AffinityFlow: Guided Flows for Antibody Affinity Maturation
Authors: Can Chen
Karla-Luise Herpoldt
Chenchao Zhao
Zichen Wang
Marcus D. Collins
Shang Shang
Ron Benson
Venue: ICML 2025 poster (2025)
Keywords: flow matching
co-teaching
protein design
antibody affinity maturation
protein property prediction
Primary area: applications->health_medicine
TL;DR: We introduce AffinityFlow, which explores guided flows for antibody affinity maturation

Abstract: Antibodies are widely used as therapeutics, but their development requires costly affinity maturation, involving iterative mutations to enhance binding affinity. This paper explores a sequence-only scenario for affinity maturation, using solely antibody and antigen sequences. Recently AlphaFlow wraps AlphaFold within flow matching to generate diverse protein structures, enabling a sequence-conditioned generative model of structure. Building on this, we propose an \textit{alternating optimization} framework that (1) fixes the sequence to guide structure generation toward high binding affinity using a structure-based predictor, then (2) applies inverse folding to create sequence mutations, refined by a sequence-based predictor. A key challenge is the lack of labeled data for training both predictors. To address this, we develop a \textit{co-teaching} module that incorporates valuable information from noisy biophysical energies into predictor refinement. The sequence-based predictor selects consensus samples to teach the structure-based predictor, and vice versa. Our method, \textit{AffinityFlow}, achieves state-of-the-art performance in proof-of-concept affinity maturation experiments.

Affinity Flow:
Guided Flows for Antibody Affinity Maturation
Can (Sam) Chen
Karla-Luise Herpoldt? Chenchao Zhao? Zichen Wang? Marcus Collins? 2 Shang Shang 2
Ron Benson
Abstract
enhanced through somatic hypermutation and clonal selec- tion (Victora & Nussenzweig. 2022). When developing a therapeutic antibody, in vitro affinity maturation- througg targeted mutation and selection-imprect improves the binding affin- ity of existing antibodies to target antigens (Tabasinezhad et al., 2019; Chiu & Gilliland, 2016).
Antibodies are widely used therapeutics, but their development requires costly affinity matu- ration, involving iterative mutations to enhance binding affinity. This paper explores a sequence- only scenario for affinity maturation, using solely antibody and antigen sequences. Recently Al- phaFlow wraps AlphaFold within flow matching to generate diverse protein structures, enabling a sequence- conditionod generative model of struc- ture. Building on this, we propose an alternat- ing optimization framework that (1) fixes the se- quence to guide structure generation toward high binding affinity using& structure-baset affinity predictor, then (2) applies inverse folding to cre- ate sequence mutations, refined by sequence- based affinity predictor for post selection. A key challenge is the lack of labeled data for training both predictors. To address this, we develop a co- leaching module that incorporates valuable infor- mation from noisy biophysical energies into pre- dictor refinement. The sequence-based predictor selects consensus samples to teach the structure- based predictor, and vice versa. Our method, Affin- iryFlow, achieves state-of-the-ea art performance in proof-of-concep affinity maturation experiments.
These in vitro methods, such as random mutagenesis, are labor-intensive and time-consuming. Recent advancements in deep learning have propelled in silico affinity maturation forward. One line of research enhances affinity prediction for mutated antibodies (Shan et al., 2022; Liu al., 2021; Cai et al., 2024; Lin et al., 2024; Xiong et al., 2017); an- other investigates mutation strategies. Specifically, protein language models propose plausible mutations to enhance binding affinities, though they lack specificity for target antigens (Hie et al., 2024; Ruffolo et al., 2021; Shuai et al., 2021). Similarly, diffusion models guide the sampling to- wards high-affinity antibody sequences but require the often unavailable or insufficiently accurate antigen-antibodyy com- plex structure (Luo et al., 2022: Zhou et al., 2024). Our research aligns more with the second line of mutation strate- gies. In particular, we focus on enhancing antibody binding affinity through sequence mutations, relying solely on the antigen-antibody sequence.
Recognizing the crucial link between antibody structure and function, it is essential to integrate structure into the sequence mutation process. The recent release of Al- phaFlow (Jing et al., 2024) builds a ssquence-conditiio generative model of protein structure, which opens path- ways for structure- optimization of antibody sequences. Specifically, AlphaFlow repurposes AlphaFold (Jumper et al., 2021) in flow matching framework to generate di- verse protein conformations.
1. Introduction
Natural antibodics protect organisms by specifically binding to target antigens such as viruses and bacteria with high affin- ity (Murphy & Weaver, 2016), while therapeutic antibodies bind various targets inactivate them, recruit immune cells attached drug compound (Chiu & Gilliland, 2016). In vivo, antibodies undergo affinity matu- ration, where their target-binding capacity incrementally
to them, or deliver
This motivates the proposal of an alternating optimization framework, as illustrated in Figure 1: (1) We fix the se- quence to guide noisy structures toward high-affinity clean structures. Rather than re-training the entire AlphaFlow model-a process that is inherently time-consuning-vv achieve guided structure generation through predictor guid- ance (Dhariwal & Nichol, 2021). Specifically, trained structure- -bsed affinity predictor is integrated into the Al- phaFlow sampling process to direct coordinate denoising.
'Mila- Quebec Al Institute (work done during an Amazon internship) AAmazon. Correspondence Can (Sam) Chen <can.chen chen mila. or chencan421 gmail.com>, Marcus Collins <collmr@ @ amazon.com>>.
Proceedings of the 42nd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

---

Affinityloow: Guided Flows for Antibody Affinity Maturation
Predictor guidance
Predictor guidance
Predictor guidance
Noisy structure
High-affinity clean structure
M
Q
V
Q
L
V
Post selection
Inverse folding
M
Q
A
Q
L
V
M
Q
L
Q
L
V
Figure 1: Illustration alternating optimization.
(2) With the high-affinity clean structure, perform in- verse folding to introduce targeted mutations, and use sequence-basee based predictor for post selection, which identi- fies promising mutated sequences for the next iteration.
AffinityFlow achieves state-of-the-art performance in affin- ity maturation experiments.
2. Preliminaries
significant challenge training both predictors is the scarcity of labeled data. To address this, we develop a co- teaching module that leverages valuable information from noisy biophysical energies to refine the predictors, shown in Figure 2. For any antigen i and antibodies j, k, n, we use Rosetta (Alford et al., 2017) to compute the binding free energy AG' and then calculate the change in binding free energy AAGink = AG - AG to form pairwise discrete labels. The sequence-basee predictor selects pairs with which concurs, considering them likely to be ac- curate and informative, and uses these consensus samples to enhance the structure-based predictor. For instance, if the sequence-based predictor predicts AAGijk > 0, it se- lects AAGijk > 0 for training the structure-based predic- tor. Similarly, the structure-based predictor reciprocates by informing the sequence-basee based predictor; for example, it selects AAGtjm < to refine the sequence predictor, as shown in Figure 2. Noisy data, such AAGijn 0, are filtered out. This module effectively integrates biophysical insights into both predictors, enhancing their accuracy.
2.1. Problem Definition
Binding affinity between an antibody (Ab) and its antigen (Ag) is predominantly determined by the complementarity determining regions (CDRs) within these chains (Akbar et al., 2022). An antibody consists of two heavy chains and two light chains with a similar overall structure. Its specificity is determined by six variable regions known as Complementarity Determining Regions (CDRs), denoted as H1, H2, H3, L1, L,,, and L.3. Typically, heavy chain CDRs range from to 16 amino acids, while light chain CDRs range from to 10 amino acids. We model an antibody chain as a sequence of amino acids, each characterized by type a; E CA, YY)
While AffinityFlow is applicable to all antibody types, this study specifically focuses on single-domain antibod- ies (sdAb), which consist only of heavy chains (Wesolowski et al., 2009). We select sdAb for their high specificity, solu- bility, stability, and lower toxicity and immunogenicity. Our goal in affinity maturation within the context of the entire Ab-Ag sequence complex to improve binding affinity.
effectively mutate the CDRs
In summary, we introduce AffinityFlow, guided flows for affinity maturation. Our contributions are three-fold:
We present AlphaFlow based alternating optimization framework that guides structure generation towards high binding affinity through predictor guidance, followed by targeted mutations.
2.2. Flow Matching
Flow matching is robust generative modeling framework (Lipman et al., 2022; Le et al., 2024). It is characterized by conditional probability path p:(x æ1), t E [0, 1], which transitions from a prior distribution po (x x1) = g(x) to an
We propose a co-teaching module that utilizes valuable in- sights from noisy biophysical energies to refine structure- and sequence-bar predictors.
approximate Dirac delta function P1 (x x1) = 8(x - x1)
conditioned on data point œ; from Piat- The evolution
2

---

AffinityFlow: Guided Flows for Antibody Affinity Maturation
Biophysical energies
AAG isk
AAG sjm 0
>
AAGijk > 0
Sequence predictor
Sequence predictor
AAG, sjm < 0
AAGijn
Structure predictor
Structure predictor
AAG ijm 0
AAGigh isk >
Figure 2: Illustration of co-teaching.
is facilitated by a conditional vector field (x æ1). The marginal vector field v(x, t) is modeled through a neural network parameterized by 0:
prior distribution g(x)) over these positions as harmonic prior (Jing et al., 2023) to ensure that inputs to the neural network remain physically plausible. For this study, the pre- trained AlphaFlow model, which was trained using FAPE loss, is used directly without any further fine-tuning. Since AlphaFlow is trained solely on single proteins, this study connects the antibody sequence and the antigen sequence into one sequence using a linker of 32 GGGGS repeats (Lin et al., 2023). The linked sequence complex is then input into the system.
(x,, t) = u(x t) (m (x x1)]
Using this modeled vector field, can generate samples from the data distribution (a)a(x) by utilizing the corre- sponding neural Ordinary Differential Equation (ODE).
2.3. AlphaFlow
AlphaFold (Jumper et al., 2021) serves precise single- state protein structure predictor, and AlphaFlow (Jing et al., 2024) repurposes AlphaFold within flow matching frame- work to generate diverse protein conformations. Given a protein sequence a of length N, the objective is to model the structural ensemble, denoted by p(æ: a), where & e 3 represents the protein 3D coordinates.
2.4. Affinity Prediction
This paper focuses on enhancing binding affinity, deter- mined by the difference in free energy between the bound and unbound states, denoted AG. A negative value indicates that the overall free energy of the system decreases upon binding, meaning that the antibody-antigen interaction is energetically favored. Consequently, we use AG' as a mea- sure of binding affinity where sequence- and structure- predictors directly output a negative value of the binding affinity (Kd). Protein properties can be predicted from two views: sequence and structure, leading to two prediction methods: sequence-based (Xu et al., 2022) and structure- based (Gligorijević al., 2021).
AlphaFlow defines the conditional probability path by sam- pling initial noise zo from (==)) and linearly interpolating it with the data point 21:
x æτ / = (1 () so + L. 21, 2o ~ g(xo)
(2)
The vector field is derived as:
Leading sequence-based models like ESM-2 (Lin et al., 2022), AntiBERTy (Ruffolo et al., 2021), and IgLM (Shuai et al., 2023) are pre-trained on extensive unlabeled protein sequences. These models extract hidden representations to predict properties such as binding energy, denoted as fa (AG)a), where a represents the model parameters. We choose ESM-2 versatility, as the antigen is a general protein rather than an antibody. Specifically, we input the antibody and antigen sequences separately into ESM-2 to obtain embeddings, which are then concatenated and fed into a three-layer MLP for the final prediction.
( x1)= = (x1 - x)/(1 (1-11
(3)
Instead of directly parameterizing the marginal vector field as in Eq. (1), the marginal vector field is parameterized in terms of neural network Φ; (x. 0) as:
sequence- bequence-based predictor due to its
6(x: t; 0) (a (x, t; 0) x0/(1 t)
(4)
This approach allows the reuse of the AlphaFold2 tem- plate embedding stack to reconstruct the clean structure Ij from the noisy input z, with serving as an additional time embedding. The model focuses on the 3D coordi- nates of B-carbons (or c-raboon for glycine), defining the
3

---

AffinityFlow: Guided Flows for Antibody Affinity Maturation
For structure-based prediction, the GVP model is notable for utilizing features from the 3D graph of proteins to pre- dict properties, denoted as fa( AG|()) (Jing et al., 2021). Integrating the ESM2 model as feature extractor within the GVP model further enhances performance (Wang et al., 2022). Thus, we employ the ESM2-GVP model as our structure-based predictor in this study. The linked antibody- antigen complex is processed by the pre-trained ESM2 to generate residue embeddings, from which intersected residues are selected for the GVP model.
Training the predictor different time steps is resource- intensive; instead, we approximate pa(AG me; t) directly from (3 AG @ (xt),
Pi P Tes t) ~ pa & (2.),, 1).
(6)
This approximation, termed Pp ( â (m))), effective when t close to I; therefore, we primarily apply predictor guidance in the later stages of sampling.
The desired binding energy distribution is formulated as (Lee et al., 2023):
It is important to note two aspects: (1) The ESM2-GVP model may not outperform the standalone ESM-2 model due to potential unavailability of ground truth structures and the challenges making reliable structure predictions for antibodies and antigens; (2) Given that our AlphaFlow system operates solely on C3 coordinates and does not account for side-chains, we do not utilize affinity prediction models that require side chain modeling (Liu et al., 2021; Cai et al., 2024).
pa pa (x(2))) = =e (_) /2,
where is scaling factor and 7 a normalization constant, with the negative sign indicating a preference for lower binding energy. Integrating this into Eq.(5) leads to:
1 ' v (x
(( t, AG; 0) o(2,, 1: - -
(8) This vector field guides the ODE sampling process towards lower binding energy. During sampling, we target the pre- dictor guidance only to CDR coordinates rather than the full protein to simplify the system and enhance its relevance.
Related works on generative protein modeling and co- teaching are detailed in Appendix A.
3. Method
Prerector-Correctorr Given that δ represents the Cp coordinates of the protein structure, which subject to energy constraints, we apply Amber relaxation (Lindorff- Larsen et al., 2010) to adjust क at each iteration before initiating guided structure generation. This correction step is essential, as predictor guidance on clashed protein struc- tures is ineffective. This approach aligns with the Predictor- Corrector methods described in (Allgower & Georg, 2012: Song et al., 2020), and we therefore adopt the same ter- minology. Predictor corresponds to the protein coordinate generation process governed by the learned vector field, and Corrector refers to the Amber energy minimization used to refine the coordinates. Additional related techniques are discussed in Appendix C.
In this section, we introduce AffinityFow, designed to en- hance the binding affinity of antibodies through targeted sequence mutations. Our method, built on AlphaFlow, em- ploys an alternating optimization framework for sequence mutation via predictor guidance, as detailed in Section 3.1. To overcome the challenge of limited labeled data, we pro- pose co-teaching module in Section 3.2. This module leverages useful knowledge from noisy biophysical energies to improve our predictors.
3.1. Alternating Optimization
Initially, the sequence is fixed while we guide the Ab struc- ture generation to achieve high binding affinity, supple- mented with predictor-correcto refinement. Based on the generated structure, we then use inverse folding to introduce targeted mutations into the Ab, with the sequence- based pre- dictor selecting promising sequences for the next iteration.
Using the generated structure as a ref- erence, employ inverse folding with ProteinMPPNN (Dau- paras et al., 2022) to identify potential mutations in the CDR regions. At each iteration, we apply single-, double-, and triple-point mutations using ProteinMPNN, For cach posi- tion, we calculate the probability difference between the cur- rent and alternative amino acids, selecting the mutation with the highest difference. Double- and triple-point mutations build sequentially on prior mutations. A requence-based predictor selects the top K (K 3) sequences at each stage for further refinement. Since the generated structure is con- ditioned on the sequence, we avoid multiple simultancous mutations to preserve the protein structure and minimize disruptive changes. However, under our alternating opti- mization framework, we can introduce a few mutations per
Sequence Mutation
Guided Structure Generation While AlphaFlow gener- ates structures unconditionally, we aim to steer structure generation toward improved binding affinity using predic- tor guidance. Following Lemma in (Zheng et al., 2023), predictor guidance in flow matching is formulated as:
1 1-1
'
5(2,, 1, AG; 0) ū (Fr, 1; 0)+ Vn, log ær, ().
(5)
where PA xee t) denotes the target binding energy distribution. The derivation details are in Appendix B.

---

AffinityFlow: Guided Flows for Antibody Affinity Maturation
iteration, gradually accumulating enough mutations over successive iterations.
4. Experiments
4.1. Benchmark
3.2. Co-teaching
Dataset We conduct our experiments using a sdAb subset of the SAbDab dataset (Dunbar et al., 2014). Following the protocol of (Luo al., 2022), we exclude structures with resolution poorer than 4A and antibodies targeting non-protein antigens. Our study focuses on sdAbs, selecting PDB files of 120 labeled sdAb-antigen pairs to initially train our predictors using mean squared loss. From these files, we extract 77 sdAbs and 54 antigens, resulting in 4, 158 docked complex structures generated by GeoDock. Rosetta is then used calculate the AG for these complexes. For maturation testing, we select 60 sdAb-antigen PDB files, ensuring that each antigen is unique and these antigens and antibodies were not included in the training set.
A primary challenge is the scarcity of labeled data for train- ing both structure-based and sequence-basee affinity predic- tors. To address this, we enhance the predictors by incorpo- rating insights from noisy biophysical energies.
Complex Generation To compute biophysical energies, initial protein complexes are required. We extract A sdAb structures and B antigen structures from existing PDB files, and then use the docking tool GeoDock (Chu et al., 2023) to generate AB complex structures. Next, we employ Rosetta (Alford et al., 2017) to calculate the binding free energy AG for each complex.
Pairwise Discrete Data Instead of relying on pointwise continuous samples, which can be highly variable and noisy, we generate robust pairwise discrete data. For the i-th anti- gen, we pair antibody j with antibody k and compute the change in binding free energy as AAG = AG A We assign a pairwise label Yij as 1 if AAGijk > 0, in- dicating stronger binding by antibody k, and 0 otherwise. This approach provides a more reliable measure than using absolute property values.
Evaluation Our evaluation considers mutations in CDR- HI, CDR-H2, CDR-H3, and the entire CDR region. Each comparative method generates three mutated sequences per antigen, resulting in a total of 180 sequence designs.
We measure performance using three metrics: functional- ity, specificity, and rationality, following (Ye et al., 2024). Functionality is assessed by the Improvement Percent- age (IMP) as described in (Luo et al., 2022). IMP re- flects the proportion of mutated sdAbs with reduced bind- ing energy compared the original. Structures are pre- dicted using IgFold (Ruffolo et al., 2023), docked with GeoDock (Chu et al., 2023), and binding energies are an- alyzed via Rosetta (Alford et al., 2017). We report IMP instead of absolute values to ensure robustness, where a higher IMP indicates better performance. Specificity mea- sures the sequence similarity among antibodies targeting different antigens. An effective method should generate distinct antibodies for different antigens, lower similarity (Sim) indicates better specificity. Rationality is evaluated using inverse perplexity calculated by AntiBERTy (Ruffolo et al., 2021). This metric, also referred to as naturalness (Nar), indicates that higher values of Nat generally reflect better rationality.
Sample Selection Given the potential noise from unreli- able biophysical energy calculations, we implement a re- ciprocal filtering approach to refine the quality of input for each predictor. Each predictor selects samples that align with its predictions to inform the other. Specifi- cally, the sequence-based predictor (AGi)) computes Tie (AA > 0). If Y = Yijk- this indicates prob- able accuracy, prompting us to use this consensus sample for the muncture-base predictor. The structure- -haued predic- tor undergoes& similar process, creating a cyclical filtering system. This ensures both predictors receive well-vetted, high-quality samples for improved reliability.
Fine-tuning With the selected samples, we aim to en- hance the performance of our predictors. For the sequence- based predictor, we minimize the following loss function:
4.2. Comparisons with Other Methods
[(a=
Σ ig.k
Yisk log Po (Yejk = 1)
In this paper, we primarily benchmark our method against language model-based methods, given our focus on se- quence design. Since our method incorporates additional biophysical energies for training, we ensure fair compar- isons by applying the same trained sequence-based predictor across all methods, unless stated otherwise. Each method generates a pool of candidate designs, and the sequence- based predictor selects the top three for final evaluation.
(9)
+ (1 - Y Y(sk) log(1 - Pa (Yijk = 19)]
where Pa Pa (Yize 1) = ar (A - ad%) and of)) is the sigmoid function. The structure-based predictor undergoes a similar fine-tuning process. Through this co-teaching module, both predictors exchange valuable biophysical in- formation, significantly improving their effectiveness.
We consider the following language model-based methods:
5

---

AffinityFlow: Guided Flows for Antibody Affinity Maturation
1. ESM (Hie et al., 2024): This method uses pre-trained language model to identify potential mutations. Mutation consensus among six ESM models is assessed, and all promising sequences are collected over nine rounds.
iteration introduces single-point, double-point, and triple- point mutations. This allows for producing 1 to 9 mutations in total. We set the AlphaFlow sampling steps T to 3 per iter- ation with a schedule of [1.0, 0.6, 0.3. 0.0] and use default scaling factor 7 of 5. We employ ESM2-8M, followed by a hidden-dim-322 three-layer MLP, as the sequence-based pre- dictor parameterized by a. For the structure-based predictor parameterized by B. we use a five-layer GVP model, which takes the structure and ESM2-8M residue embeddings as input. For the co-teaching module, we use batch size of 256 and a learning rate of 1 x 10-4 with the Adam opti- mizer (Kingma, 2014). Computational efficiency is detailed in Appendix D, and hyperparameter sensitivity is addressed in Appendix E.
AbLang (Tobias H. Olsen & Deane, 2022): Specifi- cally trained on antibody sequences, the AbLang model includes separate models for heavy and light chains. For our purposes, we utilize the heavy chain model to iden- tify promising mutations across nine rounds.
3. nanoBERT (Hadsund et al., 2024): Given our focus on sdAbs, nanoBERT, a model pre-trained on sdAb se- quences, employed. We conduct nine rounds of muta- tion identification.
4.4. Results and Analysis
Beyond language model- based methods, we include an ad- ditional sequence-design baseline:
In Table 1, we present the experimental results on four set- tings CDR-HI, CDR-H2, CDR-H3 and all design positions. Delineating lines are drawn to distinguish between different groups of methods. The best and second-best performance are highlighted in bold and underlined, respectively.
4. dWJS (Frey et al., 2023): handles discrete sequences by learning smoothed energy function, sampling from the smoothed data manifold, and projecting the sample back to the true data manifold with one-step denoising.
We make the following observations: (1) As shown in Ta- ble I, our method consistently achieves the best perfor- mance in terms of IMP and Sim, thereby highlighting its effectiveness. (2) The notable IMP mainly due to our effective predictor guidance, which directs the structure sample generation towards low binding energy. (3) The low Sim scores can be attributed to antigen-specific modeling and the diversity introduced by the AlphaFlow sampling process. Language-based methods like ESM, AbLang, and nanoBERT lack this feature, as they do not incorporate spe- cific antigens into their design processes. Structure- based methods such as DiffAb, AbDPO, and GearBind consider specific antigens, but their simplistic diffusion models less effective capturing antigen information compared to our method.
We also evaluate three structure- based methods. Although our approach is sequence- sequence-based based and does not inherently require structures for design, we use AlphaFold2 (Jumper et al., 2021) to predict the structures needed for these com- parisons. The following methods are considered:
5. DiffAb (Luo et al., 2022): Trains a diffusion model on amino acid types, coordinates, and orientations. An- tibody optimization is achieved by introducing small perturbations into the existing antibody-antigen complex and subsequently denoising the structure. We generate ten designs per antigen and use our predictor select the top three for evaluation.
6. AbDPO (Zhou et al., 2024): Based on DiffAb, this model fine-tunes a pre-trained diffusion model using a residue-level decomposed energy preference to enable a low-energy protein sampling process. The sampling and selection processes are similar to those of DiffAb.
(4) The language model-based methods ESM, AbLang, and nanoBERT achieve the highest Nat scores, as they are im- plicitly trained for this metric. Beyond these methods, our approach achieves the best Nat. We attribute this to the realistic structure modeling enabled by AlphaFlow and the reliable inverse folding performed by ProteinMPNN, which together translate structures into natural sequences. (5) Ab- DPO, as a robust baseline, often achieves strong perfor- mance in IMP, likely due to incorporating energy infor- mation into its training, allowing for low-energy protein sampling. However, AbDPO requires training a separate diffusion model for each complex, adding complexity. (6) Lastly, the high IMP scores for baseline methods can largely be attributed to our trained sequence- based predictor. When using standard predictor trained only on supervised data, IMP scores drop significantly. For example, in the CDR-H3
7. GearBind (Cai et al., 2024): Utilizes multi-level geo- metric message passing and contrastive pretraining to improve predictions of affinity. We employ AbDPÓ to produce ten designs per antigen, from which GearBind selects the three most promising for assessment.
4.3. Training Details
We use a linker composed of 32 GGGGS repeats to connect the sdAb and antigen. Our method utilizes the alternating optimization framework with three iterations, where each
6

---

AffinityFlow: Guided Flows for Antibody Affinity Maturation
Table I: Overall performance comparison
CDR-HI
CDR-H2
CDR-H3
All
Method
IMPT
Sim
Natt
IMPT
Sim!
Natt
IMP1
Sim!
Natt
IMPT
Sim!
Nat
ESM
85.5%
0.559
0.347
72.9%
0.566
0.358
64.0%
0.573
0.359
84.1%
0.562
0.361
AbLang
88.0%
0.536
0.330
85.4%
0.537
0.322
88.5%
0.542
0.336
82.9%
0.548
0.349
nanoBERT
84.7%
0.534
0.322
85.9%
0.536
0.321
81.6%
0.537
0.328
86.0%
0.544
0.341
dWJS
82.7%
0.535
0.319
69.4%
0.537
0.304
1%
0.522
0.294
85.6%
0.545
0.317
DiffAb
85.5%
0.541
0.317
86.7%
0.548
0.318
85.6%
0.528
0.317
84.4%
0.540
0.316
AbDPO
88.3%
0.540
0.318
91.1%
0.545
0.318
87.8%
0.525
0.319
90.0%
0.540
0.315
GearBind
87.7%
0.543
0.315
87.1%
0.544
0.317
86.7%
0.527
0.317
88.9%
0.541
0.314
AffinityFlow
88.9% %
0.526
0.320
93.3%
0.528
0.321
89.7% %
0.514
0.322
91.2%
0.528
0.323
design setting, IMP drops from 64.0% to 22.7% for ESM, from 88.5% to 49.4% for AbLang, from 81.6% 46.7% for
Table 2: Ablation Study of AffinityFlow CDR-H3,
nanoBERT, from 66.1% to 23.9% for dWJS, from 85.6% to
Methods
IMPt
Siml
Natt
49.4% for DiffAb, from 87.8% to 50.6% for AbDPO, from 86.7% to 50.6% for GearBind, and from 89.7% to 68.3% for our method. In this context, our method demonstrates a clear advantage over the comparison methods.
one-iteration
73.3%
0.512
0.319
w/o PC
83.3%
0.521
0.316
w/o AlphaFlow
63.3%
0.528
0.314
w/o energy
66.7%
0.531
0.322
Additional Comparisons. We further conduct experiments with gg-dWIS (Ikram al., 2024b), employing the trained affinity predictor to guide sampling. Specifically, for the CDR-H3 region, gg-dWJS achieves IMP, Sim, and Nat scores of 67.2, 0.520, and 0.291, respectively, which are still worse than our method. We observe that the IMP score does not significantly improve compared to the original dWJS (which is 66.1). This suggests that the affinity pre- dictor used in the post-selection step of the original dWIS already contributes effectively guided generation.
w/o selection
76.7%
0.523
0.326
Ours
93.3%
0.514
0.330
Alternating Optimization This framework alternates be- tween updating the structure with the sequence fixed, and mutating the sequence with the structure fixed. In this study, we perform single iteration, applying multiple mutations multaneously, referred as one-iteration. We also evaluate the impact of the predictor-corrector technique by excluding the Amber relaxation step, denoted w/o PC. As shown in Table 2, both ablations reduce performance, demonstrating the predietor-corrector and Amber relaxation effectiveness.
Additionally, we implement MCMC variant: At each step, we use ESM to identify the top 20 most probable mutations, randomly choose one mutation as a proposal, and use the affinity predictor to compute its acceptance probability. We repeat this procedure for a total of 9 steps for consistency. Evaluating the resulting sequences, we obtain scores for IMP, Sim, and Nat of 65.6, 0.562, and 0.360, respectively. While the IMP score slightly improves (from the original 64.0 to 65.6). it remains inferior to our proposed method. The drop in Sim likely stems from strong guidance every step, while Nat improves due to MCMC's conservative acceptance.
We also evaluate the effect of directly removing the Al- phaFlow framework. In this variant, we perform gradient optimization the existing protein structure instead of us- ing predictor guidance. This step is followed by Amber relaxation, after which we use ProteinMPNN to identify po- tential mutations. This variant is denoted by w/o AlphaFlow in Table 2, which shows that leaving out AlphaFlow leads to the greatest performance drop compared to the other two variants. We attribute this to AlphaFlow's 's ability to capture the natural fluctuations of proteins, resulting more realis- tic structures than those generated through direct gradient ascent alone, and accessing binding conformations that may be different from either a structure determined experimen- tally or predicted by a model like AlphaFold. Less realistic structures in turn yield less natural mutated sequences, as reflected by the Nat score decreasing from 0.330 to 0.314.
4.5. Ablation Studies
We use Affinityloww as the baseline to evaluate the effect of removing specific modules, with results shown in Table 2. The ablation studies are conducted on CDR-H3, considering 10 antigens for efficiency. Our focus is primarily on the IMP metric, so the discussion centers around this metric.
7

---

AffinityFlow: Guided Flows for Antibody Affinity Maturation
a)
X
30
b)
C)
dg
WT
Gly99
Py11o
Pro105
Figure 3: Visualizations of model-generateed antibody structures bound to the SARS-CoV-2 RBD (a) Relative fixed antigen, most model-generated antibodies (green) are predicted to bind with noticeable rotation in binding pose compared to the WT conformation (blue). (b) Our model suggests several mutations frequently, in particular Ala 105Pro may stabilize the CDR loop. (c) The buried Lys99Trp mutation interacts with multiple other aromatic residues across the interface.
Co-teaching We evaluate the co-teaching module with two variants: (1) w/o energy: using the trained predictor on limited labeled data only. (2) w/o selection: training on pair- wise discrete data without sample selection. As shown in Ta- ble 2, both variants reduce the IMP metrie, highlighting the effectiveness of the module. Notably, w/o energy performs worse than w/o selection, demonstrating the value of bio- physical energy data. We also observe that a better-trained predictor improves specificity: our method achieves the best Sim, while w/o selection ranks second. This likely re- sults from the predictor's role in estimating antigen-specific binding energy, leading to greater specificity.
4.6. Case Study
To further understand how AffimitYFlow generates muta- tions to improve binding, we analyze the structures of our proposed mutants and the wild-type of a single-domain antibody (sdAb) known to bind the SARS-CoVa receptor- binding domain (RBD) (Yao et al., 2021). We generate 30 mutated structures, with half containing mutations only in the CDR3 loop and half having mutations across all CDRs, We use Rosetta to calculate binding energies (AAG) and other interface metrics relative to the wild-type structure (PDB ID 7D30).
All computed structures show AAG < O. suggesting that the designed antibodies bind the antigen more tightly than the native sequence. However, do not observe any cor- relation between AAG and which CDRs are allowed to mutate. We measure other interface metrics (dSASA, shape complementarity) for all 30 structures and compare these values with those computed for native antibody-antigen in- terfaces the PDB (Adolf-Bryfogle et al., 2018). Both metries indicate interface quality: (1) dSASA (change in acceeslee surface area) reflects how well hydropho- bic residues are buried and how closely the antibody and antigen interact, and (2) shape complementarity measures how well the two proteins fit together. The results align well with natural structures, demonstrating that our model preserves the correct shape profile of the binding surface. Interestingly, despite conserving the binding interface shape, most mutants (2 (21/30) dock with rotated binding pose of approximately 67 degrees (Figure 3a). This rotation shifts interactions away from CDRI I and toward stronger interac- tions in CDR2 and CDR3.
Additionally, we report the Spearman's 's rank correlation coefficient R (Spearmanr) on the test set. We isolate 10 antigens from the total dataset, with each antigen paired with 77 sdAbs. We calculate Spearman's ' R for each anti- gen and present the average across the 10 antigens. The models without energy data achieve values of 0.0956 for the sequence-based predictor and -0.0043 for the structure- based predictor, respectively, reflecting the limitations of the 120 labeled entries. By utilizing biophysical energy data for direct fine-tuning, the sequence-based predictor reaches a coefficient of 0.40, while the structure-based predictor achieves 0.50. While not state-of-the-ant for antibody bind- ing energy prediction in general, these values demonstrate the effectiveness of our approach when limited data is avail- able. Sample selection further improves performance, with the sequence-based predictor achieving cocfficient of 0.51 and the structure-basee predictor reaching 0.52. These re- sults highlight the benefits of using biophysical energies and sample selection to enhance prediction accuracy.
Certain mutations occur frequently across all model-
8

---

AffinityFlow: Guided Flows for Antibody Affinity Maturation
proposed antibodies, indicating that the model focuses at- tention on these residues. Notably, Lys99Gly, Ala105Pro, and Asp109Gly appear often, regardless of whether muta- tions are restricted to the CDR3 loop or allowed across all positions (Figure 3b). We believe that the Ala00 muta- tion stabilizes the CDR3 loop into an optimal conformation for this antigen. We used scikit-learn's 's RandomForester gressor with 100 decision trees, training on mutation types (input) and Rosetta- Rosetta-predicted AAG (output). Model was validated using R² on 20% held-out test set. We find that the rarer Ala1051.eu mutation contributes most to improving AAG, likely by increasing hydrophobicity at the interface and promoting assembly.
Impact Statement
Antibody affinity maturation aims to enhance the binding affinity of antibodies their target antigens, which has broad implications in therapeutic development. This re- search has the potential to significantly improve the efficacy of antibody-base treatments for various diseases, including cancer, autoimmune disorders, and infectious discases. For instance, optimizing antibodies against emerging pathogens could play a crucial role in mitigating future pandemics and saving millions of lives. While this work offers substantial societal benefits, we acknowledge the potential for dual-use concerns. Advances in antibody affinity maturation could, in principle, be misused to develop harmful applications, such as targeting specific biomolecules for malicious purposes. As researchers, we are committed to raising awareness of these risks and promoting ethical use of these methods. We firmly believe that the potential benefits of this research far outweigh the risks, given its promise to address critical global health challenges. Additionally, we emphasize the importance of community oversight and regulatory frame- works to mitigate misuse. In this study, we have focused solely on advancing machine learning methodologies for antibody optimization, and we do not foresee any immediate ethical concerns associated with this work.
Most intriguingly, one model-generated sequence includes a Lys99Trp mutation, an unusual amino acid to insert within an interface. Visual examination reveals that this tryptophan residue is inserted such that it creates πт-π interactions with two aromatic residues across the interface as well as provid- ing stabilizing interactions with a tyrosine on the antibody itself (Figure 3c). This mutation is especially interesting, as we detail below. Our case study uses the MR17 nanobody (PDB: 7D30) from (Yao al., 2021), which has a reported KD of 83.7 nM. (Li et al., 2020) later introduced a mutant, MR17m, with a Lys99Tyr substitution that improved IC50, indicating higher potency (i.e., requiring less antibody to achieve the same effect). They also suggested Lys99Trp could be even more effective- an uncommon mutation that AffinityFlow independently identified.
A Acknowledgement
We thank Everado Villasenor Rodriguez for infrastructure support. We are grateful to Maxwell Bates and Jonah Noh from Amazon for their assistance with structure prediction. We also thank Steven Atkinson, Hao Song, and Di Sun from Amazon for their valuable discussions and feedback.
Our structural analysis of mutant and wild-type antibody structures reveals several key insights into the nature of mu- tations governing antibody-antigen binding. These results validate our computational approach and also highlight its potential to guide rational design of improved antibodies against SARS-CoV-2 and other pathogens, opening new avenues for therapeutic development.
References
Abramson, J., Adler, J., Dunger, J., Evans, R., Green, T. Pritzel, A., Ronneberger, O., Willmore, L., Ballard, A. J..
5. Conclusion
Bambrick, J., et al. Accurate structure prediction of biomolecular interactions with alphafold 3. Nature, 2024.
We present AffinityFlww for optimizing antibody sequences, introducing several key innovations. First, we develop an AlphaFlow-baal based alternating optimization framework that leverages predictor guidance to steer structure generation toward high binding affinity, followed by targeted sequence mutations. Second, we propose a co-teaching module that integrates insights from noisy biophysical energies to refine both structure- and sequence-based predictors. Our method achieves state-of-ther the performance in affinity maturation experiments across functionality, specificity, and rationality metrics, demonstrating the effectiveness of AffinityFlow in advancing antibody sequence design.
Adolf-Bryfogle, J., Kalyuzhniy, O., Kubitz, M., Weitzner, B. D., Hu, X., Adachi, Y., Schief, W. R., and Dunbrack Jr, R. L. Rosettaantioodydesign (rabd): A general framework for computational antibody design. PLoS computational biology, 2018
Akbar, R., Bashour, H., Rawat, P., Robert, P. A., Smorod- ina, E., Cotet, T.-S., Kark-enrssen, K., Frank, R., Mehta, B. B., Vu, M. H., et al. Progress and challenges for the machine learning- design of fit-for-purpose mono- clonal antibodies. In MAbs. Taylor & Francis, 2022.
Alford, R. F., Leaver-Fay, A.. Jeliazkov, J. R., O' O'Meara J., DiMaio, F. P., Park, H., Shapovalov, M. V., Renfrew,
9

---

AffinityFlow: Guided Flows for Antibody Affinity Maturation
P. D., Mulligan, V. K. Kappel, K., al. The rosetta all- atom energy function for macromolecular modeling and design. Journal of chemical theory and computation, 2017.
Frey, N. C., Berenberg, D., Zadorozhny, K., Kleinhenz, J., Lafrance- Lafrance-Vanasse, J., Hotzel, I., Wu, Y., Ra, S., Bonneau, R., Cho, K., et al. Protein discovery with discrete walk- jump sampling. arXiv preprint arXiv:2306. 12360, 2023.
Allgower, E. L. and Georg, K. Numerical continuation methods: an introduction, volume 13. Springer Science & Business Media, 2012.
Gligorijević, V., Renfrew, P. D., Kosciolek, T., Leman, J. K., Berenberg, D., Vatanen, T., Chandler, C., Taylor, B. C., Fisk, I. M., Vlamakis, H., al. Structure-based protein function prediction using graph convolutional networks. Nature communications, 2021.
Bennett, N. R., Watson, J. L., Ragotte, R. J., Borst, A. J., See, D. I.., Weidle, C., Biswas, R., Shrock, E. I.,, Leung, J.J., Huang, B., et al. Atomically accurate de novo design of single-domain antibodies. bioRxiv, 2024.
Hadsund, J. T., Satlawa, T., Janusz, B., Shan, L., Zhou, L., Röttger, R., and Krawezyk, K. nanobert: deep learn- ing model for gene agnostic navigation of the nanobody mutational space. Bioinformaties Advances, 2024.
Blum, A. and Mitchell, T. Combining labeled and unlabeled data with co-training. In Proceedings of the eleventh annual conference on Computational learning theory, 1998.
Han, B., Yao, Q. Yu, X., Niu, G., Xu, M., Hu, W., Tsang, I., and Sugiyama, M. Co-teaching: Robust training of deep neural networks with extremely noisy labels. Advances in neural information processing systems, 31, 2018.
Cai, H., Zhang, Z., Wang, M., Zhong, B., Li, Q. Zhong, Y., Wu, Y., Ying, T., and Tang, Pretrainable geometric graph neural network for antibody affinity maturation. Nature Communications,225 2024.
Hayes, T., Rao, R., Akin, H., Sofroniew, N. J., Oktay, D., Lin, Z., Verkuil, R., Tran, V. Q., Deaton, J., Wiggert, M., et al. Simulating 500 million years of evolution with a language model. bioRxiv, pp. 2024 07, 2024.
Campbell, A., Yim, J., Barzilay, R., Rainforth, T., and Jaakkola, T. Generative flows on discrete state-spaces: Enabling multimodal flows with applications protein co-design. arXiv preprint 0tt.::2402.4499999 2024.
Hie, B. L., Shanker, V. R., Xu, D., Bruun, T. U., Weiden- bacher, P. A., Tang. S., Wu, W., Pak, E., and Kim, Efficient evolution of human antibodies from general pro- tein language models. Nature Biotechnology, 2024.
Chen, C., Zhang. Y., Liu, X., and Coates, M. Bidirectional learning for offline model-based biological sequence de- sign. In International Conference Machine Learning. PMLR, 2023.
Chiu, M. L. and Gilliland, G. L.. Engineering antibody therapeutics. Current opinion in structural biology, 38: 163-173, 2016.
Huguet, G., Vuckovic, J., Fatras, K., Thibodeau- Laufer, E., Lemos, P., Islam, R., Liu, C.-H., Rector-Brooks, J., Akhound-Sadegh, T., Bronstein, M., et al. Sequence- augmented se (3)-flow matching for conditional protein backbone generation. arXiv preprint 0rXiv:2405.20313, 2024.
Chu, L.-S., Ruffolo, J. A., Harmalkar, A., and Gray, J. J. Flexible protein-protein docking with multi-track itera- tive transformer. Protein Science, pp. e4862, 2023.
Dauparas, J., Anishchenko, I,, Bennett, N., Bai, H., Ragotte, R. J. Milles, L. F., Wicky, B. I., Courbet, A., de Haas, R. J., Bethel, N., et al. Robust deep learning-based pro- tein sequence design using proteinmpnn. Science, 2022.
Ikram, Z., Liu, D., and Rahman, M. S. Antibody sequence optimization with gradient-guided discrete walk-jump sampling. In ICLR 2024 Workshop on Generative and Ex- perimental Perspectives for Biomolecular Design, 2024a.
Dhariwal, P. and Nichol, A. Diffusion models beat gans on image synthesis. Advances in neural information processing systems, 2021.
Ikram, Z., Liu, D., and Rahman, M. S. Gradient- guided discrete walk-jump sampling for biological sequence generation. Transactions on Machine Learning Re- search, 2024b. ISSN 2835-8856. URL https: / openreview net
Dunbar, J., Krawezyk, K., Leem, J., Baker, T., Fuchs, A., Georges, G., Shi, J., and Deane, C. M. Sabdab: the structural antibody database. Nucleic acids research, 2014.
Ingraham, J. B., Baranov, M., Costello, 7.,, Barber, K. W., Wang, W., Ismail, A., Frappier, V., Lord, D. M., Ng- Thow-Hing, C., Van Vlack, E. R., et al. Illuminating protein space with a programmable generative model. Nature, 623, 2023.
Fernuz, N., Schmidt, S., and Höcker, B. Protgpt2 is deep unsupervised language model for protein design. Nature communications, 13(1):4348, 2022.
10

---

AffinityFlow: Guided Flows for Antibody Affinity Maturation
Jing, B., Eismann, S., Suriana, P., Townshend, R. J. L., and Dror, R. Learning from protein structure with ge- ometric vector perceptrons. In International Confer- ence on Learning Representations, 2021. URL https: ///p///o//// //openreviee net feet/formne forum? i d=1 YLJDV566J4
URL https://ww.biorxxii org/ wrt/contet//////oooooooo early/2020/09/24/2220
06.
Lin, H., Wu, L.., Huang, Y., Liu, Y., Zhang, O., Zhou, Y., Sun, R., and Li, S. Z. Geoab: Towards realistic antibody design and reliable affinity maturation. bioRxiv, 2024.
Jing, B., Erives, E., Pao-Huang, P., Corso, G., Berger, B., and Jaakkola, T. Eigenfold: Generative protein structure prediction with diffusion models, 2023.
Lin, Z., Akin, H., Rao, R., Hie, B., Zhu, Z., Lu, W., dos Santos Costa, A., Fazel-Zarandi, M. Sercu, T., Candido, S., et al. Language models of protein sequences the scale of evolution enable accurate structure prediction. BioRxiv, 2022.
Jing, B., Berger, B., and Jaakkola, T. Alphafold meets flow matching for generating protein ensembles, 2024.
Jumper, J., Evans, R., Pritzel, A., Green, T., Figurnov, M., Ronneberger, O., Tunyasuvunakool, K., Bates, R., Zidek, A., Potapenko, A., et al. Highly accurate protein structure prediction with alphafold. nature, 2021.
Lin, Z., Akin, H., Rao, R., Hie, B., Zhu, Z., Lu, W., Smetanin, N., Verkuil, R., Kabeli, O., Shmueli, Y., et al. Evolutionary-scal prediction of atomic-level protein structure with language model. Science, 379, 2023.
Kingma, D. P. Adam: A method for stochastic optimization. arXiv preprint ar 1412.6980, 2014.
Lindorff-Larsen. K., Piana, S., Palmo, K., Maragakis, P., Klepeis, J. L., Dror, R. O., and Shaw, D. E. Improved side- chain torsion potentials for the amber ff99sb protein force field. Proteins:
Krishna, R., Wang. J., Ahern, W. Sturmfels, P., Venkatesh, P. Kalvet, I., Lee, G. R., Morey-Burrowe, F. S., An- ishchenko, I., Humphreys, I. R., et al. Generalized biomolecular modeling and design with rosettafold all- atom. Science, 2024.
Structure, Function, and Bioinformatics,
2010.
Lipman, Y., Chen, R. T., Ben-Hamu, H., Nickel, M., and Le, M. Flow matching for generative modeling. arXiv 2022.
Kulyté, P., Vargas, F., Mathis, S. V., Wang, Y. G., Hernández- Lobato, J. M.. and Liò, P. Improving antibody design with force-gut greedguided sampling in diffusion models. arXiv preprint ar arXiv:2406.00 248.2222.0....22, 2024.
preprint arXiv:2210.00
Liu, X., Luo, Y., Li, P., Song, S., and Peng, J. Deep geo- metric representations for modeling effects of mutations on protein-proteit binding affinity. PLoS computational biology, 2021.
Le, M. Vyas, A., Shi, B., Karrer, B., Sari, L., Moritz, R., Williamson, M., Manohar, V., Adi, Y., Mahadeokar, J., et al. Voicebox: Text-guided multilingual universal speech generation at scale. Advances in neural informa- tion processing systems, 2024.
Luo, S., Su, Y., Peng. X., Wang, S., Peng. J., and Ma, J. Antigen-specifer antibody design and optimization with diffusion-basse generative models for protein structures. Advances in Neural Information Processing Systems, 35: 9754-9767, 2022.
Lee, S., Jo, J., and Hwang, S. J. Exploring chemical space with score-based out-of-distributioo generation. In In- ternational Conference on Machine Learning. PMLR, 2023.
Malach, E. and Shalev-Shwarte Decoupling" when to update" from" how update". Proc. Adv. Neur. Inf. Proc. Syst (NeurIPS), 2017.
Leem, J., Mitchell, L. S., Farmery, J. H., Barton, J., and Galson, J. D. Deciphering the language of antibodies using self-supervised learning. Patterns, 2022.
Murphy, K. and Weaver, C. Janeway's immunobiology. Garland science, 2016.
Li, J., Cheng, C., Wu, Z., Guo, R., Luo, S., Ren, Z., Peng, J., and Ma, J. Full-atom peptide design based on multi- modal flow matching. arXiv preprint 24NV:22006007335 2024.
Rives, A., Meier, J., Sercu, T., Goyal, S., Lin, Z., Liu, J., Guo, D., Ott, M., Zitnick, C. L., Ma, J., and Fergus, R. Bi- ological structure and function emerge from scaling unsu- pervised learning 250 million protein sequences. PNAS, 2019. doi: 10.1101/622803. URL https: //tts:://ww.... b biorxiv. wwtp:///g///ooo///o/e/o/oe 11010 220000//2222.4...
Li, T., Cai, H., Yao, H., Zhou, B., Zhang, N., Gong, Y., Zhao, Y., Shen, Q. Qin, W., Hutter, C. A., Lai, Y., Kuo, S.-M., Bao, J., Lan, J., Seeger, M. A., Wong, G., Bi, Y., Lavillette, D., and Li, D. A potent synthetic nanobody targets rbd and protects mice from sars-cov-2 infection. bioRxiv, 2020. doi: 10.1101/2020 06..0.6.99...44 143438.
Ruffolo, J. A., Gray, J. J., and Sulam, J. Decipher- ing antibody affinity maturation with language mod- els and weakly supervised learning. arXiv preprint arXiv:21 12.072,, 2021.

---

AffinityFlow: Guided Flows for Antibody Affinity Maturation
Ruffolo, J. A., Chu, L.-S., Mahajan, S. P., and Gray, J. Fast, accurate antibody structure prediction from deep learning massive set of natural antibodies. Nature communications, 2023.
Xu, M., Zhang, Z., Lu, J., Zhu, Z., Zhang, Y., Chang, M., Liu, R., and Tang, J. Peer: comprehensive and multi- task benchmark for protein sequence understanding. Ad- vances in Neural Information Processing Systems, 2022.
Shan, S., Luo, S., Yang. Z., Hong, J., Su, Y., Ding, F., Fu, L., Li, C., Chen, P., Ma, J., al. Deep learning guided optimization of human antibody against sars-cov- variants with broad neutralization. Proceedings of the National Academy of Sciences, 2022.
Yao, H., Cai, H., Li, T., Zhou, B., Qin, W., Lavillette, D., and Li, D. A high-affinity RBD-taagettng nanobody im- proves fusion partner's s potency against SARS-CoV-2. PLOS Pathogens, 17(3)11-88 18, 2021. doi: 10.1371/joung ppat. 1009328. URL ht tittps::.. : wtt.dii.oggggoooooooooooooooo //ogg///... 1371/ Journal. 100 93288
Shuai, R. W. Ruffolo, J. A., and Gray, Generative language modeling for antibody design. bioRxiv, pp. 2021-12, 2021.
Ye, F., Zheng, Z., Xue, D., Shen, Y., Wang. L., Ma. Y., Wang, Y., Wang, X., Zhou, X., and Gu, Q. Proteinbench: A holistic evaluation of protein foundation models. arXiv preprint arXiv:2409.06744 2024.
Shuai, R. W., Ruffolo, J. A., and Gray, J. Iglm: Infilling language modeling for antibody sequence design. Cell Systems, 2023.
Zheng, Q., Le, M., Shaul, N., Lipman, Y., Grover, A., and Chen, R. T. Guided flows for generative modeling and decision making, arXiv preprint arXiv:2311.13444 2023.
Song, Y., Sohl-Dickstein J., Kingma, D. P., Kumar, A., Er- mon, S., and Poole, B. Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456 2020.
Zhou, X., Xue, D., Chen, R., Zheng, Z., Wang, L., and Gu, Q. Antigen-specife antibody design via direct energy-based preference optimization. arXiv preprint Stt::2403.16576, 2024.
Su. J., Han, C., Zhou, Y., Shan, J., Zhou, X., and Yuan, Saprot: Protein language modeling with structure-aware vocabulary. bioRriv, pp. 2023-10, 2023.
Tabasinezhad, M., Talebkhan, Y., Wenzel, W., Rahimi, H., Omidinia, E., and Mahboudi, F. Trends in therapeutic antibody affinity maturation: From in-vitro towards next- generation sequencing approaches. Immunology letters, 2019.
Tobias H. Olsen, I. H. M. and Deane, C. M. Ablang: An anti- body language model for completing antibody sequences. bioRxiv, 2022. doi: https://doi.org/10.. 1.1.:/...........1010002.020.... 477061.
101/202..0120.
Victora, G. D. and Nussenzweig, M. C. Germinal centers. Annual review of immunology, 2022.
Wang, Z., Combs, S. A., Brand, R., Calvo, M. R., Xu, P., Price, G., Golovach, N., Salawu, E. O., Wise, C. J., Pon- napalli, S. P., et al. Lm-gvp: an extensible sequence and structure informed deep learning framework for protein property prediction. Scientific reports, 2022.
Wesolowski, J., Alzogaray, V., Reyelt, J., Unger, M., Juarez, K., Urrutia, M., Cauerhff, A., Danquah, W., Rissick, B., Scheuplein, F., et al. Single domain antibodies: promis- ing experimental and therapeutic tools infection and immunity. Medical microbiology and immunology. 2009.
Xiong. P., Zhang, C., Zheng, W., and Zhang, Y. Bindprofx: assessing mutation- induced binding affinity change by protein interface profiles with pseudo-counts. Journal of molecular biology, 2017.
12

---

AffinityFlow: Guided Flows for Antibody Affinity Maturation
A. Related Work
Generative Protein Modeling Generative protein modeling primarily includes sequence-based language models and structure-basee score generative models. Language models are trained on protein sequence datasets using masked predic- tion (Rives al., 2019) or auto-regressive prediction (Ferruz al., 2022). These models are often fine-tuned for specific domains like antibodies, with examples including AbLang (Tobias H. Olsen & Deane, 2022), AntiBERTa (Leem et al., 2022), LgLM (Shuai et al., 2021), and nanoBERT (Hadsund et al., 2024). Language models have also been explored for modeling tokenized protein structures (Hayes et al., 2024; Su et al., 2023).
Score-based models, such as diffusion- bassdd and flow matching models, mainly focus on generating protein structures. (1) Diffusion-basee models like RFdiffusionAA (Krishna al., 2024) and AlphaFold3 (Abramson et al., 2024) generate structures through coordinate denoising. RFdiffusionAA has been applied antibody design (Bennett et al., 2024), but its code is not open-sourced. Chroma (Ingraham et al., 2023) introduces property-specific guidance into diffusion models but does not research antibody design. Similarly, (Kulyté et al., 2024) incorporates force-fiell guidance but struggles to capture realistic structures due to the simplicity of the diffusion model. (2) Flow matching models have shown greater effectiveness and efficiency compared to diffusion models. Recent studies like AlphaFlow (Jing et al., 2024) and FoldFlow-2 (Huguet flow matching for protein structure generation. In this work, we utilize the
et al., 2024) explore sequence-conditions AlphaFlow framework for antibody sequence design due to its demonstrated effectiveness. It worth noting that ccore-based generative models have also been applied model discrete biological sequences (Camphell et al., 2024; Frey et al., 2023; Li al., 2024; Ikram et al., 2024a).
Co-teaching Co-teaching (Han et al., 2018) is robust technique for addressing label noise by utilizing two collaborative models. Each model identifies small-loss samples from noisy mini-batch to train the other. Co-teaching is conceptually related to decoupling (Malach & Shalev-Shwartz, 2017) and co-training (Blum & Mitchell, 1998), as all these approaches involve collaborative learning between two models. In this study, we adapt co-teaching to work with biophysical binding energy data rather than noisy dataset. Specifically, the sequence-based predictor identifies clean samples for training the brase predictor, and vice versa.
B. Predictor Guidance in Flow Matching
According to Lemmal in (Zheng et al., 2023),
t(; a, V.V., logpa( AG)
(10)
Based on this, we can derive:
o(z, t, AG; = a, + 6, v., log pa t) + by Va, log (apPa(AG x,,t)
(11)
ü( t; 0) + by Va. log lo (AG) x,,t)
In our case, 6, = 1-t. and this leads to:
1-t Vay log logpa(AG x,, t)-
i (rt, 1, AG; - t
(12)
C. Computation Approximation
The guided vector field is defined by:
1- 1------v V V..ffppt (
b(,,tt,A;; 0(x,, - -
(13)
We compute V Va,fa(E1 as:
V fo(E) (ā (2x,) 0ā (xx))
(14)
0E; Ox.
As approaches 1, क closely approximates 2e, allowing for the simplification:
06 (x:) da,
I,
(15)
13

---

AffinitFloww: Guided Flows for Antibody Affinity Maturation
1.04
1.02
1.02
1.01
1.00
1.00
Ratio
Ratio
0.95
0.80
IMP
Nat
IMP
Nat
Sim
0.90
Sim
0.70
0.0
2.5
5.0
7.5
10.0
2
4
5
Scaling factor Y
Sampling step T
Figure 4: The antibody metrics versus scaling factor y normalized to their values at ry to those with y 5.0.
Figure 5: The three antibody metrics versus scaling
factor T, normalized to their values at 7 = 3.
where I represents the identity matrix. Consequently, we approximate the gradient as:
0fa(E1)
V V.. f2l
(16)
D. Computational Efficiency
All experiments are conducted on a g5. 24xlage server equipped with GPUs with 23GB of memory. One iteration of our alternating optimization framework takes approximately 10 minutes for a protein of length 500. Language model-based methods more computationally efficient, with processing times of 18.3 seconds for ESM, 13.0 seconds for Ablang, and 11.4 seconds for nanoBert per sample. However, method consistently produces significantly better designs than these methods, discussed. In applications such as antibody design, the most time-consuming and costly stage is often the evaluation of properties in wet-lab experiments. Thus, the differences in computation time between methods for generating high-peeffrmance designs are less significant in practical production settings, where optimization performance is prioritized over computational speed. This is consistent with the discussions in A.7.5 Computational Cost (Chen et al., 2023).
E. Hyperparameter Analysis
This section examines the sensitivity of our method to various cattaraaamtttee-mmmmee the scaling factor (r) and the number of sampling steps (I") on CDR-H3 with 10 antigens. The reported metrics are normalized by dividing by the default hyperparameter result to facilitate comparative analysis.
Scaling Factor (7): The effect of varying y investigated with values 0.0, 2.5, 5.0, 7.5, and 10, and > = 5.0 as the standard setting. As indicated Figure 4, the Sim and Nat metrics are stable across the range of 7. However, below y ~ 5.0 the IMP metric drops substantially, presumably because there is insufficient exploration of alternate backbone conformations when small.
Number of Sampling Steps (T'): We analyze the impact of the number of sampling steps T on the effectiveness of our method. The normalized metric is plotted as a function of in Figure 5. Again the Sim and Nat metrics are relatively unaffected by the choice of T, but IMP requires 3 sampling steps for maximum benefit. Again this suggests that more exploration of the conformational space improves the final design.
14


Reviews:
[{"review_id": "SC1z19t7xL", "reviewer": "Reviewer_wAhe", "summary": "The paper proposes the AffinityFlow model and constructs an optimization framework for generating high-affinity antibodies. First, it utilizes a structure-based affinity predictor to guide the generation of antibody structures. Subsequently, it creates sequence mutations through inverse folding. This model enables a sequence-conditioned generative model of structure, iteratively guiding the generation of high-affinity antibodies. It has been validated on the SAbDab dataset.\n\n## Update After Rebuttal\nThank you for the authors' response, which has resolved my confusion. I have increased my score.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## General Reply\n\nThank you for your valuable feedback, which has greatly improved our manuscript. We have addressed each comment and will incorporate the revisions accordingly.\n\n## Claims And Evidence\n\n> I think the architecture of the model is not clearly described. There is relatively little discussion about the Predictor-Corrector and Sequence Mutation.\n\nWe provide additional details on both Predictor-Corrector and Sequence Mutation.\n\n(1) Predictor-Corrector is composed of two components. Predictor corresponds to the protein coordinate generation process governed by the learned vector field, and Corrector refers to the Amber energy minimization used to refine the coordinates. We will add the sentence in Line 180.\n\n(2) Sequence Mutation: At each iteration, we apply single-, double-, and triple-point mutations using ProteinMPNN. For each position, we calculate the probability difference between the current and alternative amino acids, selecting the mutation with the highest difference. Double- and triple-point mutations build sequentially on prior mutations. A sequence-based predictor selects the top K (K=3) sequences at each stage for further refinement. We will add this description at Line 191 for clarity.\n\n## Theoretical Claims:\n\n>  I read about Guided Structure Generation, Sequence Mutation, but I'm still confused about the overall framework of the model and how the data is connected.\n\nTo clarify the overall framework and data flow, consider this example:\n\nGiven antibody and antigen sequences, our goal is to mutate the antibody to improve binding affinity. We begin by linking the antibody and antigen sequences and inputting this linked sequence into the AlphaFlow. Without predictor guidance, AlphaFlow generates conformations consistent with the linked sequence.\n\nHowever, our objective is to obtain a protein conformation with higher binding affinity. To achieve this, we introduce predictor guidance during the AlphaFlow structure generation phase, a process we call Guided Structure Generation. This guidance steers the generated conformations toward those with high binding affinity. Once a high-affinity structure is obtained, we apply inverse folding to introduce targeted mutations—Sequence Mutation—and feed the updated sequence back into AlphaFlow. This iterative loop continues to optimize binding affinity. This process is described between Lines 42–73.\n\n## Other Strengths And Weaknesses:\n\n> The description of model architecture is not very clear.\n\nYes, the model is end-to-end. Our architecture is organized as follows:\n\n(1) ESM-2 serves as the sequence-based predictor and is applied during post-selection (as shown in Figure 1) to choose high-affinity mutants for the next iteration.\n(2) ESM2-GVP acts as the structure-based predictor and is used for predictor guidance, steering the noisy protein coordinates toward high-affinity conformations.\n(3) AlphaFlow is the core algorithm, initially trained to transform noisy protein coordinates into clean conformations based on the input sequence. In our framework, AlphaFlow is further guided by ESM2-GVP to bias the generated structures toward higher binding affinity.\n\nWe will update Figure 1 to clearly label ESM2, ESM2-GVP, and AlphaFlow, and include an overall algorithm that demonstrates the complete framework in the revised paper.\n\n> The SAbDab dataset is small. \n\nWe address this issue with the following strategies:\n\n(1) AlphaFlow: AlphaFlow is pretrained on large-scale protein structures. In our method, this pretrained model remains frozen, thereby preventing it from overfitting the small dataset.\n\n(2) Sequence-based (ESM-2) and Structure-based Predictors (ESM2-GVP): Both predictors leverage pretrained ESM-2 models, which have been pretrained on large-scale unlabeled data. During our training, we keep these pretrained backbones frozen and fine-tune only the prediction heads. This reduces the risk of overfitting due to the small number of learnable parameters.\n\n(3) Augmented Dataset via Rosetta Labeling and Co-teaching: To further improve generalization, we introduce a co-teaching module. Initially, the predictors are trained on the limited SAbDab dataset. Next, we augment the training data by generating an additional $4,158$ labeled samples using Rosetta. The co-teaching module then mitigates noise from the augmented data, providing a richer dataset and reducing the risk of overfitting.\n\nThese measures collectively ensure that our models remain robust and generalize effectively, despite the limited size of SAbDab.\n\n> lacks comparative runtime.\n\nWe address runtime in Appendix D: one iteration of our method takes around $10$ minutes for a protein of length $500$, compared to $11$–$18$ seconds for language model-based methods per sample. While these alternatives are faster, our approach yields better designs. In practical settings like antibody design, wet-lab evaluation is the major bottleneck, making optimization quality more critical than generation speed.", "claims_and_evidence": "I think the architecture of the model is not clearly described. There is relatively little discussion about the Predictor-Corrector and Sequence Mutation.", "methods_and_evaluation_criteria": "It is reasonable to conduct the evaluation and select the indicators on the SAbDab dataset.", "theoretical_claims": "I read about Guided Structure Generation, Sequence Mutation, but I'm still confused about the overall framework of the model and how the data is connected.", "experimental_designs_or_analyses": "I think the experimental design is reasonable.", "relation_to_broader_scientific_literature": "Generating antibodies with high affinity is of great importance. However, currently, it may be limited by the relatively small amount of data with known affinity labels. Therefore, research on related artificial intelligence methods is highly necessary.", "essential_references_not_discussed": "I think the relevant literature has been covered.", "other_strengths_and_weaknesses": "Pros:\n\nThe process of the alternating algorithm model generating high-affinity is both interesting and reasonable.\n\nCons:\n1. The description of model architecture is not very clear. Is the model end-to-end? How are the ESM-2, ESM2-GVP, AlphaFlow, etc. used organized? An algorithm or a framework of the model is needed for demonstration.\n\n2. The SAbDab dataset is small. How can we ensure that the model does not overfit?\n\n3. The paper lacks comparative experiments on runtime.\n\nIf you can clear up my confusion, I will raise my score because the experimental results are objective.", "other_comments_or_suggestions": "There are no other suggestions here.", "questions_for_authors": "All the questions are in \"Other Strengths And Weaknesses\".", "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": "qZzuPCfnwF", "reviewer": "Reviewer_QKfP", "summary": "The work combines classifier (gradient) guidance with Alphaflow for flow matching based antibody structure optimization to enhance binding affinity and performs inverse folding with ProteinMPNN to retrieve antibody sequences for synthesis. It also proposes a noise reduction framework (co-teaching) for labeled data whilst training affinity predictors. The authors evaluate their method's performance on SAbDab dataset which shows improvements over the baselines.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## General Reply\n\nYour insightful comments have greatly contributed to improving our manuscript, and we sincerely appreciate your time and effort. Each point you mentioned has been addressed, and the manuscript will be updated to reflect these improvements.\n\n## Methods And Evaluation Criteria:\n> Given the nature of the work which is optimization, I expect more baselines that uses optimization techniques. Methods such as ESM and AbLang are not particularly suitable for optimizing for Antigen affinity. The author's also use dWJS as a baseline. Given their method uses classifier guidance, why not use the classified guidance version of the dWJS, i.e., gg-dWJS? Given the limited nature of experiments, I think such expectation is justified.\n\nAs discussed in Section 4.2, we employ the same trained sequence-based affinity predictor for final sequence selection across all baselines, including ESM, AbLang, and dWJS. This strategy inherently enables affinity optimization, making these methods valid baselines for comparison.\n\nThank you for pointing out gg-dWJS. To clarify, we have further conducted experiments with gg-dWJS, employing the trained affinity predictor to guide sampling, following the original gg-dWJS paper. Specifically, for the CDR-H3 region, gg-dWJS achieves IMP, Sim, and Nat scores of 67.2, 0.520, and 0.291, respectively, which are still worse than our method. We observe that the IMP score does not significantly improve compared to the original dWJS (which is 66.1). This suggests that the affinity predictor used in the post-selection step of the original dWJS already contributes effectively to guided generation. We will incorporate this additional discussion into Section 4.4 to clarify this point further.\n\n## Questions For Authors:\n\n> Given the pitfalls of inverse folding (noisiness for conversion of sequence to structure) and structure optimization (unrealizability of structures), how do you guarantee their method's generated sequences are synthesizable? Did you try synthesizing any samples suggested by your method?\n\nWe address the concern regarding synthesizability from three key perspectives:\n\n(a) Realistic Structure:  (1) We use AlphaFlow as our protein structure generation framework, which has demonstrated its effectiveness in producing realistic protein conformations.   (2) In addition, our Predictor-Corrector method incorporates Amber relaxation at every iteration to refine the protein coordinates, ensuring the generated structures are physically realistic.\n\n(b) Limited Mutation Per Iteration: (1) Although the inverse folding process (mapping structure to sequence) can be noisy, we mitigate this issue by restricting mutations to only 1-3 positions per stage rather than generating the entire sequence at once. This targeted approach reduces noise; (2) Furthermore, we employ a post-selection process using a trained sequence-based predictor to filter out sequences with low predicted affinity.\n\n(c) Biologically Meaningful Case Study:\nWe present a detailed case study in Section 4.6 to demonstrate the biological relevance of our generated designs. Notably, our AffinityFlow model independently identified the Lys99Trp mutation—a mutation previously proposed in Li et al. (2020) as a promising improvement in antibody potency.\n\nThese strategies collectively enhance the likelihood that our generated sequences are synthesizable and biologically meaningful. Furthermore, we report Nat (the inverse of perplexity) as a supporting metric. As shown in Table 1, AffinityFlow achieves the highest Nat score among all non-language model-based methods, indicating stronger sequence plausibility.\n\n\n\n> Did the authors attempt any in vitro experiments?\n\nWe have not conducted in vitro experiments at this stage.\n\n> Why is flow matching a better option for this work?\n\nWe adopt flow matching primarily due to the availability of a pre-trained AlphaFlow framework, which has demonstrated exceptional performance in generating realistic protein conformations. Additionally, recent studies [1, 2, 3] show that flow matching can offer superior effectiveness and efficiency compared to diffusion models.\n\nIt is also important to note that our proposed alternative framework and co-teaching module are not inherently tied to the AlphaFlow framework; they can, in principle, be implemented within any sequence-conditioned generative model of structure.\n\n     - [1] Lipman Y, Chen R T Q, Ben-Hamu H, et al. Flow matching for generative modeling[J]. arXiv preprint arXiv:2210.02747, 2022.  ICLR 2023\n     - [2] Le M, Vyas A, Shi B, et al. Voicebox: Text-guided multilingual universal speech generation at scale[J]. NeurIPS 2023.\n     - [3] Adam Polyak, et al. Movie gen: A cast of media foundation models. 2024.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Given the nature of the work which is optimization, I expect more baselines that uses optimization techniques. Methods such as ESM and AbLang are not particularly suitable for optimizing for Antigen affinity. The author's also use dWJS as a baseline. Given their method uses classifier guidance, why not use the classified guidance version of the dWJS, i.e., gg-dWJS? Given the limited nature of experiments, I think such expectation is justified.", "theoretical_claims": "N/A", "experimental_designs_or_analyses": "See Methods And Evaluation Criteria.", "relation_to_broader_scientific_literature": "The work adds classifier guidance to flow based method for antibody sequences and uses inverse folding to convert to sequence (so that they could be synthesized).", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "Strengths\n\n- The writing in general is concise and easy to understand\n- The proposed method works as claimed shown through the experiments (although I remain unconvinced about the baselines uses, see evaluation and criteria)", "other_comments_or_suggestions": "N/A", "questions_for_authors": "- Given the pitfalls of inverse folding (noisiness for conversion of sequence to structure) and structure optimization (unrealizability of structures), how do you guarantee their method's generated sequences are synthesizable? Did you try synthesizing any samples suggested by your method?\n\n- Did the authors attempt any in vitro experiments?\n\n- Why is flow matching a better option for this work?", "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": "VrU03nht2f", "reviewer": "Reviewer_PaUw", "summary": "The authors propose a pipeline to optimize sequences with structural guidance. AffinityFlow builds on AlphaFlow, a sequence-conditioned generative model. They present a two-stage optimization process: first, structure generation using a fixed sequence to guide the structure toward high binding affinity, followed by inverse folding and updating the initial sequence. The authors employ a co-teaching module to update the sequence after the inverse folding step.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## General Reply\n\nThank you for your constructive feedback, which has improved the clarity and rigor of our paper. We have addressed all points and will revise the manuscript accordingly.\n\n## Methods And Evaluation Criteria:\n> The clarity of the methods (predictor training). \n\nTo further clarify our method, we highlight the following points:\n\n(1) Predictor Architecture: We described the predictor architecture in Section 4.3, where $\\alpha$ and $\\beta$ represent the parameters of the sequence-based and structure-based predictors, respectively. We will explicitly reiterate these parameter definitions in Section 4.3 to improve readability.\n\n(2) Predictor Training: The training of our predictors involves two phases: (a) Supervised Training: Initially, we train both predictors using labeled antibody-antigen sequence/structure data and their affinity labels. Specifically, we optimize the parameters by minimizing the mean squared error (MSE) loss: $(f_{\\alpha}(a) - \\Delta G)^2$ for the sequence-based predictor and $(f_{\\beta}(x) - \\Delta G)^2$ for the structure-based predictor. Here $a$ and $x$ denote the protein sequence and structure respectively and $\\Delta G$ corresponds to the negative of affinity. We will explicitly present these in Section 2.4. (b) Co-teaching Fine-tuning: we further refine both predictors using Rosetta-generated labeled data, optimizing the loss in Eq. (9), to further enhances performance.\n\n\n> comparisons of inference time and comparing against methods that also utilize iterative optimization or refinement (if this is not already the case).\n\nWe have compared the inference time of our method with language model-based approaches in Appendix D. For methods that do not rely on language models, their iterative optimization process takes less than $10$ seconds per sample. Although these alternative methods are more efficient, in the context of antibody design, achieving high-affinity designs is prioritized over computational speed.\n\n## Experimental Designs Or Analyses\n\n> I think it would be interesting to compare against ESM combined with your sequence predictor. \n\nThank you for the insightful suggestion. Our current ESM baseline already incorporates the sequence predictor to select the top three sequences per antigen (Section 4.2).\n\nTo further explore your idea, we implemented an MCMC variant: At each step, we use ESM to identify the top 20 most probable mutations, randomly choose one mutation as a proposal, and use the affinity predictor to compute its acceptance probability. We repeat this procedure for a total of 9 steps for consistency.\n\nEvaluating the resulting sequences, we obtain scores for IMP, Sim, and Nat of 65.6, 0.562, and 0.360, respectively. While the IMP score slightly improves (from the original 64.0 to 65.6), it remains inferior to our proposed method. The drop in Sim likely stems from strong antigen-specific guidance every step, while Nat improves due to MCMC’s conservative acceptance. We will incorporate these discussions into Section 4.2.\n\n## Essential References Not Discussed\n\n> BindCraft relevant\n\nThank you for highlighting this work. We will add the following to Appendix A:\n\n\"BindCraft adopts AF2-multimer to generate a binder backbone and sequence given a known target protein structure, subsequently optimizing the non-interface regions using ProteinMPNN. However, BindCraft is not directly comparable to our method, as it specifically targets binder design with known target structures, whereas our setting focuses on affinity maturation through mutation of existing antibody sequences without direct access to target structures. Moreover, the primary goal of BindCraft is generating new binders, rather than improving binding affinity of existing antibodies.\"\n\n## Other Strengths And Weaknesses\n\n> report inference time\n\nOur method does require more inference time due to AlphaFlow’s realistic structure modeling, as discussed in Appendix D. While less efficient than alternatives, it consistently yields better designs. In practice, where wet-lab evaluation dominates cost and time, optimization quality is prioritized over computational speed.\n\n\n## Questions For Authors:\n> how train $f_{\\beta}$ in Eq. 7\n\nWe first train $f_{\\beta}$ using the MSE loss and then fine-tune it with the loss in Eq. (9). It is not a pre-trained energy function; rather, it is a property predictor built upon the ESM2-GVP backbone. We have described this training procedure and loss in the rebuttal of \"Methods and Evaluation Criteria\".\n\n\n\n> confused with notation\n\nYes, $f_{\\alpha}(a)$ refers to the sequence-based predictor, and $f_{\\beta}(x)$ refers to the structure-based predictor.\n\n> not familiar with comparison methods\n\nAll non-language-model-based methods used for comparison—including dWJS, DiffAb, AbDPO, and GearBind—employ iterative optimization loops for refinement. Our results demonstrate that AffinityFlow consistently outperforms these approaches.", "claims_and_evidence": "The claims are supported by experimental results.", "methods_and_evaluation_criteria": "The methods utilize established tools from the literature and combine them with a predictor. The clarity of the methods could be improved, especially regarding the training of the predictor. The evaluation appears sound, although I would suggest adding comparisons of inference time and comparing against methods that also utilize iterative optimization or refinement (if this is not already the case).", "theoretical_claims": "There are no theoretical claims made in the paper.", "experimental_designs_or_analyses": "The experiments seem reasonable, as the authors consider modifications on three CDR regions of an antibody and compare against multiple existing methods. \n\nI think it would be interesting to compare against ESM combined with your sequence predictor. I believe it is possible to perform an MCMC where you use your predictor to accept or reject proposals. This could help understand which parts of the pipeline are the most important (similar to your ablation study in Table 2).", "relation_to_broader_scientific_literature": "The key contributions of the paper relate to other works on designing pipelines for generating new proteins while steering generation toward certain properties, such as binding affinities.", "essential_references_not_discussed": "I believe BindCraft is relevant to this work, as the authors optimize a sequence based on a structure network in an iterative process.", "other_strengths_and_weaknesses": "The method seems to improve on existing methods for specific tasks. \n\nHowever, I think the method may require more time during inference. I would encourage the authors to report inference time and peak memory usage for each method (at least for their method).", "other_comments_or_suggestions": "I don't have any other comments or suggestions.", "questions_for_authors": "- I might have missed it, but how do you train $f_\\beta$ in Eq. 7? Is it a pre-trained energy function? Writing the loss function used to train the structure-based predictor could improve clarity.\n\n- I am slightly confused with the notation $f_\\alpha$ and $f_\\beta$. One is for sequences and the other for structures, correct?\n\n- I am not familiar with all the methods used for comparison. Is there a method that also includes a refinement/optimization loop? It would be great to include one if that is not already the case, or directly compare with [1] BindCraft if possible.\n\n[1] Pacesa, M., Nickel, L., Schellhaas, C., Schmidt, J., Pyatova, E., Kissling, L., ... & Correia, B. E. (2024). BindCraft: one-shot design of functional protein binders. bioRxiv, 2024-09.", "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": "MEB1P0ByWS", "reviewer": "Reviewer_QVPq", "summary": "This manuscript proposes an alternating optimization framework for designing antibodies. In the first stage of the cycle, for a given fixed sequence, structures are generated with high binding affinity using a (structure-based) predictor guidance of AlphaFlow. In the second, the structures are inverse-folded to create mutated sequences and selected by a sequence-based affinity predictor. The cycles may be repeated to accumulate mutations. A key feature of the framework is co-teaching of the structure-based and sequence-based affinity predictors, based on selecting a subset of generated instances based on prediction consensus and updating the predictors based on just the selected subset. Experiments demonstrate superior affinity improvement and antigen specificity and competitive naturalness relative to methods based on protein language models trained on a large corpus, a sequence-based generative model, and structure-based generative models.\n\n## update after rebuttal\nThe authors have incorporated my comments, importantly ones concerning accessibility to the general non-bio audience. The new experiments with gg-dWJS are convincing. I've raised my score to an accept.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## General Reply\n\nThank you for your insightful comments—they’ve greatly improved our manuscript. We’ve addressed each point and will update the manuscript accordingly.\n\n## Claims and Evidence\n\n> poor mapping\n\nThank you for your feedback. We agree that the gap between in silico proxies and experimental KD is a key challenge. Accordingly, we will revise the abstract to state: \"Our method, AffinityFlow, achieves state-of-the-art performance in proof-of-concept affinity maturation experiments.\"\n\n## Experimental Designs Or Analyses\n\n> difficult to assess significance\n\nWe acknowledge that AlphaFlow's inference involves computationally expensive protein conformation modeling, which limited our ability to perform repeated runs. Nonetheless, the reported performance differences, though modest, consistently favor AffinityFlow in functionality and specificity.\n\n> dWJS should be trained on ddG<0.\n\nAs noted in Section 4.2, we use a sequence-based predictor to select top candidates for dWJS, effectively conditioning dWJS. Moreover, dWJS is trained solely on antibody sequences without antigen context, per the original paper, so filtering by ddG < 0 is not applicable. We also compare the guided version (gg-dWJS) in QKfP's rebuttal, which still underperforms our method.\n\n> trouble understanding\n\nWe have described the change in binding free energy as the difference between the free energies of the bound and unbound states in Section 2.4 (Lines 127–130). A negative value indicates that the overall free energy of the system decreases upon binding, meaning that the antibody–antigen interaction is energetically favored. We will add these in Section 2.4 (Line 127).\n\nAn antibody consists of two heavy chains and two light chains with a similar overall structure. Its specificity is determined by six variable regions known as Complementarity Determining Regions (CDRs), denoted as H1, H2, H3, L1, L2, and L3. Typically, heavy chain CDRs range from $8$ to $16$ amino acids, while light chain CDRs range from $3$ to $10$ amino acids. We will include these in Section 2.1 (Line 80).\n\n> difficult to read\n\n(1) Random forest:  We used scikit-learn’s RandomForestRegressor with 100 decision trees, training on mutation types (input) and Rosetta-predicted ΔΔG (output). Model was validated using R² on a 20\\% held-out test set. Feature importances revealed Ala105Leu as the most influential mutation.\n\n(2) Connections to prior studies: Our case study uses the MR17 nanobody (PDB: 7D30) from Yao et al. (2021), which has a reported KD of 83.7 nM. Li et al. (2021) later introduced a mutant, MR17m, with a Lys99Tyr substitution that improved IC50, indicating higher potency (i.e., requiring less antibody to achieve the same effect). They also suggested Lys99Trp could be even more effective—an uncommon mutation that AffinityFlow independently identified.\n\nWe will incorporate these discussions into Section 4.6.\n\n> predictor predict\n\nThe structure-based predictor outputs the negative value of the binding affinity (Kd). We will add this clarification in Section 2.4 (Line 131).\n\n> form of predictors\n\nWe describe the architectures of both the sequence-based and structure-based predictors in Section 2.4, with detailed hyperparameters provided in Section 4.3. To further clarify, we will include more details regarding the MLP and GVP head in Section 4.3.\n\n## Essential References Not Discussed\n\n> see the references in Meng et al. 2024.\n\nThank you for highlighting this survey. We have reviewed Section 2.2.3 (\"Hybrid generative models\") of Meng et al. (2024) and confirm that key methods such as DiffAb and Chroma have been discussed in our paper. We note, however, that most methods listed in Meng et al. (2024) do not specifically address affinity maturation. To clarify, we will add to Appendix A: \"ABGNN pre-trains a novel antibody language model and introduces a one-shot approach for generating both sequence and structure of CDRs. AbDiffuser leverages domain knowledge and physics-based constraints to enhance diffusion modeling. AlphaPanda integrates transformer, 3DCNN, and diffusion models for joint sequence-structure co-design. A more detailed overview can be found in Meng et al. (2024). Notably, these methods primarily focus on general antibody design rather than specifically targeting affinity maturation.\"\n\n## Other Strengths And Weaknesses\n\n> very difficult to read\n\nIn addition to the points in “Experimental Designs or Analyses”, we will add following clarifications: (1) dSASA (change in solvent-accessible surface area) reflects how well hydrophobic residues are buried and how closely the antibody and antigen interact; (2) Shape complementarity measures how well the two proteins fit together. Both metrics indicate interface quality. \n\nAdolf-Bryfogle et al. (2018) assessed these values for all naturally occurring antibody-antigen interfaces in PDB. The metrics we calculate using Rosetta for our designs, fit well within the distribution observed in that paper.", "claims_and_evidence": "The paper claims \"state-of-the-art performance in affinity maturation\" but only uses the in silico $\\Delta \\Delta G$ energies for guidance and evaluation. $\\Delta \\Delta G$ has often been shown to correlate poorly with affinity (as measured by the dissociation constant KD), depending on the Rosetta protocol used. Mason et al. 2021, for instance, did not observe a significant correlation, and there are efforts to improve Rosetta protocols to improve the agreement (Das et al. 2017). The key challenge in affinity maturation originates from the poor mapping between in silico proxies and experimental KD; without addressing this, I believe the paper's claim should be phrased less strongly than SOTA in \"affinity maturation.\" While guided generation based on $\\Delta \\Delta G$ is still interesting and obtaining experimental KD data would be very expensive, the experiment should be considered a proof-of-concept of the proposed framework rather than a biologically significant scientific result.\n\n```\nMason, Derek M., et al. \"Optimization of therapeutic antibodies by predicting antigen specificity from antibody sequence via deep learning.\" Nature biomedical engineering 5.6 (2021): 600-612.\n\nDias, Raquel, and Bryan Kolaczkowski. \"Improving the accuracy of high-throughput protein-protein affinity prediction may require better training data.\" BMC bioinformatics 18 (2017): 7-18.\n```", "methods_and_evaluation_criteria": "SAbDab-nano is a widely used dataset of antibody structures for sdAb. Functionality, specificity, and rationality (naturalness) are reasonable metrics capturing complementary aspects of generated designs. For functionality, it would have been instructive to evaluate on test $\\delta \\delta G $ values based on a few other Rosetta protocols.", "theoretical_claims": "The paper does not make any theoretical claim.", "experimental_designs_or_analyses": "- While AffinityFlow seems to outperform baselines in functionality and specificity, the metric values are quite close and it is difficult to assess significance without repeated runs.\n- The ablation study is comprehensive and makes it clear that all components of the framework (multiple iterations, predictor-corrector, AlphaFlow, biophysical energy data, and selection) are helpful.\n- The one sequence-based generative model baseline (dWJS) is unconditional and does not use any predictor guidance. For a \"fair\" comparison, dWJS should only be trained on the $\\Delta \\Delta G < 0$ instances.\n- Readers not familiar with antibody design will have trouble understanding the paper, as it does not introduce domain-specific concepts. Examples: change in binding free energy (what it being negative means), CDR and its regions, how many amino acids there are (not mentioned). \n- Because the metrics are all in silico, Section 4.6 (Case Study) is especially important for making the case that the generated designs are biologically meaningful. But it is currently very difficult to read without domain expertise. Details of the random forest regression are not described, even in the Appendix. Please describe thoroughly the connections to prior experimental studies such as Li et al. 2020. \n- What value does the structure-based predictor $\\hat f_\\beta$ predict? \n- There is no discussion of the form of the sequence-based and structure-based predictors.", "relation_to_broader_scientific_literature": "This work borrows from the latest developments in structural ensemble generation methods such as AlphaFlow, inverse folding (derivatives of ProteinMPNN), and guided generation (predictor guidance). It combines techniques from each of these fields under a single pipeline, to generate high-affinity antibodies in a manner informed by both sequence and structure. Simple tricks like consensus-based sample selection and correction using Amber relaxation are important contributions that improve performance.", "essential_references_not_discussed": "There is a substantial body of work in predictor guidance for both sequence-based and structure-based generative models. Please see the references in Meng et al. 2024 for a comprehensive list.\n\n```\nMeng, Fanxu, et al. \"A comprehensive overview of recent advances in generative models for antibodies.\" Computational and Structural Biotechnology Journal (2024).\n```", "other_strengths_and_weaknesses": "- While the paper is creative and grounded in its combination of existing ideas, it is currently very difficult for a non-antibody expert to read. Please see \"Experimental Designs Or Analyses\" regarding the strengths and weaknesses of the experiments, questions about experimental details, and suggestions for improving the exposition for the lay audience.\n- Please see \"Claims And Evidence\" for a discussion of the interpretation of Rosetta energies.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "Please see \"Experimental Designs Or Analyses\" regarding the strengths and weaknesses of the experiments, questions about experimental details, and suggestions for improving the exposition for the lay audience.", "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:

Meta-review: The authors present AffinityFlow, a pipeline for sequence optimization guided by structural information. Building upon AlphaFlow, a sequence-conditioned generative model, the method introduces a two-stage optimization process: (1) structure generation using a fixed sequence to enhance binding affinity, followed by (2) inverse folding to update the initial sequence. A co-teaching module further refines the sequence after inverse folding.

The manuscript is well-written, concise, and clearly presented. Experimental results validate the effectiveness of the proposed method. During rebuttal, the authors have satisfactorily addressed reviewers' concerns, including: (1) Providing additional architectural details; (2) Expanding baseline comparisons; (3) Incorporating essential references for broader context

Following the authors' thorough responses, all reviewers unanimously recommend acceptance of the manuscript in its current form. I therefore vote to accept this paper.
Decision: Accept (poster)