# Effective Protein-Protein Interaction Exploration with PPIretrieval

Chenqing Hua  Connor Coley  Guy Wolf  Doina Precup  Shuangjia Zheng

###### Abstract

Protein-protein interactions (PPIs) are crucial in regulating numerous
cellular functions, including signal transduction, transportation, and immune
defense. As the accuracy of multi-chain protein complex structure prediction
improves, the challenge has shifted towards effectively navigating the vast
complex universe to identify potential PPIs. Herein, we propose PPIretrieval,
the first deep learning-based model for protein-protein interaction
exploration, which leverages existing PPI data to effectively search for
potential PPIs in an embedding space, capturing rich geometric and chemical
information of protein surfaces. When provided with an unseen query protein
with its associated binding site, PPIretrieval effectively identifies a
potential binding partner along with its corresponding binding site in an
embedding space, facilitating the formation of protein-protein complexes. Our
codes are available on https://github.com/WillHua127/ppi_search.

Machine Learning, ICML

##  1 Introduction

Proteins are the building blocks of life, engaged in a myriad of interactions
(Whitford, 2013). Understanding how proteins interact with each other is
fundamental to unraveling the intricate machinery of biological systems (De
Las Rivas & Fontanillo, 2010; Whitford, 2013). Therefore, the ability to
predict and analyze protein-protein interactions (PPIs) not only improves our
understanding of cellular functions but also plays a pivotal role in drug
discovery (Fry, 2006; Scott et al., 2016; Athanasios et al., 2017). Current
deep learning methods try to analyze, understand, and design PPIs (Sun et al.,
2017; Gainza et al., 2020; Réau et al., 2023; Gao et al., 2023), but the
results are often constrained by the complexity of protein interactions and
the limited understanding of the underlying mechanisms. Despite the progress,
there is a pressing need for more effective strategies aimed at designing new
protein binders. This objective is crucial for advancing therapeutic
interventions and understanding the protein interactions of various biological
processes.

Geometric deep learning emerges as a potent strategy for representing and
learning about proteins, focusing on structured, non-Euclidean data like
graphs and meshes (Satorras et al., 2021; Luan et al., 2020, 2021, 2022; Hua
et al., 2022, 2023). In this context, proteins can be effectively modeled as
graphs, where nodes correspond to individual atoms or residues, and edges
represent interactions between them (Gligorijević et al., 2021; Zhang et al.,
2022). In addition, protein structures can be represented as point clouds or
meshes, wherein each point or vertex corresponds to an atom or a residue
(Gainza et al., 2020; Sverrisson et al., 2021). Indeed, representing proteins
as graphs or point clouds offers a valuable approach for gaining insights into
and learning the fundamental geometric and chemical mechanisms governing PPIs
(Réau et al., 2023; Gao et al., 2023; Wang et al., 2023). This representation
allows for a more comprehensive exploration of the intricate relationships and
structural features within protein structures (Tubiana et al., 2022; Isert et
al., 2023).

Instead of directly generating PPIs, given the limited understanding of their
underlying biological mechanisms, we draw inspiration from a previously
developed model known as Foldseek (van Kempen et al., 2023). This model aligns
the structure of a query protein against a database by representing its
tertiary structure in an embedding space. Rather than attempting to build a
generative model that may inaccurately interpret the complex mechanisms of
PPIs, we can utilize existing PPI data to develop a retrieval model for PPIs
in an embedding space.

Therefore, we introduce the first deep learning-based PPI retrieval model,
namely PPIretrieval, which leverages existing PPI data to search for potential
PPIs in an embedding space with rich geometric and chemical information. In
our approach, PPIretrieval learns surface representations of PPI complexes,
which are initially represented as two point clouds along with their
corresponding binding interfaces. Then, the embedded surface representations
with information about binding partners are stored in our database for further
comparison. When provided with an unseen query protein, PPIretrieval learns
its surface representation and retrieves the most similar surface
representation along with its known binding partner in our database.
PPIretrieval outputs the binding partner along with predicted binding
interface for the query protein, enabling the exploration of potential PPIs.
PPIretrieval operates solely within a deep learning pipeline, elimitating the
need for precomputation of protein patches. This characteristic ensures that
PPIretrieval is a fast-computing retrieval tool for efficient and effective
PPI exploration.

Overall, a visualization of training and inference workflows of PPIretrieval
is illustrated in Fig. 1. For a thorough understanding of the model
architecture, detailed discussions are provided in Sec. 1. Moreover, we
explore the optimization strategy employed by PPIretrieval to learn the lock-
and-key structure of PPI complexes, which is discussed in Sec. 4. We visualize
the retrieval results in Sec. 5, and empirically evaluate results in Sec. 6 on
real-world PPI datasets. Experimental results demonstrate the effectiveness of
PPI exploration using PPIretrieval. Most importantly, we discuss future work
and directions in Sec. 7.

##  2 Preliminaries

In the context of PPIretrieval, the objective is to identify a binding partner
$B$ with its corresponding binding interface for an unseen query protein $P$
with a known binding interface. The approach involves learning protein
interactions through their surface manifolds. Specifically, the model employs
heat diffusion on the surface, learning individual representations. The goal
is to effectively retrieve potential binding partners and their associated
binding interfaces based on the learned surface representations.

Protein Surface Representation A protein is a chain of residues
${P}=\\{\mathbf{a}_{1},...,\mathbf{a}_{N_{P}}\\}\in[0,1]^{N_{P}\times 20}$,
consisting of $N_{P}$ residues in Euclidean space
$\upsilon_{P}=\\{r_{1},...,r_{N}\\}\in\mathbb{R}^{N_{P}\times 3}$. The binding
interface $\mathbf{Y}^{\text{res}}_{{P}}\in\\{0,1\\}^{N_{P}\times 1}$ of
protein $P$ denotes a region where the protein is poised to interact with
another protein, forming a complex. The protein $P$ can be characterized by a
set of surface points $\\{x_{1},...,x_{M_{P}}\\}\in\mathbb{R}^{M_{P}\times 3}$
with unit normals $\\{n_{1},...,n_{M_{P}}\\}\in\mathbb{R}^{M_{P}\times 3}$
located on its surface. In this context, we employ the surface representation
to learn the protein, which captures its structural characteristics and
potential interactions with other proteins.

LB Operator on Protein Surface The Laplace-Beltrami (LB) operator is known for
its smooth operation on compact Riemannian manifolds (Lévy, 2006; Wang et al.,
2023). When applied to the protein surface, which can be considered as a 2D
Riemannian manifold $\mathcal{M}$ with a Laplace-Beltrami (LB) operator
$\Delta_{\mathcal{M}}$, the LB operator operates smoothly. The LB operator
$\Delta$ has an eigendecomposition $\Delta\phi_{i}=\lambda_{i}\phi_{i},\
0\leq\lambda_{1}\leq\lambda_{2}\leq...$, and the set
$\\{\phi_{1},\phi_{2},...\\}$ forms orthonormal basis for the space of
functions defined on $\mathcal{M}$. Any function on the surface can be
expressed as a linear combination of these eigenfunctions,

$\small g=\sum_{i}a_{i}\phi_{i},\ a_{i}=\langle
g,\phi_{i}\rangle_{\mathcal{M}}.$

(1)

Here, $g$ is a linear combination of basis functions, with the scalars $a_{i}$
determined by the inner product on the surface.

LB Operator-Induced Message-passing Consider $g(x,t)$ as the measure of heat
at point $x$ on the surface at time $t$. The heat operation is a message-
passing process on the surface, propagating from hot regions to cool regions.
The change in heat over time is described by the LB operator $\frac{\partial
g}{\partial t}=\Delta g$ (Lévy, 2006). After time $t$, the heat distribution
is equivariant to

$\small g(x,t)=\exp{(H_{t})}g,\ H_{t}=-\Delta t=-\lambda t.$

(2)

where $H_{t}$ denotes the heat operator at time $t$. Following Eq. 1, we can
define a function propagation operator $\mathcal{F}$ on the heat distribution
over the surface (Wang et al., 2023),

$\small\mathcal{F}g(x,t)=\sum_{i}F_{i}\exp(-\lambda_{i}t)\langle
g,\phi_{i}\rangle_{\mathcal{M}}\phi_{i},$

(3)

where $\\{F_{i}\\}$ are frequency filters, $\\{\lambda_{i}\\}$ are
eigenvalues, $\\{\phi_{i}\\}$ are eigenfunctions, and $t$ is a time parameter
for the operator. (Wang et al., 2023) propose to use a linear Gaussian filter
to learn frequency,
$F_{i}=F_{(\mu,\sigma)}(\lambda_{i})=\exp(-\frac{(\lambda_{i}-\mu)^{2}}{\sigma^{2}})$,
where $\mu,\sigma^{2}$ are learned parameters for mean and variance.

This LB operator-induced message-passing is employed for smooth and effective
information flow on the (compact) protein surface, as discussed in Sec. 3.1.

##  3 PPIretrieval

Figure 1:  An overview of PPIretrieval pipeline, demonstrating the training
and inference workflows. During training, PPIretrieval processes a PPI
complex. The encoder network (shown in grey) encodes the two proteins,
generating surface features, $\mathbf{H}_{R},\mathbf{H}_{L}$. These features,
along with information about their binding partnership, are stored in our
database. The decoder network (shown in brown) then takes these surface
features, along with the receptor’s binding interface as input, predicting the
ligand’s binding interface and generating its embedding $\mathbf{F}_{L}$, and
vice versa. During inference, PPIretrieval takes a protein $P$ with its
corresponding binding interface to the encoder network. It encodes $P$ into a
surface feature $\mathbf{H}_{P}$. Then, PPIretrieval identifies a surface
feature $\mathbf{H}_{B}$ for binding partner $B$ in our database. The decoder
network takes the surface features $\mathbf{H}_{P},\mathbf{H}_{B}$, along with
$P$’s binding interface, predicting $B$’s binding interface. A PPI complex is
predicted between the input protein $P$ with the given binding interface and
the predicted binding partner $B$ with the predicted binding interface, as
demonstrated above. Details of PPIretrieval can be found in Sec. 1, with an
overview discussed in Sec. 3.3.

The overview of PPIretrieval is demonstrated in Fig. 1. PPIretrieval follows a
specific design process. Starting with a query protein ${P}$ comprising
$N_{P}$ residues in Euclidean space $\upsilon_{P}\in\mathbb{R}^{N_{P}\times
3}$, along with its corresponding binding interface
$\mathbf{Y}^{\text{res}}_{{P}}$, we first encode the protein into a surface
representation $\textbf{H}_{{P}}\in\mathbb{R}^{M_{{P}}\times d}$. The next
step involves retrieving the most similar surface feature
$\textbf{H}_{A}\in\mathbb{R}^{M_{{A}}\times d}$ in the database. Once
identified, we locate a binding partner protein ${B}$ that binds to ${A}$,
with a surface feature $\mathbf{H}_{B}\in\mathbb{R}^{M_{{B}}\times d}$. Then,
the model decodes the pair of protein surface features,
$\textbf{H}_{{P}},\textbf{H}_{{B}}$, utilizing the known binding interface
$\mathbf{Y}^{\text{res}}_{{P}}$. The final prediction involves estimating the
binding interface $\hat{\mathbf{Y}}^{\text{res}}_{{B}}$ for protein ${B}$. In
summary, the model outputs the protein ${B}$ that is most likely to bind to
the input protein ${P}$, accompanied by the predicted binding interface
$\hat{\mathbf{Y}}^{\text{res}}_{{B}}$ .

It is important to highlight that our entire pipeline operates on a deep-
learning framework. There is no need for precomputation of protein or surface
patches, making PPIretrieval an efficient tool. This characteristic enables a
fast encoding for the input protein and facilitates effective retrieval for
the output protein within the model.

###  3.1 Surface Representation Encoder

The surface encoder network aims to encode an input protein ${P}$ into a
surface representation $\mathbf{H}_{P}\in\mathbb{R}^{M_{P}\times d}$, where
$M_{P}$ denotes the number of surface points representing $P$. This
representation captures the propagated chemical and geometric information. It
can be stored in our database for subsequent retrieval and comparison
purposes.

Protein Surface Preparation The input consists of one-hot encoded residue
types for protein ${P}\in[0,1]^{N_{P}\times 20}$ in Euclidean space
$\upsilon_{P}\in\mathbb{R}^{N_{P}\times 3}$, along with the corresponding
binding interface $\mathbf{Y}^{\text{res}}_{P}\in\\{0,1\\}^{N_{P}\times 1}$.
We apply dMaSIF (Sverrisson et al., 2021) to generate a set of oriented
surface points $\\{x_{1},...,x_{M_{P}}\\}\in\mathbb{R}^{M_{P}\times 3}$ with
unit normals $\\{n_{1},...,n_{M_{P}}\\}\in\mathbb{R}^{M_{P}\times 3}$ to
approximate a smooth manifold representing the surface of protein ${P}$.

Upon approximating the protein surface with surface points, we define the LB
operator $\Delta_{P}$ on the surface for heat diffusion. We compute the first
$k$ eigenfunctions of $\Delta_{P}$ stacked in matrix
$\Phi_{P}\in\mathbb{R}^{M\times k}$ with their corresponding eigenvalues
$\\{\lambda_{i}\\}_{i=1}^{k}$ ($k=100$), then calculate the Moore-Penrose
pseudo-inverse of the eigenfunction matrix,
$\Phi^{+}_{P}\in\mathbb{R}^{k\times M}$. The heat diffusion allows effective
information flow between surface points, crucial for operating heat diffusion
on the surface (Wang et al., 2023).

Geometric Descriptor Following the computation of surface points to represent
the input protein, we describe the local geometric features of the surface. We
approximate the per-point mean curvature, Gaussian curvature as detailed in
(Cao et al., 2019), and compute the Heat Kernel Signatures as described in
(Sun et al., 2009). The geometric features processed by a MLP,
$\mathbf{F}_{\text{Geom}}\leftarrow\text{MLP}([\mathbf{F}_{\text{Mean}},\mathbf{F}_{\text{Gauss}},\mathbf{F}_{\text{HKS}}])\in\mathbb{R}^{M_{P}\times
d_{G}}$, capture the local geometric environment for each surface point.

Chemical Descriptor We proceed to compute chemical features for surface points
based on the one-hot encoded residue types and the binding interface. The
residue-level chemical features are first encoded using a MLP with
concatenated features,
$\mathbf{F}_{\text{Res}}\leftarrow\text{MLP}([{P},\mathbf{Y}^{\text{res}}_{P}])\in\mathbb{R}^{N_{P}\times
d_{C}}$, then transformed by an equivariant-GNN (Satorras et al., 2021),
$\mathbf{F}_{\text{Res}}\leftarrow\text{EGNN}(\mathbf{F}_{\text{Res}},\upsilon_{P})\in\mathbb{R}^{N_{P}\times
d_{C}}$. The residue-level features $\mathbf{F}_{\text{Res}}$ preserve the
local information pertaining to residues and the binding interface.

Then, we project these residue-level features onto surface-level features. For
each surface point $x_{i}$, we identify its $k$ nearest neighboring residues
$\\{r^{i}_{1},...,r^{i}_{k}\\}$ with features
$\\{\mathbf{f}^{i,1}_{\text{Res}},...,\mathbf{f}^{i,k}_{\text{Res}}\\}$. A
vector of chemical features is computed by applying a MLP and summation over
the nearest neighboring residues with a distance filter111We use a cosine
cutoff function, $f_{\cos}(d)=\frac{1}{2}(\cos(\frac{\pi
d}{d_{\text{cut}}})+1)$, to smooth out the distance transition to $0$ as the
distance $d$ approaches a pre-defined cutoff distance
$d_{\text{cut}}=30\mathring{\text{A}}$.,
$\mathbf{f}^{i}_{\text{Chem}}\leftarrow\text{MLP}(\sum_{j=1}^{k}f_{\cos}(\|x_{i}-r^{i}_{j}\|)\cdot\text{MLP}([\mathbf{f}^{i,j}_{\text{Res}},1/\|x_{i}-r^{i}_{j}\|]))\in\mathbb{R}^{d_{C}}.$
By computing and stacking these per-point features, we obtain the chemical
features for the protein surface
$\mathbf{F}_{\text{Chem}}=\\{\mathbf{f}^{1}_{\text{Chem}},...,\mathbf{f}^{M}_{\text{Chem}}\\}\in\mathbb{R}^{M_{P}\times
d_{C}}$.

Finally, we use a MLP to combine the per-point geometric and chemical
features,
$\mathbf{F}_{\text{Surf}}\leftarrow\text{MLP}([\mathbf{F}_{\text{Geom}},\mathbf{F}_{\text{Chem}}])\in\mathbb{R}^{M_{P}\times
d}$. For each surface point, these features capture the local geometric and
chemical environment, along with binding interface information. These can be
effectively used in the heat diffusion process for facilitating information
flow on the approximated protein surface.

Message-passing on Protein Surface We perform heat operation on protein
surfaces for message passing. This operation can be smoothly applied to the
protein surface, treating it as a compact object (Wang et al., 2023). For a
protein with surface feature $\mathbf{F}_{\text{Surf}}$, we first project it
onto the column space of eigenfunctions,
$\mathbf{F}^{\prime}_{\text{Surf}}\leftarrow\Phi^{+}_{{P}}\mathbf{F}_{\text{Surf}}\in\mathbb{R}^{k\times
d}$, expressing features in the orthogonal basis with a reduced dimension.
Then following Eq. 3, we can perform heat operation on the surface as,

$\mathbf{H}_{P}=\Phi\underbrace{\begin{pmatrix}e^{-\frac{(\lambda_{1}-\mu_{1})^{2}}{\sigma_{1}^{2}}-\lambda_{1}t_{1}}&\cdots&e^{-\frac{(\lambda_{1}-\mu_{d})^{2}}{\sigma_{d}^{2}}-\lambda_{1}t_{d}}\\\
\vdots&\ddots&\vdots\\\
e^{-\frac{(\lambda_{k}-\mu_{1})^{2}}{\sigma_{1}^{2}}-\lambda_{k}t_{1}}&\cdots&e^{-\frac{(\lambda_{k}-\mu_{d})^{2}}{\sigma_{d}^{2}}-\lambda_{k}t_{d}}\end{pmatrix}}_{=F\exp(-\lambda
t)\in\mathbb{R}^{k\times
d}}\odot\mathbf{F}^{\prime}_{\text{Surf}}\in\mathbb{R}^{M\times d}.$

(4)

Here, each feature channel of $\mathbf{F}_{\text{Surf}}$ has its unique set of
$\\{\mu_{i},\sigma_{i},t_{i}\\}_{i=1}^{d}$. In summary, the encoder network
encodes a protein (represented by residues) into a surface representation by
applying heat diffusion on the surface, capturing both local geometric and
chemical environments.

Training Stage During training, the encoder network is fed with the paired
receptor and ligand proteins $R,L$, along with their corresponding binding
interfaces $\mathbf{Y}^{\text{res}}_{R},\mathbf{Y}^{\text{res}}_{L}$. It then
processes these inputs to generate distinct surface features for each protein,

$\mathbf{H}_{R}=\text{Enc}(R,\mathbf{Y}^{\text{res}}_{R})\in\mathbb{R}^{M_{R}\times
d},\
\mathbf{H}_{L}=\text{Enc}(L,\mathbf{Y}^{\text{res}}_{L})\in\mathbb{R}^{M_{L}\times
d}.$

(5)

Binding Interface of Surface We construct the surface-level binding interface
$\mathbf{Y}^{\text{surf}}_{P}\in\\{0,1\\}^{M_{P}\times 1}$ for surface points
based on the residue-level binding interface
$\mathbf{Y}^{\text{res}}_{P}\in\\{0,1\\}^{N_{P}\times 1}$ for protein $P$.
Here, $\mathbf{y}^{\text{surf}}_{i,P}=1$ indicates that the surface point
$x_{i}$ belongs to the binding interface. For each residue in $P$, we define a
region with a predefined radius of $r=10\mathring{\text{A}}$. All surface
points falling within this region are then labeled as part of the surface
binding interface.

###  3.2 Interactive Decoder

The decoder network operates by taking surface features as input, allowing
interaction between two proteins, and ultimately predicting a binding
interface.

We assume that input data comprises the receptor $R$ and its corresponding
binding interface $\mathbf{Y}^{\text{res}}_{R}$. The encoder network generates
a surface feature $\mathbf{H}_{R}\in\mathbb{R}^{M_{R}\times d}$.
Simultaneously, we compute the surface-level binding interface
$\mathbf{Y}^{\text{surf}}_{R}\in\\{0,1\\}^{M_{R}\times 1}$. Then, the model
identifies a binding partner $L$ and obtains its own surface feature
$\mathbf{H}_{L}\in\mathbb{R}^{M_{L}\times d}$. The objective is to predict the
binding interface for ligand $L$, expressed as
$p(\hat{\mathbf{Y}}^{\text{res}}_{L}|\mathbf{H}_{R},\mathbf{H}_{L},\mathbf{Y}^{\text{surf}}_{R})\in[0,1]^{N_{L}\times
1}$.

Cross-Attention Before computing the cross-attention, we update the surface
features for receptor and ligand using an equivariant-GNN and MLPs,
$\mathbf{H}_{R}\leftarrow\text{EGNN}(\text{MLP}([\mathbf{H}_{R},\mathbf{Y}^{\text{surf}}_{R}]),x_{R})\in\mathbb{R}^{M_{R}\times
d},\mathbf{H}_{L}\leftarrow\text{EGNN}(\text{MLP}(\mathbf{H}_{L}),x_{L})\in\mathbb{R}^{M_{L}\times
d}$. Here, $\mathbf{H}_{R}$ is updated with information about the binding
interface, providing the model with improved capabilities for locating the
binding interface of the ligand $L$ during cross-attention.

Given the updated receptor features $\mathbf{H}_{R}$ and ligand features
$\mathbf{H}_{L}$, we compute the cross-attention between two protein surface
features, enabling interaction and communication,

where $W_{\text{Q}},W_{\text{K}},W_{\text{V}}\in\mathbb{R}^{d\times d}$ are
learned parameters for the query, key, value in the attention mechanism,
respectively. This facilitates effective interaction and communication between
the receptor and ligand surface features.

Binding Interface Once we obtain the propagated surface features for the
ligand $\mathbf{F}_{L}\in\mathbb{R}^{M_{L}\times d}$, we employ a MLP with
sigmoid function directly on these features, predicting for the binding
interface,
$\hat{\mathbf{Y}}^{\text{surf}}_{L}\leftarrow\sigma(\text{MLP}(\mathbf{F}_{L}))\in[0,1]^{M_{L}\times
1}$. Thus, the prediction of surface-level binding interface for ligand $L$ is
solely conditioned by the surface features of both the receptor and the
ligand, along with the binding interface information of the receptor.

Surface Point to Residue We compute the residue-level binding interface
$\hat{\mathbf{Y}}^{\text{res}}_{L}\in\\{0,1\\}^{N_{L}\times 1}$ from
$\hat{\mathbf{Y}}^{\text{surf}}_{L}$, and embedding
$\hat{\mathbf{F}}_{L}\in\mathbb{R}^{N_{L}\times d}$ from $\mathbf{F}_{L}$. For
each residue $i$ in $L$, we define a region with a fixed radius of
$r=10\mathring{\text{A}}$ and collect a set of surface points within this
region, each with a binding interface $\hat{\mathbf{y}}^{\text{surf}}_{j}$ and
embedding $\mathbf{f}_{j}$. The residue $i$ is considered part of the binding
interface if the majority of surface points in the region are labeled as part
of the binding interface, i.e., $\hat{\mathbf{y}}^{\text{res}}_{i}=1$ if
$\text{Mean}(\sum_{j}\hat{\mathbf{y}}^{\text{surf}}_{j})>0.5$; otherwise
$\hat{\mathbf{y}}^{\text{res}}_{i}=0$. And the residue-level embedding is
obtained using the same logic, where
$\hat{\mathbf{f}}_{i}=\text{Mean}(\sum_{j}{\mathbf{f}}_{j})$.

Training Stage During training, each PPI sample is treated as two training
instances. The model first takes the receptor $R$ and its associated binding
interface $\mathbf{Y}^{\text{surf}}_{R}$ as input, predicting the ligand’s
binding interface; then the model takes the ligand $L$ and its corresponding
binding interface $\mathbf{Y}^{\text{surf}}_{L}$ as input, predicting the
receptor’s binding interface,

$\small\hat{\mathbf{Y}}^{\text{res}}_{L},\hat{\mathbf{F}}_{L}=\text{Dec}(\mathbf{H}_{R},\mathbf{H}_{L},\mathbf{Y}^{\text{surf}}_{R}),\
\hat{\mathbf{Y}}^{\text{res}}_{R},\hat{\mathbf{F}}_{R}=\text{Dec}(\mathbf{H}_{R},\mathbf{H}_{L},\mathbf{Y}^{\text{surf}}_{L}).$

(6)

###  3.3 Overview: PPIretrieval Pipeline

Training Stage During training, PPIretrieval processes a PPI complex with
their corresponding binding interface. The encoder network encodes the two
proteins, resulting in two surface features $\mathbf{H}_{R},\mathbf{H}_{L}$,
respectively. These surface representations, along with information about
their binding partnership, are stored in our database. Then, the decoder
network takes the surface features, $\mathbf{H}_{R},\mathbf{H}_{L}$, along
with the receptor’s binding interface $\mathbf{Y}^{\text{surf}}_{R}$ as input,
and predicts the ligand’s binding interface
$\hat{\mathbf{Y}}^{\text{res}}_{L}$. This process is repeated to predict the
receptor’s binding interface $\hat{\mathbf{Y}}^{\text{res}}_{R}$ vice versa.
PPIretrieval undergoes optimization to utilize the lock-and-key structures of
the PPI complex, following a specific approach discussed in Sec. 4. This
training setup ensures that PPIretrieval learns to predict binding interfaces
for both proteins involved in a PPI complex.

Inference Stage During inference, PPIretrieval takes an unseen query protein
$P$ along with a specified binding interface to the encoder network. It
encodes $P$ into a surface feature $\mathbf{H}_{P}$. Then, PPIretrieval
searches our database to retrieve the most similar surface feature
$\mathbf{H}_{A}$ using a similarity function. Once the match is found, the
surface feature $\mathbf{H}_{B}$ of the binding partner $B$ that binds to $A$
is identified. Then, the decoder network takes the surface features
$\mathbf{H}_{P},\mathbf{H}_{B}$, along with $P$’s given binding interface
$\mathbf{Y}^{\text{surf}}_{P}$, and predicts $B$’s binding interface,
$\hat{\mathbf{Y}}^{\text{res}}_{B}$. This process entails the model making
predictions on how the surface of the binding partner interacts with the
provided protein and its binding interface. Finally, PPIretrieval outputs
protein $B$ along with the predicted binding interface, indicating the most
likely binding scenario with protein $P$ and its given binding interface. A
visual demonstration of this process is illustrated in Fig. 1.

##  4 Training Objective

Consider $\hat{\mathbf{F}}_{R}\in\mathbb{R}^{N_{R}\times
d},\hat{\mathbf{F}}_{L}\in\mathbb{R}^{N_{L}\times d}$ as the propagated
surface features derived from our interactive decoder model for the receptor
and ligand proteins. Additionally, let
$\hat{\mathbf{Y}}^{\text{res}}_{R}\in[0,1]^{N_{R}\times
1},\hat{\mathbf{Y}}^{\text{res}}_{L}\in[0,1]^{N_{L}\times 1}$ denote the
predicted binding interface for the receptor and ligand protein, respectively.
The optimization aims to utilize the lock-and-key structure between the
receptor and ligand in a PPI complex.

###  4.1 Lock-and-Key Optimization

In our model, we assume an entirely rigid protein structure. Within the
protein complex, a lock-and-key structure is established between the rigid
proteins, where their structures exhibit complementary representations
(Morrison et al., 2006). To utilize the structure, we optimize the model to
learn pairwise matching between residue features
$\hat{\mathbf{F}}_{R},\hat{\mathbf{F}}_{L}$, drawing inspiration from shape
correspondences (Jain & Zhang, 2006). This enables each surface point to
identify its lock-and-key counterpart in the opposite protein, leveraging the
information encoded in the surface features. This unique feature empowers
PPIretrieval to effectively assemble two binding sits. Following a similar
approach outlined in (Lu et al., 2023) for assembling fractures in vision-
related tasks, we first compute an affinity matrix between the surface
features of the two proteins.

Affinity Metric Given $\hat{\mathbf{F}}_{R},\hat{\mathbf{F}}_{L}$, we compute
the global affinity matrix $\mathbf{A}\in\mathbb{R}^{N_{R}\times N_{L}}$ and
its corresponding doubly-stochastic matrix
$\hat{\mathbf{X}}\in[0,1]^{N_{R}\times N_{L}}$ as follows,

$\vspace{-0.2cm}\small\mathbf{A}=\exp{(\frac{\hat{\mathbf{F}}_{R}^{T}W\hat{\mathbf{F}}_{L}}{\tau_{\mathbf{A}}})},\
\hat{\mathbf{X}}=\text{sinkhorn}(\mathbf{A}),$ (7)

where $W\in\mathbb{R}^{d\times d}$ consists of learnable affinity weights and
$\tau_{\mathbf{A}}$ denotes the temperature hyperparameter. $\hat{\mathbf{X}}$
is a doubly-stochastic matrix computed by the differentiable sinkhorn layer
(Cuturi, 2013), where $\hat{\mathbf{X}}_{ij}$ measures the soft-matching score
between surface features
$\hat{\mathbf{f}}_{i}\in\hat{\mathbf{F}}_{R},\hat{\mathbf{f}}_{j}\in\hat{\mathbf{F}}_{L}$.

Lock-and-Key We construct a ground-truth matching matrix
$\mathbf{X}\in\\{0,1\\}^{N_{R}\times N_{L}}$ to optimize the soft-matching
score between two proteins as follows,

$\small\mathbf{x}_{ij}=\begin{cases}1,&\text{if }d_{ij}\leq d_{\text{cut}}\\\
0,&\text{otherwise}.\end{cases}$

(8)

Here $\mathbf{x}_{ij}=1$ only if the pairwise Euclidean distance between two
residues $i\in R,j\in L$ is within a cutoff distance
$d_{\text{cut}}=10\mathring{\text{A}}$, implying that they are close enough to
interact; otherwise $\mathbf{x}_{ij}=0$.

To optimize PPIretrieval from the lock-and-key perspective, we enforce the
soft-matching score to closely resemble the ground-truth matching matrix,

$\small\mathcal{L}_{\text{match}}=-\sum_{1<i<N_{R}}\sum_{1<j<N_{L}}\mathbf{x}_{ij}\log\hat{\mathbf{x}}_{ij}+(1-\mathbf{x}_{ij})\log(1-\hat{\mathbf{x}}_{ij}).$

(9)

The matching loss serves the dual purpose of encouraging a close alignment
between the soft-matching scores and the ground truth, as well as providing
global rigidity guidance by ensuring each residue is matched with its
complementary part in the opposite protein. This approach reinforces the lock-
and-key structure within the PPI.

###  4.2 Contrastive Optimization

In addition to the the lock-and-key optimization objective, we aim to bring
the residue features of the binding interface closer while pushing residue
features that do not belong to the binding interface farther apart. To achieve
this, we employ the contrastive loss (Xie et al., 2020) designed for point
clouds. This loss minimizes the distance between the residue features of
corresponding residues and maximizes the distance between non-corresponding
residues as,

$\small\mathcal{L}_{\text{contra}}=-\sum_{i\in S_{R}}\sum_{j\in
S_{L}}\log\frac{\exp(\hat{\mathbf{f}}^{i}_{R}\cdot\hat{\mathbf{f}}^{j}_{L}/\tau_{\text{c}})}{\sum_{k\in
S_{L}}\exp(\hat{\mathbf{f}}^{i}_{R}\cdot\hat{\mathbf{f}}^{k}_{L}/\tau_{\text{c}})}.$

(10)

Here
$S_{R}=(\mathbf{Y}^{\text{res}}_{R}=1),S_{L}=(\mathbf{Y}^{\text{res}}_{L}=1)$
are residues of binding interface for receptor and ligand, and
$\tau_{\text{c}}$ is the temperature hyperparameter. This objective
effectively minimizes the distance between residue features
$\hat{\mathbf{f}}^{i}_{R}\in\hat{\mathbf{F}}_{R},\hat{\mathbf{f}}^{j}_{L}\in\hat{\mathbf{F}}_{L}$
of corresponding binding interfaces, enhancing the proximity of relevant
residue features.

###  4.3 Binding Interface Optimization

In addition to the lock-and-key and contrastive optimization objectives, we
directly optimize the predictions of binding interfaces,
$\hat{\mathbf{Y}}^{\text{res}}_{R},\hat{\mathbf{Y}}^{\text{res}}_{L}$. Given
the ground-truth binding interfaces
${\mathbf{Y}}^{\text{res}}_{R}\in\\{0,1\\}^{N_{R}\times
1},{\mathbf{Y}}^{\text{res}}_{L}\in\\{0,1\\}^{N_{L}\times 1}$, we aim to make
the predictions close to the ground-truth values as,

(11)

This objective ensures that the model makes accurate predictions for the
binding interfaces of both the receptor and ligand proteins by minimizing the
difference between predicted and ground-truth values.

The total loss is the sum of the three loss terms
$\mathcal{L}=\mathcal{L}_{\text{match}}+\mathcal{L}_{\text{contra}}+\mathcal{L}_{\text{bind}}$.
This optimization is designed to leverage the lock-and-key structure inherent
in PPI complexes.

##  5 Retrieval Visualization

We visualize some retrieval results, showing the predictions of PPIretrieval
when provided with an unseen query protein and observing its potential binding
partner within our protein surface database. The database currently comprises
a total of $151,207$ paired proteins with $302,414$ surface representations,
trained and embedded using PPIs from PDB, DIPS, and PPBS training and
validation sets (see Sec. 6).

Figure 2: Visualization of PPIretrieval results for proteins in the PDB test
set, evaluated by dockQ. Proteins colored in blue are input query proteins;
proteins colored in red are binding partners. Left column displays the ground-
truth structures; right column shows the structures predicted by PPIretrieval.

In Fig. 2, we observe that the predicted PPIs, with interface dockQ
similarity, form a well-defined lock-and-key structure. This reliable
structure formation bolsters confidence in the potential of PPIretrieval for
exploring novel protein interactions. One can utilize our model and database
to investigate and learn about unknown protein interactions. Additional
visualizations are available in App. A.

##  6 Experiment

We use the PDB dataset from (Gainza et al., 2020; Sverrisson et al., 2021) and
the DIPS dataset from (Morehead et al., 2023). Also, we clean up PPI data from
the PPBS dataset from (Tubiana et al., 2022). To ensure data quality, we
exclude protein complexes with fewer than $40$ residues in one protein or a
minimum distance between two proteins exceeding $10\mathring{\text{A}}$. The
original PDB dataset comprises $4754$ and $933$ protein complexes for training
and testing, respectively. After excluding low-quality complexes, the PDB
dataset consists of $4420$ and $840$ protein complexes for training and
testing, with 10% of the training set used for validation following
(Sverrisson et al., 2021). The original DIPS dataset includes $33159$ and
$8290$ protein complexes for training and validation, respectively. After
excluding low-quality complexes, the DIPS dataset consists of $33028$ and
$8267$ protein complexes for training and validation, with the first $4267$
complexes of the validation set used for testing. The original PPBS dataset
comprises $101755$, $10221$, and $10911$ protein complexes for training,
validation, and testing, respectively (following homology split in (Tubiana et
al., 2022)). After excluding low-quality complexes, the PPBS dataset consists
of $99799$, $9960$, and $10742$ protein complexes for training, validation,
and testing.

For surface sampling of each protein, we use dMaSIF (Sverrisson et al., 2021)
with sampling resolution $1.0\mathring{\text{A}}$, sampling distance
$2.25\mathring{\text{A}}$, sampling number $20$, and sampling variance
$0.3\mathring{\text{A}}$. Additionally, we use $32$ hidden dims and $0.3$
dropout for all projections, use $2$ propagation layers and $2$ cross-
attention layers. We choose a learning rate of $1e-4$ and use the AdamW
optimizer with a weight decay of $5e-10$. We select the models with the lowest
validation loss $\mathcal{L}$.

Figure 3: Evaluation of PPI binding site during inference. For a PPI in the
test set, a query protein with a known binding site
$\mathbf{Y}_{\text{query}}$ seeks a binding partner with an actual binding
site $\mathbf{Y}_{\text{true}}$. However, we assume that the binding partner
is unknown to us. So, PPIretrieval aims to retrieve a potential binding
partner from the surface databse. PPIretrieval identifies protein $A$ in the
surface database, which has the most similar surface representation to the
query protein. Protein $A$ has a known binding partner $B$ with a reference
binding site $\mathbf{Y}_{B}^{\text{ref}}$ (stored in database), a binding
site $\mathbf{Y}_{B}^{\text{masif}}$ predicted by masif, and a binding site
$\mathbf{Y}_{B}^{\text{dmasif}}$ predicted by dmasif. PPIretrieval takes query
protein and $B$ as input and predicts a new binding site
$\mathbf{Y}_{B}^{\text{pred}}$. We compute
$\textit{dockQ}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{pred}}),\textit{TM}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{pred}}),\textit{rmsd}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{pred}})$,
$\textit{dockQ}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{masif}}),\textit{TM}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{masif}}),\textit{rmsd}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{masif}})$,
$\textit{dockQ}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{dmasif}}),\textit{TM}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{dmasif}}),\textit{rmsd}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{dmasif}})$,
$\textit{dockQ}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{ref}}),\textit{TM}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{ref}}),\textit{rmsd}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{ref}})$
to evaluate and compare the quality of PPI and binding interfaces.
$\mathbf{Y}_{\text{true}}$ denotes the known binding site of the ground-truth
binding partner; $\mathbf{Y}^{\text{ref}}_{B}$ denotes the known binding site
(stored in database) of the retrieved binding partner;
$\mathbf{Y}^{\text{pred}}_{B}$ denotes the predicted binding site of the
retrieved binding partner.

###  6.1 Empirical Evaluation

We empirically assess the quality of PPIs carried out by PPIretrieval during
the inference stage. For PPIs in the test set, we measure the dockQ score
(Basu & Wallner, 2016), TM score (Zhang & Skolnick, 2005), and root-mean-
square-distance (rmsd) to compare PPIretrieval reference binding site, masif-
predicted binding site (Gainza et al., 2020), dmasif-predicted binding site
(Sverrisson et al., 2021), and PPIretrieval predicted binding site with the
ground-truth binding sites. (1) dockQ score measures the quality between a
ground-truth binding site and a predicted binding site, which combines the
fraction of native contacts, the interface root mean square distance, and the
ligand root mean square distance; a higher dockQ score indicates a better
quality of the predicted binding site. (2) TM score measures the similarity
between a ground-truth binding site and a predicted binding site, which
considers both the distance and the alignment of the residues; a higher TM
score indicates higher similarity between the two binding site. (3) rmsd
measures the distance between a ground-truth binding site and a predicted
binding site after superimposition; a lower rmsd indicates higher
superimposition similarity between the two binding site. A comprehensive
visualization and explanation of our metrics to assess quality of PPI binding
sites are demonstrated in Fig. 3.

Inference Result In Tab. 1, we assess the quality of PPIs and binding
interface identified by PPIretrieval with smaller databases. The database for
each test set comprises surface representations from the training set of the
respective dataset. For example, when evaluating the PDB test set, we only
search for surface representations in the PDB training set. Also, the models
are trained on each respective dataset.

Dataset | Metrics | PDB | DIPS | PPBS
---|---|---|---|---
Site Quality | dockQ$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.4073$ | $0.4177$ | $0.5535$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.4220}$ | $\underline{0.4304}$ | $\underline{0.5946}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $0.1334$ | $0.1021$ | $0.1228$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $0.1155$ | $0.0837$ | $0.1036$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | ${0.2134}$ | $0.6617$ | ${0.4622}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.2366}$ | $\underline{0.6649}$ | $\underline{0.4735}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $0.0773$ | $0.0981$ | $0.0911$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $0.0665$ | $0.0831$ | $0.0871$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | ${11.40}$ | $11.33$ | $\underline{8.20}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{10.44}$ | $\underline{6.02}$ | $9.77$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $15.73$ | $19.66$ | $17.32$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $17.87$ | $23.55$ | $19.65$

Table 1: dockQ, TM, and rmsd for evaluation of Top1 hit binding sites
predicted by PPIretrieval in comparison with other binding sites over three
runs. The database for each test set comprises surface representations from
the training and validation sets of each respective dataset.

In Tab. 2, we evaluate the quality of PPIs and binding interface identified by
PPIretrieval with larger database. The database includes surface
representations from the training and validation sets of the PDB, DIPS, and
PPBS datasets, in total of $155,384$ paired proteins with their surface
features for retrieval. And the models are trained on all training PPIs.

Dataset | Metrics | PDB | DIPS | PPBS
---|---|---|---|---
Site Quality | dockQ$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.4250$ | ${0.4367}$ | $0.6014$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.4678}$ | $\underline{0.4410}$ | $\underline{0.6045}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $0.1345$ | $0.1026$ | $0.1249$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $0.1235$ | $0.0998$ | $0.1261$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.3222$ | ${0.6914}$ | $0.6014$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.3300}$ | $\underline{0.6944}$ | $\underline{0.6045}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $0.0833$ | $0.1002$ | $0.1004$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $0.0823$ | $0.0911$ | $0.1144$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $\underline{9.30}$ | $9.65$ | $9.96$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $10.70$ | $\underline{5.67}$ | $\underline{6.52}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $15.56$ | $19.05$ | $16.82$
| $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $16.81$ | $21.22$ | $16.08$

Table 2: dockQ, TM, and rmsd for evaluation of Top1 hit binding sites
predicted by PPIretrieval in comparison with other binding sites over three
runs. The database comprises all surface representations from the training and
validation sets of PDB, DIPS, and PPBS datasets.

By comparing the tabular results, it is evident that the qualities of the
predicted PPIs carried out by PPIretrieval improve with a larger database, as
reflected in higher dockQ and TM scores, as well as lower rmsd. This
improvement suggests that using PPIretrieval could be highly beneficial in
facilitating the discovery of novel PPIs. More experimental results can be
found in App. E

Cross-Dataset Validation In addition, we show the cross-dataset performance in
Tab. 3. We take the model trained on PDB training set only to encode the PPIs
in DIPS and PPBS training and validation sets, respectively. Then we evaluate
the cross-dataset performance on DIPS and PPBS test sets at two different hit
rates, respectively. Top10 hit means that PPIretrieval retrieves the $10$ most
similar surface representations to the query protein in the test set for
inference. Then, PPIretrieval decodes between the query protein and the $10$
potential binding partners associated with these similar proteins. The best
binding partner for the query protein is then selected based on the highest
dockQ score.

Dataset | Metrics | DIPS-Top1 | DIPS-Top10 | PPBS-Top1 | PPBS-Top10
---|---|---|---|---|---
Site Quality | dockQ$(\uparrow)$ |  $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.4030$ | $0.4156$ | $0.5231$ | $0.5611$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.4207}$ | $\underline{0.4435}$ | $\underline{0.5579}$ | $\underline{0.5857}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $0.0515$ | $0.0523$ | $0.0621$ | $0.0633$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $0.0434$ | $0.0515$ | $0.0601$ | $0.0633$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.5330$ | $0.6714$ | $0.4202$ | $0.3725$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.5419}$ | $\underline{0.6792}$ | $\underline{0.4421}$ | $\underline{0.3889}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $0.0499$ | $0.0511$ | $0.0611$ | $0.0620$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $0.0433$ | $0.0491$ | $0.0519$ | $0.0602$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $11.12$ | $\underline{7.35}$ | $\underline{8.92}$ | $\underline{8.91}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{5.84}$ | $10.50$ | $11.76$ | $10.49$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $20.73$ | $19.21$ | $19.81$ | $19.55$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $23.89$ | $22.05$ | $20.66.$ | $20.04$

Table 3: dockQ, TM, and rmsd for evaluation of Top1, Top10 hit binding sites
predicted by PPIretrieval in comparison with other binding sites on cross-
datasets over three runs. The database for each test set comprises surface
representations from the training and validation sets of each respective
dataset.

We observe solid cross-dataset validation results, with improvements in dockQ
scores compared to the baseline results in Table 1. This improvement indicates
that our model and training strategy demonstrate generalizability to unseen
PPI structures. Furthermore, the trained models can be directly employed to
encode new PPIs and conduct inference without the need for retraining. We
provide more comparison in Tab. 12 and visualization in Fig. 9.

Computational Resources Our models are trained on a single Nvidia 48G A40 GPU.
Regarding training time, PPIretrieval takes approximately $0.35$s to train a
protein complex. In terms of inference time, PPIretrieval requires about
$0.11$s for a protein complex.

###  6.2 Ablation Study

In Tab. 4, we present experimental results for PPIretrieval at five different
hit rates, increasing from Top1 to Top100. The models are trained on PDB
training set only.

PDB Dataset | Metrics | Top1 | Top10 | Top20 | Top50 | Top100
---|---|---|---|---|---|---
Site Quality | dockQ$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.4073$ | $0.4362$ | $0.4379$ | $0.4411$ | $0.3507$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.4220}$ | $\underline{0.4375}$ | $\underline{0.4459}$ | $\underline{0.4569}$ | $\pagecolor[rgb]{ .573, .816, .314}\underline{0.4688}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $0.1334$ | $0.1338$ | $0.1355$ | $0.1401$ | $0.1405$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $0.1155$ | $0.1194$ | $0.1212$ | $0.1247$ | $0.1301$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.2134$ | $0.2078$ | $0.2059$ | $0.2059$ | $0.2108$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.2366}$ | $\underline{0.2266}$ | $\underline{0.2241}$ | $\underline{0.2231}$ | $\underline{0.2265}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $0.0773$ | $0.0775$ | $0.0774$ | $0.0758$ | $0.0702$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $0.0665$ | $0.0668$ | $0.0679$ | $0.0698$ | $0.0701$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | ${11.40}$ | $9.74$ | $9.59$ | ${9.50}$ | $9.34$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{10.44}$ | $\underline{9.33}$ | $\underline{8.94}$ | $\underline{8.52}$ | $\pagecolor[rgb]{ .573, .816, .314}\underline{8.16}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $15.98$ | $15.88$ | $15.84$ | $15.76$ | $15.53$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $17.87$ | $17.31$ | $17.03$ | $16.55$ | $16.02$
Cost |  PPIretrieval runtime($\downarrow$) | second/protein | $0.29$ | $0.91$ | $1.97$ | $4.64$ | $9.44$

Table 4: dockQ, TM, and rmsd for evaluation of Top1, Top10, Top20, Top50,
Top100 hit binding sites predicted by PPIretrieval in comparison with other
binding sites in the PDB test set over three runs. The database comprises
surface features from training and validation sets from PDB dataset only.

We observe an improvement in the quality of predicted PPIs, measured by dockQ,
TM scores and rmsd, as the hit rate increases from Top1 to Top100. Notably,
with 100 similar representations, the predicted PPIs exhibit high quality in
terms of the dockQ and TM scores. This suggests potential PPI exploration with
PPIretrieval.

Furthermore, we present experimental results for PPIretrieval at five
different hit rates, increasing from Top1 to Top100, in Tab. 5. The models are
trained on all PDB, DIPS, and PPBS training set, and the database comprises
surface representations from training and validation sets of them.

PDB Dataset | Metrics | Top1 | Top10 | Top20 | Top50 | Top100
---|---|---|---|---|---|---
Site Quality | dockQ$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.4126$ | $0.4331$ | $0.4480$ | $0.4491$ | $0.4490$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.4235}$ | $\underline{0.4402}$ | $\underline{0.4531}$ | $\underline{0.4649}$ | $\pagecolor[rgb]{ .573, .816, .314}\underline{0.4708}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $0.1433$ | $0.1436$ | $0.1455$ | $0.1458$ | $0.1478$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $0.1225$ | $0.1266$ | $0.1301$ | $0.1398$ | $0.1405$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.3944$ | $0.3877$ | $0.3833$ | $0.3554$ | $0.3422$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.4041}$ | $\underline{0.3969}$ | $\underline{0.3863}$ | $\underline{0.3625}$ | $\underline{0.3528}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $0.0787$ | $0.0766$ | $0.0750$ | $0.0721$ | $0.0709$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $0.0536$ | $0.0548$ | $0.0588$ | $0.0582$ | $0.0601$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | ${10.41}$ | $9.73$ | $9.70$ | $9.49$ | $9.32$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{10.04}$ | $\underline{8.97}$ | $\underline{8.66}$ | $\underline{8.20}$ | $\pagecolor[rgb]{ .573, .816, .314}\underline{7.35}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{masif}}_{B}$ | $15.73$ | $15.71$ | $15.54$ | $15.26$ | $15.19$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{dmasif}}_{B}$ | $17.75$ | $17.22$ | $17.02$ | $16.40$ | $16.11$

Table 5: dockQ, TM, and rmsd for evaluation of Top1, Top10, Top20, Top50,
Top100 hit binding sites predicted by PPIretrieval in comparison with other
binding sites in the PDB test set over three runs. The database comprises
surface features from training and validation sets from PDB, DIPS, and PPBS
dataset.

We observe improved predicted interface quality in terms of dockQ, TM scores,
and rmsd, with larger surface database. The robust experimental results
suggest that PPIretrieval has the potential to facilitate and expedite the
discovery of novel PPIs, identifying candidates with higher dockQ scores.
However, it is important to note that the computational time has also
increased significantly. As a retrieval model, there exists a trade-off
between performance and efficiency, and this trade-off becomes evident with
higher hit rates. More ablation studies can be found in App. E

###  6.3 Case Study

We explore the practical application of PPIretrieval in facilitating the
discovery of novel PPIs. In real-world scenarios, a protein can have a binding
site that interacts with multiple partners. While some of these binding
partners may be unknown, others might already be known and stored in our
database. PPIretrieval can be effectively used to identify these binding
partners by finding similar surface representations within the database. A
case study demonstrating this application is visualized in Fig. 4.

In our case study, the query protein has two binding partners: one is already
stored in our surface database (pdb id: 5J28), while the other is not (pdb id:
1DGC). It is important to note that, although the query protein in the two
ground-truth structures shares the same sequence representation, there are
slight differences in their geometric configuration.

Figure 4:  Case study using PPIretrieval. The query protein, highlighted in
blue, successfully identifies a binding partner within our surface database
using PPIsearch.

Given the query protein, PPIretrieval identifies the protein in the database
that most closely matches in both sequential and geometric representation.
Thus, it successfully predicts the corresponding binding partner for this
query protein.

##  7 Future Work

Improving Model Size and Training A potential work is to train a larger model
with increased parameters to better approximate the protein surface manifold.
Also, we can explore larger models with more hidden dimensions and
incorporating more propagation and cross-attention layers.

Dataset Development We aim to continuously integrate more high-quality PPI
data into the collection of protein complex surface representations. As
demonstrated in Tab. 3, PPIretrieval exhibits the ability to generalize to
unseen proteins. Therefore, future efforts involve training our existing
PPIretrieval model on new PPI data, enabling direct encoding and storage of
these data in our existing database.

## Impact Statements

PPIretrieval presents work whose goal is to advance the field of AI in drug
discovery by designing and finding protein binders, which can potentially
improve our understanding of protein complex interactions. We encourage the
exploration of novel PPIs findings using PPIretrieval, as it offers
significant potential and high impact in this field.

Our goal is to establish a webserver for PPIretrieval, following the service
of Foldseek (van Kempen et al., 2023). As a retrieval model, our objective is
to offer a convenient service for individuals interested in exploring novel
PPIs using PPIretrieval.

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##  Appendix A Protein-Protein Interaction Visualization

We visualize additional predicted PPIs carried out by PPIretrieval.

Figure 5: Visualization of PPIretrieval results for proteins in the PDB test
set, evaluated by dockQ. Proteins colored in blue are input query proteins;
proteins colored in red are binding partners. Left column displays the ground-
truth structures; right column shows the structures predicted by PPIretrieval.

In Fig. 5, we observe that the predicted PPIs, with interface dockQ
similarity, form a well-defined lock-and-key structure. This reliable
structure formation bolsters confidence in the potential of PPIretrieval for
exploring novel protein interactions. One can utilize our model and database
to investigate and learn about unknown protein interactions.

##  Appendix B Additional Experiments on Empirical Evaluation

In additional to
$\textit{dockQ}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{pred}}),\textit{TM}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{pred}}),\textit{rmsd}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{pred}})$,
$\textit{dockQ}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{ref}}),\textit{TM}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{ref}}),\textit{rmsd}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{ref}})$,
$\textit{dockQ}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{masif}}),\textit{TM}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{masif}}),\textit{rmsd}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{masif}})$
used in Sec 6, we evaluate
$\textit{dockQ}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}),\textit{TM}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}),\textit{rmsd}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}})$,
$\textit{dockQ}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{B}^{\text{ref}}),\textit{TM}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{B}^{\text{ref}}),\textit{rmsd}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{B}^{\text{ref}})$,
$\textit{dockQ}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{B}^{\text{pred}}),\textit{TM}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{B}^{\text{pred}}),\textit{rmsd}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{B}^{\text{pred}})$as
demonstrated in Fig. 6

Figure 6: Evaluation of PPI quality during inference. For a PPI in the test
set, a query protein with a known binding site $\mathbf{Y}_{\text{query}}$
seeks a binding partner with an actual binding site
$\mathbf{Y}_{\text{true}}$. We compute
$\textit{dockQ}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}),\textit{TM}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}),\textit{rmsd}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}})$
to measure quality of the ground-truth PPI. However, the binding partner is
unknown to the PPIretrieval surface database. So, PPIretrieval aims to find a
potential binding partner from the surface databse. PPIretrieval identifies
protein $A$ in the surface database, which has the most similar surface
representation to the query protein. Protein $A$ has a known binding partner
$B$ with a binding site $\mathbf{Y}_{B}^{\text{ref}}$. We compute
$\textit{dockQ}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{B}^{\text{ref}}),\textit{TM}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{B}^{\text{ref}}),\textit{rmsd}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{B}^{\text{ref}})$
to assess quality of the PPI, and
$\textit{TM}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{ref}}),\textit{rmsd}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{ref}})$
to evaluate quality of the binding sites. PPIretrieval takes query protein and
$B$ as input and predicts a new binding site $\mathbf{Y}_{B}^{\text{pred}}$.
We compute
$\textit{dockQ}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{B}^{\text{pred}}),\textit{TM}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{B}^{\text{pred}}),\textit{rmsd}(\mathbf{Y}_{\text{query}},\mathbf{Y}_{B}^{\text{pred}})$
to assess quality of the PPI,
$\textit{dockQ}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{pred}}),\textit{TM}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{pred}}),\textit{rmsd}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{pred}})$,
$\textit{dockQ}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{ref}}),\textit{TM}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{ref}}),\textit{rmsd}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{ref}})$,
$\textit{dockQ}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{masif}}),\textit{TM}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{masif}}),\textit{rmsd}(\mathbf{Y}_{\text{true}},\mathbf{Y}_{B}^{\text{masif}})$
to evaluate and compare quality of the binding sites.

In Tab. 6, we assess the quality of PPIs and binding sites identified by
PPIretrieval with smaller databases. The database for each test set comprises
surface representations from the training set of the respective dataset. For
example, when evaluating the PDB test set, we only search for surface
representations in the PDB training set. Also, the models are trained on each
respective dataset.

Dataset | Metrics | PDB | DIPS | PPBS
---|---|---|---|---
PPI Quality | dockQ$(\uparrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $0.4596$ | $0.4797$ | $0.4949$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.4039}$ | $\underline{0.4042}$ | $\underline{0.4092}$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.3907$ | $0.3935$ | $0.4040$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $0.4552$ | $0.5909$ | $0.5767$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.2196}$ | ${0.4211}$ | $\underline{0.3167}$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.1950$ | $\underline{0.4346}$ | ${0.3105}$
| $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $7.38$ | $6.70$ | $6.70$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $11.60$ | $\underline{8.99}$ | $11.07$
| $\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $\underline{10.80}$ | $10.34$ | $\underline{10.27}$
Site Quality | dockQ$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.4220}$ | $\underline{0.4304}$ | $\underline{0.5946}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.4073$ | $0.4177$ | $0.5535$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.2366}$ | $\underline{0.6649}$ | $\underline{0.4735}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | ${0.2134}$ | $0.6617$ | ${0.4622}$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{10.44}$ | $\underline{6.02}$ | $9.77$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | ${11.40}$ | $11.33$ | $\underline{8.20}$

Table 6: dockQ, TM, and rmsd for evaluation of PPIs and binding sites of Top1
hit predicted by PPIretrieval in comparison with ground-truth structures over
three runs. The database for each test set comprises surface representations
from the training and validation sets of each respective dataset.

Dataset | Metrics | PDB | DIPS | PPBS
---|---|---|---|---
PPI Quality | dockQ$(\uparrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $0.4596$ | $0.4797$ | $0.4949$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.4110}$ | $\underline{0.4394}$ | $\underline{0.4400}$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.4061$ | $0.4093$ | $0.4130$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $0.4552$ | $0.5909$ | $0.5767$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.2649}$ | $\underline{0.4507}$ | $\underline{0.4148}$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | ${0.2507}$ | $0.4394$ | $0.4009$
| $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $7.38$ | $6.70$ | $6.70$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $10.78$ | $\underline{8.84}$ | $\underline{9.11}$
| $\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $\underline{9.88}$ | $10.09$ | $11.01$
Site Quality | dockQ$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.4678}$ | $\underline{0.4410}$ | $\underline{0.6045}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.4250$ | ${0.4367}$ | $0.6014$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.3300}$ | $\underline{0.6944}$ | $\underline{0.6045}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.3222$ | ${0.6914}$ | $0.6014$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $10.70$ | $\underline{5.67}$ | $\underline{6.52}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $\underline{9.30}$ | $9.65$ | $9.96$

Table 7: dockQ, TM, and rmsd for evaluation of PPIs and binding sites of Top1
hit predicted by PPIretrieval in comparison with ground-truth structures over
three runs. The database comprises all surface representations from the
training and validation sets of PDB, DIPS, and PPBS datasets.

Dataset | Metrics | DIPS-Top1 | DIPS-Top10 | PPBS-Top1 | PPBS-Top10
---|---|---|---|---|---
PPI Quality | dockQ$(\uparrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $0.4797$ | $0.4797$ | $0.4949$ | $0.4949$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.4334}$ | $\pagecolor[rgb]{ .573, .816, .314}\underline{0.4432}$ | $\underline{0.4098}$ | $\pagecolor[rgb]{ .573, .816, .314}\underline{0.4447}$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.4054$ | $0.4316$ | $0.4040$ | $0.4051$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $0.5909$ | $0.5909$ | $0.5767$ | $0.5767$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.3965}$ | $\pagecolor[rgb]{ .573, .816, .314}\underline{0.4691}$ | $\pagecolor[rgb]{ .573, .816, .314}\underline{0.3219}$ | $\underline{0.3021}$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.3708$ | $0.4357$ | $0.2903$ | $0.2780$
| $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $6.70$ | $6.70$ | $6.70$ | $6.70$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{8.71}$ | $10.49$ | $12.09$ | $10.25$
| $\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $11.68$ | $\underline{9.26}$ | $\underline{10.71}$ | $\underline{10.13}$
Site Quality | dockQ$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.4207}$ | $\underline{0.4435}$ | $\underline{0.5579}$ | $\underline{0.5857}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.4030$ | $0.4156$ | $0.5231$ | $0.5611$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.5419}$ | $\underline{0.6792}$ | $\underline{0.4421}$ | $\underline{0.3889}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.5330$ | $0.6714$ | $0.4202$ | $0.3725$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{5.84}$ | $10.50$ | $11.76$ | $10.49$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $11.12$ | $\underline{7.35}$ | $\underline{8.92}$ | $\underline{8.91}$

Table 8: dockQ, TM, and rmsd for evaluation of PPIs and binding sites of Top1,
Top10 hit predicted by PPIretrieval in comparison with ground-truth structures
on cross-datasets over three runs. The database for each test set comprises
surface representations from the training and validation sets of each
respective dataset. Figure 7: Comparison of PPI qualities in the test set of
PDB dataset, considering ground-truth, predicted, and reference PPIs,
evaluated using the dockQ score at Top1, Top10, Top50, Top100 hit. The
database comprises surface representations from training and validation sets
from PDB dataset only.

In Tab. 7, we evaluate the quality of PPIs and binding sites identified by
PPIretrieval with larger database. The database includes surface
representations from the training and validation sets of the PDB, DIPS, and
PPBS datasets, in total of $155,384$ paired proteins with their surface
features for retrieval. And the models are trained on all training PPIs.

In Tab. 8, we show the cross-dataset performance. We take the model trained on
PDB training set only to encode the PPIs in DIPS and PPBS training and
validation sets, respectively. Then we evaluate the cross-dataset performance
on DIPS and PPBS test sets at two different hit rates, respectively. Top10 hit
means that we identify the $10$ most similar surface representations to the
query protein in the test set for inference. Then, PPIretrieval decodes
between the query protein and the $10$ potential binding partners associated
with these similar proteins. The best binding partner for the query protein is
then selected based on the highest dockQ score.

Additionally, we show the quality distribution of PPIs predicted by
PPIretrieval in comparison with ground-truth and reference at different hit
rates in Fig 7. For dockQ score (Basu & Wallner, 2016), a score in the range
(0, 0.23) denotes incorrect interaction, [0.23, 0.49) denotes acceptable
interaction, [0.49, 0.8) denotes medium interaction, and [0.8, 1) denotes good
interaction. In Fig 7, we divide these ranges into sub-ranges for better
visualization of the quality distribution, (0, 0.23)$\rightarrow$(0,
0.1)$\cup$[0.1, 0.23), [0.23, 0.49)$\rightarrow$[0.23, 0.31)$\cup$[0.31,
0.4)$\cup$[0.4, 0.49), [0.49, 0.8)$\rightarrow$[0.49, 0.57)$\cup$[0.57,
0.65)$\cup$[0.65, 0.73)$\cup$[0.65, 0.73)$\cup$[0.65, 0.8),[0.8,
1)$\rightarrow$[0.8, 0.9)$\cup$[0.9, 1).

We observe that more predicted PPIs fall into the medium-quality category as
hit rates increase from Top1 to Top100, surpassing the number of ground-truth
PPIs of acceptable and medium qualities. This consistent quality distribution
of PPIs predicted by PPIretrieval indicates a strong potential for novel PPI
findings. Furthermore, we compare the results of using cosine similarity in
Tab. 11 and Fig. 8.

##  Appendix C Additional Experiments on Euclidean Distance vs. Cosine
Similarity

We show additional results and visualize more quality distributions carried
out by PPIretrieval using Euclidean distance and cosine similarity in this
section.

In Sec. 3.3 and Fig. 1, we present the PPIretrieval inference strategy to find
a binding partner for a query protein. We identify a similar surface
representation to the query protein in the PPIretrieval database using the
Euclidean distance function for the surface embeddings,

$d(\mathbf{H}_{P},\mathbf{H}_{A})=\sqrt{\sum_{i=1}^{d}\left(\frac{1}{N}\sum_{j=1}^{N}\mathbf{H}_{P}^{j,i}-\frac{1}{M}\sum_{k=1}^{M}\mathbf{H}_{A}^{k,i}\right)^{2}}\in\mathbb{R}.$
(12)

Here, $\mathbf{H}_{P}\in\mathbb{R}^{N\times d}$ represents the surface
embedding of the query protein, and $\mathbf{H}_{A}\in\mathbb{R}^{M\times d}$
represents the surface embedding of a protein in our PPIretrieval database. In
addition to the Euclidean distance, we can use cosine similarity to find the
surface representation that is the most similar to the query protein.

In Tab. 11, we present experimental results for PPIretrieval using Euclidean
Distance and Cosine Similarity at five different hit rates, ranging from Top1
to Top100. The models are exclusively trained on the PDB training set. Our
observations reveal an improvement in the quality of predicted PPIs, as
measured by the dockQ score and rmsd, when employing Cosine Similarity to find
similar surface representations compared to using Euclidean Distance for the
same purpose in the PPIretrieval database. During the inference stage, we
leverage Cosine Similarity as an alternative method for retrieving similar
surface representations for the query protein, in contrast to the original
approach using Euclidean distance.

PDB Dataset | Metrics | Top1 | Top10 | Top20 | Top50 | Top100
---|---|---|---|---|---|---
PPI Quality | dockQ$(\uparrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $0.4596$ | $0.4596$ | $0.4596$ | $0.4596$ | $0.4596$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.4039}$ | $\underline{0.4352}$ | $\underline{0.4428}$ | $\underline{0.4532}$ | $\underline{0.4614}$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.3907$ | $0.3920$ | $0.3943$ | $0.3963$ | $0.3968$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $0.4552$ | $0.4552$ | $0.4552$ | $0.4552$ | $0.4552$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.2196}$ | $\underline{0.2183}$ | $\underline{0.0.2174}$ | $\underline{0.2168}$ | $\underline{0.2159}$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.1950$ | $0.1938$ | $0.1944$ | $0.1950$ | $0.1958$
| $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $7.38$ | $7.38$ | $7.38$ | $7.38$ | $7.38$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $11.60$ | $\underline{9.52}$ | $\underline{9.17}$ | $\underline{8.73}$ | $\underline{8.42}$
| $\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $\underline{10.80}$ | $9.77$ | $9.65$ | $9.65$ | $9.56$
Site Quality | TM$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.2366}$ | $\underline{0.2195}$ | $\underline{0.2174}$ | $\underline{0.2154}$ | $\underline{0.2156}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.2134$ | $0.1986$ | $0.1960$ | $0.1955$ | $0.1957$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $11.52$ | $10.01$ | $9.84$ | $9.62$ | $\pagecolor[rgb]{ .573, .816, .314}\underline{9.42}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $\underline{10.50}$ | $\underline{9.69}$ | $\underline{9.62}$ | $\underline{9.53}$ | $9.47$

Table 9: Retrieval Using Euclidean Distance

PDB Dataset | Metrics | Top1 | Top10 | Top20 | Top50 | Top100
---|---|---|---|---|---|---
PPI Quality | dockQ$(\uparrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $0.4596$ | $0.4596$ | $0.4596$ | $0.4596$ | $0.4596$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.3907}$ | $\underline{0.4381}$ | $\underline{0.4472}$ | $\underline{0.4601}$ | $\underline{0.4683}$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.3147$ | $0.3319$ | $0.3388$ | $0.3407$ | $0.3422$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $0.4552$ | $0.4552$ | $0.4552$ | $0.4552$ | $0.4552$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.2009}$ | $\underline{0.2101}$ | $\underline{0.2085}$ | $\underline{0.2089}$ | $\underline{0.2095}$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.1838$ | $0.1857$ | $0.1861$ | $0.1934$ | $0.1941$
| $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $7.38$ | $7.38$ | $7.38$ | $7.38$ | $7.38$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $11.08$ | $\underline{9.15}$ | $\underline{8.86}$ | $\underline{8.39}$ | $\underline{7.99}$
| $\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $\underline{11.01}$ | $9.91$ | $9.81$ | $9.92$ | $9.79$
Site Quality | TM$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $\underline{0.1981}$ | $\underline{0.2084}$ | $\underline{0.2082}$ | $\underline{0.2049}$ | $\underline{0.2055}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.1818$ | $0.1832$ | $0.1860$ | $0.1923$ | $0.1919$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $11.05$ | $9.56$ | $9.42$ | $9.13$ | $\pagecolor[rgb]{ .573, .9, .314}\underline{9.09}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $\underline{10.90}$ | $\underline{9.93}$ | $\underline{9.83}$ | $\underline{9.80}$ | $9.87$

Table 10: Retrieval Using Consine Similarity

Table 11: dockQ, TM, and rmsd for evaluation of PPIs and binding sites of
Top1, Top10, Top20, Top50, Top100 hit predicted by PPIretrieval in comparison
with ground-truth structures on PDB dataset over three runs. The database
comprises surface representations from training and validation sets from PDB
dataset only.

(a) Retrieval Using Euclidean Distance (b) Retrieval Using Cosine Similarity

Figure 8: Comparison of PPI qualities in the test set of PDB dataset,
considering ground-truth, predicted, and reference PPIs, evaluated using the
dockQ score at Top1, Top10, Top50, Top100 hit. The database comprises surface
representations from training and validation sets from PDB dataset only.

In addition to the tabular results in Tab. 11, we visualize the quality
distribution of predicted PPIs by PPIretrieval using Euclidean Distance and
Cosine Similarity in Fig. 8. Our observations reveal that, as hit rates
increase from Top1 to Top100, more predicted PPIs fall into the medium-quality
category when using cosine similarity to retrieve surface representations
similar to the query protein. This trend exceeds the number of ground-truth
PPIs of acceptable and medium qualities. The consistent quality distribution
of predicted PPIs by PPIretrieval suggests a robust potential for novel PPI
exploration with PPIretrieval. Additionally, we provide Cosine Similarity as
an alternative choice to the Euclidean distance in our approach.

##  Appendix D Additional Experiments on Cross-Dataset Validation

We show additional results and visualize more quality distributions carried
out by PPIretrieval on the cross-dataset validation. Following the cross-
dataset validation results in Tab. 3, we provide a thorough experimental
analysis and visualization here.

In Table 12, we present the cross-dataset validation results for Top1 and
Top10 hits on the PPBS test set. We utilize two models for this analysis: one
is trained on the PPBS training set and validated on the PPBS test set, and
the other is trained on the PDB training set and cross-validated on the PPBS
test set. With Top1 hit, we find that PPIretrieval is capable of generalizing
to unseen protein complexes, as evidenced by the second model exhibiting
better PPI quality compared to the first model in terms of dockQ and TM
scores. When we expand our retrieval space to Top10 hit, the first model
(trained on the PPBS training set) predicts PPIs with improved quality.

Dataset | Metrics | PPBS-Top1 | PPBS-Top1 (PDB Cross-Dataset) | PPBS-Top10 | PPBS-Top10 (PDB Cross-Dataset)
---|---|---|---|---|---
PPI Quality | dockQ$(\uparrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $0.4949$ | $0.4949$ | $0.4949$ | $0.4949$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | ${0.4092}$ | $\underline{0.4098}$ | $\pagecolor[rgb]{ .573, .816, .314}\underline{0.4513}$ | $0.4447$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.4040$ | $0.4040$ | $0.4345$ | $0.4051$
TM$(\uparrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $0.5767$ | $0.5767$ | $0.5767$ | $0.5767$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | ${0.3167}$ | $\underline{0.3219}$ | $\pagecolor[rgb]{ .573, .816, .314}\underline{0.3245}$ | ${0.3021}$
$\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.3105$ | $0.2903$ | $0.3219$ | $0.2780$
| $\mathbf{Y}_{\text{query}},\mathbf{Y}_{\text{true}}$ | $6.70$ | $6.70$ | $6.70$ | $6.70$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{pred}}_{B}$ | $11.07$ | $12.09$ | $9.46$ | $10.25$
| $\mathbf{Y}_{\text{query}},\mathbf{Y}^{\text{ref}}_{B}$ | $10.27$ | $10.71$ | $9.53$ | ${10.13}$
Site Quality | TM$(\uparrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | ${0.4652}$ | $0.4421$ | ${0.4323}$ | ${0.3889}$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $0.4747$ | $0.4202$ | $0.4396$ | $0.3725$
rmsd$(\downarrow)$ | $\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{pred}}_{B}$ | $9.77$ | $11.76$ | $8.95$ | $10.49$
$\mathbf{Y}_{\text{true}},\mathbf{Y}^{\text{ref}}_{B}$ | $8.20$ | $8.92$ | $8.15$ | ${8.91}$

Table 12: dockQ, TM, and rmsd for evaluation of PPIs and binding sites of
Top1, Top10 hit predicted by PPIretrieval in comparison with ground-truth
structures on cross-datasets over three runs. The database for each test set
comprises surface representations from the training and validation sets of
each respective dataset.

(a) PDB Model Cross-Validated on PPBS Test Set (b) PPBS Model Validated on
PPBS Test Set

Figure 9: Comparison of PPI qualities in the test set of PPBS dataset,
considering ground-truth, predicted, and reference PPIs, evaluated using the
dockQ score at Top1, Top10 hit. (a) presents results from the model trained on
the PDB training set and cross-validated on the PPBS test set. (b) presents
results from the model trained on the PPBS training set and validated on the
PPBS test set.

In addition to the results presented in Table 12, we also provide a
visualization of the quality distribution of predicted PPIs by PPIretrieval
for the cross-dataset validation in Fig. 9. Fig. 9(a) displays the results of
the model trained on the PDB training set and then cross-validated on the PPBS
test set, while Fig. 9(b) shows the results of the model trained on the PPBS
training set and then validated on the PPBS test set. With Top1 hit, it is
noticeable that both models predict PPIs of approximately the same quality, as
evidenced by comparing the quality distributions. This visual representation
demonstrates that PPIretrieval possesses the capability to generalize to
unseen protein complexes and accurately predict their interactions.

##  Appendix E Additional Experiments on Binding Interface Prediction

We show additional results on the binding interface prediction task.

We evaluate the models on PDB and PPBS datasets (details reported in Sec. 6).
For baseline comparisons, we train MaSIF-search (Gainza et al., 2020) and
dMaSIF-search222The MaSIF and dMaSIF models were originally designed without
prediction capabilities for binding interfaces of protein complexes. We have
modified their architectures to enable the models to make predictions for
binding interfaces. (Sverrisson et al., 2021) to predict the binding
interfaces of receptor and ligand proteins in a complex. The comparisons are
summarized and highlighted in Tab. 13. MaSIF (Gainza et al., 2020) and dMaSIF
(Sverrisson et al., 2021) offer model variants, namely MaSIF-search and
dMaSIF-search, for predicting interactions between protein complexes. To
enable these models to make predictions for the binding interfaces of protein
complexes, we extract their final embeddings, denoted as
$\mathbf{F}_{R}\in\mathbb{R}^{M_{R}\times d}$ and
$\mathbf{F}_{L}\in\mathbb{R}^{M_{L}\times d}$, just before the output layer.
Employing the strategy outlined in Sec. 3.2 to predict the surface-level
binding interface, we employ a MLP with sigmoid function directly on these
embeddings, resulting in
$\hat{\mathbf{Y}}^{\text{surf}}_{R}\leftarrow\sigma(\text{MLP}(\mathbf{F}_{R}))\in[0,1]^{M_{R}\times
1},\hat{\mathbf{Y}}^{\text{surf}}_{L}\leftarrow\sigma(\text{MLP}(\mathbf{F}_{L}))\in[0,1]^{M_{L}\times
1}$. We then compute the residue-level binding interfaces, denoted as
$\hat{\mathbf{Y}}^{\text{res}}_{R}\in\\{0,1\\}^{N_{R}\times
1},\hat{\mathbf{Y}}^{\text{res}}_{L}\in\\{0,1\\}^{N_{L}\times 1}$ from
$\hat{\mathbf{Y}}^{\text{surf}}_{R},\hat{\mathbf{Y}}^{\text{surf}}_{L}$,
respectively. For each residue $i$ in $R$, we define a region with a fixed
radius of $r=10\mathring{\text{A}}$ and collect a set of surface points within
this region, each with a binding interface
$\hat{\mathbf{y}}^{\text{surf}}_{j}$ and embedding $\mathbf{f}_{j}$. The
residue $i$ is considered part of the binding interface if the majority of
surface points in the region are labeled as part of the binding interface,
i.e., $\hat{\mathbf{y}}^{\text{res}}_{i}=1$ if
$\text{Mean}(\sum_{j}\hat{\mathbf{y}}^{\text{surf}}_{j})>0.5$; otherwise
$\hat{\mathbf{y}}^{\text{res}}_{i}=0$. The residue-level binding interface
$\hat{\mathbf{Y}}^{\text{res}}_{L}$ for $L$ is computed by the same method. In
terms of training strategy, these baseline models are directly optimized
through the binding interface optimization in Sec. 4.3.

Dataset | PDB | PPBS
---|---|---
Model | Acc$(\uparrow)$ | ROC$(\uparrow)$ | Acc$(\uparrow)$ | ROC$(\uparrow)$
MaSIF-search | $22.93$ | $20.10$ | $20.45$ | $19.79$
dMaSIF-search | $20.86$ | $20.74$ | $22.35$ | $21.08$
PPIretrieval | $\mathbf{92.76}$ | $\mathbf{92.61}$ | $\mathbf{93.55}$ | $\mathbf{94.98}$

Table 13: Accuracy and ROC of PPIretrieval in comparison with MaSIF-search and
dMaSIF-search on datasets over 5 runs.

In Table 13, we observe that PPIretrieval surpasses MaSIF-search and dMaSIF-
search, achieving improvements of $69.83\%,71.90\%$ in accuracy, and
$72.51\%,71.87\%$ in ROC on the PDB dataset. Additionally, PPIretrieval
outperforms MaSIF-search and dMaSIF-search by $73.10\%,71.20\%$ in accuracy,
and $75.19\%,73.90\%$ in ROC on the PPBS dataset.

#### Abalation Study

In Tab. 14, we conduct an ablation study to examine the effectiveness of our
training objectives for the PPIretrieval model, which includes the lock-and-
key goal $\mathcal{L}_{\text{match}}$, the contrastive goal
$\mathcal{L}_{\text{contra}}$, and the binding interface goal
$\mathcal{L}_{\text{bind}}$.

Dataset | $\mathcal{L}_{\text{match}}$ | $\mathcal{L}_{\text{contra}}$ | $\mathcal{L}_{\text{bind}}$ | Acc$(\uparrow)$ | ROC$(\uparrow)$
---|---|---|---|---|---
PDB |  |  | $\checkmark$ | $91.10$ | $90.88$
PDB |  | $\checkmark$ | $\checkmark$ | $92.11$ | $91.13$
PDB | $\checkmark$ |  | $\checkmark$ | $90.86$ | $91.95$
PDB | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\mathbf{92.76}$ | $\mathbf{92.61}$

Table 14: Ablation study of PPIretrieval optimization. A checkmark
$(\checkmark)$ indicates that an objective is used to optimize the model.

We observe that, overall, PPIretrieval performs better in terms of both
accuracy and ROC when all three optimization objectives are combined. This
suggests that PPIretrieval successfully learns the lock-and-key structure
between the receptor and ligand in a protein complex under our training
strategy.

In Fig. 10, we visualize protein surface sampling with different dMaSIF
parameters.

Figure 10: Visualization of dMaSIF parameters for surface sampling. The
bracket includes (Resolution, Distance, #Sample, Variance).

We can observe that lower sampling resolution, higher sampling distance, and a
greater number of sampling points contribute to a more accurate approximation
of the protein surface manifold. However, due to limited computational
resources, we can only perform sampling and training shown in Fig. 10(c).
Training PPIretrieval on more precise surface sampling with more computing
resources is a potential direction for exploration.

In Tab. 15, we present the performance of PPIretrieval with different dMaSIF
sampling parameters.

Dataset | Resolution | Distance | #Sample | Variance | #Surf Point | Acc$(\uparrow)$ | ROC$(\uparrow)$
---|---|---|---|---|---|---|---
PDB | 1.00 | 2.25 | 8 | 0.30 | 2175 | $90.16$ | $90.96$
PDB | 1.00 | 2.25 | 12 | 0.30 | 2425 | $91.44$ | $90.99$
PDB | 1.00 | 2.85 | 20 | 0.30 | 2632 | $92.03$ | $91.55$
PDB | 1.00 | 2.25 | 20 | 0.30 | 2680 | $92.76$ | $92.61$

Table 15: Ablation study of dMaSIF parameters for PPIretrieval. #Surf Point
denotes the average number of surface points of a protein sampled by dMaSIF
across the training set.

PPIretrieval exhibits improved accuracy and ROC on PDB, with more precise
protein surface sampling. Once again, these results motivate further
exploration for future enhancements.

#### Computational Resources

Our models are trained on a single Nvidia 48G A40 GPU. Regarding training
time, dMaSIF-search takes approximately $0.29$s to train a protein complex,
while PPIretrieval takes around $0.35$s for the same task. In terms of
inference time, dMaSIF-search requires about $0.10$s for a protein complex,
while PPIretrieval takes approximately $0.11$s.