samples are drawn from the disturbed distribution (Cueg: x 00) ~ tations, labeled type Cueg. As positive and negative data are sampled equally, the NCE objective for a single positive data point is:
p( ()) by adding large spatial noises to the ground truth positions and orien-
exp g0,e (x,, O O
I(c, x. O) log Ee cxp J (x, O T) + p(Cneg: I. 0 T)
(4)
As common practice Gutmmann & Hyvärinen 2012), we fix the negative probability p(Cneg: O T') as a constant, simplitying the evaluation of log-likelshods for negative samples. The final loss function is given by:
CNC = -E+ [[c, x. O T)] E_ [Mnng .0 [T)
(5)
Sampling In the founding stage, we sample k hot-spot residues from the learned energy-based distribution, where & is kept small relative to the peptide length (c.g.. k = ~ 3 in our experiments). Since hot-spots are assumed be sparsely distributed along the peptide (Bogan & Thorn 1998), we approximately sample them independently. For each hot-spot residue, we employ the Langevin MCMC Sampling algorithm (Welling & Teh (2011), starting from an initial guessed position x" and orientation 0", and iteratively update them using the following gradients:
2
a <x0
V Va (xr 0º O'1T) + e2 2/ NO Ia),
2
t+ e
Σ Vogo. 0' T) + Z,)), Z (0,
1+1 ~softmax (ar (T).
(8)
Since orientation lies in the SO(3) space, we employ the exponential map and a Riemannian random walk the tangent space for updates (De Bortoli et al. 2022). The summation of all possible
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residue types ensures that transition from regions of low occurrence probability to regions of higher probability. Finally, after each iteration, the residue type e is sampled conditioned on the updated position and orientation.
4.2 EXTENSION STAGE
The extension stage expands fragments into longer sequences, starting from the sampled hot-spot residues. At each extension step. we add a new residue either the left or right of fragment F. Based on the relationship between adjacent residues (Eq 12). the backbone structure of the new residue inferred from its dihedral angles and the structure of the adjacent residue, which is either the N-terminal or C-terminal residue of the fragment. Specifically, when connecting new residue to residue Rs in the j th fragment F), we model the dihedral angle distribution P(V. d, Ri, E), where d E L, R} indicates the extension direction and E' represents the surrounding residues, including target T and other residues in the currently generated fragments.
11,)) d L, P( Φ d, Rag. E3) = P(Wi, 01,+1), d d= R.
Since multiple angles are involved, the dihedral angle distribution is modeled as a product of pa- rameterized von Mises distributions (Lennox al., 2009). which use cosine distance instead of L2 distance to measure the difference between angles, behaving like circular normal distributions. For example, when L, we have:
( P( 1, 1, 0i,)) =JvM (11 1. Kive (Vvi(dssi Moby i Kigzy
(10)
fvM(1r, 11: M (
2 2 exp (Kvey-- cos cos(uurr 12 1))_
(11)
[vaaldigi Poi, kei;)) 2nr To (Hie))))
exp (Kas, cos(uer, - (b,))
(12)
Here, Io(-) denotes the modified Bessel function of the first kind of order O. The four distribution parameters are predicted by a neural network ho, called the prediction network. Similarly, for = R, the network predicts another set of four parameters:
(M 1 Kwn, Mong Kod (Mure Medry Mey + Koygtt)
d L, d = R.
ho Riy; F.) F3)= =
(13)
Network Implementation The prediction network ha uses the same IPA backbone to extract fea- tures. However, to avoid data leakage during training, we employ directional masks in the Attention module since the neighboring backbone structures analytically. For instance, if the direction Left, residues can only attend to their neighbors on the right during attention updates, and vice versa for Right.
known and dihedral angles can be derived
Training We optimize the network parameters using Maximum Likelihood Estimation (MLE) over directions d {L, R} and peptides in the peptide-target complex dataset. The MLE objective is given by:
MLE = -E [lg P(W. & d, Ri,, F))
(14)
Sampling During the extension stage, we generate k fragmmets corresponding to i hot-spot residues from the founding stage. The extension process is iterative, where fragments are autoregressively extended until the total peptide length (the sum of fragment lengths) reaches a predefined value (e.g., the length of the native peptide). Consider one-step extension of fragment F in direction L implies adding residue the left of
d. The starting residue R., depends on the direction: the fragment, making R; the N-terminal residue (first residue); d = R implies adding to the right, making Rg the C-terminal residue (last residue). The other residues in the fragment and target form the environment E. We then sample the dihedral angles for the new residue in the chosen direction from the predicted distribution, using he. For example, when = L:
Vi ~fvM(Vi -1 hold L,, Rí E)), 0i ~fvM(di, hold = R, Ru, E)).
(15)
(16)

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Next, the backbone structure of the newly added residue R,,-1 is reconstructed using the transfor- mations in [q The residue type is then estimated by the density model go used during the founding stage:
( Oiş-1) Le, Oi, the - dig)
(17)
Ci--1 ~softmax go (0 (1) 01,-1 E).
(18)
Finally, the process is repeated for another randomly selected fragment and direction.
4.3 CORRECTION STAGE
Although we autoregressivelyy extended each fragment, the resulting fragments may not form valid peptide with accurate geometry. For example, some fragments may not maintain proper distances between each other, leading to broken peptide bonds, while others may have incorrect dihedrals or residue types in relation to the whole peptide and the target protein. Some fragments may also exhibit atom clashes within the target protein. Inspired by traditional methods using hand-crafted energy functions (Alford et al. 2017), we introduce correction stage as a post-processing step to refine the generated peptides. Rather than relying on empirical functions, we use the learned, network-parunne parametrrra distributions from the first two stages to regularize the peptides.
For a generated peptide D = [(e,, I1, Oi), .... (cN, æN ON)], the dihedrals of each residue are derived based on the backbone structures of adjacent residues. To ensure self-consistency between dihedrals and backbone structures, we use them to estimate new backbone structures and compare them with the original ones. The distance between these backbone structures reflects the validity of the generated peptide with respect to peptide bond properties and planarity. We define the distance between two residues' backbone structures separately for position and orientation and derive the backbone objective considering both directions:
d((z;, O:), (z,, 0,)) = ||= 12 +1 log(O,))1
(19)
Toe d(Left(x; Or, ()) (e:-1,0--111 d (Right(x;, O, tha, 0.+1) - (0 O++1)).
1=2
(20)
Additionally, the dihedral angles must conform to the learned distribution P(w,, Φ) to ensure correct geometric relationships between neighboring residues. This leads to the dihedral objective, which similar Eq. [4 However, in Eq. [14] we optimize the network parameters fit the angle distribution, whereas here, we keep the learned networks fixed and update the dihedrals instead:
N-1
Jang Σ logg(
Σ
PoWs, 01+1).
(21)
The final optimization objective a weighted sum of the backbone and dihedral objectives. We iteratively update the peptide's backbone structures by taking gradients, similar to the founding stage, but we optimize the entire peptide at each timestep. The density model go predicts the residue types the end of each update step. Unlike the founding stage, where started from random structures, the correction stage begins with the complete peptide.
Jeorr =bs + Xang
(22)
(a
4+1 update(aa), Oú Vn No.JJ), ~softmax 0º E).
(23)
(24)
EXPERIMENTS
Overview We evaluate PepHAR and several baseline methods on two main tasks: (1) Peptide Binder Design and (2) Peptide Scaffold Generation. In Peptide Design, co- generate both the structure and sequence of peptides based on their binding pockets within the target protein. However, in real- world drug discovery, prior snowledge-ssuhh key interaction residues at the binding interface or

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initial peptides for optimization often available. Therefore, introduce Peptide Scaffold Gen- eration to assess how well models can scaffold and link these key residues into complete peptides, reflecting more practical applications. Details are included in the Appendix E
Dataset Following Li et al. (2024a), we construct our training and test datasets. This moderate- length benchmark is derived from PepBDB (Wen al. 2019) and Q-BioLip (Wei et al. 2024), with duplicates and low-quality entries removed. The binding pocket defined as the residues in the target protein which has heavy atoms lying in the 10Aradius of any heavy atom in the peptide. The dataset consists of 158 complexes across 10 clusters from mmseqs2 (Steinegger & Söding 2017). with an additional 8, 207 con-hooologous examples used for training and validation.
5.1 PEPTIDE BINDER DESIGN
In Peptide Binder Design, we co-generate peptide sequences and structures conditioned on the bind- ing pockets of their target proteins. The models provided with both the sequence and structure of the target protein pockets and tasked with generating bound-state peptides.
Table 1: Evaluation of methods in the peptide design task. K 1, is the number of hot spots.
Valid %
RMSD à
SSR %
BSR %
Stability %
Affinity 1
Novelty %
Diversity 15
Success S%
RFDiffusion
66.04
4.17
63.86
26.71
26.82
16.53
53.74
25.39
25.38
ProtcinGenerator
PepFlow
40.27
2.07
33.46
86.89
18.15
21.37
50.26
20:23
27.96
PepGLAD
55.20
3.83
80.24
19.34
20.39
10.47
75.07
32.10
14,05
PepHAR (K 1)
57.99
81.21
23.00
PepHAR
79.07
PepHAR (K
59.31
2.68
84.91
86.74
16.62
20.53
79.11
29.58
23.54
10
Design Scaffold
PDB: Javn
PDB: 2drk A.::244224
A3:-33.41
8-
RMSD
APKPVPEPRG
SHKIDNLD
RMSD:2.72
RMSD: 1.08
AG:-37.40
AG:-25.16
AAR: 0.4
A.R:0.375
K=1
K-2 Hot Nums
K-3
OSGPPPRGRE
GPKLDALS
Figure 3: RMSD of generated pep- tides, considering different tasks and numbers of hotspots. More hotspot residues lead to better results.
Figure 4: Two examples of generated peptides, along with RMSD and binding energy. PepHAR generate native-like peptides with better bind- ing affinities.
Metrics A robust generative model should produce diverse, valid peptides with favorable stability and affinity. The following metries employed: (1) Valid measures whether the distance be- tween adjacent_ree residues is consistent with peptide bond formation, considering C. atoms within 3.8A valid (Chelvanayagam
al. 1998; Zhang al. 2012). (2) RMSD (Root-Mean-Square Deviation) compares the generated peptide structures to the native ones based on C₂ distances af- ter alignment. (3) SSR (Secondary Structure Ratio) evaluates the proportion of shared secondary structures between the generated and native peptides labeled by DSSP (Kabsch & Sander 1983). (4) BSR (Binding Site Rate) assesses the similarity of peptide-target interactions by measuring the overlap of binding sites. (5) Stability calculates the percentage of generated complexes that are more stable (lower total energy) than their native counterparts, based on rosetta energy functions Chaudhury et al. 2010 Alford et al. 2017). (6) Affinity measures the percentage of peptides with higher binding affinities (lower binding energies) than the native peptide. Beyond geometric and en- ergetic factors, the model should also exhibit strong generalizability in discovering novel peptides.
(7) Novelty is the ratio of novel peptides, defined by two criteria: (a) TM-score & 0.5 (Zhang & Skolnick 2005) and (b) sequence identity 0.5. (8) Diversity quantifies structural and sequence
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variability, calculated the product of pairwise (1-TM-score and (1 (1-sequence identity) across all generated peptides for a given target. (9) Success rate evaluates the proportion of AF2 AF2-predicted complex structures with a whole ipTM value higher than 0.6.
Baselines We compare PepHAR against three state-of- sate-of-theearr peptide design models. RFDiffusion (Watson et al. 2022) uses pre-trained weights from RoseTTAAold (Baek et al. [021] and generates protein backbone structures through a denoising diffusion process. Peptide sequences are then re- covered using ProteinMPNN (Dauparas et al.] 2022). ProteinGeneratoo augment RFDiffusion with sequence-structure jointly generation (Lisanza et al. 2023). PepFlow (Li et al. 2024a) models full- atom peptides and samples peptides using a flow- mmtthhinnng framework on a Riemannian manifold. PepGLAD (Kong et al., 2024) employs equivariant latent diffusion networks to generate full-atom peptide structures.
Results As shown in Table PepHAR effectively generates peptides that exhibit valid geome- tries, native-like structures, and improved energies. While RFDiffusion produces valid peptides due to its pre-trained protein folding weights. PepFlow, which is trained solely peptide datasets, struggles with generating valid peptides, making it challenging for practical applications. In con- trast, PepHAR's autoregressive generation based on dihedral angles ensures the production of valid peptides and allows for precise placement at the binding site with accurate secondary structures. Similar to previous work (Li et al. 2024a), RFDiffusion excels at generating stable peptide-target structures, while PepHAR demonstrates competitive performance compared to PepFlow. Addition- ally, PepHAR shows impressive results in terms of novelty and diversity, highlighting its potential for exploring peptide distributions and designing a wide range of peptides for real-worke applica- tions. Figure iillustraees two examples of peptides generated by PepHAR, which closely resemble the structures and binding sites of native peptides while exhibiting low binding energies, indicating high affinities for the target.
5.2 PEPTIDE SCAFFOLD GENERATION
Compared to designing peptides from scratch, more practical approach involves leveraging prior knowledge, such as key interaction residues. We introduce this as the task scaffold generation, where certain hot spot residues in the peptide peptide by connecting these residues. In this context, the generated peptide should incorporate the hot spot residues in the correct positions, effectively scaffolding them. Hot spot residues are selected based on their higher potential for interacting with the target protein. To identify these, we first calculate the energy of each residue using an energy function (Alford et al., (017), then manually select residues that are both energetically favorable and sparsely distributed along the peptide sequence. These selected residues are fixed as the condition for scaffold generation.
fixed, and the model must generate complete
Table 2: Evaluation of methods in the scaffold generation task. spots.
1,2,3 is the number of hot
Valid
2.
SSR 56
Stability
Affinity
Novelty
Divensty
Success
RFDilfusion (K 3)
69.88
4.09
26.83
20.07
21.26
55.03
26.67
23,15
ProteinGeenertoo (K 3)
68.52
3.95
65.86
24.17
20.60
22.80
50.73
20.52
20:42
RepFoo (K 3)
42.68
2.45
81.00
82.76
11.17
18.27
50.93
16.97
24.54
PspGLAD (K =3)
53.51
3.84
76.26
19.61
12.22
18.27
50.93
30.99
14.85
PopHAR (K = 1)
56.01
5.72
80.61
78.18
17.89
19.94
81.61
29.79
20.43
PopHAR
74.76
22.09
PoplIAR
72.56
21.45
Baselines and Metrics We use the same baselines and metrics as in the Peptide Design task. Specif- ically, for RFDiffusion and Protein Generator, the known hot spot residues, along with the target, are provided as an additional condition. For PepFlow, we modify the ODE sampling process by initializing it with the ground truth hot spot residues and ensuring the model only modifies the re- maining residues. In our method, we replace the sampled hot spot residues with the known ground truth residue.
Results As shown in Table 2 PepHAR demonstrates excellent performance in scaffolding hot spot residues into complete peptides. Given that the hot spot residues have functional binding capa- bilities. In contrast, the scaffold residues contribute primarily to structural integrity, the generated peptides are expected to possess valid, native structures with high stability. PepHAR successfully generates valid and native-like structures, ensuring that scaffold residues do not disrupt interactions between hot spot residues, achieving the best scores in SSR and BSR. Moreover, PepHAR achieves

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Published as a conference paper at ICLR 2025
Hot Spots
Generated
Reference
ENKIDVLQ
RHAVEVKN
HKDIDDST
DEKIDNLD
3av:
Energy::-13.55 -33.59
-212.84
Energy:- 150.26
Energy:-140.73
RMSD: 1.78
RMSD: 2.66
RMSD: 2.08
GEKPDEPEPP Energy:-73.84 RMSD: 1.02
GSCPSEPSEP
YEKPALPRKR
5ih2
Energy: -8199
Energy:-72.60 RMSD: 1.33
Energy: -72.15
RMSD: 1.67
Figure 5: Examples of generated scaffolded peptides by PepHAR. PepHAR can scaffold hotspot residues, leading to more stable complexes with native-like valid geometries
competitive stability compared to RFDiffusion, which is trained on larger PDB dataset. Addition ally. PepHAR produces novel and diverse scaffolds. Figure 5 presents two examples of scaffolded peptides alongside native peptides and given residues. The generated scaffolds exhibit similar struc- tures to the native ones, while displaying variations in geometry and orientation at the midpoints and ends the peptides, indicating flcxibility in the scaffolding regions. Furthermore, the gener- ated scaffolds often have lower total energy than the native peptides, suggesting enhanced stability of the complex and improved interaction potential.
5.3 ANALYSIS
Table 3: Ablation results of PepHAR peptide design task.
Valid %
RMSD A
SSR %
BSR
Stability
Affinity %
Novelty
Divensty
PepHAR (K' 3)
59.31
2.68
84.91
86.74
16.62
20.53
79.11
29.53
PopHAR w/o Von Mosics
56.21
3.10
80.86
82.21
17.24
15.68
79.44
29.65
PepHAR w/o Spot
55.62
3.99
74.17
12.21
81.51
PepHAR w/o Correction
53.66
3.41
80.46
81.43
15.72
14.85
82.75
37.87
Effeet of Hot Spots Comparing Tables [ and 2 we observe that introducing hot spots as prior knowledge significantly boosts PepHAR's performance while providing little benefit to RFDiffusion and PepFlow. This highlights PepHAR's versatility across different design tasks. We also investigate the effect of varying the number of hot spots, denoted K 1, 3. As shown in Tables and Figure 3] increasing the number of hot spots improves geometries and energies, regardless of whether the hotspots are estimated by density models or provided as ground truth; however, it negatively impacts novelty and diversity. This illustrates a trade-off between designing low-diversity but high-quality peptides (in comparison to the native) and high-diversity but varied peptides (Luo et al. 2022
et al. 2024a).
Ablation Study Table presents our ablation study. which assesses the effectiveness of different components in PepHAR. "PepHAR w/o Hot Spot" refers to the model where hot spots sampled from the density model are replaced with randomly positioned and typed residues. "PepHAR w/o Von Mises" indicates using direct angle predictions instead of modeling angle distributions. We also removed the correction stage from "PepHAR w/o Correction." " Our findings reveal that generated hot spots are crucial for Valid, RMSD, SSR, and BSR metrics, underscoring their importance for achieving valid geometries and interactions. Modeling angle distributions also contributes positively by accounting for the flexibility of dihedral angles. Lastly, the final correction stage is vital in en- hancing fragment assembly, leading to peptides with higher affinity and stability, which are essential for effective protein binding.
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CONCLUSION
In this work, we presented PepHAR, a hot-spot-based autoregressive generative model designed for efficient and precise peptide design targeting specific proteins. By addressing key challenges in peptide design-such as the unequal contribution of residues, the geometric constraints imposed by peptide bonds, and the need for practical benchmarking scenarios- PepHAR provides compre- hensive approach for generating peptides from scratch or assembling peptides around key hot spot residues. Our method leverages energy-based hot spot sampling, autoregressive fragment extension through dihedral angles, and an optimization process to ensure valid peptide assembly. Through extensive experiments on both peptide generation and scaffold-based design, we demonstrated the effectiveness of PepHAR in computational peptide design, highlighting its potential for advancing drug discovery and therapeutic development.
ACKNOWLEDGEMENTS
This work was supported by the National Key Plan for Scientific Research and Development of China (2033YFC0043300; China's Village Science and Technology City Key Technology fund- ing, and Wuxi Research Institute of Applied Technologies, Tsinghua University under Grant 00242001120.
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A HOT SPOT RESIDUES
In the context of protein interactions, hot spots refer to specific amino acid residues within a protein- protein interface that significantly contribute to the binding affinity and stability of the complex (Bogan & Thorn 1998 Moreira et al.] 2007; Keskin et al.) [005; Guo et al.). These residues are often characterized by their energetic contributions, with a few critical interactions having a dispro- portionate effect on the overall binding energy. These regions typically have a higher likelihood of binding events and are characterized by favorable structural and energetic features. Identifying and understanding these hot spots is crucial for the design of effective inhibitors or modulators that selectively target protein-proteio interactions (PPIs). Several classic examples illustrate the concept of protein interaction hot spots:
p53 and MDM2: The interaction between the tumor suppressor protein p53 and its negative regulator MDM2 is a well-studied example. Key residues in p53, such as Leu-22, Trp-23, and Phe- 19, have been identified as hot spots for binding to MDM2. Disruption of this interaction is promising strategy for cancer therapy (Vassilev 2004).
Aniiooy-Anttignn Interactions: The binding of antibodies to their specific antigens often involves hot spots that are essential for the specificity and affinity of the interaction. For example, the interaction between the antibody 1G12 and the HIV-I envelope glycoprotein gp120 features specific residues on both molecules that contribute significantly to binding (Zhou et al. 2007).
Receptor-Peptide Interactions: The interaction between the CD4 receptor and the HIV-1 gp120 envelope protein is another notable example. Specific residues on CD4, such as Asp368 and Tyr371, serve as hot spots that facilitate binding, leading to viral entry into host cells (Sattentau & Moore 1993).
The interaction between cytokines and their receptors is crit- ical for immune signaling. For instance, the binding of interleukin-6 (IL-6) to its receptor IL-6R involves hot spot residues that are crucial for signal transduction and biological ac- tivity (Rose-John et al. 2007).
Cytokine- Binding:
In addition to hot-spot residues, which directly mediate protein-protein interactions, the remaining residues in the interface are referred to as scaffold residues. These scaffold residues play a crucial role in providing structural support to maintain the stability and conformation of the interface. While scaffold residues do not typically contribute significantly to the binding free energy, they ensure that the hot spots are properly positioned to interact with their binding partners. This structural framework is essential for maintaining the overall architecture of the protein complex and facilitating specific interactions at the hot-spot regions. For example, scaffold residues often help to shield hot spots from solvent exposure, thereby preserving their high binding affinities.
In our context, we focus on the hot-spot residues on the peptides that are crucial for key interactions with their target, as they are thought to be structurally conserved. While there are also hot spots on the target proteins, we do not model them here. Some works, however, focus on designing binders that specifically target these hot-spot residues on the proteins, treating them as critical interaction points (Watson et al. 2022 Zambaldi et al. 2024).
In our peptide design task, since we aim to design peptides from scratch, we lack prior knowledge about the ground-truth hot-spot residues, which are typically defined by energy functions and con- served interactions. Instead, we employ a density model to identify statistically favorable residues as hot spots. Essentially, our energy function is represented by neural network. For the scaffold generation task, we first use the Rosetta energy function (Raveh et al. 2011 Alford et al., 2017) to compute the factorized binding energies of each peptide residue at the binding interface. We then manually select key residues with lower binding energy contributions, ensuring they are uniformly distributed along the peptide. This approach is important because, in scaffold generation, aim to link these hot spots with a feasible and evenly distributed scaffold structure, ensuring the stability and functionality of each fragment.
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B ADJACENT RESIDUE RECONSTRUCTION
B.1 PEPTIDE BOND AND PLANAR
Peptide bonds are the key linkages between amino acids in proteins, formed through a condensation reaction between the carboxyl group of one amino acid and the amino group of another. This bond is an amide bond, specifically between the carbonyl carbon (C=0) of one amino acid and the nitrogen (N-H) of another. The nature of the peptide bond plays a crucial role in determining the structure and stability peptides and proteins.
One significant characteristic of the peptide bond is its partial double bond nature. Although it's formally a single bond, resonance between the lone pair of electrons on the nitrogen and the car- bonyl group gives the bond partial double-bond character. This resonance limits rotation around the peptide bond, which leads to a rigid and planar structure between the alpha carbon atoms of the amino acids involved in the bond. As result, the peptide bond creates flat, coplanar arrangement of the six atoms involved: the nitrogen, hydrogen, carbon, oxygen, and the two alpha carbons (one from each amino acid).
This planarity is crucial because it helps constrain the protein's 's overall folding pattern. The rigid planes of successive peptide bonds are connected by flexible single bonds at the alpha carbons, allowing the polypeptide chain to fold into its specific secondary structures like alpha helices and beta sheets. The restricted rotation around the peptide bond imposes dihedral angles, and th, which define the conformation of the polypeptide backbone and are critical in shaping the overall dire-diiensional structure of proteins.
In summary, the partial couble-bond character of the peptide bond is a key factor in maintaining the planarity and rigidity the peptide backbone, which in turn plays a fundamental role in determining the folding and function of proteins.
B.2 DIHEDRAL ANGLES
In proteins, the dihedral angles-gt & and e' define the conformation of the protein backbone by describing the rotation around specific bonds in the peptide chain. These angles crucial for understanding the three-dimensional structure of a protein. Below is a detailed explanation of how these angles are calculated:
General Formula for Dihedral Angle Calculation consecutive atoms (A, C, D), the steps are:
To calculate a dihedral angle between four
1. Compute the bond vectors:
AB AB B
CC CD CD=D-C
2. Calculate the normal vectors of the two planes formed by the atoms:
i AB x BC, 1h = BC x CD
3. Use the dot product find the angle between the planes:
angle arctan [CC (Mg x n2), n1 722)
(25)
This general method can be applied to calculate & and & dihedral angles across a protein's 's backbone.
Phi (dx) Angle The oi angle is the dihedral angle around the bond between the nitrogen (N) and alpha carbon (C.) of residue i. It is defined by the following four atoms:
Cj-1: Carbonyl carbon of the previous residue
Nj Amide nitrogen of the current residue
Ca Alpha carbon of the current residue
Cj Carbonyl carbon of the current residue
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The dihedral angle de is caleulated as the angle between the planes formed the atoms (C,-1, N,, Ca.s) and (N₂, Ca.i, Cj):
Φ angle between planes (C:-1; Nr, Ca.s) and (N,, Ca.i. Ci)
(26)
Psi (1b;) Angle The v/ angle describes the dihedral angle around the bond between the alpha
carbon (Ca) and the carbonyl carbon (C) of residue is defined by the following four atoms:
Nj Amide nitrogen of the current residue
Ca Alpha carbon of the current residue
* Cj: Carbonyl carbon of the current residue
M411: Amide nitrogen of the next residue
The dihedral angle 1/, is calculated as the angle between the planes formed by the atoms (Na, Ca.ir C:) and (Ca.i, C₁, N++1):
1/4 = angle between planes (N, Ca.i, Ct) and (Co.i, Ci N(41)
(27)
Psi (1/-1) of Previous Residue The w angle is calculated similarly to 3 but for the previous residue. involves the following four atoms:
Ni-1: Amide nitrogen of the previous residue
Ca.-1: Alpha carbon the previous residue
Ci-1: Carbonyl carbon of the current residue
Nj: Amide nitrogen of the current residue
The dihedral angle oi:- is calculated as:
4411 angle between planes (N--1, Ca C--1) and (Ca,i-1, C1-1,
(28)
Phi (0:+1) of Next Residue The det1 angle is similar to but for the residue. It involves the following four atoms:
Cj Carbonyl carbon of the current residue
Ni41: Amide nitrogen of the next residue
Ca.t+i: Alpha carbon of the next residue
C++1: Carbonyl carbon of the next residue
The dihedral angle Φ++1 calculated as:
di+1 = angle between planes (Ci, No41, Ca.+1) and (Net1, Ca,411, C..1
(29)
C ADIACENT STRUCTURE RECONSTRUCTION
Reconstructing the backbone structures of adjacent residues R;-1 and RG+1 involves two main steps. First, we use dihedral angles to rotate the standard residue coordinates in the local frame. Then, we transform the local frame coordinates back the global frame based the position and orientation of the given residue. As an example, let's consider the Right operation, where we use the coordinates of R2 and the associated dihedral angles dy and d:+1 compute the structure of R
C.1 CALCULATING X, AND O
To convert local coordinates into global coordinates, we first need to calculate the translation vector x; and the orientation matrix O, for residue R.
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Translation Vector The translation vector x; defines the global position of residue R, and it is typically chosen as the position of a key atom within the residue. common choice is the a-carbon (CA,), which is centrally located in the backbone of the residue, providing stable reference point for the rest of the structure.
X; CA:
(30)
This ensures that the relative coordinates of other atoms in R₃ can be translated into the global coordinate system.
Orientation Matrix O; The orientation matrix O; defines the local frame of reference for residue R2 and allows us to rotate local coordinates into the global frame. To construct Oj we use the positions of three key atoms: C, (carbonyl carbon), CA, (alpha carbon), and N, (amide nitrogen). These atoms form the backbone of the residue, and their relative positions define the orientation of the local coordinate system.
The steps to compute O are as follows:
1. Compute the vector from C; to CA,, and normalize it to obtain the first basis vector e1
V1 = C; CA.
(31)
V1
G1
(32)
v1ll
Compute the vector from N, to CA,, and remove the projection this vector onto e₁ to get the component orthogonal e1. Normalize this to obtain the second basis vector eg:
V2 N; CA,
(33)
112
V2
||e
el
(34)
U2
e2
||u2|
(35)
3. Compute the third orthogonal vector C3 as the cross product of ej and e2!
e3 ej e2
(36)
The orientation matrix O is formed by combining these three orthonormal vectors into a matrix:
O; [ei, e2, ea]
(37)
This orientation matrix O defines the local coordinate system for residue R and can be used to transform the local coordinates neighboring residues into the global frame.
C.2 LOCAL COORDINATE RECONSTRUCTION
Given a reference peptide structure, we apply dihedral angle transformations to compute the new coordinates based on the angles uhs and Φ++1.
Rotation Matrix Definition The rotation matrix for an arbitrary axis (dz, dyy dz) and angle 0 is given by the Rodrigues' rotation formula:
R(d, 0) I sin(O) (1 ())))
(38)
where is the skew-symmetrie matrix of
0
- d2
dy
K
d_
0
dr
(39)
-dy
dg
0
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Initial Reference Coordinates
The initial reference coordinates for the peptide follows:
N1 = (-0.572, 1. 1.337, 0.000),
CA1 = (0.000, 0.000, 0.000), C1 = (1.517,1.0000 0.000, 0.000)
N2 (2.1114, 1.1887, 0.0000), CA2 (3.5606, 1.3099, 0.0000),
C2 = (4.0913, -..1112, 0.0000)
Note: The above coordinates are derived from the standard structure of glycine (GLY), one of the simplest amino acids. GLY chosen because it lacks a side chain (only a hydrogen atom as side chain), making it ideal reference for constructing peptide backbone geometries. Additionally, the peptide bond between C1 and N2 assumed to be planar, with 11 = d2 0%, reflecting the rypical rigidity of peptide bonds. This simplifies the geometric model by aligning the peptide bond in 00180-111000 degree plane.
Rotate C2 around CA2 N2 axis (6.-1) We first rotate C2 around the axis from CA2 to N2 by the dihedral angle Φ++1. The axis is defined as:
N2 CA2
d d22-CA12 |N2 CA22
(40)
The new position of C2 after applying the rotation matrix R(6++1) is:
C2' CA2 + R(dN2-CARR P++1) (C2 CA2)
(41)
Rotate C2 around CA1 C1 axis (1:)) Next, rotate C2 around the axis from CA1 to C1
by the dihedral angle 14. The axis is defined as:
C1 - CA1
dC1-CA1
(42)
|| CA1]
The new positions of C2, CA2, and N2 after applying the rotation matrix R(w)) are:
C2 CA1 + R(dCI-CAL, v/) (C2' - CA1)
(43)
CA2 CA1 + R(dCI-CAL v.) (CA2 CA1)
(44)
N2 = CA1 + R(d wh) (N2 - -CA1)
(45)
C.3 CONVERTING RELATIVE COORDINATES TO GLOBAL COORDINATES
Once the relative coordinates have been calculated, we transform them back into global coordinates using a combination of rotation O, and translation o; We use the calculated relative coordinates of C22, C2, and N2 and transform them into the global coordinate system.
This transformation is applied to each of the atoms C'22, C2, and N2:
CA1+1 = CAA = 3; + O, CA2
(46)
C++1 = C2global x; + O C2
(47)
N1+1 = N2 globall = + O N2
(48)
After getting backbone atoms, the side-chain atoms are reconstructed by side-chain packing algo- rithms, in our implementation, we use PackRotamersMove in Pyrosetta (Chaudhury et al. (010)) to pack side-chains for the newly added residue, which is based on rotamer library and rosetta energy
function (Shapovalov & Dunbrack 2011 Alford et al. 2017).
D VON MOSIES DISTRIBUTION
The von Mises distribution is continuous probability distribution defined on the circle, commonly used to model angular or directional data. It is sometimes referred to as the "circular normal dis- tribution" due to its similarity to the normal distribution on a plane, but it is defined for angles or directions. The von Mises distribution is often referred to as the circular normal distribution because it shares several properties with the normal distribution, such as being unimodal and sym- metric around the mean. As K approaches infinity, the von Mises distribution approaches a normal distribution in terms of angular deviation.
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D.1 PROBABILITY DENSITY FUNCTION (PDF)
The probability density function (PDF) of the von Mises distribution is given by:
1
f(0 p. 2TIO(K)
exp cos 14))
where:
[0, 2T) is the random variable ((an angle measured in radians),
μ is the mean direction of the distribution, the central angle around which the data clustered,
K 2 0 is the concentration parameter,analogouu to the inverse of the variance the normal distribution, which controls how tightly the data are clustered around the mean direction. When O, the distribution is uniform around the circle, while larger values of indicate that the data are more tightly concentrated around
[x) is the modified Bessel function of the first kind of order O, which serves as a normal- ization constant to ensure that the total probability integrates over the circle, defined as:
1 f e cos(d) do
(K(K)
The concentration parameter к controls the spread the distribution around the mean direction fa:
When x = O, the von Mises distribution becomes a uniform distribution on the circle.
As - oc, the distribution becomes increasingly concentrated around μ and approaches normal distribution for small angular deviations.
D.2 CUMULATIVE DISTRIBUTION FUNCTION (CDF)
The cumulative distribution function (CDF) of the von Mises distribution does not have a simple closed-form expression. However, can be computed numerically as:
F(8 p. = 2T L" exp (Is cos(t - (4)) dt
where the integral is typically evaluated numerically due to the complexity introduced by the Bessel function and the circular nature of the distribution.
D.3 MEAN AND VARIANCE
The mean direction μ is the central tendency of the von Mises distribution, and the concentration parameter x influences how closely the data are clustered around The variance of the distribution related as follows:
Var(0) = 1 41 (x)
(x)
where I, (I)) is the modified Bessel function of the first kind of order 1.
In our implementation, we use VonMises distribution implemented in pytorch package for sampling angles and evluating likelihood.
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E PEPHAR IMPLEMENTATIONS
E.I NETWORK DETAILS
The network used in our method includes the density model go in the founding stage and the predic- tion model he in the extension stage. Both networks use an Invariant Point Attention (IPA)-based encoder to encode hidden representations of peptide residues (Yim et al., 2023a Luo et al. 2022 Li et al. 2024a; Wu et al. 2024b). The input to the network consists of the backbone coordinates and residue types of the peptide-targe complex. Several shallow MLPs (multi-layer perceptrons) are applied to transform these inputs into initial feature representations. The network outputs node embeddings and node-pair embeddings.
For the node (residue) embeddings, we use a combination of the following features:
Residue type: A learnable embedding is applied.
Atom coordinates: This includes both backbone and side-chain atoms.
These features are processed by separate MLPs. The concatenated features are then transformed by another MI.P to produce the final node embedding.
For the edge (residue-pain embeddings, we use combination of the following features:
Residue-type pair: A learnable embedding matrix of size 20 20 is applied.
Relative sequential positions: learnable embedding of the relative position between the two residues is applied.
Distance between two residues.
Relative orientation between two residues: The inter-residue backhone dihedral angles are calculated to represent the relative orientation, and sinusoidal embeddings are applied.
Similarly, these features are processed by separate MLPs, concatenated, and then transformed by another MLP produce the final edge embedding.
Starting from the node and edge embeddings, the IPA encoder further encodes these representations. The density model then applies classification layer classify residue types, while the prediction model uses a regression head to predict parameters of the angle distributions. Since we use two separate models instead of single model, set the embedding size to 128 for node embeddings and 16 for edge embeddings, ensuring comparable parameters to our baseline models (Li et al., 2024a). The IPA encoder consists of 4 layers, each with query heads and a hidden dimension of 32.
E.2 TRAINING DETAILS
Both the density and prediction models are trained on 8 NVIDIA A100 GPUs. As we found these two models prone overfitting, we employed an early stopping strategy, training the density model for 1400 iterations and the prediction model for 2400 iterations. This results in training time that significantly shorter than the baseline models. We set the batch size to 64, using Adam as the optimizer with a learning rate of 10 To prevent overfitting, we also applied dropout rate of 0.5 at each layer the IPA.
E.3 SAMPLING DETAILS
For the sampling process, we use 10 iterations with an update rate of 0.01 in the founding stage to sample anchors by default, followed by 100 fine-tuning steps with update rate of 0.1 in the correction stage. In the scaffold design task, we replace the sampled hotspot residues with predefined ground truth residues.
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F EXPERIMENTAL DETAILS
In each task, for every method, generate 64 peptides for each target protein, and the evaluation metrics are averaged across all generated peptides.
F. METRIC DETAILS
Valid This metric checks whether the distance between adjacent residues is consistent with peptide bond formation. Specifically, the distance between the C., atoms of adjacent residues must be within 3.8 for the peptide be considered valid (Chelvanayagam et 1998 Zhang et al. 2012).
RMSD The Root-Mean-Squant Deviation (RMSD) is a widely used metric to assess structural similarity between two protein conformations. In our evaluation, the generated peptide is aligned with the native peptide using the Kabsch algorithm Kabsch (1976), focusing only on the peptide portion of the complex for superposition, After aligmment, we compute the RMSD by calculating the normalized distance between corresponding C. atoms in the generated and native peptides. A lower RMSD value indicates a closer alignment to the native structure, with implying perfect alignment.
SSR The Secondary Structure Ratio (SSR) measures the similarity between the secondary struc- tures of the generated peptide and the reference peptide. It is computed by comparing the secondary structure labels of the two peptides. These labels are assigned using the DSSP software Kabsch & Sander (1983). The ratio of matching secondary structure assignments between the generated and native peptides then calculated. higher SSR value indicates that the generated peptide preserves the secondary structure of the native peptide more closely.
BSR Binding Site Rate (BSR) quantifies how well the binding interactions of the generated peptide with the target protein resemble those of the native peptide. We define residue as part of the binding site if its Cs atom within 6Åradius any atom in the peptide. The BSR calculated as the overlap ratio of binding site residues between the generated peptide and the native peptide. A higher BSR indicates that the generated peptide interacts with the protein target in a manner similar to the native peptide, which could suggest similar functional properties.
Stability Stability refers the proportion of designed peptides that achieve lower energy score than the native appiide-protiin complex. A lower energy score generally implies greater structural stability. We use the FastRelax protocol in followed by evaluation using the REF2015 scoring function. It is then computed the fraction of complexes where the designed peptide leads to a lower total energy compared to the native complex, indicating improved stability.
et al. (2010) to relax each complex,
Affinity Binding Affinity evaluates the percentage designed peptides that exhibit stronger bind- ing interactions with the target protein compared to the native peptide, as determined by their binding energy. Higher binding affinity usually suggests enhanced peptide functionality. Using PyRosetta's s AnteffaceAnllyzeMMover Chaudhhrry et al. (2010), we calculate the binding energy after relaxing the complex and defining the interaction interface. Affinity is the percentage of peptides that show lower binding energy (and thus higher affinity) relative to the native peptide.
Novelty Novelty measures the proportion of generated peptides that are structurally and sequen- tially distinct from the native peptide. A peptide is considered novel if it satisfies conditions: (a) the TM-score (a structural similarity score) between the generated and native peptides is less than or equal to 0.5 (Zhang & Skolnick (005), and (b) the sequence identity between the two peptides is less than or equal to 0.5. A higher novelty score indicates that more generated peptides are different from the native peptide.
Diversity
Diversity assesses the variability among the generated peptides in terms of both structure and sequence. It is calculated as the product of pairwise (1 TM--ccre) and (1 sequence identity)
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across all generated peptides for given target. A higher diversity score indicates greater struc- tural and sequence diversity among the generated peptides, suggesting a broader range of potential functional variations.
Success Success evaluates the quality of predicted complex structures using the confidence score from AlphaFold2. Specifically, we employ AlphaFold2 Multimer (Evans et al. (2021) to pre- dict the structures of peptides and their full-length receptors. The success rate calculated as the proportion of complexes with an overall ip'TM score greater than 0.6.
F.2 BASELINE DETAILS
In the scaffold geneartion task, we set all baseline hot spot residues K 3, the highest hot spot numbers in our experiment.
RFDiffusion For RFDiffusion (Watson et al. 2022). we use the official implementation along with the pretrained weights for the complex version. Specifically, we apply 200 discrete timesteps during the diffusion process, generating 64 peptides for each target protein. In the peptide design task, we use the official binder design scripts for sampling. For the scaffold design task, we provide the ground-truti hotspot residues as additional information, instructing the model to inpaint the remaining peptide structure. After sampling the peptide backbone, we use ProteinMPNN (Dauparas) al. 2022 to generate the corresponding peptide sequences.
ProteinGenerator ProteinGenerator jointly samples protein backbone structures and sequences (isanza et al.) (202)). We utilize the official inference scripts, employing 200 diffusion timesteps to design 64 peptides for each target protein.
PepFlow We employ the released Model No.1 from PepFlow (Li al., 2024a), which a full- atom peptide design model based on multi-modal flow matching. In the peptide design task, we utilize the official implementation for sampling. For the scaffold generation task, we modify the sampling process ensure that the hotspot residues are constrained to their ground-truth values during each update step. For each generation, we perform 200 discrete time steps for sampling 64 peptides of each target.
PepGLAD We utilize the released inference script and co-design model from PepGLAD (Kong et al. 2024). which leverages latent diffusion models to generate full-atom peptide structures. For the scaffold generation task, we modify the inference script so that the input peptide includes certain known masked blocks instead of all blocks being masked. We maintain the same hyperparameter settings as described in the original paper.
G ADDITIONAL RESULT
G.1 TM-SCORE AND AAR
Table 4: TM-Score and Sequence Recovery Rate in peptide design and scaffold generation tasks.
Table 5; Peptide Design Task
Table 6: Scaffold Generation Task
Method
TM
AAR
Method
TM
AAR
RFDiffusion
0.44
40.14 14
RFDiffusion (K=3)
0.46
31.14
ProteinGenerator
0.43
45.82
ProteinGenerator (K=3)
0.48
32.05
PepFlow
0.38
51.25
PepFlow (K=3)
0.37
51.90
PepGLAD
0.29
20.59
PepGLAD
0.30
21.48
PepHAR (K=1)
0.33
32.32
PepHAR (K=1)
0.33
32.90
PepHAR (K=2)
0.32
39.91
PepHAR (K=2)
0.35
35.06
PepHAR (K=3)
0.34
34.36
PepHAR (K=3)
0.38
35.34
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G.2
CUMULATIVE ERROS
Scatter Plat of Pep Length vs RMSD (Original Datal
Data Paints Segreedon
8950
11
10
Pep Length
Figure 6: Scatter Plot of peptide length and RMSD value.
We analyzed the relationship between the length of the generated peptides and their corresponding RMSD values compared to native structures. As shown in the figure, peptide length demonstrates a strong positive correlation with RMSD, indicating that the autoregressive generation process accu- mulates errors as peptide length increases. Specifically, during the extension stage, dihedral angle predictions are used iteratively add residues to the peptide structure. However, these predictions are not always precise. For example, when predicting the dihedral angles for new residue, small deviations from the ground truth can occur. These deviations lead to slight inaccuracies the re- constructed residue's 's backbone conformation. Once residue is added with structural bias, the error propagates to subsequent extension steps. For instance, if the incorrect backbone conformation po- sitions the residue slightly off from its ideal location, the next prediction step will use this biased structure as imput. This can result in further deviation in the predicted dihedral angles for the next residue, introducing additional distortions the growing peptide. Over multiple iterations, these small inaccuracies accumulate, leading to increasing structural deviations from the native confor- mation. This accumulation of structural errors explains the observed increase in RMSD with longer peptide sequences. The inherent dependency of the autoregressive process on previously generated fragments makes it particularly susceptible error propagation during residue-by-resine exten- sion. Addressing this limitation is crucial to improving the accuracy of peptide structure generation in future work.
Future work could address this accumulation issue in our autoregressive extension model. First, we can improve the precision of each prediction step by employing more accurate dihedral prediction models. Given the limited peptide datasets, leveraging pretrained models trained on larger datasets or incorporating traditional energy relaxation methods at each extension step to correct backbone bias could be beneficial. Second, advancements in autoregressive language modeling could be ap- plied, such as predicting multiple dihedral angles simultaneously (Qi et al., 2020; Gloeckle et al,, 2024]. injecting noise during training (Pasini et al.), using diffusion models to refine the predicted posterior distribution (Li et al.) (024c). Third, non-autores ann-autoreeressive approaches, such as generative modeling (Kenton & Toutanova 2019 Chang al., 2022) or diffusion models (Wu et al., (0024)), could be explored to generate all dihedral angles simultaneously and refine predictions iteratively.
G.3 DIFFERENT K VALUES OF BASELINES
As shown in Table 7 unlike PepHAR, which benefits from increasing K in terms of geometry and energy metrics, the baseline models show only marginal improvements or even performance degradation. We believe this is due their training schemes, which do not explicitly condition known hotspots. Optimizing their training and inference processes for the scaffold setting could potentially improve their performance.
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Table 7: Evaluation of methods in the scaffold generation task. K = 1, 2, 3 is the number of hot spots.
Valid %
RMSD A
SSR %
BSR
Stability X
Aftinity
Novelty 36
Diversty X
Success %
RFDiflusin (K 1)
65.30
3.51
63.19
23.56
17.73
20.58
66.17
22.46
19.19
RFDiftusion (K 2)
68.68
2.85
65.68
31.14
18.69
22.34
45.53
24.14
21,59
RFDiffasion (K
26.83
20,07
21.26
55.03
23.15
PeteiinGnneraoe
ProteinGemeator
65.86
24.17
50.73
34.90
RepFkw (K 1)
40.35
2.51
79.58
$6.40
10.55
18.13
30.46
16.20
26.46
Popflow (K 2)
49.29
2,22
79.23
$5.05
10.19
18.20
$1.74
19.52
24,03
PopFkw (K 3)
42.68
2.45
81.00
$2.76
11.17
13.64
50.93
16.97
24.54
PopGLAD
50.46
13.56
PspGLAD
(K
PspHAR 1)
56.01
3.72
80.61
78.
17,89
19.94
80.61
29.79
20.43
ReHHAR 2)
55.36
2.85
82.79
85.80
19.18
19.17
74.76
22.09
PopHAR (K
55.41
2.15
83.02
$8.02
20.50
20.65
72.56
19.68
21.45
Figure 7: Upper Left: Human Endothelin type B receptor in complex with the ETI peptide binder. Upper Right: Receptor in complex with PepHAR- peptide binder. Lower Left: HISI6 in the ETI peptide is identified hotspot residue. Lower Right: PepHAR recovers this hotspot residue in the peptide design task.
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G.4 CASE STUDY ON PICR-PEPTIDE INTERACTION
Here, we present a case study of generating a peptide binder for the human Endothelin type B receptor (PDB: 5GLH) (Shihoya al. 2018). As shown in Fig. the designed peptide exhibits secondary structures (helix) similar to the native peptide binder (ET1 peptide), interacting with the receptor residues at the top and within the receptor. Through per-residue energy calculations and manual inspection, the HIS16 residue in the ETI peptide is identified as hotspot residue, playing a crucial role in contacting the receptor's s extracellular loop regions. Remarkably, PepHAR recovers this HIS 16 residue in the generated peptide. The orientation of the functional group in the generated HIS closely resembles that of the native hotspot residue, demonstrating that PepHAR can effectively recover hotspot interactions during the design process.
G.5 SECONDARY STRUCTURE ANALYSIS
Table 8: Secondary structure composition evaluation.
Method
Coil %
Helix %
Strand %
Native
75.20
11.47
13.15
PepHAR (K = 3)
89.42
10.36
0.21
Hotspots
90.13
9.48
0.22
We analyzed the secondary structure proportions of native peptides, generated peptides, and hotspot residues in the test set, as shown in Table
Compared native peptides, proportion of coil regions (bonded turns, bends, or loops) while maintaining similar proportions of helix regions. However, the proportion of strand regions significantly lower compared native peptides, indicating that strand regions in the native structure are often replaced by coil regions in the generated peptides. This could be due to subtle differences in structural parameters required for forming strands. We believe that further energy relaxation using tools like Rosetta, OpenMM, or FoldX could help refine the peptide structures to form more accurate secondary structures.
peptides and hotspots tend to exhibit a higher
Regarding hotspot occurrences, observe that hotspots are predominantly located in coil and helix regions, with almost no presence in strand regions. This aligns with interaction principles, where strand regions may represent structural transitions, while the irregular coil regions or the relatively stable helix regions are more likely to serve as functional interaction sites.
H CURRENT WORKS ON PEPTIDE DESIGN METHOD
Recent advancements in computational peptide binder design have significantly benefited from deep learning. |Bryant& & Elofsson 2022) introduced EvoBind, an in silico directed evolution platform that utilizes AlphaFold to design peptide binders targeting specific protein interfaces using only sequence this, Li et al. (2024b) developed EvoBind2, which extends EvoBind's
information. Building capabilities by enabling the design of both linear and cyclic peptide binders varying lengths solely from a protein target sequence, without requiring the specification of binding sites or binder sizes. Using MCTS simulations and reinforcement learning, Wang et al. (2023) engineers peptide binders and achieves comparable result EvoBind. Chen al. (2023) proposed PepMLM, target- sequence-conditionee generator for linear peptide binders based on masked language modeling. By employing a novel masking strategy. PepMLM effectively reconstructs binder regions, achieving low perplexities and demonstrating efficacy in cellular models. Leveraging geometric convolutional neural networks to decipher interaction fingerprints from protein interaction surfaces, Gainza et al. (220)) developed MaSIF. Subsequently. BindCraft (Pacesa et al.) 2024) combined AF2-Multimer sampling with ProteinMPNN sequence design to optimize protein- protein interaction surfaces. Sim- ilar to our approach of defining key hotspot residues, AlphaProteo (Zambaldi et al. (024) also aims to generate high-affinity protein binders that specifically interact with designated residues on the target protein. PepGLAD (Kong al. 2024) encodes full-atom peptide structures and sequences using an equivariant graph neural network, and applies latent diffusion on the peptide embedding space explore peptide generation.
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Reviews:
[{"review_id": "vZJB8G00d6", "reviewer": "Reviewer_k8mv", "summary": "This paper introduces PepHAR (Hotspot-driven Autoregressive peptide design), a novel three-stage approach for designing peptides that can bind to specific target proteins. The method acknowledges the critical role of \"hot spot\" residues in peptide-protein binding and addresses key challenges in computational peptide design. The three stages consist of: (1) a founding stage that uses an energy-based density model to identify and sample key hot spot residues, (2) an extension stage that autoregressively builds peptide fragments from these hot spots using a dihedral angle-based approach ensuring proper geometry, and (3) a correction stage that refines the complete structure through optimization. The authors also introduce a new \"scaffold generation\" task that better reflects real-world peptide drug development scenarios. When compared to state-of-the-art baselines (RFDiffusion, ProteinGenerator, PepFlow), PepHAR demonstrates superior performance across multiple metrics including structural validity, geometric accuracy, binding site accuracy, and novelty/diversity of generated peptides, while maintaining competitive stability and binding affinity.", "questions": "Major:\n1. For different sampling K values, does the binder length remain constant for the same target protein?\n\n2. RMSD might be somewhat misleading since peptides can still bind effectively with very different geometries, which is actually desirable - valid binders that show different binding modes from native ones.\n\n3. Regarding Novelty, especially for sequences, what is the source of this novelty? Does it primarily come from scaffold sites or contact sites? If changes are mainly in scaffold sites compared to native ones, this metric might be misleading and trivial for a designed binder.\n\n4. In the Dataset section, the binding pocket is defined using a 10Å radius, while for BSR in the supplementary material, binding sites are defined using a 6Å radius. Why are different values used?\n\nMinor:\n1. Authors should specify that they are performing peptide binder design, not peptide design, as these are distinctly different tasks.\n\n2. In the Dataset section (Lines 276-377), please clarify the distinction between the 158 examples and the 8,207 additional examples.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "- Novel Problem Decomposition: The work introduces a clever way to break down peptide design into a three-stage process based on biological understanding. By focusing on hot spot residues first, then extending and refining, it makes the problem more tractable while maintaining biological relevance.\n\n\n- Strong Geometric Constraints: The method explicitly handles peptide bond geometry through dihedral angles. Uses von Mises distribution (and others) to model angle distributions properly.\n\n- Novel Energy-Based Density Model: Introduces an innovative energy-based model to identify hot spot residues. Uses noise contrastive estimation for effective training without needing explicit normalization. Employs Langevin dynamics sampling to efficiently explore the residue distribution space.\n\n- Autoregressive Fragment Extension: Enables bidirectional growth from hot spots through Left/Right operations\n\n\n- Hybrid Optimization Framework: Creates a novel joint optimization objective combining backbone and dihedral constraints. Introduces an iterative refinement strategy that can handle multiple fragments simultaneously", "weaknesses": "Overall, this work is well written with clear logic and reasonable benchmarks.\n\n1. Many recent works of peptide binder design use AlphaFold2 for scoring (e.g., pAE or iptm). I would like to see the evaluation of designed peptides with such metrics.\n\n2. Regarding Novelty score, can author also show separate metrics for it in supplementary as well: TM-score and sequence identity.\n\n3. For all examples provided, I will suggest authors to also provide the peptide sequence for reference for better understanding.\n\n4. To enhance further the evaluation and discussion, I would suggest authors to include following works for discussion and potentially use them for benchmarking as well.\n\n[1] EvoBind: https://www.biorxiv.org/content/10.1101/2022.07.23.501214v1 (Discussed, but not benchmarked?)\n\n[2] EvoBind2: https://www.biorxiv.org/content/10.1101/2024.06.20.599739v2\n\n[3] PepMLM: https://arxiv.org/abs/2310.03842\n\n[4] EvoPlay: https://www.nature.com/articles/s42256-023-00691-9\n\n[5] AlphaProteo: https://arxiv.org/abs/2409.08022 (very recent)\n\n[6] MASIF: https://www.nature.com/articles/s41592-019-0666-6", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "TpQrUZQTcx", "reviewer": "Reviewer_UnBf", "summary": "This paper proposes a method for peptide sequence and structure generation for peptide design with target protein. The methodology includes three parts: the hot-spot residue generation, the autoregressive generation of fragments based on the hot-spot residues to complete the chain, the correction stage that refine the peptide structure. Experiments have been performed on the peptide design and peptide scaffold generation tasks, and compared with baseline models like RFdiffusion, Pepflow, and demonstrate good performance in novelty and diversity, but not as good in the validity or quality of the generated structures.", "questions": "- In the correction stage, are the terms in J_bb only non-zero in those residues that stay at the connection of two fragments? Because other residues in the middle of the fragments should be complying with the consistency constraint from construction. The authors should clarify this.\n- How does the correction method proposed in this work (using models directly from the first and second stages) compare with the correction by some empirical methods (like some energy function)?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "- The methodology is novel, which divide-and-conquer the peptide design task into three stages: hot-spot residue generation, fragment completion and correction.\n- Utilizing the information of hot-spot residues helps to improve the generation quality\n- Experiments have been performed on the curated dataset and benchmarks, with comprehensive metrics, and comparison with relevant models.\n- The method achieves the highest novelty and diversity compared with different baselines.", "weaknesses": "- The quality of the generated peptide is not good, on the metrics such as validity and stability the method is significantly worse.\n- In the first stage, each hotspot generation is independent and do not consider other generated hotspot, or a joint generation. And in the second stage, the completion of each fragment only depends on the target protein and the generated residues of the current fragment. Not taking other hotspots or fragments into account in the two stages could make the model ignorant of important information for the geometry and validity.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "B0R88JbVKC", "reviewer": "Reviewer_mmeW", "summary": "The paper introduces PepHAR, a hot-spot-driven autoregressive generative model for designing peptides targeted at specific protein binding sites. The authors propose a three-stage approach: 1) hotspot residue sampling using an energy-based model, 2) fragmented autoregressive extension of peptide structure using dihedral angles, and 3) correction through gradient-based optimization to ensure overall peptide geometry validity. Through experiments, PepHAR demonstrates competitive performance in scaffold-based peptide design, showing improvements in structure and binding accuracy when compared to state-of-the-art models like RFDiffusion and PepFlow on metrics including binding site overlap, novelty, and stability.", "questions": "- I expect the author to quantify the impact of the cumulative errors from autoregressive generation. \n- Figure 4 shows the designed peptides are all loops. Given that, I wonder if the SSR % is still meaningful if most of the native and designed peptides are just loops. Because in that case, the model can just produce all loopy structures and get a very high SSR.\n- I suggest that the author further design the sequences for those generated peptide structures using for example, ProteinMPNN and report the recovery rate. This could reflect the peptide structure quality since low-quality structures would result in low sequence recovery or low-quality sequences generated such as repetitions.", "limitations": "", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The paper attempt to solve an important protein design problem with significant biomedical applications.\n\nThe hotspot-driven approach combined with an autoregressive fragment assembly model is novel within peptide design, providing a unique perspective on addressing protein-peptide design problem.\n\nThe paper offers a detailed breakdown of the approach, supported by schematics and visualizations that help clarify the generation process.\n\nThe paper uses comprehensive metrics (e.g., validity, stability, affinity, diversity, novelty), which cover structural, energetic, and novelty aspects of peptide design.", "weaknesses": "- The autoregressive fragment extension process might introduces cumulative geometric errors, especially for longer peptides. \n\n-  Although PepHAR outperforms some baselines, the reported improvements are incremental and may not justify the added model complexity and limitations. For a conditional generation task, the primary metric is RMSD, which quantifies the structural similarity between the generated structures and native structures. where PepHAR is worse than the baseline PepFlow. \n\n- The claim of the paper is purely using the frame representation for peptide might break the validity of the protein structures like bond formulation. However, Table 1 shows that RFDiffusion, which is a frame-representation-based method, exhibits higher Valid %.\n\n- I would expect open source code to support the methodology and experimental results. \n\n- Regarding the equation, the author should add period to the end if it closes a sentence. I notice that the author missed that in most of the equations in this paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "l3A4HS5e06", "reviewer": "Reviewer_4QbP", "summary": "The paper introduces PepHAR, a state-of-the-art generative model for peptide design. It employs an energy-based density model to precisely sample key residues, extends peptides with an autoregressive approach based on dihedral angle estimation, and refines fragment assembly through an iterative optimization process. The paper proposes a new experimental setting, scaffold generation, to mimic practical scenarios, and demonstrate the competitive performance of PepHAR in both peptide design and scaffold generation tasks.", "questions": "1. In Section 5.2, Table 2, it would be insightful to see the performance of the baseline models under different conditions, specifically for K=1 and K=2, which are currently not included. Additionally, to thoroughly understand the influence of hotspot count on peptide design and the tradeoff with diversity mentioned in Section 5.3, it would be valuable to conduct experiments with a broader range of K values, or explain the insights behind the choice of these values.\n2. The current study employs RFDiffusion and PepFlow as baseline models. Given the recent advancements in diffusion or flow-based peptide design, it would be valuable to include additional baseline models such as PepGLAD\n3. Why does PepHAR underperform RFDiffusion and PepFlow in metrics such as valid% and RMSD, and what is the tradeoff involved?\n4. The paper mentions tasks such as HIV-1+CD4 and p53+MDM2 interactions, which are known for their hotspot-mediated binding. It would be beneficial to see PepHAR's performance demonstrated on these specific systems.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "- The paper innovatively integrates hotspot residues into peptide design, a concept well-supported by biological theories, enhancing the model's relevance and novelty in the field.\n- The three-stage approach, including the use of dihedral angles and the correction stage, is a robust technical framework that ensures the generation of structurally sound peptides.\n- The model demonstrates excellent performance in SSR, Affinity, Novelty, and Diversity, indicating its ability to produce high-quality, functional, and diverse peptides.", "weaknesses": "1. **Performance in Specific Metrics**: As shown in Section 5.1, Table 1, PepHAR underperforms RFDiffusion in the Valid metric by a significant margin (10%). This suggests that PepHAR may not always generate peptides with geometries that are fully consistent with the formation of peptide bonds. Additionally, PepHAR's Affinity metric indicates room for improvement, potentially due to the density model's limitations in sufficiently approximating the complex energy landscapes involved in peptide-target interactions.\n2. **Limited Exploration in Scaffold Generation**: The scaffold generation scenario only considers a small number of hotspots (K=1, 2, 3), with baseline comparisons limited to K=3. This narrow exploration may not capture the full spectrum of possible hotspot configurations, potentially limiting the generalizability of the findings to more complex scenarios.\n3. **Density Model Limitations**: The energy-based density model used in PepHAR might not fully approximate the intricate energy landscapes of peptide interactions, which could impact the model's ability to generate peptides with optimal binding affinities.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "3mAXOtuZpU", "reviewer": "Reviewer_Gac7", "summary": "The authors present a novel de-novo peptide design method, PepHAR, aimed at generating binders for specific sites on a target protein. The method leverages the concept of \"hotspots\", a small number of residues at protein-protein interfaces that contribute most of the binding energy, with other residues acting as \"scaffolds\" to stabilize the interface. PepHAR’s peptide prediction process is based on three main components: (1) A neural network trained using a noise contrastive estimation (NCE) loss to differentiate between real interface residues (ground truth) and noisy counterparts altered with spatial perturbations. The authors use Langevin dynamics to sample from this energy-based model. (2) A second neural network that builds a polypeptide chain autoregressively by predicting the phi-psi dihedral angles for each subsequent residue. This model, trained using maximum likelihood estimation (MLE), predicts angles for residues extending either direction along the chain. (3) A final correction step to refine the predicted peptide structures, addressing minor inaccuracies like dihedral angle errors, steric clashes, or chain breaks. This stage optimizes dihedrals based on neighboring residues and rebuilds the peptide, comparing it to the initial prediction. An objective function minimizes the distance between the rebuilt and predicted structures while ensuring angles align with the learned dihedral distribution.\nPepHAR was evaluated for de-novo peptide generation with up to three hotspots, comparing favorably to other leading methods like RFdiffusion, PepFlow, and ProteinGenerator. An ablation study also confirmed the significance of each method component. Overall, PepHAR generated peptides with lower RMSD to the native structure than other methods, showing its effectiveness in autoregressively designing peptides for target protein interfaces.", "questions": "I have two minor questions, primarily out of curiosity:\n\n(1) In the benchmarks where PepHAR was tested, could you provide more insights into the nature of the predicted structures? For instance, do the predictions tend to cluster around helical bundles, or is there a broader range of conformations? Additionally, are the k=3 hotspots located within disordered regions, or are they typically in helices, where the backbone might be easier to infill? I would suggest to include a brief analysis of the secondary structure composition of the generated peptides and compare it to native structures (or a representative set of native structures), as well as an examination of where the hotspots tend to be located in terms of secondary structure elements.\n\n(2) When multiple hotspots are specified, fragments are grown from each hotspot. How does the network ensure that these initially disconnected fragments will eventually fit together? Is this addressed during the extension phase or in the polishing stage? Furthermore, is there a risk that extended chains from different fragments might fail to converge into a closed structure? It could be useful to elaborate on the fragment assembly method, and add statistics on how often fragments successfully connect and if there are any strategies used to ensure proper assembly or safeguard this process.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "The paper is well-written, with ideas and concepts clearly explained. Given the ongoing challenges in de-novo peptide binder design, this novel and original approach is both relevant and significant. I especially appreciated the clear presentation of the derivations and fundamental principles underlying the neural network design and training.", "weaknesses": "The paper is well-written, with few notable weaknesses.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)