Antigen-Specific Antibody Design via Direct Energy-based Preference Optimization
Authors: Xiangxin Zhou
Dongyu Xue
Ruizhe Chen
Zaixiang Zheng
Liang Wang
Quanquan Gu
Venue: NeurIPS 2024 poster (2024)
Keywords: direct preference optimization
diffusion model
antibody design
Primary area: machine_learning_for_other_sciences_and_fields

Abstract: Antibody design, a crucial task with significant implications across various disciplines such as therapeutics and biology, presents considerable challenges due to its intricate nature. In this paper, we tackle antigen-specific antibody sequence-structure co-design as an optimization problem towards specific preferences, considering both rationality and functionality. Leveraging a pre-trained conditional diffusion model that jointly models sequences and structures of antibodies with equivariant neural networks, we propose direct energy-based preference optimization to guide the generation of antibodies with both rational structures and considerable binding affinities to given antigens. Our method involves fine-tuning the pre-trained diffusion model using a residue-level decomposed energy preference. Additionally, we employ gradient surgery to address conflicts between various types of energy, such as attraction and repulsion. Experiments on RAbD benchmark show that our approach effectively optimizes the energy of generated antibodies and achieves state-of-the-art performance in designing high-quality antibodies with low total energy and high binding affinity simultaneously, demonstrating the superiority of our approach.

Antigen-Specific Antibody Design via
Direct Energy-based Preference Optimization
Xiangxin Zhou 2,24,
Dongyu Xue
Ruizhe Chen
Zaixiang Zheng!
Liang Wang
Quanquan Gu
School of Artificial Intelligence, University of Chinese Academy of Sciences New Laboratory of Pattern Recognition (NLPR). State Key Laboratory of Multimodal Artificial Intelligence Systems (MAIS), Institute of Automation, Chinese Academy of Sciences (CASIA) *College of Computer Science and Electronic Engineering, Hunan University 4 BByteDance Research
Abstract
Antibody design, a crucial task with significant implications across various disci- plines such as therapeutics and biology, presents considerable challenges due its intricate nature. In this paper, we tackle antigen-specific antibody sequence- structure co-design sidering both rationality and functionality. Leveraging a pre-trained conditional diffusion model that jointly models sequences and structures of antibodies with equivariant neural networks, we propose direct energy-based preference optimiza- tion to guide the generation of antibodies with both rational structures and consid- erable binding affinities to given antigens. Our method involves fine-tuning the pre-trained diffusion model using a residue-level decomposed energy preference. Additionally, we employ gradient surgery to address conflicts between various types of energy, such as attraction and repulsion. Experiments on RAbD benchmark show that our approach effectively optimizes the energy of generated antibodies and achieves state-of-the-art performance in designing high-quality antibodies with low total energy and high binding affinity simultaneously. demonstrating the superiority of our approach.
optimization problem towards specific preferences,
Introduction
Antibodies, vital proteins with an inherent Y-shaped structure in the immune system, are produced in response to an immunological challenge. Their primary function is discern and neutralize specific pathogens, typically referred to as antigens, with a significant degree of specificity (39]. The specificity mainly comes from the Complementarity Determining Regions (CDRs), which accounts for most binding affinity to specific antigens (24] 29] Hence, the design of CDRs is a crucial step developing potent therapeutic antibodies, which plays an important role in drug discovery.
Traditional silico antibody design methods rely on sampling or searching protein sequences over large search space to optimize the physical and chemical energy, which inefficient and easily trapped bad local minima [ 31 (47) Recently, deep generative models have been employed to model pro- tein sequences in nature for antibody design [7]. Following the fundamental biological principle
Equual contribution (this work was done during Xiangxin and Ruizhe's internship at ByteDance Research). Corresponneecee to: Quanquan Gu <quanquan, gu @ bytm
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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that structure determines function numerous efforts have been focused on antibody sequence-structung co-design [22 21 36 29
30 371, which demonstrate superiority over sequence design- -asedd methods. However, the main evaluation metrics in the aforementioned works are amino acid recovery (AAR) and root mean square de- viation (RMSD) between the generated antibody and the real one. This is con- troversial because AAR is susceptible to manipulation and does not precisely gauge the quality of the generated antibody se- quence. Meanwhile, RMSD does not involve side chains, which are vital for antigen-antibody interaction. Besides, it is biologically plausible that a specific anti- gen can potentially bind with multiple ef- ficacious antibodies [45] [2]. This moti- vates to examine the generated struc- tures and sequences of antibodies through the lens of energy, which reflects the ra- tionality of the designed antibodies and their binding affinity the target antigens. We have noted that nearly all antibody sequence-structure co-design methods struggle to produce antihodies with low energy. This suggests the presence of irrational structures and inadequate binding affinity in antibodies designed by these methods (see Fig. [T). We attribute this incapability to the insufficient model training caused by a scarcity of high-quality data.
Figure The third CDR in the heavy chain, CDR-HB (colored in yellow), of real antibody (left) and synthetic antibody (right) designed by MEAN (2] for given antigen (PDB ID: 4cmh). The rest parts of antibodies except CDR-H3 are colored in blue. The antigens are colored in gray. We use red (resp. black) dotted lines to represent clashes between CDR-H3 atom and a frame- work/antigen atom (resp. another CDR-H3 atom). We consider clash occurs when the overlap of the van der Waals radii of two atoms exceeds 0.6Å.
To tackle the above challenges and bridge the gap between in silico antibody sequence-structure co-design methods and the intrinsic need for drug discovery, we formulate the antibody design task antibody optimization problem with a focus better rationality and functionality. Inspired by direct preference optimization [DPO, 41) and self-play fine-tuning techniques [10) that achieve huge success in the alignment of large language models (LL.ss), we proposed direct energy-based preference optimization method named ABDPO for antibody optimization. More specifically, we first pre-train a conditional diffusion model on real antigen-antibody datasets, which simultancously captures sequences and structures of complementarrty-deteriii cquivariant neural networks. We then progressively fine-tune this model using synthetic antibodies generated by the model itself given an antigen with energy based preference. This preference defined fine- aneeggrineed residue level, which promotes the effectiveness and efficiency of the optimization process. To fulfill the requirement of various optimization objectives, we decompose the energy into multiple types so that we can incorporate prior knowledge and mitigate the interference between conflicting objectives (e.g., repulsion and attraction energy) to guide the optimization process. Fine-tuning with seff-synthesized energy-based antibody preference data represents a revolutionary solution to address the limitation of scarce high-quality real-world data, significant challenge in this domain. We highlight our main contributions as follows:
regions (CDR) in antibodies with
We tackle the antibody sequence-structure co-design problem through the lens of energy from the perspectives of both rationality and functionality.
We propose direct residue-level energy- based preference optimization to fine-tune diffusion models for designing antibodies with rational structures and high binding affinity to specific antigens.
We introduce energy decomposition and conflict mitigation techniques to enhance the effectiveness and efficiency of the optimization process.
Experiments show ABDPO's 's effectiveness in generating antibodies with energies resembling natural antibodies and generality in optimizing multiple preferences.
2 Related Work
Antibody Design. The application of deep learning to antibody design can be traced back to at least (35 43
3. recent years, sequence-structure co-design of antibodies has attracted increasing attention. Jin et al. (22] proposed to simultaneously design sequences and structures of CDRs in an autoregressive way and iteratively refine the designed structures. Jin al. (2T) further utilized the epitope and focused on designing CDR-H3 with hierarchical message passing equivariant

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Valtes
Volaimetes
Residue
Paltepshes
Gradient Surgery
Residuel
Residue
Fine-tuning
Antibody Pair
Palfera
Loa
CoR-AE Kawwin
cottAa Sou
Pafke
Antibody Diffusion Model
Pakkr
Energy
Sampling
Energy Decomposition
Synthebic
enegy Rancian
Energy
Antibodies
Figure 2: Overview of ABDPO. This process can be summarized as: (a) Generate antibodies with the pre-trained diffusion model: (b) Evaluate the multiple types of residue-level energy and construct preference data; (c) Compute the losses for energy- energy-based preference optimization and mitigate the conflicts between losses of multiple types of energy; (d) Update the diffusion model.
network. Kong et al. 22 incorporated antigens and the light chains of antibodies as conditions and designed CDRs with E(3)-equivarian graph networks via progressive full-shot scheme. Luo et al. [36] proposed diffusion model that takes residue types, atom coordinates and side-chain orientations into consideration to generate antigen-specific CDRs. Kong et al. 300 focused on epitope-binding CDR-H3 design and modelled full-atom geometry. Recently, Martinkus et al. [37 proposed AbDiffuser, novel diffusion model for antibody design, that incorporates more domain knowledge and physics-basee constraints and also enables side-chain generation. Besides, Wu and Li 48). Gao et al. [19 and Zheng et al. [52] introduced pre-trained protein language model to antibody design. Distinct from the above works, method places stronger emphasis designing and optimizing antibodies with low energy and high binding affinity.
Alignment of Generative Models. Solely maximizing the likelihood of training data does not always lead model that satisfies users' preferences. Recently, many efforts have been made on the alignment of the generative models to human preferences. Reinforcement learning has been introduced learning from human/Al feedback to large language models, such as RLHF 40) and RLAIF [33]. Typically, RLHF consists of three phases: supervised fine-tuning, reward modeling, and RL fine-tuning. Similar ideas have also been introduced text-to-image generation, such as DDPO 77. DPOK [16] and DiffAC 53 They view the generative processes of diffusion models as multi-step step Markov Decision Process (MDP) and apply policy gradient for fine-tuning. Rafailov et al. [11 proposed direct preference optimization (DPO) to directly fine-tune language models on preference data, which matches RLHF performance. Recently, DPO has been introduced to text-to-image generation [46 6) Notably, in the aforementioned works, models pre-trained with large-scale datasets have already shown strong performance, in which case alignment further increases users' satisfaction. In contrast, in our work, the model pre-trained with limited real-world antibody data is insufficient in performance. Therefore, preference optimization in our case is primarily used to help the model understand the essence of nature and meet the requirement of antibody design.
Method
In this section, we present ABDPO, a direct energy-based preference optimization method for designing antibodies with reasonable rationality and functionality (Fig. 2}. We first define the antibody generation task and introduce the diffusion model for this task in [Sec. 3.1 Then we introduce residue-level preference optimization for fine-tuning the diffusion model and analyze its advantages in effectiveness and efficiency iecS. 3.2 Finally, in |Sec. 3.3) we introduce the energy decomposition and describe how mitigate the conflicts when optimizing multiple types of energy.
3.1 Preliminaries
We focus on designing CDR-H3 of antibody given antigen structure as CDR-H3 contributes most to the diversity and specificity of antibodies [49 2 and the rest part of the antibody including the frameworks and other CDRs. Following Luo al. [36, each amino acid is represented by its C, coordinate
type s, E (ACDEFGHIKLMMNPORSTWWW
R3, and frame orientation

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O E SO(3) 228,, where i = I.....N N and N is the number of the amino acids in the protein complex. We assume the CDR-H3 to be generated has m amino acids, which can be denoted by R {S}, x, ز,)li = n + 1 ...;; n + m), where n + 1 is the index of the first residue in CDR-H3 sequence. The rest part of the antigen-antibody complex can denoted by P = ((s,, x, O,)li E
In++ (n 1, n m)) The antibody generation task can be then formulated as modeling the conditional distribution PP).
{1. ....... NJ
Denoising Diffusion Probabilistic Model [DDPM. 20 have been introduced to antibody generation by Luo et al. [3). This approach consists of forward diffusion process and reverse generative process. The diffusion process gradually injects noises into data as follows:
(($}1s}) = C (1(s)) a' ( (5)) 311/K),
(xx) xx)) N (x)/ B').
q (0))) (0)) = I9 (0) ScaleRot (Vo,0)) B²),
where (s), x 0.) are the noisy-free amino acid at time step with index j. and (5), 0)) are the noisy amino acid at time step t. I[-) is the one-hot operation. { ) is the noise schedule for the diffusion process (20), and we define á² = II=
(8) and 3r = 1- at. K is the number of amino acid types. Here, C(.). and Z9 (+) are categorical distribution, Gaussian distribution on RR, and isotropic Gaussian distribution on SO(3) (32 respectively. ScaleRot scales the rotation angle with fixed rotation axis to modify the rotation matrix [18].
Correspondingly, the reverse generative process learns to recover data by iterative denoising. The denoising process p 1R', P) from time step t to time step t 1 is defined follows:
"R', P) = C(s) (s, (R', P)Li), (Rt P) = Nxx fo, (R', P) 1
(2)
IG (fo, ()))).)))
(3)
is the noisy sequence and structure of CDR-H3 at time step f, fo So.Je Te Sog are parameterized by denoising neural networks. We utilize SE(3)-equivariant networks 23 221 as denoising networks because proteins are structures in three- dimeessinnii space, and their properties and characteristics should remain invariant regardless of their observation views. f(D) denotes the output that corresponds to the j-th amino acid. The training objective of the reverse generative process is to minimize the Kullback-Leible (KI.) divergence between the variational distribution and the posterior distribution as follows:
where RD Xs, 03 -=t++
DKL (i(R" RD, (2) p))
== -=ER
Σ
(4)
m
j=++1
With some algebra, we can simplify the above objective and derive the reconstruction loss time step & as follows:
mitm Σ
(1s)5-11s), 'IR', pT)
4
ER
(a(s)
(5)
m
4/
ER
|| - (RR' p)]1 (P)
(6)
j=n-1
L6
Exg
(1,)) Fog (R', P)b] 1122
(7)
m
j=++1
where RR ~ (RR) and RD ~ P(R(P), and || .|e is the matrix Frobenius norm. Note that as Luo al. [36] mentioned, Eqs. ① and (3) are an empirical perturbation-denssii rigorous one. Thus the terminology KL-divergence may not be proper for orientation O. Nevertheless, we can still approximately derive an empirical reconstruction loss for orientation O as above that works in practice. The overall loss is I ~ Em-up,,y [74 + I + L.). After optimizing this loss, we can start with the noises from the prior distribution and then apply the reverse process to generate antibodies.
process instead of

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3.2 Direct Energy-based Preference Optimization
Only the antibodies with considerable struuccue rationality and binding affinity can be used as effective therapeutic candidates. Fortunately, these two properties can be estimated by biophysical energy. Thus, we introduce direct energy-based preference optimization to fine-tune the pre-trained diffusion models for antibody design.
Inspired by RLHF 40],
fine-tune the pre-trained model to maximize the reward as:
maxER=~<p [r(R)]] 3DKL (po(R))) (PPra((RR)))))))
where pe (resp. Pief) is the distribution induced by the model being fine-tuned (resp. the fixed pre-trained model), 8 is hyperparameter that controls the KL divergence regularization, and r(-) is the reward function. The optimal solution to the above objective takes the form:
Po- (R.) = Z (Peer(R") exp ()(RR))
Following Rafailov et al. [41, we tum to the DPO objective as follows:
Pe (R)) Pret (RT)
log Prerl (R2) )}
Pe R2))
LDPO - L S Rg log (Ssgn(R). R2)
log
where o-) is sigmoid and sgn(R), R2) indicate the preference over Ri and R2. We use "x" to denote the preference. Specifically, sgn(R). R2) = (resp. -1) if R > R2 (resp. R2 < RD) in which case we call Ri (resp. R2) the "winning" sample and R2 (resp. R4) the "losing" sample, and sgn(R) (R. R2) = O if they tie. R and Ry are a pair of data sampled from the Bradley-Terry [BT model with reward r()), i.e., p(R] > R2) (r(()) r(R))). Please refer Appendix for more detailed derivations.
Due to the intractable "R",, following Wallace et al. 446] we introduce latent variables R 1:T and utlize the evidence lower bound optimization (ELBO). In particular, LDro can be modified follows:
po (R ( -log
Po (
(R2:7)
LpPO-Diflusion Diflusion = - Egg. p.....g
log a [BERYT RRATT (R), R!)
logg Prer (R!=) Peot (RQ:2)
where RI:TT Po (R (R)) and R.:TT po po (R.:TRR))
Following Wallace al. [46), we can utilize Jensen's 's inequality and convexity of function log o to derive the following upper bound of LiPo-Diffusion
DPPo-Diftusion -E, R.R.R.R....R 1 (R))) (.R))
Pret (R)- (R() log - 1R2))
po (R-- (R] (R))
Prer (R² R25) )
log a [TsggnRR) R2)) log
where ~ 2000 T), (R--1 (R) and (R 1 R2))
are sampled from reverse generative process of Ri and Ry, respectively, i.e., (RI-1RR) po R((R)) and (R) Rτ) po (R) 1-1 (Q))
In our case, the antibodies with low energy desired. Thus, define the reward r(-) as E(-)/T.
where {-) is the energy function and T is the temperature. Different from the text-to-image generation where the (latent) reward is assigned to complete image instead of pixel [46] we know more fine-grained credit assignment. Specifically, it is known that E(R²) Σ S E(R) (j). ie.. the energy of an antibody is the summation of the energy of its amino acids 44. Thus the preference can be measured at the residue level instead of the entire CDR level. Besides, we have log Po = -j=++1 log Po [)) which a common assumption of diffusion models. Thus we can derive a residue-level DPO-Diffusion loss:
Trresidue DPO- Diffusion
- EE (.R. (.)_)_____RR)).._-....
log a BT f
n+m SeweanissnnnnRPnM
log -
log ( ; [ [[] Per( 3 [ -
5

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Thus, by Jensen's inequality and the convexity of - log c, we can further derive Lresidue -residue-DPO-Diiee DPO-Diffusion which is an upper bound of residuue-DPe DPO. Diffusion
Lresidue-Dro Dioiiuus (, Rg. (.1... (.1)).
(01 log - (()) )]
E Emt log (Rlsg RQLi) log (r ([]()() (M2(22 [(11(14)
The gradients of DPPoDiiftusinn and Dresidno-DPO--iiftusiin w.r.t the parameters 0 can be written as:
V VeLDPO-Diffusion = - - -, R() 2nj=n S (g, R2)
- Vo log (8ologpo(R11 [b]( Ve log (R5 (1))))
and
V L Lresidue-DPO-Difiiee = -3TE, |, RQ..R. (.) .R5)
>u 1gn sgn
((((R]L) - - Ve log (i Ve logpo (R)
[i]
where f(-) = log(pe (-)rrer()), which can be viewed as the estimated reward by current policy pe-
We can see that LeLDPo-Diftssoon actually reweight Ve peg P [ R') with the estimated reward of the complete antibody while V VoLnesidee-Do-Diiie amino acid itself. In this case, V Diffusiin will increase (resp. decrease) the likelihood of all amino acids of the "winning" sample (resp. "losing") at the same rate, which may mislead the optimization direction. In contrast, V V DPo-iduee-DD-Diifeiiie does not have this issue and can fully utilize the residue-level signals from estimated reward to effectively optimize antibodies.
does this with the estimated reward of the
We further approximate the objective Deotitio by sampling from the forward diffusion process instead of the reverse generative process Pa to achieve diffusion-like efficient training. With further replacing log Pe with - log 2 + log Phe which is exactly -Dx (gllp))) ) + Dx z (g) Pett
Phe when taking expectation with respect to q, we can derive the final loss for finettuning the diffusion model as follows:
Pe
LandPo RE (... (05)) RR))
Extm log or (-BTTgnnRR)) R(D1)
1 L (xllprer)
(gllp))))) ( [it}]
where RJ, Rd ~ (R), (Ri-1, 1 and (R RR)) are sampled from forward diffusion process of Ry and R2, respectively, which can be much more efficient than the reverse generative pro- cess that involves hundreds of model forward estimation. Here we use DD (Qllpe)ii to denote DKL. (xR [ RR) (R[
Similar for D& (g Pret [7]. (1 and
Dk., (4llpaa)))) These KL divergence can be estimated as in Eqs.
3.3 Energy Decomposition and Conffict Mitigation
The energy usually consists of different types, such attraction and repulsion. Empirically, direct optimization on single energy will lead some undesired "shortcuts". Specifically, in some cases, repulsion dominates the energy of the antibody so the model will push antibodies as far from the antigen as possible to decrease the repulsion during optimization, and finally fall into a bad local minima. This effectively reduces the repulsion, but also completely eliminates the attraction between antibodies and antigens, which seriously impairs the functionality of the antibody. This motivates us explicitly express the energy with several distinct terms and then control the optimization process towards our preference.
Inspired by et al. [51), we utilize "gradient surgery" to alleviate interference between different types of energy during energy preference optimization. More specifically, we have E(.) >V W,, (-), where is the number of types of energy, and w, is constant weight for the v-th kind of energy. For each type of energy (.). compute its corresponding energy preference gradient VoL, as

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Table Summary of AAR, RMSD, CDR E CDR-Ag AG (kcal/mol), pLL, PHR, and Nuucess of antibodies designed by our model and baselines. (L) (1) denotes smaller larger number is better.
Methods
AAR (1)
RMSD (L)
CDR Evoal (1) CDR-Ag AG (1)
pLL (1)
PHR ())
Naucess (t)
HERN
32.38%
9.18
10887.77
2095.88
-2.02
40.46%
MEAN
36.20%
1.69
7162.65
1041.43
-1.79
30.62%
dyMEAN
40.04%
1.82
3782.67
1730.06
-1.82
43.72%
DiffAb
34.92%
1.92
1729.51
1297.25
-2.10
41.27%
0
ABDPO 31.25%
1.98
629.44
307.56
-2.18
69.67%
9
ABDPO+
36.27%
2.01
1106.48
637.62
-2.00
44.21 %
5
Eq. (8) and then alter the gradient by projecting it onto the normal plane of the other gradients (in random order) if they have conflicts. This process works as follows:
VOL +- VoL, min (VeL, VoLu. 0) VoLu:
V 12
where (1,..., V) and Shuffle(1,...,
Experiments
4.1 Experimental Setup
Dataset Curation To pre-train the diffusion model for antibody generation, we use the Structural Antibody Database [SAbDab. [Σ under IMGT (34) scheme as the dataset. We collected antigen- antibody complexes with both heavy and light chains and protein antigens and discarded the duplicate data with the same CDR-L3 and CDR-H3 sequence. The remaining complexes are used to cluster via MMseqs2 [44] with 40% sequence similarity as the threshold based on the CDR-H H3 sequence of each complex. We then select the clusters that do not contain complexes in RAbD benchmark [I] and split the complexes into training and validation sets with a ratio of 9:1 (1786 and 193 complexes respectively). Specifically, the validation set is composed of clusters that only contain one complex. The test set consists of 55 eligible complexes from the RAbD benchmark (details in Appendix (D.2).
For the synthetic data used in ABDPO fine-tuning, 12 samples are randomly sampled for each antigen--ntiboul complex the we use pyRosetta 19] to apply the side-chain packing for these samples.
using the aforementioned pre-trained diffusion model. Then,
Preference Definition To apply ABDPO, we need to build the preference dataset and construct the "winning" and "losing" pair. The accurate relationship between preferences based in silico with wet-lab experimental results a scientific issue that remains unresolved, with a wide range of opinions. ABDPO's is solution to this open question is to provide generic framework that allows for arbitrary definitions and combinations of preferences to satisfy various requirements in antibody design.
To demonstrate the effectiveness of ABDPO, we define the preferences as lower total energy and lower binding energy. The two energies are defined on residue level, specifically. (1) RESCDR Evoal is the total energy of each residue within the designed CDR, and is used represent the overall rationality of the corresponding residue; (2) RescdR-AA AG is the interaction energy between each designed CDR residue and the target antigen, representing the functionality of the corresponding residue. RescoR-Ag AG is further decomposed into (2.1) RescoR-Ag EnonRep- the sum of the interaction energies except repulsion between the designed CDR residue and the antigen, and (2.2) RescDR- Ag ERep. the repulsion energy between the design CDR residue and the antigen.
As generic framework, ABDPO also supports non-energy- based preferences. To verify this, demonstrate an advanced version named ABDPO+. ABDPO+ incorporates two additional prefer- ences: pseudo log-liieldhood (pLL) from AntiBERTy [42) and the percent of hydrophobicity residues (PHR). Different from the previously mentioned energy-based preferences, pL.. and PHR are defined on the whole CDR level. For pl..,, higher value considered better and is designated "winning". conversely; for PHR, a lower value is preferable.
Baselines We compare our model with various representative antibody sequence-strucun co-design basclines. HERN [1 designs sequences of antibodies autoregressively with the iterative refinement
7

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Reference AMPOPDAFDI
ANDPO ASOOGVELDV
Referanos ARWINDYY
ASDPO ARWYORY
Rufurenoe ARDTYMSOMDY CDR Hew!
ADOPO ARDOWNOOMDV
CDR Row!
CDR Four 57,4347
CDR CDR-Ag &O -2490
CDR Fow!
CDR-Ag AG: -54266 5,4766
CDR-Ag ao: -..22
CDRiAg aG 6,0688
CDR-Ag AG:- 72134
CDR-Ag -
Figure 3: Visualization of reference antibodies in RAbD and antibodies designed by ABDPO given specific antigens (PDB ID:: liqd (left), 1ic7 (middle), and 2dd8 (right)). The unit of energy annotated is kcal/mol and omitted here for brevity.
of structures; MEAN [29] generates sequences and structures of antibodies via a progress full- shot scheme; dyMEAN 50 designs antibodies sequences and structures with full-atom modeling; DiffAb (36] models antibody distributions with a diffusion model that considers the amino acid type, C. positions and side-chain orientations, which is more rigorous generative model than the above baselines. The side-chain atoms are packed by pyRosetta. For dyMEAN, we (1) provide the ground-truth framework structure as input like other methods, (2) only use its generated backbones and pack the side-chain atoms by pyRosetta for a more fair comparison.
Evaluation Following the previous studies, preliminarily evaluate the generated sequence and structure with AAR and Co RMSD. Besides, we carry out series more reasonable metrics. We utilize the preferences affrrementioeed to evaluate the designed antibodies from multiple perspectives, but at the whole CDR level. Specifically, (1) CDR Event. the total energy of the designed CDR, is utilized evaluate the rationality by aggregating all RESCDR Evoal of residues within the CDR; (2) CDR-Ag AG' denotes the difference in total energy between the bound state and the unbound state evaluate the functionalityy. PHR and pLL remain the same definition as above. All methods are able to generate multiple antibodies for specific antigen (a randomized version of MEAN, rand-MFANN, used here). We employ each method to design 192 antibodies for each complex, and we report the mean metrics across all 55 complexes. We further report the number of successfully designed antibody- anttien complexes, Naucess: to evaluate their rationality and functionality comprehensively. The design for an antibody-antign complex is considered as "successful" when at least one generated sample holds energies close to or lower than the natural one, i.c., for both of the two energy types, Egenerated < Emaural + std mutural pall--complxess
of the CDR and antigen, which is calculated
4.2 Main Results
We report the evaluation metrics in Tab. [ As the results show, ABDPO performs significantly superior to other antibody requence-structure co-design methods in the two energy-based metrics, CDR Exoual and CDR-Ag AG, while maintaining the AAR and RMSD. With the two additional pref- erences, ABDPO+ avoids the expense of the increased PHR while achieving better performance than DiffAb remaining metrics (even surpassing DiffAb in AAR). This demonstrates the effectiveness and compatibility of ABDPO in terms of optimizing multi-objectives simultaneously. We have also provided the detailed evaluation results for each complex in Appendix
We do not consider AAR and RMSD as the main reference evaluation metrics as their inadequacy (refer to Appendix A for more details). With the new evaluation methods, issues that used to be hidden by AAR and RMSD are exposed. It is observed that structural clashes can not be avoided completely in any method, resulting in the high energy values of generated antibodies, even for ABDPO and ABDPO+. The structural clashes between CDR and the antigen finally lead to the unreasonable high CDR-Ag AG. However, the primary goal in antibody design is to generate least one effective antibody. Given the complexity of protein interactions, it is not plausible that every generated antibody will yield effectiveness. Therefore, Nsuceess a more valuable metric. AB DPOP and ABDPO+ are the only two to achieve successful cases, with 9 and successful cases out of 55 complexes, respectively. Following this concept, we also rank the designed antibodies for each complex by uniform strategy (see Appendix D.3). calculate the metrics of the highest-ranked design for each complex, and report the mean metries across the 55 complexes (see Appendix E.T Notably, ABDPO is the only method that achieves CDR-Ag AG lower than 0.

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A0DPO
W/O residue level DPO
W/ Energy Decompasition
wic Gradient: Surgery
CDR.AQ
CDR CDRLAQ
CDR
Stap
Step
Stop
Step
Figure 4: Changes of median CDR E EmnnRep ERep= and CDR-Ag AG (kcal/mol) over- optimization steps, shaded indicate interquartile range (from 25-th percentile to 75-th percentile).
We also visualize three cases (PDB ID: I liqd, lic7, and 2dd8) in Fig. S It is shown that ABDPO can design CDRs with both fewer clashes and proper relative spatial positions towards the antigens, and even better energy performance than that of natural antibodies.
We conduct another two experiments to demonstrate further the generality of ABDPO: (1) directly incorporate auxiliary training losses for those properties of which gradients are computable; (2) introduce energy minimization before energy calculation, which is more in line with the real workflow. ABDPO shows consistent performance and demonstrates its generality. Please refer to Appendix for related details.
4.3 Ablation Studies
Our approach comprises three main novel designs, including residue-level direct energy-based preference optimization, energy decomposition, and conflict mitigation by gradient surgery. Thus perform comprehensive ablation studies to verify our hypothesis on the effects of each respective design component. Here take the experiment Here, we apply more fine-tuning steps and additionally introduce EnonRep (aggregation of RescDR-Ag EnonRep within the designed CDR), Exep (aggregation of ReScDR-Ag L'Rep) for more obvious and detailed comparison. More cases of ablation studies can be found in Appendix G
complex (PDB ID: 1a14) as the example.
Effects of Residue-level Energy Preference Optimization We hypothesize that residue-level DPO leads to explicit and intuitive gradients that can promote effectiveness and efficiency compared with the vanilla DPO 466 as the analysis in [Sec. 3.2, To validate this, we compare ABDPO with its counterpart with the CDR-level preference instead of residue-level. As Fig. shows, regarding the counterpart (blue dotted line), the changes in all metrics are not obvious, while almost all metrics rapidly converge an ideal state in ABDPO (red line). This demonstrated the effects of residue-level energy preference in improving the optimization efficiency.
Effects of Energy Decomposition In generated antibodies, the huge repulsion caused by clashes accounts for the majority of the two types of energy. This prevents from using the ÅG as an optimization objective directly as the model is allowed to minimize repulsion by keeping antibodies away from antigens, quickly reducing the energies. To verify this, we compared ABDPO with a version that directly optimize AG. As shown in Fig. 4 without energy decomposition (green dashed line), both EREP and EnonRep quickly diminish to O, indicating that there is no interaction between the generated antibodies and antigens. Conversely, ABDPO (red line) can minimize ERep to 0 while maintaining EnonRep- which means the interactions are preserved.
Effects of Gradient Surgery To show the effectiveness of gradient surgery in mitigating conflicts when optimizing multiple objectives, surgery. As Fig. shows, the counterpart (purple dashed line) can only slightly optimize CDR-Ag EmonRep but incurs strong repulsion (i.e., FRRE)), learning to irrational structures. ABDPO (red line) can converge to a state where CDR Favul and ERep achieve a conspicuously low point, suggesting the generated sequences and structures are stable, and EnonRop still significantly less than zero, showing that considerable binding affinity is kept.
compare ABDPO and its counterpart without gradient
Comparison with Supervised Fine-tuning Supervised Fine-tuning (SFT) can be an alternative way of generating antibodies with lower energy. For SFT, we first select the top 10% high-quality samples from ABDPO training data on complex (PDB ID: la14). We fine-tune tune the diffusion model under the same settings as ABDPO. Results Tab. 2 show that SFT only marginally surpasses pre-trained diffusion model, and ABDPO performs significantly superior to SFT. We attribute the performance of ABDPO to the preference optimization scheme and the fine- grained residue-level energy rather than the entire CDR.

---

Table 2: Comparison of ABDPO and supervised fine fine-tuning (SFT) on la14.
CDR
Emaa (C)
CDR-Ag AG (L)
Methods
Avg.
Med.
Avg.
Med.
DiffAb
1314.20
1133.36
534.21
248.28
DiffAbseT
1053.82
869.37
374.27
144.25
ABDPO
336.02
226.25
88.64
0.10
Conclusions
In this work, we rethink antibody sequence-structtre co-design through the lens of energy and propose ABDPO for designing antibodies meeting multi-objectives like rationality and functionality. The introduction of direct energy-based preference optimization along with energy decomposition and conflict mitigation by gradient surgery shows promising results in generating antibodies with low energy and high binding affinity. With ABDPO, existing computing software and domain knowledge can be easily combined with deep learning techniques, jointly facilitating the development of antibody design. Limitations and future work are discussed in Appendix
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A Motivation for Choosing Energy as Evaluation
There are many inadequacies in using AAR and RMSD as the main evaluation metrics in Al-based antibody design. Antibody design is a typical function-oriented protein design task, necessitating a more fine enn-grai measure of discrepancy compared to general protein design tasks. Especially when the part of the antibody to be designed and evaluated, CDR-H3, is usually shorter, more precise evaluation becomes particularly important.
A
B
RAbD CDR-H3 sequences
10
AR
D
SGG
DY
probebitt
XONIAAI
Y
Tyr
Phe
Gly
Trp
00
50
20
posilion
Figure 5: A: Tyr (Y) and Phe (F) differ by only one oxygen atom. In contrast, there a substantial difference between Gly (G) and Trp (W). Gly lacks side chain, whereas Trp possesses the largest side chain of all amino acids. B: the visualization of the frequency of occurrence of each amino acid at various positions in RAbD CDR-H3 sequences. The sequences are initially aligned using MAFFT [26] and subsequently visualized with WebLogo [[]. The width of each column corresponds to the frequency of occurrence at that position.
For AAR, there are two main limitations in measuring the similarity between the generated sequence and the reference sequence. The first limitation is located in measuring the difference in different incorrect recoveries. Among the 20 common amino acids, some have high similarity between them, such as Tyr and Phe, while others have significant differences, such as Gly and Trp (Fig. [AA). When an amino acid CDR is erroneously recovered to different amino acids, their impact will also vary. However, AAR does not differentiate between these different types of errors, only identifying them as "incorrect".
A further, more serious issue is that AAR is easily hacked. Although the CDR region is often considered hypervariable, mild conservatism in sequence still exists (Fig. (B), which allows the model to obtain satisfactory AAR using a simple but incorrect way directly generating the amino acids with the highest probability of occurrence at each position, while ignoring the condition of the given antigen which is extremely harmful to the specificity of antibodies. We made a simple attempt by simply counting the amino acids with the highest frequency of occurrence various positions in all samples in SAbDab, and then composing them into a CDR-H3 sequence, which looks roughly like "ARD + rYn G)* + FDY", achieving an AAR of 38. 77% on the RAbD dataset.
CDR-Ag Enenrtup
CDR-Ag Enso
residue
200
aductin Sioosiochuin mel. 2.50
Count
6.0
ang
from dktechin avg. 10.00
frome whold rosiduu 12 86
40
1.00
from whole resi med
6.32
-28
23
30
-22 -2
-16
Figure 6: The distribution of CDR-Ag EnoeRep (left) and CDR-Ag FRep (right) formed by the whole CDR atoms (colored in red) and solely by CDR side-chain atoms (colored in blue) among SAbDab dataset.
While RMSD fails to measure the discrepancies on side-chain atoms, in general, the calculation of RMSD focuses on the alpha carbon atom or the four backbone atoms due to their stable existence in any type of amino acid and thus ignores the side-chain atoms. However, side-chain atoms in the CDR region are extremely important as they contribute to most of the interactions between the CDR and the antigen. Our analyses on the SAbDab dataset also prove the importance of the side chain in CDR- Antigen interaction in terms of energy. As shown in Fig. 6 the distribution of energies formed
14

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by the whole residues in CDR is colored in red while the distribution of energies formed only by side-chain atoms of CDR is colored in blue. The interaction energy formed by side-chain atoms accounts for the vast majority of the total interaction energy in both types of energy.
The above reasons have led us to abandon AAR and RMSD learning objectives and evaluation metrics, and instead use energy as our goal. Energy can simultancously consider the relationship between structure and sequence, distinguish different generation results in more detail, and impor- tantly, reflect the rationality and functionality of antibodies in a more fundamental way. Despite the various shortcomings of AAR and RMSD, have demonstrated that the antibodies generated by ABDPO achieve lower AAR and comparable RMSD compared to those generated by other methods However, in practice, ABDPO-generale differing from reference antibodies, and demonstrate significantly better energy performance than those produced by other methods. This further highlights the inadequacies of using AAR and RMSI) as evaluation metrics in antibody design tasks, exposing their vulncrability to being "hacked".
antibodies exhibit distinct binding patterns to antigens,
B Energy Calculation
In ABDPO, we conduct the calculation on RESCDR Evst residue level, and more fine-grained calculation on the two functionality assoccated energies at the sub-residue level. We use Rosetta to calculate all types of energies in this paper.
We denote the residue with the index i in the antibody-antigen complex as A,, then ArC and A represent the side chain and backhone of the residue respectively.
For the energies in the proposed preference, we describe the function for energies of Single residue as ES, and ESuuaa is the sum of all types of energy with the default weight in REF15 A. The function for interaction energies between Paired residues is described EP, which consists of six different energy types: EP bhond EP att EP rep-
EP Eos
EP Ploce and EPIK-
Following the settings previously mentioned Sec. 3.1 the indices of residues within the CDR-H3 range from n + + m, and the indices of residues within the antigen range from g + 1 to g + Then, for the CDR residue with the index j. the three types of energy are defined as:
ReSCDR 1y EStonal (Aj),
(10)
g g-k
RescdR-AS Ag Fj
Σ
Σ
(EP (P,5 AA")).
(11)
nomRep
i=g-1 1 oF lol..c.
g+
RescDR-AS
Ag Ekep
reppp( A, )+ + EP
rep (Apc. Ab)
++1
+ 2 EPrep (4 AAT) + x EP Ereep (A)5 A!h))
(12)
It can be observed from Eqs. 11 and (12) that the two aaatiionllit-asssciiane energies, namely RescDR-Ag EnonRep and RescdR-Ag Erep- which collectively describe the interaction energy between CDR and the antigen, are computed at the level of side-chain and backbone. RescnR-Ag EncnRep only calculated on the interactions caused by the side-chain atoms in the CDR-H3 region, while RescdR-Ag Rapp assigns greater cost to the repulsions caused by the backbone atoms in the CDR-H3 region. This modification is carried out according to the fact that the side-chain atoms contribute the vast majority of energy to the interaction between CDR-H HH and antigens (Fig, 6 and EnonRep exhibits a benefit in interactions, while Exep could be regarded as a cost.
The fine-grained calculation of RescDR-Ag EnonRep and ResCDR-AS LRee is indispensable. With- out the fine-grained calculation, the model tends generate poly-G CDR-H3 sequences, such as "GGGGGGGGGGG" for any given antigen and the rest of the antibody. The most likely reason for this is that G, Glycine, can maximize the reduction of clashes and gain satisfactory CDR Exoua and RescdR-AS Ag EROP as it doesn't 't contain side chain and simultaneously form weak attraction to the antigen solely relying on its backbone atoms.
We emphasize that the two imnciionlity-aasociill energies, RESCDR -Ag FrnonRe and ResCDR FRee calculated exclusively at the sub-residue level when serving as the determination of preference in
15

---

guiding the direct energy mergy-based preference optimization process. However, when these energies are used evaluation metrics, they are calculated at the residue level, in which the greater cost the repulsions attributed to the backbone atoms is negated.
C Theoretical Justification
In this section, we show the detailed mathematical derivations of formulas in Sec.. 3.2] Although many of them are similar to Rafailov et al. [41] we still present them in detail for the sake of completeness. Besides, we will also present the details of preference data generation.
First, we will show the derivation of the optimal solution of the KL-constrained reward-maximization
objective, i.e., maXpo ER-~ [r(]))] 3D (pe (R") Prer (R)) as follows:
max Roo (r(RR) 31DxL (po (T2) (IP))t(RR))
Pe
po (RO)
max E Ro Pe
r(R²) 3 llg Pref (RU)
log po (R.)
1
min Exp po
(RR_)
Prer (R))
3
po (
min Egawpo
log (P exp (2r(R)))
log Z
Po
where Z is the partition function that does not involve the model being trained, i.e., Po. And we can define
p" PR(R)) z Prer (R.) exp (R)))))
With this, we can now arrive at
Po Po (R
min Ro
log
log Z
Pe
p" (Ro)
min E Epo
[TK (Po [1pT)
Z
Pe
Since Z does not depend on Pe. we can directly drop it. According to Gibb's inequality that KL- divergence is minimized at 0 if and only if the two distributions are identical. Hence arrive the optimum as follows:
1 Pa- (R (R²) 7 Pror( (R) exp (F)(R2))
(13) Then we will show that the objective that maximizes likelihood on preference data sampled from p(R] > R2) (r(())) r(RR)), which is exactly I.PO leads to the same optimal solution. For this, we need to express the pre-defined reward r(-) with the optimal policy p":
p² (RRO)
T(R)) = 3 log
+ Z
Pee (RO)
The we plugin the expression of r()) into p(R) > R2) = ((((R)) - r((R)) as follows:
PRR > R2) o (r(R)) - -(R)))
o 3 log R()
p" (R(
p¹ (RRR)
3 log
Pret (
where Z is canceled out. For brevity, we use the following notation for brevity:
(R > RB) = o Boo (R() 3 log
po (R2)
Prer(R))
Pref Pref (RQ)
With this, have
min LiPo min -ERg R$
(R) - R2)
max Exg Rg~ R2 > Ry)
min DxL ((R R2) po po R2)
Pe
16

---

Again with Gibb's inequality. we can easily identify that po > R2) = p(R) > R2) achieves the minimum. Thus p" (R") = (ree((R)) exp (t)(R)) is also the optimal solution of LOPO.
D
Implementation Details
D.1 Model Details
The architecture of the diffusion model used in our method is the same Luo et al. [3]. The input of the model is the perturbed CDR-H3 and its surrounding context, i.e., 128 nearest residues of the antigen or the antibody framework around the residues of CDR-H3, The input is composed of single residue embeddings and pairwise embeddings. The single residue embedding encodes the information of its amino acid types, torsional angles, and 3D coordinates of all heavy atoms. The pairwise embedding encodes the Euclidean distances and dihedral angles between the two residues. The sizes of the single residue feature and the residue-pair features are 1285 and 64, respectively Then the features are processed by Multiple Layer Perceptrons (MLPs). The number of layers is 6. The size of the hidden state the layers is 128. The output of the model is the predicted categorical distribution of amino acid types, C. coordinates, and so(3) vector for the rotation matrix.
The number of diffusion steps is 100. We use the cosine 3 schedule with 0.01 suggested in Ho et al. 20 for amino acid types, Ca coordinates, and orientations.
D.2 Training Details
Pre-training Following Luo et al. [36.. the diffusion model is first trained via the gradient descent method Adam (7 with init anit_llarning learning_rateeeee----- 14, betas= (0.9, O. 999), batch_size-1s During the training phase, the weight of rotation loss, position
and clip-gradd peaddienttnorm-100 loss, and sequence loss are each set to 1.0. We also schedule to decay the learning rate multiplied by factor of 0.8 and minimum learning rate of 5e 6. The learning rate is decayed if there is no improvement for the validation loss in 10 evaluations. The evaluation is performed for every 1000 training steps. We trained the model on one NVIDIA A100 80G GPU and it could converge within 30 hours and 200k steps.
Test set The original RAbD dataset contains 60 antibody-antigen complexes. In this study, we hope all the complex consists of an antibody heavy chain and light chain, and at least one protein antigen chain. In practice, 2ghw and 3uzq lack light chains, while 3h3b lacks heavy chains. 5d96 was excluded because of the incorrect chain ID information in rabd_ summary.ison where heavy chain and light chain do not bind to antigen chain A. As for 4etq, we actually conducted the training (CDR 70.55, CDR-Ag AG=-4.57), but HERN reported an error when running for this complex, so we did not report it.
Pair data construction In terms of the construction of "winning" and "losing" data pair, we did not pre-define "prefered" and "non-preferedd datasets but rather constructed unified data pool. During each training step, the paired data used for DPO training is randomly sampled from the data pool. Although their energies and properties have been pre-calculated, the "winning" and "losing" labels are determined real time. In practice, we used several labels, involving three different preferences related to energy and two preferences related to non-energy-bas -baed properties. The "winning" and "losing" labels among these preferences are not necessarily consistent. Therefore, the loss for each type of energy/preference is calculated separately and then aggregated with different weights to update the entire model. Moreover, as the training progresses, we continuously sample new data, calculate their energy, add them the data pool, and discard some of the older addt- data simultaneously to ensure that the data stays in sync with the policy.
Fine-tuning For ABDPO fine-tuning, the pre-trained diffusion model is further fine-tuned via the gradient descent method Adam with init_nneittttt seat__earninggaee 1.. betas= (0.9, 9,0.999) and siap-gradient norm= 1arm=1000 100. The batch size is 48. More specifically, in a batch, there are 48 pairs of preference data. We do not use decay learning
and do not weight decay in the fine-tuning process. And we use 3 = 0.01 and 0.005 in Eq. (8). We use the hyperparameter search space as follows. As for the three energies introduced in Sec.. 4.1 use 8:8:2 to reweight them (i.e., RescoR Emtal, ReScnR-Ag EnonRep, and RescDR-Ag BREp), and reweight PLL and PHR in ABDPO+
jsonl
17

---

to 1. In practice, different antibody- antiggn complexes prefer different hyperparameters. For fair comparison with baselines, we do not carefully picked the optimal hyperparameter for each complex but use uniform hyperparameter. We fine-tune the pre-trained diffusion model on four NVIDIA A800 40G GPUs for 1,800 steps for each antigen, separately.
D.3
Ranking Strategy
To rank the numerous generated antibodies with multiple energy labels, we applied a simple ranking strategy based on single energy metrics. The CDR Evoal and the CDR-Ag AG of each antibody are ranked independently. Then, a composite ranking score for each antibody is defined as the sum of its CDR Fanaal rank and CDR-Ag AG rank (for ABDPO+, PHR and pL.. also involved). Finally, the antibodies are ranked according to these composite scores. We acknowledge that this ranking strategy has several limitations. For instance:
1. Equal weights are assigned to all energy types and properties, despite them having differing importance in reality.
2. The distribution patterns of different energy types and properties can vary, with these distri- butions usually being non-uniform. This could result in scenarios where minor numerical differences in the top-ranking CDR-Ag AG values coincide with larger differences in CDR Eioal potentially leading to the selection of samples with suboptimal CDR Evstal-
However, addressing these issues would require extensive and in-depth exploration of antibody binding mechanisms and energy calculation methodologies. We chose this straightforward, yet impartial, ranking strategy for two key reasons:
1. The primary goal of this work is to reformulate the antibody design task as an energy-focusee optimization problem and propose a feasible implementation, rather than to delve into the mechanisms of antibody-antiget binding;
2. Our approach is designed to avoid introducing statistical biases or preferences based on potentially erroneous prior knowledge or favoritism towards particular antibody design methods.
E More Evaluation Results
E.1
Evaluation Results for Ranked Top-1 Design
In Tab. [ we have reported the average results of all antibodies designed by our method and other baselines. Here we provide the evaluation results for the ranked top-1 design in Tab, 3 (refer to the ranking strategy in Appendix D.3).
Table 3: Average performance of top-1 designs of 55 complexes designed by baselines and our model.
Methods
CDR Eveat ()) CDR-Ag AG (L)
PHR (1)
pLL (1)
AAR (1)
RMSD (L)
RAbD
5.25
-13.04
45.78%
-2.20
100.00%
0.00
HERN
8495.56
1296.22
48.18%
-2.01
33.29%
9.21
MEAN
3867.47
207.99
36.91%
-1.72
38%
1.70
dyMEAN
2987.93
1283.97
46.27%
-1.79
40.74%
1.81
DiffAb
381.82
58.84
49.19%
-2.03
37.99%
1.62
ASDPO
68.51
-4.96
69.97%
-2.15
32.92%
1.58
ABDPO+
332.10
29.27
32.81
-1.54
39.55%
1.67
E.2 Detailed Evaluation Results for each Complex
In Tab. and Tab. 5 we list the CDR Eusal- CDR-Ag AG, PHR and pL. of the reference antibody in RAbD and the average/ranked top-1 antibodies designed by HERN, MEAN, dyMEAN, DiffAb, ABDPO, and ABDPO+ for each complex in the test set separately. Tab. 5 we highlight the energy values of the designed complexes that surpass the natural one in terms of two energies simultaneously with bold text.
18

---

Table 4: Detailed evaluation results for reference antibodies and average evaluation results for antibodies designed by HERN, MEAN, dyMEAN, DiffAb, ABDPO. and ABDPO+ for 55 complexes. The data source is the same as that in Tab. [I] For simplicity, we use A, B, C, and D to stand for CDR Emnal: CDR-Ag AG, PHR, and pLJ. respectively in this table. The unit of the two energies kcal/mol and omitted for brevity.
1.78
-1.4
-3.1
1.40
-244
313
211
222
-162
38 29 227
251
1197
-185
-308
215
200
188
200
325
1888
300
212
196
320
220
200
325
-220
1.50
350
330
155
2002
01
35.999
51,515
6391
36
2216
31.91
0.458
550
53.550
160
70
43
840
69 28
035
70.00
AnDPO.
35.92
89
45
02
53
36
34
39
52
09
58
34.34
50.70
367.36
3602
686
591.70
199
30.50
110
152
27365
115007
000
506
148
500
251
664
286
190
828
25555
15
197
27 170
20200
26462
100
0.6
25435
12
255
880
440
74400
340
010
79.
66.
151
1451
800.66
800
038
34
10
318.00
744.88
055.66
280
1858
116 145
266
1033
1670
355
535
26
009
21
940
27
935
892
172
830
877
62
27
226
19
129
100
389
913
650
902
362
680
39047
27
192
1008
1200
22
2221
55
772
600
105
480
826
060
920
525
169
2.00
-191
-241
188
-2/5
-23
232
327
315
160
200
211
200
210
250
200
200
190
220
250
190
87 17 500
224
120
230
07 190
240
23
228
260
242
200
220
218
310
-20
ARDPO
76.84%
48 185
41
4/5
85 19
79 22.2%
65
04
66988
19
26.99
51
63 22
27.60
48
57
89 228
1000
664
65 396
57 35.
38 52
58
25
27.
37.00
82
02.28
70 2000
74 25
62
45
78 20
15 01
1048 77064
01
24.2%
88
52.99
64
11
860
06
21
11
54
88.64
925
257
11.19
73.23
158.66
29
281
18107
33.45
125
10047
500.30
1161
127
17223
4077
0908
00412
100
228.56
95.0
55
170522
52.58
3936
86.07
057.6
6701
7548
010
0707
06
77274
1944
122
412
22531
137779
06
10.5
30399
0618
2500
02
1067
336,02
247
167.0
800.35
23
91
52
12
24.85
38
541
121
622
1402
300.5
378
521
27
400.0
212
631
1322
417
407
467
25153
251
156
40
390
38
185
126
62000
195
212
36
38
1625
28
288
61
104
128
15
500
129
16
178
15
319
48.
205
400.0
384
55
105
1242
1.88
-121
-3.4
1.25
-236
-216
-319
235
222
257
216
218
215
190
21N
311
1.84
200
205
201
200
214
214
100
41.99 200
500
219
189
215
213
200
207
210
322
-22
162
173
-310
225
321
214
-21
-114
B,C,
35%
19%
45 65
46 07.
49 586
56.758
17/888
35 85
44 250
40 398
5009
21
39 35
121 118 35
14
37 068
36 50.
38 989
099
45
502
31
4.5
36 22
45 29
4.758
44
45 55.99
1744
25.21
DIFAb
31
46
42
40
45
58 40
40
46
40
47
55421
5000
00001
102.53
121819
67567
2413
166.56
31524
217112
556
116.14
12
536.00
20.565
40100
421
187
340
2052
130
3124
67150
149963
1000
200911
1906
53935
7158
331
00
096
62280
3014
0.30
50
280
2311
65622
25
366
100
19452
1050
235
36
35995
2964
131433
538
065.00
45
1277
1366.5
2797
173
08
1408
21
1522
255
923
1208
10
925
39
1941
162
130
200
1034
100
1000
21
31
198
2710
155
560
712
553
53
18
350
2522
537
1000
60
400
21
966
20
200
890
26
3665
1320
1422
100
132
986
2009
b)
1.99
-1280
1.45
-197
-205
2215
2344
-237
1.50
150
130
155
420
210
133
100
120
160
189
180
257
140
200
120
220
150
1.97
150
180
150
780
160
220
242
160
160
230
231
244
2115
015
55 25.315
42 50
S8
53 656
32 5806
139
50000
35
456
4545
55
190
160
08
460
09 95
41 288
62 286
24
11
77
290
54 83
02 23300
38 725
4yMEAN
57.5
0/
59
48
52
26
55
55
38
58
33
39
40
38
47
48
54
187.7
4004
255.00
144,17
20.96
931
182.00
53/389
4489846
1001
757
256000
109938
105455
17056
138828
00700
4387
260
515
1968
1478
21821
120226
1321230
140030
31 56524
072.37
0.47
00340
075
13808
121144
10342
50.224
46.25
215105
254050
261
21
14230
10.0
99428
1021
1116
60000
140234
101361
30008
5284.77
70
307300
559.55
661
54
2621
0650
46675
126.
40
5378
50
150
23080
151184
525945
57662
304
965
56
1000
400017
999246
2224
11
9644
5226.5
1968
3060
517.32
74047
208
312455
1853
2043
6710.5
10
1067
29
4291
403
479977
4206
135000
700020
420
19926
174602
4.57
1.90
-135
1.78
151
1390
1.00
3380
1999
155
224
155
4.50
4300
4.50
491
2340
228
18
2.00
230
3.74
5.52
160
220
1.57
220
220
166
2.19
2355
4.50
222
775
4.5
3.47
4.50
4.90
1.71
-130
-237
MEAN
31,
39
33.25%
25 576
16%
52
525
07
48.38
29
30
18:00
36
22
16
25225
929
38
200
22
165
81
600
29
29
56
57
226
20
38
1900
00
07005
206
21
186
49
07
158
3331
4.2
94224
17.22
17.2
51 515
25
250.02
75.95
865
59.31
664
773.06
2161 26
2093.0
190
126663
35 92.9
194
43
262
35
198
59
22
60 527.0
680
240
28
90
120
41
869
24
25
285
29
1855
59.55
5598
76
1009
13
155
41
02
586
50
185
1110
40
08
956
902
1710
547
50
309
69
1012
7114.7 76
3722 91
54
1699
55
51
4922
30
0009
2800
04
27
07
5262
1072
0012
22
0000
01
81
1328
76
4552
42
6007
502
1746
52
22
6500
0333
72
688
74
13
31
180
80
5047
19
308
668
68
11
2007
48
87
2000
5560
28
0000
86
41
256
65
1015
260
670
5155.0
0011.0
48
7367
27
501
660
16
1.57
1.25
-2.5
1.54
22
23
199
22
3.06
2.24
36
30
205
31
16
200
99
2.0
2.00
-1
208
21
90
20
96
208
25
200
27
45
16
-00
2.0
90
1.66
34
49
40.87%
42.08%
6.17 43.405
41.77%
281 72 43.7%
38.988
19/00
40.009
106
31 11%
25 42,405
56 41558
188
24 443
40
4520%
50485
30
4.308
571 11 41028
52A26
15 43258
29278
443
50.228
50 38505
65 1991
30006
31 439
56 40000
42423
4141
3731
706
380
30090
40 40140
12
4042
55 38628
30468
3955%
38346
96 4250%
64 37156
35598
4129%
68 40.5%
46
HERN
65-75
163.75
216 80
115.08
145
1055-00
1085
30545
57.7
236
668.1
1066
114638
1200
45.5
112
70
1547
50
55
52.50
08.11
28.71
736
702
1747
59
265
04
42 30920
16-21
100
300
20
730
15
136
97
881
1055
200
957
1059
220.00
2276.1
87
15 1706
3511
600
59.8
641
5084.22 26
50087 (4
4000000 (L
32
5500
00028
46
7472
36
1509
08
14
34
5963
10000
36
15635
81
00822
31
5012
79
17700
1980
1002035
3070
25
13
85
11409
11
61
15005
2099
63
10211
1211-30
2277
38
22
8822
560
12500
11025
32
362222
12
16882
18
92
007000
9108
96
268
01
44375
31
10
3908
5090
24
11559
699
21
396
16
540.50
1997
12600
91
55502
20
61
5000
15795
1.56
300
-261
2.49
446
250
4.78
210
340
322
3.00
227
170
260
25
14
121
250
100
322
350
240
200
201
250
165
231
230
290
180
192
260
180
250
120
255
18
122
351
350
266
155
2.5
-316
-1
RABD (Reforene)
45
146
08
406
359
47.75
676
08
158
23
55
41
53658
200
966
46
576
46
450
010
67
636
21.05
44
57,
70
3
36
58
50
38
75
36
38
67
48
60
4.73
-1.0
14.50
2.02
5.47
3.0
11
15.9
11
16
4:0
7221
12.90
16.14
12.35
14.57
18
19.00
28.54
40
18.41
544
1313
060
21
481
01
12
3.55
31.00
35
15.21
18.25
-99
84
16
1800
18
10.4
-240
-2118
25.79
1996
43.36
4188
20
1.39
8.6
20.47
531
5.5
04
-1032
366
1996
472
3.47
18.7
1188
-7558
21.35
0121
-601
.005
19.15
235
4.77
26
33500
0130
-980
11.9
14.11
18.37
-31.5
411
4687
-638
596
15
0.58
061
15.55
10.95
-6675
PDB
16l4
Inly
16X
1k7
1igh
165
1855
18.3
2675
200
200
3633
3095
400
46g
460
4.5m
4000
58%g
3W67
501
500
515
510
Spus
Sque
19

---

Table 5: Detailed evaluation results for reference antibodies and top-1 antibodies designed by HERN. MEAN, dyMEAN, DiffAb, ABDPO, and ABDPO+ for 55 complexes. The data source is the same as that in Tab. 3 For simplicity. we use A, B. C. and D to stand for CDR Exsal: CDR-A, Ag AG, PHR, and PLL respectively in this table. The unit of the two energies is keal/mol and omitted for brevity.
3.00
-1.35
-1.25
0.88
-181
-151
1M
-1.57
-10
-00
-135
1115
-10
-10
-133
-161
1288
-1.
1151
-198
-102
-180
1166
1:0
-161
-100
-082
12
-1.6
1.00
-120
100
-135
-151
26,778
20000
22.28
42.90
20
20000
35.
27.278
31674
16.00 33.558
4.3 56.304
50000
263306
22
27.55
55.506
41838
25
50026
4619
35
-222 53.558
180 50096
267 1862
-40 54500
25009
18755
227
38
21485
21.58
200
15
46155
27.29
466
33338
53
AnDrO
98
38
1.23
4.12
3.57
47.9
40
2211
488
0.2
6.1
358
4.38
310
38.30
86
8.50
130
-6
42
400
1300
360
3.5
345
360
-559
340
100
3.76
3.5
2600
4.27
25
440
3.0
330
110
390
-220
-314
180.00
74.95
667/06
10
100
28
184-7
75000
75524
25730
502.55
343.0
1692
65488
39988
20
460
175
58
201
56
2008
942
286.0
020
275
37.90
555
071
25
12500
3008
9681
660
72.2
2032
33293
156
402.0
3984
311
31106
916
916
51226
38
01
184
150
57.52
134
15
11
201
50000
2225
-443
-340
1453
-22
2358
3.00
238
488
329
336
122
221
211
329
194
225
255
180
330
150
330
250
230
180
200
251
210
213
200
216
190
223
220
220
1161
204
358
1.83
330
154
211
2315
ARDPO
66.77%
36
33.
31.
71.458
98
009
38
265
28
18
63
626
38
63
83
63
008
86
45
40
03
58
356
81
00
71
141 66.05
-41 85
75
389
77
22
88
60
86
60
656
51
250
68
280
68
36
92
23
66
71.
25.25
666
68
1300
545
5583
3.58
4.11
3.50
-7.36
3300
-11
555
750
-10
-60
4.74
4555
740
460
290
4.57
5565
3.00
722
400
460
360
546
534
231
140
355
522
500
461
220
3.3
4.00
4.00
7.0
457
465
3.0
5.4
400
3.54
455
4.00
A
4465
20:87
122.36
1.63
1271
10641
19837
5001
1502
8261
85.66
13420
2007
236
2311
1510
5006
3544
0025
19.54
1886
7300
2047
5841
1028
3155
10821
5033
212 41.5
1309
151 4125
15
3198
1192
25452
24225
2001
70.33
12144
4033
8836
1864
3425
80.25
5516
55.0
20.09
13607
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20

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C-N bond length in CDR-H3
C-N bond length KDE
1500
1250
80
Count
Density
750
40
500
250
1.29
1.30
1,31
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1.35
1.36
1.37
1.29
1.30
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1.34
1.35
1.36
1.37
Figure 7: Left: the distribution of peptide bond length within CDR-H3 in the SAbDab dataset; Right: the kernel density estimation (KDE) function fit on the natural peptide bond length distribution.
Arbitrary Preferences
F1 Incorporating Auxiliary Loss
predominant advantage the ABDPO is its unique capacity to seamlessly integrate traditional bioinformatics, computational biology, and computational chemistry tools - -olssthhoss those incapable of directly computing gradients - into the training regimen of AI models. This integration significantly broadens the ABDPO's 's applicability and versatility in antibody design. However, it is pertinent to acknowledge the existence of antibody energies/properties for which gradient calculations are feasible. Indeed, fundamental geometric characteristics, such as bond lengths, angles, and torsion angles, alongside more intricate properties predicted by deep-learning models, are gradient-computable. These gradient-computable features offer explicit direction for optimization, potentially enhancing the effectiveness and efficiency of the model optimization process.
In light of this, we initiated another experiment aimed at exploring ABDPO's compatibility with traditional gradient- losses, extending beyond the DPO loss. Specifically, we propose a special version based on ABDPO+ ABDPO++, which incorporates an auxiliary loss about peptide bond length. As covalent bond, the variation range of peptide bond lengths is very limited, and thus we can consider the length of peptide bonds to be fixed value and then utilize an MSE loss to directly penalize the unreasonable peptide bond length in generated antibodies.
In practice, we consider the ground truth peptide bond length to be 1.3310 (the average length of peptide bonds within CDR-H3 in SAbDab, the distribution could be seen in Fig. left) and apply the auxiliary loss only when the sampled t is near 0 (t < 15 in this experiment while T is 100), and the weight is set to 0.25. The peptide bond length is caleulated based on the predieted (sf, xh. 09) which is denoised with one step from xs). Of), then an MSE loss peptide bond length can be calculated. Finally, this auxiliary loss, together with various DPO losses, updates the model through the conflict mitigation mentioned Sec. 3.3
Table 6: Summary of CDR Evoaa CDR-Ag AG (kcal/mol), pLL, PHR, C-N AAR, and RMSD of reference antibodies and antibodies designed by ABDPOW/O and baselines the experiment involves auxiliary loss. (L) (1) denotes smaller larger number is better.
Methods
CDR Evoal (1) CDR-Ag AG
pLL (t)
PHR (L) C-N (1)
AAR (1)
RMSD (J)
HERN
10887.77
2095.88
-2.02
40.46%
0.12
32.38%
9.18
MEAN
7162.65
1041.43
-1.79
36.20%
1.68
36.30%
1.69
dyMEAN
3782.67
1730.06
-1.82
43.72%
2.08
40.04 %
1.82
DiffAb
1729.51
1297.25
-2.10
41.27%
3.85
34.92%
1.92
ABDPO
629.44
307.56
-2.18
69.67%
2.55
31.25%
1.98
ABDPO+
1106.48
637.62
-2.00
44.21%
2.95
36.27%
2.01
ARDPO++
1349.39
747.89
-1.99
44.46%
4.51
36.30%
1.95
21

---

To evaluate the consistency of generated antibodies' peptide bond length to the natural antibodies, we fit Kernel Density Estimation function using the length of peptide bonds found within the CDR-H3 region of natural antibodies (shown in Fig. rright,, then the density of the generated peptide bond length, SuNee is used to represent the consistency. We report the average experiment result in Tab. 66. It can be observed that ABDPO+ significantly optimized the length of the peptide bond, achieving the best C-resore of 4.51, while maintaining the optimization to the other 4 preferences. The experimental result demonstrates the compatibility of AbDPO with traditional gradient-basel losses, indicating that AbDPO has a wider scope in actual application.
F.2 Incorporating Energy Minimization
Energy minimization is indispensable in the standard protein design protocol and is typically applied the raw co-crystal structure and the generated structure. Most existing Al-based antibody design methods have not undergone similar operations, but to verify the performance of ABDPO in a more realistic workflow environment, we have also proposed another version based on ABDPO+ that integrates energy minimization, ABDPOW/O.
For the minimization of the raw co-crystal structure, compared the performance of baseline meth- ods trained with and without minimized co-crystal structure but observed no significant difference. possible reason for this is that most of the methods do not generate the side chain and thus not sensitive to energy minimization, which mainly optimizes the side-chain conformation. Thus we follow the previous studies, and directly use co-crystal structure to train the baseline models and the pre-trained model in ABDPO.
We carry out minimization during the evaluation phase and apply the minimization to the generated antibodies before energy calculation. Therefore, the preference dataset used in ABDPOw/O is built upon the minimized energy. The energy minimization process consists of two parts, peptide bond length rectification and loop refinement. We first set the length of the peptide bond to 1.3310, the average length of the peptide bonds within CDR-H3 in the SAbDab dataset. Then we use GhopMover_Refine CCD from pyRosetta to refine the structure of the designed CDR loop. To reduce time consumption in loop refinement, we set the outer_ cccles to and max_ini maxx__nner_eee cener__ycles to 10 (a bigger number of cycles will lead to better energy performance undoubtedly, but also makes the time consumption uncontrollable).
Another modification of ABDPOW/O compared to ABDPO+ is that the decomposition of ReSCDR AG into RescdR-Ag EaonRep and RescdR-Ag Exep is canceled. Energy decomposition is indispensable in the main experiment because of the huge repulsion, and is not necessary in this experiment the repulsion would be diminished by the post-minimization process.
Table 7: Summary of CDR Exotal, CDR-Ag AG (kcal/mol), PHR, and pLL of reference antibodies and antibodies designed by ABDPOW/O and baselines in the experiment involves energy minimization. / (f) denotes smaller / larger number is better.
Methods
CDR Evtal (L)
CDR-Ag AG (L)
PHR (L)
pLL (1)
RAbD
-0.6699
-10.2772
0.4578
-2,0466
HERN
2765.5834
0.8332
41.41%
-2.0499
MEAN
1162.0961
0.0508
30.63%
-1.7936
dyMEAN
611.1203
-2.051
43.73%
-1.8187
DiffAb
82.6216
-0.2734
38.58%
-2.0933
ARDPOW/O
69.8181
-3.0007
36.71%
-2.0251
In Tab. 7 we report the average values of the evaluation metrics for all the generated antibodies in this experiment. Given that the peptide bond length has been rectified, measuring the C-N score is deemed unnecessary in this context. It can be observed that the post- most-minimization eliminates most of the clashes between the designed antibodies and the corresponding antigens, making CDR-Ag AG fall within a reasonable range of value. ABDPOW/O still achieves the best performance in the two energy-based metrics, CDR Exual and CDR-Ag AG, and surpasses DiffAb in all metrics. This experiment proves (1) the effectiveness of ABDPO in more realistic setting, and (2) the ability of ABDPO to optimize the energies/properties not directly calculated from the generated antibodies. The values of the two sequence-relater metrics, PHR and pLL, for the baseline methods slightly
22

---

differ from those in Tab. 1 This discrepancy arises because we imposed maximum processing time during the loop refinement phase, leading to the exclusion of samples whose refinement was incomplete within the allocated time.
G Extended Ablation Studies
Due to the massive training cost in the RAbD benchmark, we investigate the effectiveness and necessity of each proposed component on five representative antigens, whose PDB IDs are 1a14, 2dd8, 3cx5, 4ki5, and 5mes. From the results in Fig. 8 it is clear that ABDPO can significantly boost the overall performance of ablation cases. Note that moving averages are applied to smooth out the curves to help identifying trends, including Fig. 4
We present observations and constructive
insights of the three proposed components as follows:
1.
The residue-level DPO is vital for training stability specifically for CDR Evstal As aforemen- tioned in Section 3.2 the residue-level DPO implicitly provides fine-grained and rational gradients. In contrast, vanilla DPO (without residue-level DPO) may impose unexpected gradients on stable residues, which incurs the adverse direction of optimization. According to each energy curve in Figure by at least one energy term.
[8] we observe that residue-level DPO surpasses vanilla DPO
2. Without Energy Decomposition, all five cases appear undesired "shortcuts" aforementioned in Section 3.3 We observe that the energy of CDR Evstl exhibits slight performance improvement over the ABDPO after the values of attraction and repulsion reach zero. We suppose that is the result of the combined effects of low attraction and repulsion. Because the generated CDR-H3 is far away from the antigen in this case, the model can concentrate refining CDR Evai without the interference of attraction and repulsion.
3. The Gradient Surgery can keep a balance between attraction and repulsion. We can see the curves of EnooRep are consistently showing decline, while the curves of ERep are showing an increase. This observation verifies that ABDPO without Gradient Surgery is unable optimize EmonRop and Egep simultaneously. Additionally, the increase in attraction significantly impacts the repulsion, causing the repulsion to fluctuate markedly.
H Limitations and Future Work
Diffusion Process of Orientations As Luo et al. [36 stated and we have mentioned in See. 3.1 Eq. (T) is not rigorious diffusion process. Thus the loss in Eq. ( cannot be rigorously derived from the KL-diiergeece in Eq. D. though they share the idea of reconstructing the ground truth data by prediction. However, due to the easy implementation and fair comparison with the generative baseline, i.c., DiffAb (36), we adopt Eq. 7 in the ABDPO loss in Eq. (8). In practice, we empirically find that it works well. FrameDiff [50]. protein backbone generation model, adopts a noising process and a rotation loss that are well compatible with the theory of score-based generative models (also known diffusion models). In the future, we modify the diffusion process of orientations as Yim et al. (50) for potential further improvement.
Energy Estimation In this work, we utilize Rosetta/pyRossee already one of the most authoritative energy simulation software programs and widely used in protein design and structure prediction, the final energy value is still difficult to perfectly match the actual experimental results. In fact, any computational energy simulation software, whether it is based on force field methods such as OpenMM [14] or statistical methods like the Hiyazawwa-ernigal potential 38). will exhibit certain biases and cannot fully simulate reality. Sometimes there is a significant difference between the energy calculated by the software and the results observed experimentally. One possible reason is that theoretical calculations often rely on the designed sequence and structure of antibodies; meanwhile, in actual experiments, the actual folding of the CDR region into the designed structure can be difficult, which leads to significant discrepancies in theoretical calculations. An in vitro experiment the only way verify the effectiveness of the designed antibodies. However, due to the significant amount of time consumed by in vitro experiments and considering that the main goal of our work is to propose novel view of antibody design, we did not perform the vitro experiment.
calculate energy, although it is
Future Work on Preference Definition The preferences used in ABDPO determine the tendency of antibody generation, and we will strive to continue exploring the definition of preference to more
23

---

AddPD
-... W/b residue-leve DPD
-...
We Enengy Decompostion
who Gradient Surgery
COR
CDRAg
CDR A0
Step
Step
PDB ID: 1a14
CDltagg Factee
CDR Ar AG
Stap
Step
POB ID: 26d8
Stup
Step
CDRT
CDR Ag
CDR
Stop
Stop
Stop
Stop
CDR Ag
Stop
Step
Stop
Stop
A4 Evee
CDR Ag 2/5
CDR.
Stop
Step
PDB
Step
Step
Figure 8: Changes of median CDR Evcal CDR-Ag EnonRep. CDR-Ag DRep' and CDR-Ag AG (kcal/mol) over-optimization steps, shaded to indicate interquartile range (from 25-th percentile to 75-th percentile). The rows represent PDB lal4, 2dd8, 3ex5, 4ki5, and 5mes respectively, in top-down order.
closely align the antibody design process with the real-world environment antibody activity. Further, aim synchronize the preference with the outcomes of in vitro experiments and expect that our method will ultimately generate effective antibodies real-world applications. The exploration of preference can be divided into two aspects: enhancing existing preferences and integrating components or energies.
1.
The improvement to current preference: (1) performing more fine- ane-grained calculations on the current three types of energy, such as decomposing CDR Fioal into interactions between the CDR and the rest of the antibody, interactions within the CDR, and energy at the single amino acid level; (2) exploring the varying importance of preferences for antibodies and determining the relative weights each preference during the optimization and ranking of generated antibodies.
2. The incorporation of new components or energies is intended to address additional chal- lenges in antibody engineering, focusing on aspects such as antibody stability, solubility, immunogenicity, and expression level. Additionally, we consider integrating components that target antibody specificity.
24

---

I Potential Societal Impacts
Our work on antibody design can be used in developing potent therapeutic antibodies and accelerate the research process of drug discovery. The generality of our method extends beyond its current application; it is adaptable for various computer-aided design scenarios including, but not limited to, small molecule, material, and chip design. is also needed ensure the responsible use of our method and refrain from using it for harmful purposes.
25

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Reviews:
[{"review_id": "9xPiYeNAPh", "reviewer": "Reviewer_i9FY", "summary": "This paper applies direct preference optimization to antibody design. Specifically, it uses Rosetta binding energy to guide a pre-trained diffusion model to generate antibody CDR structures with low binding energy.", "questions": "* Can you report your model performance by running Rosetta relaxation multiple times with different random seeds and report standard deviation of the reported binding energy for each method?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* Optimizing antibody binding energy is an important problem.\n* The proposed gradient surgery procedure is technically interesting.", "weaknesses": "* To evaluate binding energy using Rosetta, it is necessary to run side-chain packing and energy minimization to clean up the predicted structure. Therefore, it usually takes couple of minutes to evaluate binding energy using Rosetta for just one structure. In other words, it is computationally expensive to guide diffusion models using Rosetta.\n* Rosetta side-chain packing is stochastic and non-deterministic. Therefore, if we relax the structure generated by diffusion model multiple times, the calculated Rosetta energy will be very different, and the standard deviation can be very high (sometimes it can be twice or three times higher than the mean). In other words, it is very tricky to construct a preference dataset because you need to compare the binding energy distribution between two CDR sequences, and their standard deviation is very high. \n* Despite the high standard deviation, the reported binding energy in this paper does not have standard deviation. It seems like the authors only calculate Rosetta binding energy once for each structure instead of running side-chain packing or energy minimization multiple times and take the average. Therefore, the reported results may not be statistically significant.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your feedback. Please see below for our responses to the comments.\n\n**Q1: It is computationally expensive to guide diffusion models using Rosetta.**\n\nA1: Yes, the computational expense is indeed a drawback of Rosetta. We are aware of Rosetta's limitations and have discussed them in the appendix. However, despite these issues, the time cost of optimizing AbDPO for a single antigen is less than a day. Additionally, AbDPO is not specific to Rosetta. For example, other packing tools (like DiffPack) and energy calculation methods (such as OpenMM, which is significantly faster than Rosetta) can also be used. In fact, AbDPO supports optimization of any type of property, and we chose Rosetta because it can perform both packing and energy calculations and is widely used.\n\n**Q2: Rosetta side-chain packing is stochastic and non-deterministic. Therefore, if we relax the structure generated by diffusion model multiple times, the calculated Rosetta energy will be very different, and the standard deviation can be very high (sometimes it can be twice or three times higher than the mean). In other words, it is very tricky to construct a preference dataset because you need to compare the binding energy distribution between two CDR sequences, and their standard deviation is very high.**\n\nA2: We recognize that the same CDR-H3 (with the same sequence and structure) may result in different side-chain conformations after packing, and there will be energy differences between these side-chains. We observed this in our early exploration but still only performed the side-chain packing for each sample once. The reasons are as follows :\n- The differences between different samples generated by existing methods (such as DiffAb) are generally much larger than the energy differences between different side chain conformations of the same sample. For natural antibodies, total energy is relatively low due to their reasonable structure, so different side chains may have a significant impact on total energy. However, for generated antibodies with several clashes, the influence of side-chain conformations is not significant as the total energy could be extremely high.\n- Repeating the packing process on the same sample can indeed yield more accurate energy labels, but it will consume more time and we do not want the excellent performance of AbDPO to be based on a large amount of meticulously selected data. Although sampling only once may lead to incorrect judgments of win-lose relationships between two samples, this usually occurs when the two samples are quite similar. As long as the better sample has a higher probability of being sampled at lower energy, the model will generally be optimized toward generating antibodies with lower energy.\n- DPO is derived based on the Bradley-Terry model. In the Bradley-Terry model, the labels of winner and loser are not deterministic but exist in probabilistic form. We perform packing for each sample only once, which is similar to sampling winner and loser once. This is also theoretically justifiable.\n\nFurthermore, we use 1a14 as an example and sample 100 synthetic data from the 1a14 training dataset. For each synthetic sample, we repeat packing 128 times with different random seeds. Then we can compare the deviation between different synthetic data and different sidechains from the same synthetic data. The results are shown in Fig. 1 in the uploaded pdf, and the deviation between different synthetic data (the red line) is far greater than the deviation between different sidechains from the same synthetic data (the blue violin plot indicates the distribution of deviation within each synthetic data). This further supports our justification.\n\n**Q3: Can you report your model performance by running Rosetta relaxation multiple times with different random seeds?**\n\nA3: We repeat the optimization process 32 times with different random seeds for each AbDPOw/O generated sample. The average $\\text{CDR} E_{\\text{total}}$ and $\\text{CDR-Ag} \\Delta G$ of all generated antibodies are 65.19 and -2.67, which are slightly different from the reported values of 69.82 and -3.00.  Therefore, the experiment results reported in our paper are reliable. The reason we did not report the averaged results over multiple runs is due to time cost considerations.\n\n**Q4: Can you report standard deviation of the reported binding energy for each method?**\n\nA4: Thanks for your reminder, we provide the standard deviation of two energies for each method below. It could be seen that significant deviations are commonly present in the results generated by each method, and the deviation of AbDPO is smaller than that of DiffAb.\n\n|  | CDE$E_{\\text{total}}$ avg | CDE$E_{\\text{total}}$ std | CDR-Ag$\\Delta G$ avg | CDR-Ag$\\Delta G$ std |\n|----------|-----------------|-----------------|---------------|---------------|\n| HERN     | 10887.77        | 1313.08         | 2095.88       | 1051.85       |\n| MEAN     | 7162.65         | 2421.58         | 1041.43       | 1322.44       |\n| dyMEAN   | 3782.67         | 482.51          | 1730.06       | 544.91        |\n| DiffAb   | 1729.51         | 883.14          | 1297.25       | 1016.96       |\n| AbDPO    | 629.44          | 446.02          | 307.56        | 378.59        |\n| AbDPO+   | 1106.48         | 678.9           | 637.62        | 631.99        |\n| AbDPO++  | 1349.39         | 754.61          | 747.89        | 692.09        |\n| AbDPOw/O | 69.82           | 59.17           | -3            | 6.61          |", "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": "cvBb9vzhu2", "reviewer": "Reviewer_X6SE", "summary": "The paper proposes an approach for fine-tuning diffusion models for the design of antibodies. The core diffusion-based generative model comes from Luo et al. [36] and to my understanding there are no technical changes to it. The second component is direct preference based optimization, inspired by fine-tuning of large language models. This is the main technical contribution and builds entirely on the works by Rafailov et al [41] and Wallace et al [46]. The reward signal comes from binding free energy that is decomposed at the residue level. Different components include attraction and repulsion forces that can be linked to antibody function. To overcome possibly diverging gradients associated with different energy components, the authors propose to leverage gradient surgery from Yu et al [51] that essentially increases cosine similarity between gradients for different tasks/energy components.\n\nEmpirical evaluation is focused on qualitative aspects and whether the approach is able to discover better binders than initially given complexes, measured using binding free energy.", "questions": "Could you also list how many mutations from the original CDR sequence are the improved binders (Table 1)?  \n\nCan you share the structural similarity scores between epitopes in the train and test folds?\n\nIf you limit the fraction of hydrophobic residues (PHR) to the value for the original complex and accept only designs with lower score, how does Table 1 look? Can you list relative to how many test fold complexes each method achieves better binding free energy (e.g., MEAN wins on N, AbDPO wins on 20, etc.)?\n\nHow does Table 1 look like if you apply ITA to the vanilla baselines?", "limitations": "NA", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "I think it is an interesting approach to merry molecular simulations and physics based energy calculations with diffusion and generative models. Especially given the small number of available crystal structures in the SAbDAB database.\n\nAdding energy-based signal via direct preference optimization is an interesting re-purposing of that method.\n\nEmpirical evaluation goes beyond amino-acid recovery rate and RMSD metrics. The “success” at generating better binders quantified via improvement in binding free energy relative to the initial complex is an interesting metric.", "weaknesses": "Table 1 indicates that the approach is able to design better binders, measured via binding free energy relative to the initial complex. However, this comes at the expense of increasing the number of hydrophobic residues which is typically associated with non-specific binding. This would in all likelihood be useless binders and from the perspective of function no better than baselines.\n\nIt would be interesting to see the results of a baseline that “fine-tunes” relative to ddG score directly. In my understanding, the results in Table 1 are vanilla baselines. None of them (e.g., MEAN, dyMEAN, HERN) has for instance been used in combination with iterative improvement algorithm and some physics based simulator. How would this compare to fine-tuning relative to the directed preference optimization?\n\nIt would be interesting to see the results relative to different physics-based simulators. I’m not sure how many different simulators were used to generate “fine-tuning” signal?\n\nWould it be possible to include additional metrics such as lDDT, TM, and some metrics characterizing the fit on angles?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your detailed feedback. Please see below for our responses to the comments.\n\n**Q1: The approach can design better binders, but comes at the expense of increasing the number of hydrophobic residues which is typically associated with non-specific binding.**\n\nA1: This is exactly why we included PHR as an optimization objective in AbDPO+. We will show the performance of each method when limiting the PHR in A6, and AbDPO still performs better.\n\n**Q2: It would be interesting to see the results relative to different physics-based simulators. I’m not sure how many different simulators were used to generate “fine-tuning” signal?**\n\nA2: All the three energy signals were calculated using Rosetta, which is capable of both energy calculation and side-chain packing, and is widely used by researchers. In early stages, we also tried using OpenMM for energy calculations and obtained consistent results.\nAdditionally, we used OpenMM to calculate the potential energy of the antigen-antibody complex where CDR-H3 is generated by AbDPO fine-tuned according to Rosetta energy. For 6 complexes tested, AbDPO achieved lower energy in 5 compared to DiffAb. (the remaining 49 complexes raise errors in OpenMM workflow when adding Hydrogens, and are not influential in Rosetta workflow that does not require Hydrogens)\n\n**Q3: Would it be possible to include additional metrics such as lDDT, TM, and some metrics characterizing the fit on angles?**\n\nA3: For the antibodies generated by all methods, we measured both the TM-score[1] on the heavy chain (Hc_TM-score) and the torsion performance (Torsion-score) of residues on the CDR-H3. For Hc_TM-score, there is not much difference in methods other than HERN. The Torsion-score is derived from a two-dimensional KDE function, which is based on the joint distribution of Phi and Psi torsions observed in natural CDR-H3s. Diffusion-based methods, DiffAb and AbDPO, perform significantly better than other methods.\n\n| |Hc_TM-score|Torsion_score|\n|--|--|--|\n|HERN|0.92|0.14|\n|MEAN |0.98|0.34|\n|dyMEAN|0.98|0.68|\n|DiffAb|0.97|0.98|\n|AbDPO|0.97|0.86|\n|AbDPO+|0.98|0.90|\n|AbDPO++|0.97|0.89|\n\nReference:\n\n[1] Zhang, Yang, and Jeffrey Skolnick. \"TM-align: a protein structure alignment algorithm based on the TM-score.\" Nucleic acids research.\n\n**Q4: Could you also list how many mutations from the original CDR sequence are the improved binders (Table 1)?**\n\nA4: Yes, we calculate the minimum number of mutations of the generated samples that exhibit energy levels close to the natural samples (i.e., the \"successful\" samples in Table 1) and the corresponding CDR lengths.\n\n|pdb_id|CDR_length |N_mut_min|\n|--|--|--|\n|1a14|15|7|\n|1ic7|7|3|\n|1iqd|10|7|\n|2b2x|12|6|\n|2dd8|11|3|\n|3bn9|9|8|\n|4ffv|10|6|\n|4qci|13|8|\n|5d93|9|6|\n\n**Q5: Can you share the structural similarity scores between epitopes in the train and test folds?**\n\nA5: We follow the metric widely used in protein structure design tasks to calculate the structural similarity scores. The similarity between two protein sets is defined as the average TM-score of each sample in one set to its most similar protein in another set. The similarity between the train and test folds is 0.6965. Following MEAN, the epitope is defined as the 48 residues of the antigen closest to the paratope.\n\nAdditionally, we believe there is a misunderstanding here. The training data only appears during the pre-training phase, while in the optimization phase, we only used synthetic data.\n\n**Q6: If you limit the fraction of hydrophobic residues to the value for the original complex and accept only designs with lower score, how does Table 1 look?**\n\nA6: We perform an evaluation only on the samples that contain hydrophobic residues not exceeding the natural one, and the results are shown below. It can be seen that under this setting, the energy performance of almost all methods has deteriorated, but AbDPO and AbDPO+ still perform the best in terms of the two energies.\n\n| | AAR| CDR $E_{\\text {total}}$ | CDR-Ag$\\Delta G$ | pLL| PHR|\n|--|--|--|--|--|--|\n|HERN| 32.30% |11953.56|1949.35|-1.95|25.81%|\n|MEAN| 37.42% |8127.87|1412.02|-1.93|23.85%|\n|dyMEAN| 38.33%|6253.15|2906.5|-1.94|31.84%|\n|DiffAb|34.47%|2129.9|1646.6|-2.14|27.22%|\n|AbDPO|31.24%|907.18|453.71|-2.25|31.24%|\n|AbDPO+|32.91%|1464.53|815.14| -2.09|32.91%|\n\n**Q7: Can you list relative to how many test fold complexes each method achieves better binding free energy?**\n\nA7: Sure. For each complex, if a method achieves the best performance, it was considered a \"win\" for that method on that specific complex. We record the number of \"win\" complexes, N_win. We also observe that there are instances where none of the samples have a PHR lower than that of the natural sample. Therefore, we also list the number of complexes, denoted as N_phr, for which the method can generate samples with a PHR not exceeding that of the natural sample. The specific results are as follows:\n\n| | N_win | N_phr |\n|--|--|--|\n|HERN|8|35|\n|MEAN|2|32|\n|dyMEAN|3 | 12|\n|DiffAb| 1 | 38|\n|AbDPO| 20 | 36|\n|AbDPO+| 18| 52|\n\n**Q8: How does Table 1 look like if you apply ITA to the vanilla baselines?**\n\nA8: We follow the ITA setting from the MEAN codebase and implement ITA for MEAN, dyMEAN, and DiffAb. We adapt $\\text{CDR}E\\_{\\text{total}}$ and $\\text{CDR-Ag}\\Delta G$ as two targets to gather high-quality candidates for each antibody. We observe that directly generating high-quality candidates can negatively affect other preferences. This further demonstrates the effectiveness of AbDPO in optimizing multiple objectives simultaneously.\n\n|  | AAR | RMSD | CDR $E_{\\text {total}}$ | CDR-Ag$\\Delta G$ | pLL | PHR | N_success|\n|--|--|--|--|--|--|--|--|\n| MEAN   |32.56% |2.19| 4731.58 |  363.26 |-1.83 |75.12% |0 |\n| dyMEAN |39.69% |2.00|6105.83 |1665.72 |-1.63 |42.09% |0 |\n| DiffAb |35.93% | 2.15 |1288.67 |814.93 |-1.82 |59.57% |0 |\n| ABDPO| 31.25% |1.98 |629.44 |307.56 |-2.18 |69.67% |9 |\n| ABDPO+ | 36.27% |2.01 |1106.48 |637.62|-2.00 |44.21% |5 |", "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": "3hxPNyu47m", "reviewer": "Reviewer_FkeK", "summary": "This paper proposes a new perspective for antibody design-- incorporating the energy factors aiming to minimize the overall energy of designed sequence and structure. It involves diffusion to maintain the sequence-structure co-design. Towards the variance of energy factors, the paper proposes the idea of gradient surgery to simplify it. The paper conducted extensive experiments, showing its performance towards other baselines. The paper is easy to follow.", "questions": "* This paper relies heavily on energy function and sidechain packing methods in pyrosetta. Would it be helpful to directly train the diffusion model from scratch by optimizing the loss function using pyrosetta?\n* There are several other tasks except for CDR-H3 design, as the paper aims to optimize the energy of the complex, would it be helpful to test the method with other downstream tasks that may be closely related to the energy(refer to dyMEAN)?", "limitations": "As stated in the article.", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "* The paper proposes an energy-based preference optimization approach to achieve better rationality and binding affinity, which is inspiring in the field of antibody design.\n* The paper decomposites the energy factors, simplifying the gradient calculation process.\n* The paper achieved significantly lower energy than other approaches, reflecting the effectiveness of the model design.\n* The paper clearly states why it chooses energy as the main evaluation metric with strong statistical evidence.\n* The paper provides a detailed sample-level comparison of existing baseline approaches, which is a solid solution and beneficial to successive works.", "weaknesses": "* Although the authors stated why they chose energy as the main metric, the AAR is about 10% lower than dyMEAN. The authors did not provide a solid reason for what caused the result (Are all the lower results considered hacked or biased? Maybe a sample-level analysis would be more convincing.)\n* The derivation of the final loss for fine-tuning could be simplified.\n* The adaptation of RLHF into this approach should be further clarified.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your helpful feedback! We address your questions as follows.\n\n**Q1: AAR is about 10% lower than dyMEAN. The authors did not provide a solid reason for what caused the result.**\n\nA1: As mentioned in Appendix A, AAR is easily hacked and conceals numerous issues. Certain intrinsic patterns within CDR-H3 sequences enable the model to achieve a seemingly satisfactory AAR by memorizing these patterns (also noted in the Limitations section of dyMEAN). However, this leads the model to produce highly similar sequences for all antigens, which is highly impractical. The possible reason is the severe lack of data, causing the model to merely learn the marginal distribution of residue types at each position. dyMEAN is a typical example of this scenario. To illustrate the sequences generated by dyMEAN with over 40% AAR, we reproduced dyMEAN, generated CDR-H3 for 55 antigens, and visualized the sequences. As shown in Fig. 2 in the uploaded pdf, through alignment (aligned and visualized by MAFFT[1]), it is evident that dyMEAN generates almost identical sequences, while AbDPO+ is considerably better. In this case, AAR is not a meaningful measure.\n\nAs for why AbDPO did not achieve a high AAR, we believe it is due to the different learning objectives between AbDPO and the baselines. The learning objective of baselines is to generate antibodies consistent with natural antibodies in terms of sequence and structure. Therefore, they perform better on metrics like AAR, which measures similarity to natural ones. However, AbDPO's learning objective is to better meet specific preferences, while not optimizing for consistency with natural ones. Consequently, its AAR is lower than dyMEAN. Nevertheless, sequence pLL leads to a significant improvement in AAR (31.25% to 36.27%) when used as an optimization objective.\n\nReference:\n\n[1] Madeira, Fábio,et al. \"The EMBL-EBI Job Dispatcher sequence analysis tools framework in 2024.\" Nucleic Acids Research.\n\n**Q2: The adaptation of RLHF into this approach should be further clarified.**\n\nA2: We can consider the antibody generation model obtained through conventional training methods as a pre-trained model. However, this pre-trained model does not meet our requirements, such as physical energy. This situation is similar to the challenges faced in current generative AI, where pre-trained models often require further alignment to match human preferences. Therefore, we can leverage methods like RLHF to align the antibody generation models with the desired properties, essentially optimizing the model. In AbDPO, we optimize the pre-trained model using such methods, allowing us to generate antibodies that satisfy multiple preferences.\n\n**Q3: Would it be helpful to directly train the diffusion model from scratch by optimizing the loss function using pyrosetta?**\n\nA3: Directly training the diffusion model from scratch is not practical. \n\nThe reasons are twofold: \n\n1. Since the loss function using pyrosetta is not differentiable, RL algorithms can be applied, such as policy gradient methods. In this case, the antibody design problem is formulated as a high-dimensional non-linear decision making problem. The search space for this problem is large and involves both continuous and discrete variables. Directly training from scratch is hard due to its instability. Specifically, useless efforts might be made, especially at the beginning of the training, when the policy can only generate samples with unsatisfactory rewards. A feasible solution to address this challenge is to use a pre-trained policy that can significantly prune the search space and accelerate the convergence rate, which has been validated on many applications, such as [1] and [2]. And this solution is the pretraining-finetuning paradigm that we utilized in our work. The pre-trained diffusion model can be viewed as an expressive policy. \n\n2. Another reason is that low pyrosetta energy is not our only purpose. We aim to generate valid antibodies with low energy. Some intricate properties cannot be explicitly formulated as rewards but can be learned from data by generative modeling. Our optimization objective is equivalent to maximizing rewards with regularization with reference model. The regularization term keeps knowledge learned from data, which cannot be achieved by training from scratch by optimizing the energy function. \n\nReferences:\n\n[1] Silver, David, et al. Mastering the game of go without human knowledge. Nature\n\n[2] Haarnoja, Tuomas, et al. Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor. ICML.\n\n**Q4: Would it be helpful to test the method with other downstream tasks that may be closely related to the energy**\n\nA4: We test our method on the affinity optimization. Specifically, we test AbDPO, along with its counterpart, DiffAb by evaluating the best $\\Delta\\Delta G$ against the reference antibodies among 300 generated samples using [1] on 16 randomly selected antigens in the test set. **Note that we do not use the metric as the signal in fine-tuning**. The results are shown as follows:\n\n|pdb id|DiffAb|AbDPO|\n|--|--|--|\n|1a14|-3.91|**-5.46**|\n|1n8z|-5.23|**-6.80**|\n|1w72|0.34|**-1.82**|\n|2cmr|-3.12|**-3.62**|\n|3bn9|-2.44|**-4.42**|\n|3mxw|-4.12|**-5.45**|\n|3rkd|-6.21|**-6.99**|\n|4dvr|-5.28|**-5.77**|\n|4fqj|**-4.57**|-4.39|\n|4g6m|-5.94|**-5.97**|\n|4ki5|-3.17|**-4.83**|\n|4xnq|-6.78|**-7.71**|\n|5bv7|-6.19|**-7.66**|\n|5en2|-3.33|**-5.54**|\n|5f9o|-5.10|**-5.32**|\n|5nuz|-2.49|**-5.28**|\n\nOur results significantly outperform DiffAb, which shows the generalizability on other tasks. *We believe that our method can perform even better if we consider the metric itself, ie., predicted $\\Delta\\Delta G$ against the reference antibodies, in our preference definition when fine-tuning*.\n\nReference:\n\n[1] Shan Sisi, et al. \"Deep learning guided optimization of human antibody against SARS-CoV-2 variants with broad neutralization.\" Proceedings of the National Academy of Sciences", "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": "tQAM53adMg", "reviewer": "Reviewer_d9wd", "summary": "This paper uses a pre-trained conditional diffusion model for antibody design. This diffusion model is fine-tuned using a direct energy-based preference optimization method, focusing on optimizing residue-level energy preferences to enhance the generation of antibodies with desirable structures and high binding affinities. The authors also compared their method with SOTA baselines on 55 cases from RAbD benchmarks and showed good results.", "questions": "1. Why we need to use SE(3)-equivariant neural network? \n2. What is the inference time for generating one sample or one batch?", "limitations": "Limitations are adequately addressed.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The proposed algorithm is novel and interesting. The authors combine diffusion models and DPO to solve the specific problem of antibody design. \n2. The algorithm is clear. The authors both define the diffusion process and DPO formation with very clear definitions. Meanwhile, all the figures with protein structure are very clear and informative. \n3. The results are convincing. AbDPO archives good results on CDR total energy compared to other methods.\n4. The experiments part is very detailed. The authors conduct experiments on 55 of 60 antibodies on both their methods and the compared baselines.", "weaknesses": "Lack of explanation of SE(3)-equivariant neural network. The author uses the diffusion model with such an equivariant neural network from Luo et al. Lacking such an explanation may hurt the understanding of the whole method. \n\n**Minor:**\n- There are some writings inconsistent. For example, equations under line 130 are not marked with numbers, but equations under line 138 have numbers. The ABDPO in everywhere this paper is written as \\textsc{AbDPO}, but in line 242 is \"ABDPO\". In line 235, the first letter in pyRosetta should be capitalized since it is a proper noun. Checking these format issues will improve the consistency in the future published version.\n\nReference:\n----------------------------------\nLuo et al: Shitong Luo, Yufeng Su, Xingang Peng, Sheng Wang, Jian Peng, and Jianzhu Ma. 2022. Antigen-Specific Antibody Design and Optimization with Diffusion-Based Generative Models", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your strong support! Please see below for our responses to the comments.\n\n**Q1: Lack of explanation of SE(3)-equivariant neural network. The author uses the diffusion model with such an equivariant neural network from Luo et al. Lacking such an explanation may hurt the understanding of the whole method.**\n\nA1: Thanks for your valuable suggestion. We will complete the explanation in the revision.\n\n**Q2: There are some writings inconsistent.**\n\nA2: Thanks for your careful inspection, we will fix it in the revision.\n\n**Q3: Why we need to use SE(3)-equivariant neural network?**\n\nA3: SE(3)-equivariance is a crucial property in protein design because the structure of proteins is independent to the observation view. Utilizing SE(3)-equivariance can ensure stable and predictable performance in the presence of nuisance transformations of the data input[1]. In addition, we chose to build our method on DiffAb, which uses equivariant neural networks. Other baselines, such as MEAN and dyMEAN, are also E(3)-equivariant. Therefore, we retained the equivariant neural networks to ensure a fair comparison. Nevertheless, we would like to emphasize that our proposed method is not specific to equivariant NNs and can be applied to other base models beyond equivariant NNs.\n\nReference:\n\n[1] Fuchs, Fabian, Daniel Worrall, Volker Fischer, and Max Welling. \"Se (3)-transformers: 3d roto-translation equivariant attention networks.\" Advances in neural information processing systems 33 (2020): 1970-1981.\n\n**Q4: What is the inference time for generating one sample or one batch?**\n\nA4: Our model could be regarded as an aligned model to the specific preference of a pre-trained model, so the inference time will not be changed. We record the detailed time cost in each antigen-antibody complex and show them below (batch_size=16, single A100 40G GPU).\nThe inference time consists of two parts: model inference time and .pdb file reconstruction time. The inference time is related to data length. Most antigen-antibody complexes are truncated to 256 residues when fed into the model, and the corresponding inference time is around 16-17s. The reconstruction time is determined by the total number of residues in the complex. For the complex with 500 residues, the  reconstruction time of one batch of samples is around 2s. We list the detailed time cost below (the last few rows are dropped due to the limitation of space)\n\n| pdb_id | infer_time (s) | data_length | reconst_time (s) | pdb_length |\n|--------|----------------|-------------|------------------|------------|\n| 1a14   | 16.73          | 256         | 2.36             | 612        |\n| 1a2y   | 16.76          | 256         | 1.29             | 351        |\n| 1fe8   | 16.86          | 256         | 2.28             | 610        |\n| 1ic7   | 16.76          | 256         | 1.25             | 349        |\n| 1iqd   | 16.73          | 256         | 2.09             | 563        |\n| 1n8z   | 16.75          | 256         | 3.6              | 1015       |\n| 1ncb   | 16.75          | 256         | 3.28             | 823        |\n| 1osp   | 16.73          | 256         | 2.44             | 682        |\n| 1uj3   | 16.88          | 256         | 2.44             | 635        |\n| 1w72   | 16.73          | 256         | 2.81             | 707        |\n| 2adf   | 16.73          | 256         | 2.28             | 615        |\n| 2b2x   | 16.71          | 256         | 2.19             | 607        |\n| 2cmr   | 16.8           | 256         | 2.35             | 604        |\n| 2dd8   | 16.81          | 256         | 2.49             | 623        |\n| 2vxt   | 16.75          | 256         | 2.21             | 575        |\n| 2xqy   | 16.72          | 256         | 3.26             | 897        |\n| 2xwt   | 16.76          | 256         | 2.43             | 661        |\n| 2ypv   | 16.75          | 256         | 2.67             | 655        |\n| 3bn9   | 16.81          | 256         | 2.45             | 662        |\n| 3cx5   | 16.8           | 256         | 1.74             | 418        |\n| 3ffd   | 6.44           | 144         | 1.79             | 444        |\n| 3hi6   | 16.78          | 256         | 2.34             | 606        |\n| 3k2u   | 16.81          | 256         | 2.46             | 655        |\n| 3l95   | 16.77          | 256         | 3.5              | 661        |\n| 3mxw   | 16.76          | 256         | 2.26             | 585        |\n| 3nid   | 16.74          | 256         | 3.33             | 883        |\n| 3o2d   | 16.72          | 256         | 2.26             | 615        |\n| 3rkd   | 16.73          | 256         | 2.21             | 577        |\n| 3s35   | 14.93          | 240         | 2.14             | 539        |\n| 3w9e   | 16.74          | 256         | 2.4              | 654        |\n| 4cmh   | 16.73          | 256         | 2.41             | 668        |\n| 4dtg   | 10.09          | 192         | 1.87             | 499        |\n| 4dvr   | 16.71          | 256         | 2.74             | 718        |\n| 4ffv   | 16.79          | 256         | 4.74             | 1144       |\n| 4fqj   | 16.72          | 256         | 2.68             | 731        |\n| 4g6j   | 16.81          | 256         | 2.19             | 578        |\n| 4g6m   | 16.85          | 256         | 2.31             | 583        |\n| 4h8w   | 16.76          | 256         | 2.82             | 760        |\n| 4ki5   | 16.77          | 256         | 2.23             | 587        |\n| 4lvn   | 16.79          | 256         | 2.99             | 758        |\n| 4ot1   | 15.79          | 248         | 2.08             | 558        |\n| 4qci   | 13.17          | 224         | 1.94             | 511        |\n| 4xnq   | 16.84          | 256         | 2.39             | 627        |\n| 4ydk   | 16.86          | 256         | 2.94             | 785        |\n| 5b8c   | 15.83          | 248         | 1.32             | 346        |\n| 5bv7   | 16.8           | 256         | 3.2              | 809        |", "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:
We would like to thank all the reviewers for your constructive feedback. We placed Figure 1 and Figure 2 in the PDF file.

Meta-review: After some discussion and extensive additional results provided by the authors, the reviewers' agree that the authors' method of combining energy based calculations and generative modelling is an interesting approach for optimizing binding energy. My only real comment here is to of course be sure to include the new results in the final version of the paper.
Decision: Accept (poster)