Towards Stable Representations for Protein Interface Prediction
Authors: Ziqi Gao
Zijing Liu
Yu Li
Jia Li
Venue: NeurIPS 2024 poster (2024)
Keywords: protein interface
graph learning
adversarial training
stable representation
Primary area: machine_learning_for_other_sciences_and_fields
TL;DR: We regard the protein flexibility as an attack on the trained model and aim to defend against it for improving protein interface prediction.

Abstract: The knowledge of protein interactions is crucial but challenging for drug discovery applications. This work focuses on protein interface prediction, which aims to determine whether a pair of residues from different proteins interact. Existing data-driven methods have made significant progress in effectively learning protein structures. Nevertheless, they overlook the conformational changes (i.e., flexibility) within proteins upon binding, leading to poor generalization ability. In this paper, we regard the protein flexibility as an attack on the trained model and aim to defend against it for improved generalization. To fulfill this purpose, we propose ATProt, an adversarial training framework for protein representations to robustly defend against the attack of protein flexibility. ATProt can theoretically guarantee protein representation stability under complicated protein flexibility. Experiments on various benchmarks demonstrate that ATProt consistently improves the performance for protein interface prediction. Moreover, our method demonstrates broad applicability, performing the best even when provided with testing structures from structure prediction models like ESMFold and AlphaFold2.

Towards Stable Representations for Protein Interface Prediction
Ziqi Gao Zijing Liu", Yu Li', Jia Li Honn Kong University of Science and Technology Hong Kong University of Science and Technology (Guangzhou) International Digital Economy Academy (IDEA)
Abstract
The knowledge of protein interactions is crucial but challenging for drug discovery applications. This work focuses protein interface prediction, which aims determine whether pair of residues from different proteins interact. Existing data-driven methods have made significant progress in effectively learning protein structures. Nevertheless, they overlook the conformational changes (i.e., flexibility) within proteins upon binding, leading poor generalization ability. In this paper, we regard the protein flexibility as an allack on the trained model and aim to defend against it for improved generalization. To fulfill this purpose, we propose ATProt, an adversarial training framework for protein representations to robustly defend against the attack of protein flexibility. ATProt can theoretically guarantec protein representation stability under complicated protein flexibility. Experiments various benchmarks demonstrate that ATProt consistently improves the perfor- mance for protein interface prediction. Moreover, our method demonstrates broad applicability, performing the best even when provided with testing structures from structure prediction models like ESMFold and AlphaFold2.
1 Introduction
(A)
Training Bound structures
Structure change
Testing (B)
Protein
Protein
Unbound structures
Frotein
Protsin unbound
Interface
Positive
Negative
bound
Figure 1: (A). The task illustration. PIP involves predicting if there is an interaction between two residues from different proteins. (B). The task challenge. During training, the input consists of bound structures of two proteins. However, for testing, one can only access their unbound structures.
Protein-protein interactions are important for understanding biological processes, and for the design of novel therapies [48 [6] and drugs [47). The protein interface refers to the surface region of protein where the interaction occurs. It therefore holds key to revealing the specific interaction mechanism and understanding protein functions. In this work, tackle the problem of protein
"Conrepondencee to: Zijing Liu (liuzi edu, cn) and Jia Li (jialeeQust.n))
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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AUC (1)
18
94
SASNet
NEA
91.6
92
1.2
1.4
1.5
SASNeE
Tesibbuudd
Classifisston Loss
1.8
2.0
Then-douund
bound
1.5
1.2
1.4
Teat-unbound
bound
Olossffication
1.1
1.0
90
88.5
1.0
0.0
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68
67.6
8
0.9
1.4
0.4
0.8
122
0.2
8.U 8-8
B:U 8-9
B-U
20
100
(A)
(B)
Figure 2: The impact of flexibility on results with the DB5.5 dataset 45 (A) The testing results of two baselines (SASNet [43, NEA [3]) and our method. 'B-U' represents the popular formulation, i.e., training with bound structures and testing with unbound ones. 'B-B' refers to the formulation where both training and testing are conducted with bound structures. (B) Loss trends for three method.
interface prediction (PIP) (shown in Figure A)); predicting whether two residues, each from an individual protein, interact with each other, given the separate structures of two proteins.
For years, data-driven methods based on deep learning (DL) have made significant progress in response to this critical task by effectively learning protein structures using geometric graph neural networks (GNN) 15 33 3D CNN 43 etc. Limited by the difficulty in accessing protein structure data, they typically follow a formulation of training on bound (after binding) structures and testing on unbound (before binding) ones, as depicted in Figure BB). For training, large-scale datasets like
the Database of Interacting Protein Structures (DIPS) 43 typically consist of only bound structures, which are directly extracted from the PDB database 4 In contrast, in the practical inference scenario, the model cannot access the bound structures but can only be provided with unbound ones [K] 15 33]
In this paper. we empirically find that this training (bound)-testing (unbound) formulation leaves significant room for performance improvement. In Figure 2 exploratory experiments show that prevailing PIP methods are sensitive to flexibility. Utilizing the bound version structures for testing can greatly boost their performance. Based on these findings, we aim to answer the question in this paper-how to handle the mismatch between bound and unbound structures for PIP?
Since it is usually impractical to access the protein bound structures for testing, the most intuitive solution is to explicitly learn the mapping relationship from unbound to bound structures of proteins. However, this is challenging due the following two factors: (1) The amount of pairwise unbound and bound structure data for proteins is extremely limited [10] (to our knowledge, only DB5.5 (45)). (2) A protein's bound structure is not unique and depends on its binding partner, so diverse training data is necessary. To address this issue, we take a different route. We consider any potentially complicated flexibility in a protein as an attack (29 24.. which can harm the testing performance of model trained on bound structures. Therefore, our core idea is to enable protein representations with adversarial robustness, which can defend against the attacks of protein flexibility. In simple terms, for a protein with both unbound and bound versions, the model outputs similar (stable) representations.
In this work, we take an important step forward in mitigating the impact of flexibility on PIP. We propose ATProt, an end-to-end adversarial training (AT) framework for protein representations, to effectively defend against protein flexibility in PIP. Inspired by the recent protein graph representation methods [17 (33 [15, our model comprises graph-basee feature extractors (encoders) for protein graphs. Our ATProt framework does not require computationally expensive data augmentation and can be smoothly applied to most existing protein graph encoders. Specifically, we implement differentiable AT regularizations for various protein representation encoders. Importantly, we introduce novel and expressive graph encoder for protein representations and propose its theoretical regularization form for the first time. ATProt can produce stable representations for the same protein with different structure versions (e.g., bound, unbound, and generrtee ones). Extensive experiments on several protein interaction benchmarks verify that our ATProt method consistently outperforms advanced PIP methods. The results demonstrate the effectiveness of the AT regularization. Furthermore, ATProt maintains excellent performance even when tested with structures generated by AlphaFold2 (5] and ESMFold [3), allowing for user-friendly inference without the need for native structures.
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2 Related Work
Protein interface prediction. Protein interface prediction (PIP), a well-studied problem, focuses on determining whether there is an interaction between amino acids from two different proteins. Recently, a series of methods based on protein 19 17
20 14 or amino acid representation [39 46 learning have achieved significant success. NEA [SS pioneers the use of protein graphs to address PIP, where protein structure information is represented and aggregated, followed by the dense layers. SASNet [3 considers embedding the hierarchical structures of proteins, integrating atomic and amino acid information into 4D-grid data, and employs 3D CNN for learning. To further enhance performance, more fine-grained structure information modeling, specifically surface geometry [46] [39], introduced to effectively learn amino acid representations. Existing methods have effectively represented proteins from various perspectives of protein information. However, we have observed that protein flexibility, which is overlooked by most methods, poses significant performance bottlenecks for them. We focus this key issue of mitigating the bound-unbound mismatch in protein structures to improve model generalization.
Modelling protein flexibility. Recently, pioneer works in biology confirm that protein-proteie interaction (PPI) conforms to the "induced fit" theory (7 38) Specifically, proteins undergo structure changes due to residue-level forces, and they adjust structures achieve the best binding state. More importantly, proteins with PPI typically undergo larger structure changes at the interface compared to non-interface regions [O] II
52 [2]. which will exacerbate the generalization challenge of the PIP task. Modelling flexibility directly is challenging, whether using traditional computational or deep learning (DL) approaches. Traditional methods often rely on finding the lowest energy state 42 51 or introducing an induced fit model (specifically, the elastic network model) 12 3) to guide structure deformations. The optimization space these methods is vast, making them very comecconumiing DL-based methods (10] struggle to achieve satisfactory accuracy in learning the distribution mapping of nound-unbound states due limited training data (i.e., 253 complexes in the DB5.5). As directly predicting bound structures is challenging, in the context of the PIP task, we choose to eliminate the influence of different versions of the same protein structure on the task.
Preliminaries
In this section, (1) we present the definition of the protein interface prediction (PIP). Then, (2) verify the importance of representation stability through empirical and mathematical views. Finally, (3) we investigate to ensure protein representation stability within the adversarial training framework.
Problem definition. We are given as input two proteins pl and frlppppccoopo consisting of M and residues, respectively. The proteins represented their residue sequences and 3D structures, which are posed of a-carbon atom locations of all residues. The goal of the PIP is to classify all possible pairs of residues from separate proteins. More formally, the set of data is ((P), PJ), Vig J iissMMISiS where p! represents the i-th residue in protein pl and Vij E (0, 1}.
3.1 The importance of protein representation stability
We verify the importance of stable protein representations from both empiri- cal and theoretical perspectives. For clarity, we use the notations x 1: x to
91
represent the native bound structures of proteins pl and p2, while X X represent their structures used for testing. After using a protein graph en-
Test-
AUC
bound
coder, we have their representations, denoted as H H² H H. We
89
Test
denote the protein representation perturbation as || 1p + || 1ollpp- where H²
88
unbound
8, H H 82 H' -H',.
0.0 Representation perturbetion
0.3 0.4
From an empirical perspective, in Figure B we quantify the test results of the NEA method [15] under flexibility. We gradually increase the structure change of test samples and calculate the representation perturbation. We note that the test performance is negatively correlated with the represen-
Figure 3: AUC vs. repre- sentation perturbation.
tation perturbation caused by flexibility. Moreover, testing with bound structures yields the best results.
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From theoretical perspective, we draw the consistent conclusion that stable representations lead to improved PIP results. Following [5], we model PIP as a pairwise classification problem. Specifically, we concatenate the i-th and j-th rows of H and H22 into a vector embedding, which is then sent to the PIP classifier f. In this case, the following proposition describes the impact of representation perturbations on PIP results.
Proposition 3.1. For two proteins with M and N residues respectively, the classification results obtained using hound and unbound structures are the same. This is true if N ||ō: + M A(f.p), p), where A(f,p) can be constant depending only on the PIP classifier f and the norm I1-1ly-
[| <
We detail P().p) and prove Proposition 3.1 in Appendix B.1 This proposition tells that stable protein representations (i.e., smaller || Ilp and || under flexibility are necessary for achieving high performance. Thus, to effectively address the structure mismatch in PIP, an intuitive idea is to perform adversarial training for protein representation learning.
3.2 Adversarial training
Here, we introduce the concept of adversarial training (AT) [ 1 18 5 and establish a connection between it and the stability of protein representations. We consider a classification task with a given dataset D {(rr, y4) |= consisting of K classes. We assume that the entire prediction pipeline includes a representation model (e.g., encoder) and a classifier. The concept of adversarial training (AT) requires the entire pipeline to perform well not only on D but also on the worst-case distribution near D, as determined by a specific distance metric. More concretely, the AT that we primarily focus on in this paper the éy-robustness. For a given p value and finite e >> 0, AT aims train a pipeline that can correctly classifies (x + 5, v) for any ||ó||p S c, where (z, y) belongs to DD
Among all AT methods, Lipschitz neural networks belong to common and effective category. Specifically, an encoder function is considered to have Lipschitz continuity if a slight perturbation to the input of the encoder does not significantly change its output.
Formally, the definition of Lipschitz continuity is given by:
Definition 3.1. (Lipschitz continuity in adversarial training) An encoder function ENC is said to be C-Lipschitz continuous w.r.l. norm ||-|| if for any two versions of imputs 31, 22.
(ENC(=)) - ENC(#2)] S C C| - -
(1)
Lipschitz continuity explains the requirements of AT for a general representation learning encoder. In the context of protein graph representation, this can be modified to become the definition below. Definition 3.2. (Lipsehitz continuity for protein representations) A protein representation encoder (-) has C-Lipschitz continuity w.r.t. norm II-II if for any two versions of structure inputs X X and the invariant residue feature input F.
((F - ((F x sC
x ----X x*
(2)
3.3 How to ensure Lipschitz continuity for protein graph representations?
As expressive representation, graph structured data is widely used for representing input pro- with residues acting as nodes and physical interactions as edges. Let G = (V, E) be an undirected graph with nodes V = {I,..., N}. edges & C V2, graph signal F E Nxd and a graph shift operator L E gg.Vx.
teins 17 22 19
(i.e., node connectivity). We consider any variant of the spectral GNN (e.g..
GCN (6 30 ChebNets [[3], BWGNN 41 40 that follows the concept of learning filter coef-
ficients for graph convolution. By constructing the filter h (L) = Σk 0g I (0g are learnable
parameters), the protein graph representation can be defined as H Σ K O.L = hL
Here, we extend the Definition 3.2 to the scenario of using GNN models. To achieve this, we assume L is perturbed to become L due to the protein flexibility, and introduce the key factor (GNN filter stability constant Cr), for achieving GNN-based stable protein representations.
Definition 3.3. (GNN filter stability constant) Given a graph spectral filter h: (0, 2] + [0, 1). it defined as Lipschitz with constant Cj > 0 for any pair of points X1, A2i
[h(A1) - h()2)) S Shh AA1 -221,
(3)

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Ls
max
18
8(+1
big
00
H
Cross Attention
MAS s KLs
Protein
Edge
Node Feature
bf
0
BCC
Feature
by
O2
Graph Convolation
PIP Clussifier
:
h(-)
0x
Cross Attention
H
Bersteen
Leamable
Filter
Protein
Stabllity-regularized GNN
Figure 4: The framework overview with the BernNet encoder. The whole framework contains the
graph encoder for stable protein representations, the cross attention layers for communication and the final binary classifier. ATProt takes in two protein graphs as inputs, and extracts features with the pre-defined graph encoder (BernNet is taken as an example here). The PIP results obtained after the learned representations have passed through the cross attention module and classifier. The Ls loss for stability regularization and classification loss LBC jointly optimize the model.
which introduces main theorem below.
Theorem 3.1. (Protein graph stability with GNNs) Let the perturbation to L is finite such that L-L -
e. e. The protein graph encoder (+) always stable with a polynomial filter h if for
pp some finite Oj.
(FFFL) ((F || s A(()) 11
(4)
where A(V) is a constant determined by the model (e.g., layer number and feature dimension).
Based on Eq. g and Eq. 4 the lower bound of the left term in Eq. is solely determined by the maximum of CA (denoted as Cj), To be more intuitive, Cß equal to the maximum absolute slope (MAS) the filter (the straightforward proof the Appendix B.2).
Therefore, we conclude the core idea for designing our ATProt framework as follows:
We can enhance the stability of protein representations by decreasing the MAS value of h.
4
Method
Overview. We propose ATProt, an end-to-end framework (illustrated in Fig. 4 to boost PIP from view of representation stability. Specifically, our model inputs two proteins whose structures can be provided in various sources (e.g., native bound, native unbound, AlphaFold2, ESMFold). ATProt incorporates protein graph representation encoder and a targeted diffcrentiable regularization scheme to theoretically guarantee the representation stability. Our ATProt framework can be implemented with at least four protein graph encoders, and we provide specific examples of these cases. Lastly, for the PIP task, we apply cross-attention module to facilitate communication between the protein representations and use a simple linear classifier for final prediction.
Protein representation. We represent protein as an undirected weighted graph g = (V,E). Each node v. E V representing one residue has d-dimensional feature vector F; E TR (i.e., residue type) and 3D coordinate X, E R² (i.e., the a-carbon atom location). Edges & = {i are constructed with a k-nearest-neighbor (k-NN) graph using Euclidean distance. To distinguish the edges, follow 17 to construct the SE(3)-invariant edge features {et, V(i.j) E EJ.
The goal ATProt. According to Definition 3.2 we aim to achieve representation stability, which means that the perturbation in the representation caused by protein flexibility is constrained. In
5

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addition, it is also important to ensure the commonly encapsulated that the representation of the protein not affected by rotation or translation. Formally, we represent single protein d consisting of N residues, with its residue-level feature matrix F E N and residue-level structure X TR. N33 We wish our model (-() to ensure the following property.
which means
Given Z. H VFF, X); Z H' (FF, QX + +
we have || H S C- ||XX||] (C-Lipschitz continuity)
(5)
AQ E SO(3), Vg E RR, E R 3C E R.
4.1 Adversarial training regularizations for various encoders
The Fourier transform is powerful tool in the representation of both structured [50 26 49 28
and unstructured data [9] 21 31]. Our main focus is on employing spectral graph encoders for representing protein graphs. These encoders adhere to the principle of utilizing a graph spectral Σ
filter I(A) ko (A) learn effective protein representations. Here, (ba) is the pre- defined filter basis and {0 is the learnable parameters. For graph convolution, the filter h(.) will be applied to the whole Laplacian matrix L. which is calculated from the protein structure data. Specifically, to construct L, we first apply Multi-Layer Perceptron (MLP) reduce the dimensionality of E to I, and incorporate the results into the edge weight matrix W:
MLP (eis),
(1,5) E
Wi
(6)
0.
(1,5) E
Then the Laplacian matrix L is obtained by = 1/2 W D D-IDD-/2 1/2 where D the degree matrix, i.e., D diag E, W Wig..,,, W N.j)-
The protein graph representation can be defined as:
K
=
Σ (=
where the result of h()) represents the graph spectral response.
In this paper, we introduce four types of top graph encoders (i.e., Simple GCN 49). Chebynet 13 Low-pass filter 34], and BernNet (23) along with their corresponding stability regularizations.
Case 4.1. (Simple GCN encoder
49 The Simple GCN encoder (SGC) utilizes a spectral filter in
the monomial function form:
=())=KK
(8)
Since the spectrum X lies in 1),,1), it is clear that the maximum absolute slope (MAS) that h(A) can reach is K. Therefore, the stability regularization of the SGC encoder does not involve any loss function. We can directly constrain the size of the order K.
Case 4.2. (Chebynet encoder 13) The Chebynet encoder utilizes spectral filter in the polynomial function form:
M(A)
Σ 02t.
The stability regularization of Chebynet can be implemented by the loss function Lg =EK k|1* Case 4.3. (Low-pass filter encoder (34)) The Low-pass filter (LPF) encoder utilizes a spectral filter in the low-pass filter function
h(A)= = =1+
(10)
The stability regularization of LPF can be implemented by the loss function Ls = O.
Case 4.4. (BernNet encoder (23)) The BernNet encoder utilizes Bernstein basis, the state-of-the-ar graph spectral basis, to construct the graph spectral filter:
K
K
h(A)= Σ
K (14+1)
0k
(2I
(11)
2k
k
0=
A=U

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According to Theorem 3.1 the BernNet encoder easily satisfies the representation C-Lipstchiz continuity in Eq. 4 provided that the filter h(A) always has finite MAS. However, in Eq. [ the analytical relationship between MAS and (0g [0x] k== is intractable, suggesting the difficulty of constraining C with a gradient descent manner. Thus, our next goal discover a differentiable method for constraining the minimum of C in the training process.
The stability of the BernNet is still unclear in these four cases, prompting us to investigate its regularization form. To the best of our knowledge, it the first investigation of the Lipsthhíz continuity for Bemstein-based spectral filters.
4.2 Guarantecing stability of the BernNet encoder
For clarity, rewrite the Eq. 4 as H - S C. C- ||AXI Cn A(W)) ||X|| [[]]], where, referring to Eq. 3 A(V)) is determined by the model architecture hyperparameters and remains constant. We say the overall model & is of C-Lipstchiz continuity and the learned spectral filter h(A) = E k OabE (A) is of -i-Lipstchiz continuity. We aim to constrain the minimum of constant C2 (denoted as C with {0x} by discovering the underlying relationship between them. Finally, we propose an auxiliary differentiable regularization of [0e]=o to constrain Cj to a controllable bound, for any AX.
Theorem 4.1. Given an arbitrary polynomial function s ((A) on E [0, 2] and suppose its K-onler
K
Bernstein polynomial is denoted as l((A) =E ((2))
(2 - AR. For any point pair
k
λι A2 [0,2], if there exists constant Cj for [f(Ai) [ S CfllA - >22. then l((A) always
holds C C-piptccciz continuity for all K 2 1: [m(A1) - h(x2)) s Cy |A1 A21-
(12)
We introduce Theorem 4.1 which describes the stability relationship between the filter h(A) and an auxiliary function j (A). It tells that with Berstein basis, the MSA of ((A) will never exceed that of the auxiliary function f()). Due to f( = O2. for all k E [0, K] n Z, f(A) can be any 2-D curve passing through all points of {{ 2k
K 0x)] K Therefore, the MAS of f(A) is analytically
tractable, and we can subsequently provide the bounds for the MAS of (A). We have the following proposition, which is accompanied by a detailed derivation in Appendix B.3
Proposition 4.1. Suppose h(A) is approximated with Bernstein basis, i.e., h(A)= Ek Denoting the MAS (minimum Lipschitz constant) of h as Cj₁, it can be upper bounded by
k=o O&b (A).
C
S max xE --jjZ
K - 10; - 0s+1/-
(13)
To summarize, Bernstein basis applied to our ATProt guarantees finite MAS, and more importantly, we can further enhance the stability of the BernNet encoder with the following objective:
Ls
max
10;
0.+1/-
(14)
*E K Innz
4.3 Protein interface prediction
Given proteins PI, P2 with their initial feature F1, F2 and coordinates X1, X2, ATProt produces their stable representations under respective structure perturbations.
H1S E Mxd ATProt Fi); H2 Mxd ATProt (x,, F2).
(15)
We apply a cross-attention layer (shown in Appendix D to enable communication between proteins and obtain their final representations H' Hy Next, we aim predict whether pairs of inter-protein residues belong to the interface, which involves performing pairwise binary classification. Concretely, 10N;
for each training pair of proteins, have a set of 10N, labeled pairs {((HH))) (H2))) vz) i=1 where y: E {0, 13. /' is the number of positive residue pairs and 9 negative ones are downsam- pled. We take the element-wise product of two residue representations and feed it to another MLP with the Sigmoid function to compute the probability p:. Weighted cross-entropy loss is used for training.
C1
Σ
Σ
2N ==
3 logpt k - (1- vē log((1 24)).
(16)
Dirain y E'eenan
7

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Experiments
5.1 Experimental setup
Datasets and processing. We evaluate our method on the complexes from Docking Benchmark 5.5 (DB5.5) [5), gold standard dataset with high-quality, and Database of Interacting Protein Structures (DIPS) 43 which collects 41,876 complexes mined from PDB [4]. DB5.5 only contains 253 complex structures manually curated by domain experts, which cover both native unbound and bound structures. In comparison, DIPS has significantly larger data size, but it only includes bound structures of proteins. The two datasets are randomly divided into training, validation, and testing sets with the following sizes: 203/25/25 (DB5.5) and 39,937/974/965 (DIPS).
For both datasets, we test using various versions of protein structures as imputs for PIP. To accomplish this, we prepared three versions of the testing set for DB5.5, including native unbound structures, structures produced by AlphaFold2. and structures produced by ESMFold. We use Native -Bund, Native-Unbound ESMFold, AlphaFold2 to denote these four settings respectively.
As for DIPS, since it does not have native unbound structures, we only used ESMFold prepare unbound structure inputs for its testing set. AlphaFold2 is not considered due to its high computational cost for the entire testing set of DIPS.
Baselines. We compare our ATProt method with state-of-the-art conventional machine learning method BIPSPI (36), the CNN-based methods Siamese Atomic Surfacelet Network (SASNet) [R), Inttsiion-Conoluution Neural Networks (DCNN) (2). differentiable molecular surface interaction fingerprinting (dMaSIF) [39], and a set of GNN-based methods Deep Tensor Neural Networks (DTNN) 37,. and NEA 15
Setup and metrics. We consider three experimental setups: (1) performing training and testing both on the DB5.5; (2) performing training and testing both on the DIPS; and (3) performing pre-training on the DIPS, fine-tunie fine-tuning on the DB5.5 and testing on the DB5.5. For our proposed ATProt method, we consider graph encoders of Simple GCN, Chebynet, Low-pass pasp filter and BernNet (denoted as ATProt-SGC. -herry,-Cheb,, ATProt-LPP, and ATProt-Bern, respectively).
For each complex in the testing set, assuming that the two proteins have M and N residues, re- spectively, we test all its M N binary classification samples and calculate the Area Under the ROC Curve (AUC) value. Following [15], we report the median AUC score (MedAUC) across all complexes as the final evaluation metric.
Table 1: Training and testing on the DB5.5. Mean and standard deviation values of the MedAUC scores of all baselines, computed from three random seeds. The best performance is in bold and the second best one is underlined. 'SR' means the proposed stable regularization Ls.
Methods
Native Bound
Native NattiveUUbbound
ESMFold
AlphaFald2
BIPSPI
36
0.937 (0.008)
0.911 (0.017)
0.896 (0.008)
0.887 (0.013)
SASNei 4
0,902 (0.007)
0.876 (0.017)
0.887 (0.025)
0.881 (0.020)
dMaSIF 39
0.928 (0.005)
0.912 (0.009)
0.906 (0.003)
0.892 (0.012)
DTNN 37
0.912 (0.005)
0.886 (0.007)
0.883 (0.010)
0.878 (0.021)
NEA LS
0.916 (0.015)
0.895 (0.009)
0.902 (0.010)
0.883 (0.012)
ATProt-SGC
0.925 (0.015)
0.918 (0.004)
0.909 (0.012)
0.924 (0.014)
ATProt-Cheby
0.928 (0.017)
0.922 (0.007)
0.922 (0.005)
0.924 (0.011)
ATProi-LPP
0,915 (0.017)
0.919 (0.019)
0.911 (0.009)
0.911 (0.010)
ATProt-Bern
0.932 (0.017)
0.928 (0.014)
0.929 (0.014)
0.925 (0.011)
ATProt-Bem w/o SR
0.934 (0.009)
0.901 (0.011)
0.897 (0.010)
0.901 (0.012)
Results. T and T in Appendix) show the model performance for PIP. We find that our method is competitive and outperforms the majority of baseline methods with native bound structures. Under this Seative-Bount setting, although ATProt is slightly less effective than BIPSPI, demonstrates the ability to learn sufficiently powerful protein representations (especially with BernNet and Chebynet). Notably, all the baselines fail significantly when using non-bound structures
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Table 2: Pre-training on the DIPS, fine-tuning on the DB5.5 and finally testing on the DB5.5.
indicates that the model performs better/worse than without pre-training (i.e., results in Table I
Methods
Native-Boure
-ubboun
ESMFold
AlphaFold2
BIPSPI 36
0.945 (0.017)
0.913 (0.009)
0.907 (0.007)
0.903 (0.010)
SASNet 43
0.916 (0.003)
0.899 (0.011)
0.900 (0.016)
0.878 (0.012)v
dMaSIF 39
0.922 (0.006)
0,903 (0.012)
0.901 (0.006)
0.910 (0.007)
DTNN 37
0.919 (0.003)
0.893 (0.004)
0.896 (0.013)
0.898 (0.015)
NEA 15
0.926 (0.013)
0,911 (0.009)
0.897 (0.014)
0.892 (0.014)
ATPrtt w/o SR
0.939 (0.013)
0,910 (0.016)
0.902 (0.01 l)
0.904 (0.014)
ATProt-Bern
0.939 (0.011)
0.934 (0.014)
0.937 (0.012)
0.928 (0.012)
as inputs, whereas our method maintains similar performance compared to that under As can be from the results of ATProotBernNNet w/o SR', the robustness to structure perturbation is attributed to the proposed SR (stable regularization) strategy. Overall, the experiments on DB5.5 demonstrate that our method does not rely native bound or unbound structure data for inference, but can directly utilize structure prediction software to achieve satisfactory PIP results. From Table 2 3 we note that although DIPS has a larger data scale than DB5.5, it is difficult to achieve better results. However, pre-training on DIPS can improve most of the testing results on DB5.5.
In summary, all three tables show consistent performance degradation for all baselines with the non-bound structures. In contrast, our method can defend against this bound-unbound mismatch and achieve performance similar to, or even better than that with Native-Bouus
Benefits representation stability. Jisows shows the dimensionality reduction visualization of residue representations with t-SNE [44]. We observe that ATProt leads to a "clustering" effect in the representations, which is the result of stability regularization. Importantly, this ultimately generates clearer classification boundary in visualization and quantification (i.e., the Silhouette Score (35)).
The
ATProt- Barn
ATProt-Ber
Nagatin
Nogatino
Nugatins
Silboaette: 0.4120
Silbauttte: 0,4127
Silbourlee: 0.5457
Figure 5: The t-SNE visualization for the last layer representations. The x and y axes all three subplots are uniformly scaled to (0, 1).
6 &Conclusion
In this paper, we present ATProt, an end-to-end learning framework for protein interface prediction (PIP). By highlighting the importance of protein representation stability for the PIP task, we tailor the stability regularization for four types of spectral graph encoders, theoretically ensuring that the ATProt framework exhibits Lipschitz continuity properties. Our method demonstrates competitive empirical performance compared to leading deep learning- basclines, especially when dealing with significant bound-unbound structure gaps. Importantly, ATProt demonstrates the ability to perform inference in native-structure free scenarios.
Limitations. To present a clear and focused issue, we do not incorporate adversarial vaining-based classifiers into our framework. However, is expected that their inclusion could further enhance the performance of ATProt, as they have shown promising results in the field of computer vision.

---

Acknowledgement
This work was supported by HKUST-HKUSTGGZ) 20 for 20 Crosscampus Collaborative Research Scheme C019, and Shenzhen Hetao Shenzhen- Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone under Grant No. MTTHZQSWS-KKCCYB-2222
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Supplementary of "Towards Stable Representations for Protein Interface Prediction"
A Representing proteins with graph data
Let 9 = (V,E) be an undirected graph with nodes V [I,..., Nj, edges & C V2, graph signal F E R.xd and a graph shift operator E NNNN (i.e., node connectivity). We construct edges with the k-nearest neighbor (k-NN) algorithm and each node in G is connected to the 10 closest nodes within physical distance of less than 30 Å. The edge attributes are distances between o-carbon atoms encoded with Gaussian basis functions. The nodes have two kinds of attributes: the one-hot encoding of amino acid type and the surface-awar features at the residue level. The latter is defined by [77] to distinguish residues closer to the protein surface from those the interior. Notably, we do not introduce any biochemically related attributes of atoms or amino acids featurization. Instead, protein graphs are constructed solely using their a-carbon coordinates.
B Proofs of main propositions
B.1 Proof of Proposition 3.1
Assuming we model the protein interface prediction as a pairwise classification problem. Basically, this proposition provides perturbation radius, within which if the perturbations of two protein representations fall, the predicted correspondences of all pairs of inter-protein residues will be robust.
Formally, we apply the model V/ to obtain d-dimensional protein representations H1 (P)) Mxd H2 = (P22) E Nx The i-th row of H1 and j-th row of H₂ are concatenated into (01) E Rd which is the pairwise residue representations. We then use a neural network f to calculate the probability of the presence of residue correspondence, and define the classifier as g(x(6))= == arg max, fu fa (x))) Assuming that the structure changes of two proteins cause perturba- tions 8,, 52 on Hi and 22 respectively, the interface prediction robustness can be determined by the following proposition. First, we rewrite Proposition
3.1 iinto a more formal expression.
Proposition B.1. For all i [1 n Z and j E [1, n Z, the interface classifier g is provably robust for arbitrary x((i) (i.e., g is robust for all residue pairs Pi and P2) if N || Il + M 1| 1
A(f.p), where A(f.p) p) can be a constant depending only on f and the norm I1-I1pp
Proof. We denote x as variable for convenience to represent the pairwise residue representation. Let g(x)) = y. Suppose there exists perturbation 5 such that g(æ: + 5) * g(æ:) and fī(x + 5) 2 fa + 8) for some + y. We first prove that | 2
8/2 mfrgin(f(x:)) where C' is the lipschitz constant of f. margin( is the margin between the largest and second runner-up output logits. Define z' f(x 5), then 2/ 2/,- The difference between outputs and f(x) can be lower bounded by
2C
| - f())lp 2 [|(2) 21) (f - (t) +12
(17)
In the above equation, we utilize the fact that setting certain elements of a vector to zero can only decrease its p-norm. Let us now consider the following optimization problem:
min 224 - (1=) + 1=3 [z))
s.t. 2 z
(18)
When =/ (z)(z) + fy (2)) we have the minimum of (2) and the update for (11):
22 (x) fx))
2 - -f())) > || 211² ((())
(19)
2
14

---

According to the Lipschitz constant of f. we have
> f(z)), =
(20)
Considering (3) and (4), we have the initial conclusion as follows
42 margin(f(x)))
"
|| 2
(21)
2C
Then we consider the complete residue pair representation set {x((9) bejl,,]nnee((...yg
M
M
N
22 2C
margin mF
(22)
j=1
We denote the perturbations on protein representations H1 and H as o1 and 82, respectively. 8(8)
actually the concatenation of the i-th row of di and the i-th row of 82, i.e., g(6) AGG( 62). Thus the left term of (6) is equal to N 1| p + M 1|62l1p- Finally, we conclude the proof:
M
22 2C
V2 2C
16 M 1022
mfrgin(((zx()))
.MN
margin" (f(z))
j=1
(23)
where margin" (f(x)) is the average value of all margins w.r.t the MN concatenated residue repre- sentations.
B.2 Proof of the statement after Theorem 3.1 that C is equal to the MAS.
Proof. We prove this based on the definition of graph Lipschitz filter, which is continuously differen- tiable due to the polynomial approximation.
Let Cj be the Lipschitz constant of h, and let u(A) = [A)). We want to show that C% is minimized when C₁ sup, u()).
Suppose there exist A and 22 such that |A Aal > and (h(At) h(A2)l > C. A Azl. Then, by the mean value theorem, there exists À between d1 and such that hh' [h'(As) C₁. But this contradicts the assumption that Cn is the Lipschitz constant of h. Therefore, C₁ must be greater than or equal to sup, u(A).
To show that C₁ minimized when C₁2 = supx u(A), suppose there exists Lipschitz constant C₁ such that C₁ < sup, u(A). Then, for any A1 and Ag. have
(h(Ar) 1(A2)1 S C/ A2l
< sup - -X2l X
(24)
< IM (Ma))) -ee
where Ag is some point between A and A2. But this contradicts the definition of u(A) as the maximum of (A)]. Therefore, Cs. must be equal to sup, u(A).
Thus, we have shown that C₁ is minimized when C₁ sup, u(A), as desired. For readability, we denote the minimum of C₁ as Cj and sup, u(A) as the MAS (maximum absolute slope) of h. respectively.
B.3 Proof of Proposition 4.1
start the analysis with the unique -eiiiitt-ppeservattionn property the Bernstein basis shown in
Theorem 4.1 Simply put, during Bernstein polynomial approximation, the outcome polynomial h(A) least as stable as the target function (2). This crucial as it tells that the MAS of an exact function f fA) can always serve as upper bound for Cj,
15

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(A)
Maximum absolute slope (MAS)
Any version of ft Broken line
1.0
MAS;
(1.0, 0,)
0.5 (0,700 0))
MAS < MAS, VA
Stability: h 2 fu vi
K =
C S MAS MASbroken broken
0
0.5
1.0
1.5
2.0
Figure 6: The way to find upper bound of Cj case to explain Proposition 4.1
The relationship between (A) and {8k [0 k= Setting the polynomial order to K, our model learns a set of K + 1 weights {0x === that acts as the coefficients for polynomial approximation, such that f( 2k K = 0g. for all l E [0. K] n Z. Put differently, any 2-D curve passing through all points of (0/K, 80). (2/K, ().,, (2K K, 0k) can be regarded as a possible version of f()) for polynomial approximation. Consequently, given any set of (0x {8x]k=o> k= the stability of h(A) is not worse than the most stable version among all possible ('()).
Formally, we naturally extend the Theorem 4.1 to the following proposition, which provides a theoretical upper bound for Oj of h(A). directly using the learnable coefficients {0x]
As is at least as stable as the most stable f. the MAS of h can be upper bounded by the minimum MAS among all possible f functions, which is infinitely close to the MAS of the broken line passing through points {kk/ K, 0x)]k (egure6/hely to better understand Proposition 4.1 For example, let us set K to any curve passing through (0, 0.) and (2,01) can be version of Out of all possible
versions, the line segment directly connecting two points has the minimum MAS (i.c.,
[0g- 01
2
We have introduced in the main text the relationship between f fA) and k= Based on this, the proof of Proposition 3.2 is equivalent to proving the following lemma.
Lemma B.1. Given K + points (0, 0g). (2. 01) ...., (2x, ,0K),, suppose there are infinitely many functions f(A) that pass through these K + points. The maximum absolute slope (MAS) of any
version of a function (A) is not less than the MAS of the piecewise linear function passing through
these K + points.
Proof. Let fbroken (A) be the piecewise linear function passing through the given K 1 points. The slope of foroken between two consecutive points 2
02) and
2(++1)
K 0.+1) is given by:
0,41 8, 0:41
0
m, 2
(25)
2
K
K
K
The MAS of fbraken (A) is the maximum of the absolute values of these slopes:
MAStroken
max 0Si
|msl
(26)
Now, consider any function f(A) that passes through the K + points. Since f(A) is differentiable,
by the mean value theorem, for each interval
2(i-1) K
there exists a point X; such that:
K
2((+1)
K
O 0,
(A):))
(27)
2(++1)
24
K
Since f(A) passes through all the given points, we have:
MAS,
max
[f))) = max
|m. MAS
(28)
DSiSK-1
osigk-1
Thus, the MAS of any function ((A) satisfying the conditions is greater than or equal to the MAS of the piccewise linear function foroken (A) passing through the points.
16

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C Results on DIPS
Table BaaeeBsshoon shows the results on DIPS. Kindly note that we train and test all methods both on the DIPS dataset.
Table 3: Training and testing on DIPS.
Methods
Native-Boun
ESMFold
BIPSPI 36
0.891 (0.003)
0.883 (0.012)
SASNet 43
0.895 (0.002)
0.878 (0.013)
dMaSIF 39
0.909 (0.012)
0.885 (0.004)
DTNN 37
0.902 (0.009)
0.870 (0.014)
NEA 15
0.911 (0.015)
0.875 (0.009)
Ours w/o SK
0.909 (0.013)
0.882 (0.013)
Ours
0.909 (0.007)
0.906 (0.007)
D
The cross-attention layer used
(H (WWW)) Vd (H₂WQ) (H,WQ)H,,<k)) k)
H softmax
(H2Wv).
(29)
H 2 softmax
(H(Wv).
(30)
E
Hyper-parameters
The training process takes around 0.5 hours with 1 Nvidia 4090 GPUs with 24GB RAM. The hyper-parameters used in this paper are listed in the following table.
Hyperparameters
Values
Graph node degree (k-NN)
10
Filter coefficient number for BernNet
10
Dimension of MLP. in Eq.
27, 1
Number of layers in BernNet
Dropout rate Number of attention head Weight of loss Li
0.2
4
1.0
Weight of loss Ls with BernNet Batch size
0.35
Learning rate Optimizer
3 X 10 Adam
Table 4: Hyperparameter choices ATPROT.
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NeurIPS Paper Checklist
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Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification:
The contributions are included in the abstract and the introduction.
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Question: Does the paper discuss the limitations the work performed by the authors?
Answer: [Yes]
Justification: See Section 6
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Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
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Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
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Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
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Justification: This paper presents work whose goal is advance the field of Machine Learning. There are some potential societal consequences of our work, none of which we feel must be specifically highlighted here.
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Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
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Justification: This paper does involve crowdsourcing nor research with human subjects.
19


Reviews:
[{"review_id": "GHl3Bw2U74", "reviewer": "Reviewer_kBXn", "summary": "This paper considers the generalization issue caused by the conformational changes of two proteins before and after binding in the PIP task. The authors view protein flexibility as an attack on the model and aim to defend against it for better generalization. Hence, an adversarial training framework for protein representation is proposed, termed ATProt. ATProt is theoretically proven to ensure protein representation stability under complex protein flexibility. Experiments on the DB5.5 and DIPS datasets further validate the effectiveness of ATProt, especially when using unbound structures as input.", "questions": "* What about the experimental results for the removal of 'SR' in the other three encoders? Clearly demonstrating the performance improvement brought by 'SR' in the other three encoders would better validate the effectiveness of the framework.\n* Considering visualizing the changes in interface prediction before and after adding 'SR' could more intuitively validate the proposed framework..\n* Showcasing the hyperparameter tuning process for “the weight of loss $L_{s}$ with BernNet” would be beneficial, as it is the core idea of ATProt.\n* Providing the number of epochs and the number of cross-attention layers would help readers better reproduce the results.", "limitations": "The authors have thoughtfully addressed the limitations of their study, particularly highlighting the absence of adversarial training-based classifiers in their framework.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "* The concept of viewing protein flexibility as an attack on the model and utilizing an adversarial training framework to address this issue is both interesting and brilliant.\n* Experiments on the DB5.5 and DIPS datasets effectively validate ATProt's performance improvement in unbound scenarios.\n* ATProt provides a novel perspective for robust predictions with real unbound inputs. Combining ATProt with protein structure prediction models such as AlphaFold and ESMFold might aid in advancing sequence-based PIP tasks.", "weaknesses": "* Although the idea of ATProt is interesting and effective, the model's architecture adopts a combination of existing methods, BernNet and Cross-attention.\n* The ablation experiment targeting 'SR' was conducted only within the 'ATProt-BearNet' combination.\n* Lacking some visualization experiments. No examples are presented to show which residue pairs are predicted more accurately before and after incorporating ATProt.\n* In Supplementary.E, some hyperparameters are missing, such as the number of epochs and the number of Cross-attention layers.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely appreciate the reviewer **kBXn**'s recognition of our paper and valuable comments. We will respond to reviewer's insightful suggestions point-by-point.\n\n**[Cons 1. Novelty of Model's Architecture]**\nThanks for the valuable comment. We sincerely clarify that the novelty of this paper is three-fold.\n\n1. **Various protein graph encoders:** We fully agree with your feedback that we did not pay enough attention to the design of new protein representation models. However, **the proposed method (strategy) is plug-and-play**. Although we only demonstrate four cases, the GNN encoders applied for protein-related tasks are far more numerous [1,2]. The concept of stability regularization (SR) has the potential to be widely applied to **various existing encoders** to address the challenges posed by protein flexibility.\n\n2. **Various protein-related tasks:** Through empirical and theoretical validation, we show that in the protein interface prediction (PIP) task, we can avoid simulating the exact distribution of protein flexibility and instead use **simple yet effective regularizations**. In other protein-related tasks, this strategy might also address distribution shifts caused by structural changes. For example, SR has the potential to resolve the distribution shift between AlphaFold 2 and native structures mentioned in [3]. \n\n3. **New proposition for stable BernNet:** BernNet is a widely applied model with strong expressive power. Here, we introduce the Lipschitz regularization for BernNet for the first time (to our knowledge), achieving state-of-the-art performance on the PIP task. Due to the analytical difficulties caused by the complex polynomial structure of BernNet, we respectfully believe it is a relatively fundamental contribution to the field of stable GNNs.\n\n**[1]** Protein representation learning by geometric structure pretraining. ICLR, 2023.\n\n**[2]** Structure-based protein function prediction using graph convolutional networks. Nature communications, 2021.\n\n**[3]** SaProt: Protein language modeling with structure-aware vocabulary. ICLR, 2024.\n\n**[Cons 2. Need More Ablation Experiments]**\nWe really appreciate the reviewer's detailed comments. We include the added experimental results in Table 3,4 in one-page PDF.\n\nFrom the results, we can see that:\n\n(1) In the Native-Bound (ideal and virtual) scenario, the proposed SR is ineffective, while in the remaining (real-world) scenarios, SR significantly improves all four cases of encoders.\n\nFurthermore, we have made a new discovery that:\n\n(2) The gain of SR on the SGC encoder is relatively small among the four cases, which may be due to the direct reduction of the polynomial order $K$ in SGC caused by SR. Therefore, the expressive power is explicitly diminished.\n\n**We will add all of these results to our revised manusrcipt.**\n\n**[Cons 3. Residue-Level Visualizations]**\nThank you for your insightful comments regarding this issue. To address your concern, we add the residue-level visualization, and the figure is included in one-page PDF. Due to space constraints, we select two out of the 25 samples from the DB5.5 testset.\n\nThe baseline method we select is NEA in our manuscript. First, we categorize the misclassified samples by NEA into **false negatives (FN)** and **false positives (FP)**. Due to the imbalanced nature of the PIP problem, we observe that there are notably more FP samples than FN samples. Therefore, in the added figure, we visualize all FN samples and some of the FP samples. Please kindly note that all of the visualized pair samples are misclassified by NEA but correctly classified by ATProt.\n\nFrom the figure we add, it can be seen that the residues involved in the shown samples (especially the FN samples), exhibit significant structural changes.\n\nIn addition, we quantify the average structural changes of residues corresponding to correct and incorrect predictions for both NEA and ATProt. This is performed with all of the DB5.5 testset samples. For NEA, the average structural changes of correctly and incorrectly classified residues are 0.563 and 0.972, respectively. For ATProt, the respective values are 0.589 and 0.597. In simple terms, the structural changes impair the performance of NEA but have little impact on ATProt.\n\nThis insightful comment highlights the advantages of the proposed method, and **we will include this interesting part in our revised manuscript**.\n\n**[Cons 4. Some Hyperparameters are Missing]**\nThanks for your very thorough review. Table 5 in one-page PDF is a comprehensive summary of the hyperparameters. The **bolded** rows are newly added.\n\n**[Question 1. Effectiveness of SR]**\nThanks for the feedback, and we have added more experimental results in the response to **[Cons 2]**.\n\n**[Question 2. The Prediction Changes after Using SR]**\nThanks for the valuable comment. In the response to **[Cons 3]**, we conducted visualizations and quantitative experiments, both of which show the robustness of ATProt to structural changes.\n\n**[Question 3. Hyperparameter Tuning Process for Weight of $\\mathcal{L}_S$]**\nThank you very much for this question. For the overall training objective $\\beta\\mathcal{L}_I + \\gamma\\mathcal{L}_S$, we fix $\\beta$ at $1.0$ and search for $\\gamma$ in the range of $0.1$ to $10$. For fairness, we ensure that all baselines and our methods conduct hyperparameter search with ```n_trials=50``` in the Optuna API. \n\nWe provide the results on the DB5.5 dataset in Table 6 in one-page PDF. \n\nWe observe that all three cases exhibit a similar pattern: with the increase of $\\gamma$, **the performance first increases and then decreases**. The difference is that the optimal weight ranges for the three types of encoders are not the same.\n\n**[Question 4. More Detailed Hyperparameters]**\nThanks for your detailed suggestion, and we have provided more hyperparameter results in the response to **[Cons 4]**. The complete hyperparameter table will be added to our revised appendix.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "CnuW7eQsR1", "reviewer": "Reviewer_RLcQ", "summary": "This paper first identifies a commonly overlooked issue in protein docking: protein flexibility, and proposes an improved method to address it. This approach utilizes an adversarial training framework to maximize Lipschitz continuity. Experimental results demonstrate the effectiveness of this method.", "questions": "None", "limitations": "Excessive emphasis on ensuring Lipschitz continuity may limit the expressive power of the network ($L_S$). The article is meaningful and interesting. However, excessive restriction on the network's expressive ability could potentially prevent this method from becoming the ultimate solution. Therefore, I believe this article does not reach the level of spotlight or oral presentation.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "The overall quality of this paper is very high. The addressed issue - protein flexibility - is highly meaningful. The methods are sound. Therefore, I believe this paper should be accepted.", "weaknesses": "The writing in one part of the paper is not very clear. I hope the authors can adjust it. The paper discusses a method of adversarial training to ensure Lipschitz continuity, but the specific training objectives of adversarial training are not explicitly stated here. Adversarial training typically refers to having two competing objectives, which are contradictory. However, I did not see this aspect described in the paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer **RLcQ** for acknowledging our method as \"meaningful and interesting\", the quality of our paper as \"very high\" and our methods as \"sound\". Many thanks for the constructive feedback especially for the questions about the writing part. These all help us to further enhance the readability and the quality of our paper.\n\n**[Cons. Description of Adversarial Training]**\n\n***Our explanation:***\n\nThanks for the constructive feedbacks. We strongly agree with you that adversarial training (AT) typically involves two or more conflicting training objectives. Many cases of literature indicate that a more accurate statement is: Lipschitz continuity regularization is a popular and effective method for **Adversarial Robustness (AR)**. \n\nFrom the formulation of the training objectives, two losses only exhibit intuitive conflicts, as $\\mathcal{L}_S$ acts by constraining the slope of the GNN filter, which limits the expressive power of the GNN (as mentioned in the Limitation section). Moreover, from the empirical perspective, the regularization loss slightly reduces the model's performance on the 'Native-Bound' structure, implying that there may be an **implicit conflict** in the training objective. Therefore, we acknowledge that the two objectives do not have explicit or theoretically provable conflicts.\n\nIn our work, robustness is the model's performance when facing such flexibility 'attack', that is, when we test on unbound, ESM-Fold or AF2 structures. Therefore, while our training objectives ($\\mathcal{L}_I$ and $\\mathcal{L}_S$) have implicit conflicting nature, we believe that AR will be a more conducive expression for promoting readability.\n\n***Our adjustment:***\n\n1. Firstly, as shown in Table 3,4 in one-page PDF, we note that the proposed regularization slightly impairs performance in the standard, i.e., Native-Bound scenario. Thus, we validate the conflicting nature of the objectives in the empirical perspective.\n\n2. Additionally, we will supplement the formulation analysis of the objective conflicts, i.e., how constraining the slope of the GNN filter affects its expressive power.\n\n3. We will adopt the use of \"adversarial robustness\" instead of \"adversarial training\" which will involve the Preliminaries section. As a result, the training objective for protein representation stability will have a more rigorous description.\n\n**[Cons. Ablation Study]**\nThanks for the valuable suggestions. \n\n***About baselines:***\n\nWe have added various baselines, and all results can be found in Table 7 in the one-page PDF. We have added the following baselines: **EBMdock, Pair-EGRET, PesTo, ProtMD-FT, ProtMD-LP, ESM-Fold, AF2 and AF2-Train**.\n\n***About regularization:***\n\nWe perform ablation study on the effectiveness of the stability regularization. The results are shown in Table 3,4 in the one-page PDF.\n\n**We will include all newly added experiments to our revised manuscript**", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "w1FBo9DPvp", "reviewer": "Reviewer_RNrt", "summary": "This work focuses on protein interface prediction, i.e., determining whether a pair of residues from different proteins interact. It notices the conformational change within the protein upon binding and regards the flexibility as an attack on the trained model. An adversarial training framework named ATProt is introduced to defend against this kind of attack with a theoretical guarantee. Experiments demonstrate consistent improvements. However, I am not completely certain about many unignorable points, such as the experimental setting, the missing of up-to-date baselines, and etc. I am absolutely fond of the idea of being robust to conformational changes and give a score between 4 and 5 (leave the decision to other reviewers and AC).", "questions": "(1) In Figure 3, how do the authors increase the structure change of test samples? I agree with Equ. 5 to use \\Delta X to represent the structure perturbation. However, I suppose there are some constraint in this \\Delta X. Notably, the protein flexibility is not entirely random. The atoms' movement need to follow some physical rules. See [A] for illustration. \n\n[A] Fractional denoising for 3d molecular pre-training. ICML 2023. \n\n(2) As far as I am concerned, dMasif is a surface point cloud-based mechanism, and it only outputs the prediction of surface points instead of residues. How do the authors make the comparison compatible? \n\n(3) The conformational change is fancy without doubt and many studies have been trying to do relevant analysis. For instance, ProtMD [A] pretrains the DL model on MD data to learn the protein flexibility with continuous time domain. Can the authors do an additional experiment to see whether this category of pretraining is effective to mitigate the negative effect of conformation change for PIP? \n\n[A] Pre-training Protein Geometric Models via Molecular Dynamics Trajectories. Advanced Science, 2022. \n\n\n(4) It looks weird to me that the pretraining on DIPS brings a negative impact on dMasif but positive impacts for all the others. After pretraining, dMasif drops from 0.928 to 0.922 for native-bound, from 0.912 to 0.903 for native-unbound, etc. Can the authors explain this counterintuitive phenomenon?", "limitations": "Yes, the limitation is addressed.", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "(1) This paper pinpoints an important topic in computational biology, that is, the domain shift for bounded and unbounded structures when evaluating deep learning models. It is a real-world dilemma that scientists do not hold bound-form structures for new proteins. \n\n(2) ATProt is proposed to achieve stability-regularization. It has a theoretically upper bound associated with the Bernstein basis and a stability-oriented objective is introduced. The overall framework can be generalized to many sorts of GNNs, which is also a big strength. \n\n(3) The author conducted many different experimental settings, including native unbound structures, and structures produced by AF2, and ESMFold. The results showcase the superiority of ATProt and demonstrate the decrease of DL models when using predicted or native structures as inputs.", "weaknesses": "(1) The problem formulation is kind of confusing. The authors target classifying all possible pairs of residues from separate proteins. I suppose this may not be the regular version of protein interface prediction (PIP). The standard one would be to classify whether each residue on the ligand and receptor is on the interface or not. The PIP task in this paper is more challenging than the standard PIP task, and is very close to (but easier than) the protein-protein docking problem. Because once the pairwise interactions are recognized, the docking pose is nearly known. I recommend the authors reconsider the problem definition and formulate it more carefully. \n\n(2) No adequate ablation study. I believe a more proper ablation analysis is needed to showcase the contribution of each component. For instance, it would be interesting to see ATProt-SGC/CHEBY/LPF's performance without the stability regularization. \n\n(3) More baselines are required. I notice that all baselines are pretty old, containing NEA (2017), dMasif (2021), BIPSPI (2019), SASNet (2019), DTNN (2017), and DCNN (2016). It is not convincing enough to select these old-school algorithms as competitors. There has been a surge of interest in developing DL models for interface identification. Please see below. Moreover, it is necessary to also evaluate ESM-Fold and Alphafold-2 (if possibly, AF3) in this problem, because they can also immediately output the complex structures (so the interface is given) from sequences. These structure prediction models completely do not suffer from structural perturbation. \n\n[A] Epitope 3D: a machine learning method for conformational b-cell epitope prediction. Brief in Bioinformatics, 2022. \n\n[B] ScanNet: an interpretable geometric deep learning model for structure-based protein binding site prediction, Nature Methods, 2022. \n\n[C] PesTo: parameter-free geometric deep learning for accurate prediction of protein binding interfaces. Nature Communications, 2023. \n\n[D] SEMA-2.0: Antigen b-cell conformational epitope prediction using deep transfer learning. Frontiers in Immunology, 2022 \n\n[E] Pair-EGRETt: enhancing the prediction of protein-protein interaction sites through graph attention networks and protein language models. ICLR Workshop, 2023. \n\n(4) I really appreciate the authors' efforts in attacking the structure change's bad effect in DL models. However, there is an unavoidable issue that I want to discuss with the authors and AC. If our concentration is to bridge the gap between training (bound) and test (native/unbound) datasets, why does not the author directly train the model on unbound or predicted structures? To be specific, we can use AF2/ESMFold to obtain unbound structures and leverage them as the training data. Moreover, it is also feasible to rely on Rosetta, PyMol, OpenMM, etc. to relax the bound structures with some force fields and approximate the unbound circumstance. In the AI4S community, I believe the solution is more flexible and we should consider more simple but effective methods to solve the problem. There have already been some works [A] that mention this representation shift between real structures and predicted structures. \n\n[A] Protein 3D Graph Structure Learning for Robust Structure-Based Protein Property Prediction. AAAI 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely appreciate the reviewer's thorough review and insightful feedbacks. We also appreciate the reviewer's recognition for the core idea and contribution of this paper. We will respond to these comments point-by-point.\n\n**[Cons. 1 Problem Formulation]** \nThank you for your professional comments, which we fully agree with. We will make some adjustments to avoid confusion. To address your concerns, we make the following efforts.\n\n1. Firstly, we clarify that existing research related to our task falls into three categories: partner-specific interface prediction (PS-IP), partner-specific binding site prediction (PS-BSP), partner-agnostic binding site prediction (PA-BSP). \n\n    **PS-IP** is the problem of our paper, which is to predict whether there is an interaction between a pair of residues of two different proteins. In many cases (e.g., NEA, SASNet, BIPSPI, HOPI), this task is referred to as 'protein interface prediction'.\n\n    **PS-BSP**, as mentioned in your comment, predicts whether the residues belong to the interface. For this task, the interface of a protein is conditioned on its partner.\n\n    **PA-BSP** predicts all possible binding sites of a protein. It is the main setting of ScanNet and PesTo, which does not assume knowledge of the partner. \n\n2. Although the applications of the three tasks differ, they are strongly related. We will mention the above three tasks and their differences in the abstract and introduction sections. Importantly, in the related work section, we will provide descriptions of baseline methods belonging to each.\n\n**[Cons. 2 More Ablation Study]**  Thanks for the valuable suggestion. To address the your concerns, we show ablation results on stability regularization (SR) in Table 3,4 in the one-page PDF.\n\nWe find that:\n\n(1) In the Native-Bound scenario, SR is ineffective, while in the remaining (real-world) scenarios, SR significantly improves all four cases.\n\n(2) The gain of SR on the SGC encoder is relatively small among the four cases, which may be due to the direct reduction of the polynomial order $K$ in SGC. Therefore, the expressive power is explicitly diminished.\n\n**[Cons. 3 More Baselines]**\nThanks for the constructive feedback. Regarding the five papers provided, we find that except for Pair-EGRET, they are all designed for the task of 'partner-agnostic binding site prediction'. However, we find that PesTo can perform the PIP task after simple code modifications.\n\n**In this way, we consider Pair-EGRET, PesTo, ESM-Fold and AF2 as additional baselines.**\n\nThe results are shown in Table 7 in the one-page PDF. We find that ATProt can still outperform AF2 (actually AF-Multimer) and ESM-Fold.\n\n**[Cons. 4.1 Use AF2 to Generate Training Data]**\nThis is a very worthy topic for discussion. Frankly speaking, this is our initial attempt. Table 7 in one-page PDF shows the results. The results indicate that using the suggested methods is difficult to achieve SOTA.\n\nRegarding this, our insights are:\n\n1. There may still be distribution shift between the training and testing sets. This is because the cropping process of AF2 considers monomers and multimers. This results in AF2's training set being a mixture of bound and unbound structures. Thus, using AF2 to generate both training and test sets may not necessarily guarantee consistent distribution.\n\n2. It is not very practical to use AF2 to generate training structures on a large-scale dataset (e.g., DIPS with over 40,000 dimers), as it would be very time-consuming. \n\n3. Our method allows **training only once** and then testing on **various versions of structures**. This uniformity and wide applicability are also a potential advantage.\n\n**[Cons. 4.2 Relax the Bound Structures]**\nPerforming force field optimization based on First Principles is a very insightful idea and has been proven effective[1]. However, molecular dynamics (MD) often requires huge computational cost. Thus, applying MD to large-scale datasets is a challenge.\n\n[1] Benchmarking Refined and Unrefined AlphaFold2 Structures for Hit Discovery. ACS, 2023.\n\n**[Cons. 4.3 Representation Shift]**\nThanks for providing this literature called SAO. SAO indicates that there is room for improvement when training and testing both on AF2-structures (i.e., its TonP baseline). Although tasks are different, the deep motivations of ATProt and SAO are similar: both to enable effective inference using structures from various source.\n\n**[Q1. How to Change Structures]** We strongly agree with your point that flexibility cannot be arbitrarily generated. We applied a dynamics guided method called ProDy. It can sample structures that differ from the initial structure by a specific value (RMSD).\n\n**[Q2. About dMaSIF]** The main point of dMaSIF is to generate point cloud representations. However, the dMaSIF paper also contributes a geometric convolutional model, enabling it to address structure-related downstream tasks. Importantly, the PIP task is implemented in the dMaSIF paper.\n\n**[Q3. ProtMD]**\nThanks for providing this valuable literature, which has a user-friendly open-source nature. \n\nIn Table 7 of the one-page PDF, we present the experimental results of ProtMD. We consider the results of fine-tuning (ProtMD-FT) and linear probing (ProtMD-LP). Surprisingly, its performance slightly exceeds the baseline specifically designed for PIP.\n\n\n**[Q4. Pre-training with dMaSIF]**\nThanks for the thorough findings. The quality of the DIPS and DB5.5 dataset differs slightly. The latter is an expert-annotated \"gold standard dataset\", while the dimers mined in DIPS are mainly from multimers in PDB, which do not reflect pure **binary interaction knowledge**. Facing such gap, negative transfer (where pre-training has a negative impact) is common for some models because they are not designed for the pretraining-finetuning paradigm.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
Dear reviewers,

We sincerely appreciate your valuable time and constructive feedbacks. 

**Please see the attached one-page PDF with a summary of added experimental results.** It contains:

Figure 6: Visualization of the changes in interface prediction results before and after using stable regularization (SR).

Table 3,4: The ablation study on the effectiveness of SR.

Table 5: Hyperparameter choices.

Table 6: The tuning process of the weight of $\mathcal{L}_S$.

Table 7: Results of the newly added baselines (EBMDock, Pair-EGRET, PesTo, ProtMD-FT, ProtMD-LP, ESM-Fold, AF2 and AF2-Train). In this table, to address the concern of **Reviewer RNrt**, AF2-Train represents using the training structures generated by the AF2. 

Please see our reviewer-specific feedback for more information.

Meta-review: The paper proposes ATProt, an adversarial training framework for protein interface prediction, designed to enhance model robustness against protein flexibility by treating it as an attack, with experiments showing improved performance across various benchmarks. Reviewers appreciated the novel approach of treating protein flexibility as an adversarial attack, the theoretical grounding and soundness of the framework, and its demonstrated robustness across different datasets. Reviewers criticized the lack of clarity in the problem formulation, the limited novelty in the model architecture, inadequate ablation studies, missing up-to-date baselines, and the need for more detailed experimental settings and visualizations to substantiate better the claims made in the paper. The authors addressed many of these issues during the discussion period, and subsequently, the reviewers unanimously recommended that the paper be accepted. Therefore, we accept the paper, but we urge the authors to carefully incorporate all the additional updates and results in the final revision.
Decision: Accept (poster)