arXiv DOI Advance Access Publication Date: August 28, 2024 Review

Rogers et al.

[$\ast$]Corresponding author<EMAIL_ADDRESS><EMAIL_ADDRESS>
# Growing ecosystem of deep learning methods for modeling protein–protein
interactions

Julia R. Rogers0000-0003-3269-6375  Gergő Nikolényi0000-0003-0581-7864
Mohammed AlQuraishi0000-0001-6817-1322  Department of Systems Biology,
Columbia University, New York, New York, USA, 10032

(2023; 2023)

###### Abstract

Numerous cellular functions rely on protein–protein interactions. Efforts to
comprehensively characterize them remain challenged however by the diversity
of molecular recognition mechanisms employed within the proteome. Deep
learning has emerged as a promising approach for tackling this problem by
exploiting both experimental data and basic biophysical knowledge about
protein interactions. Here, we review the growing ecosystem of deep learning
methods for modeling protein interactions, highlighting the diversity of these
biophysically-informed models and their respective trade-offs. We discuss
recent successes in using representation learning to capture complex features
pertinent to predicting protein interactions and interaction sites, geometric
deep learning to reason over protein structures and predict complex
structures, and generative modeling to design de novo protein assemblies. We
also outline some of the outstanding challenges and promising new directions.
Opportunities abound to discover novel interactions, elucidate their physical
mechanisms, and engineer binders to modulate their functions using deep
learning and, ultimately, unravel how protein interactions orchestrate complex
cellular behaviors.

###### keywords:

protein–protein interactions, deep learning, protein complex structure
prediction, binder design, representation learning

##  1 Introduction

Protein–protein interactions underpin numerous molecular processes that are
essential to cellular functions ranging from metabolism and growth to motility
and development. For example, the enzyme responsible for producing chemical
energy assembles from two multisubunit protein motors (Guo et al., 2019);
nearly one thousand protein subunits form nuclear pore complexes to regulate
traffic of genetic messages into the cytoplasm (Mosalaganti et al., 2021); and
networks of actin filaments provide a structural and mechanical support system
that enables cellular motion (Reynolds et al., 2022). A comprehensive
understanding of protein interactomes thus promises fundamental insights into
cellular behavior. Such knowledge is key to ultimately deciphering how
aberrant protein interactions manifest in disease (Cheng et al., 2021) and
engineering protein interaction modulators for therapeutic applications (Lu et
al., 2020).

Protein interactions coordinate such a wide array of cellular processes by
utilizing an equally varied set of molecular recognition mechanisms. For
example, very strong—effectively permanent with negligible probability of
being unbound—obligate interactions ensure the stability of essential,
multisubunit enzymes, whereas weak, transient interactions involving
regulatory or signaling proteins allow for rapid responses to environmental
stimuli (Acuner Ozbabacan et al., 2011; Kastritis and Bonvin, 2013). These two
examples sit at extremes of a continuous spectrum of direct, physical
interactions (Peng et al., 2017; Mosca et al., 2013) with varied affinities,
interfacial sizes, and structural properties (Fig. 1A).

Figure 1: Diversity of protein interactions. (A) Direct, physical interactions
involve a protein and peptide (typically defined by lengths of less than 25
residues) or a pair of proteins. Interaction affinity, as quantified by
dissociation constant ($K_{\rm D}$), distinguish weak, transient interactions
with $K_{\rm D}\geq\mu$M from strong, permanent interactions with $K_{\rm
D}\ll\mu{\rm M}$. Interaction surface areas are smallest for protein–peptide
interactions and range from $500-1,500$ Å for weak protein–protein
interactions to $10,000$ Å for obligate ones. (B) Proteins assemble into
higher-order complexes through combinations of direct, pairwise interactions.
Examples illustrate a homodimeric complex with two direct protein–peptide
interactions and a heterooligomeric protein tetramer. Solid black lines
indicate direct interactions while dashed gray ones indicate indirect ones
where molecular surfaces are not in physical contact.

Strong protein interactions often exhibit large, hydrophobic interaction
surfaces, whereas transient ones display a larger fraction of polar and
charged residues that can favorably interact with solvent molecules in their
unbound states (Acuner Ozbabacan et al., 2011; Kastritis and Bonvin, 2013).
Interactions mediated by short peptidic motifs of roughly ten contiguous
residues exemplify the weak end of the spectrum (with affinities in the
micromolar range) employed to dynamically control protein localization,
activation, and degradation (Van Roey et al., 2014). Often a few interfacial
‘hot spot’ residues contribute substantially to interaction affinity and
specificity; however, residues distant from the interaction surface can also
impact binding, for instance by altering unbound monomers’ conformational
ensembles (Kastritis and Bonvin, 2013). Indeed, some proteins undergo large
conformational changes upon binding, and many peptidic sites found within
intrinsically disordered regions only adopt well-defined structures upon
binding to a receptor (Van Roey et al., 2014). Yet other proteins maintain
‘near-rigid’ structures, exhibiting only minor fluctuations in side chain
orientations upon binding (Kastritis and Bonvin, 2013). One example is the
subpicomolar-affinity binding of protease inhibitors to their cognate enzymes
(Kastritis and Bonvin, 2013), which is well approximated by a lock-and-key
model.

To catalogue and characterize the full span of pairwise interactions that
organize proteins into functional complexes (Fig. 1), multiple approaches,
with varying trade-offs, have been employed. High-throughput, qualitative
experimental assays enable large-scale mapping of protein interaction networks
(Luck et al., 2020; Huttlin et al., 2021) at reduced sensitivity and
specificity relative to low-throughput methods (Acuner Ozbabacan et al., 2011;
Davey et al., 2023). Nevertheless, these interaction maps remain sparse
drafts—for example they are estimated to encompass only $2-11$% of all
pairwise interactions in humans (Luck et al., 2020)—and biased towards stable
interactions involving high-abundance proteins in well-studied cell types and
model organisms (Acuner Ozbabacan et al., 2011; Davey et al., 2023; Huttlin et
al., 2021). While high-resolution, quantitative experiments enable reliable
and precise detection of protein interactions, including weak, transient ones,
their expense prohibits large-scale application (Acuner Ozbabacan et al.,
2011). Computational methods have the potential to inexpensively fill in
existing gaps and yield a more comprehensive picture of protein interaction
networks. Deep learning methods in particular can leverage both heterogeneous
data and basic physical knowledge about protein interactions to model diverse
molecular recognition mechanisms. This makes them well-suited for this task
compared to other modeling techniques. On the one hand, molecular simulations
rooted in statistical mechanics offer detailed physical insights into protein
interaction specificities, thermodynamics, and kinetics, but are too
computationally expensive to apply proteome-wide (Spiga et al., 2014; Wang et
al., 2022a). On the other hand, purely bioinformatic approaches predict
interactions based on known sequence and structural homology or functional
associations, but have difficulty generalizing to poorly characterized regions
of interaction space (Tsuchiya et al., 2022; Peng et al., 2017; Xue et al.,
2015; Kelly and Stumpf, 2008).

In this review, we first describe how deep neural networks have been tailored
to model protein interactions and, in particular, how the choice of inputs
provided and their internal model representations, target outputs, and network
architecture determine the types of interactions modeled and biological
questions addressed. We then report on recent progress in using deep learning
to accomplish three long-term goals: (1) discovery of protein interactions
that have yet to be experimentally detected, (2) elucidation of the residues,
molecular surfaces, and atomic structures that underpin protein interactions,
and (3) design of protein binders and oligomeric assemblies for basic and
translational applications. Throughout, our focus is on approaches suitable
for bottom-up inference (and design) of interaction networks from physical and
molecular determinants. Remarkable successes have been recently achieved using
deep learning to structurally resolve protein interactomes (Burke et al.,
2023; Humphreys et al., 2021; Gao et al., 2022; O’Reilly et al., 2023) and
computationally design picomolar affinity binders (Vázquez Torres et al.,
2022). Nonetheless, generalizing interaction prediction and design beyond
sequences and structures well-represented in training data remains a challenge
(Bernett et al., 2023; Tsishyn et al., 2023). We conclude by discussing
promising ideas across multiple aspects of model development: from compiling
larger, higher-quality datasets to better incorporating biophysical priors
within network architectures and integrating varied training schemes. We
believe these ideas will help overcome existing challenges, including
predicting interaction affinities and variant effects at scale, and expand the
scope of current methods to include protein complexes mediated by highly
transient interactions, intrinsically disordered regions, and post-
translational modifications.

##  2 Properties of protein interactions inform modeling approaches

Geometric and chemical complementarity of interacting surfaces often plays a
defining role in molecular recognition. These functional interfaces are more
evolutionary conserved than other surface sites, and their complementarity is
maintained through co-evolution of residues on binding partners (Ghadie et
al., 2018). Yet, within this basic framework, the specific biophysical
mechanisms responsible for molecular recognition are highly diverse (Acuner
Ozbabacan et al., 2011; Kastritis and Bonvin, 2013). Such diversity makes it
challenging to compile a set of comprehensive and predictive rules from first
principles to describe dimeric protein interactions, let alone how
combinations of pairwise interactions assemble proteins into higher-order
complexes (Fig. 1B). In this case, it can be advantageous to use statistical
approaches to capture the physicochemical, structural, and evolutionary
patterns underpinning protein interactions directly from data. Neural networks
accomplish this by learning to transform raw input representations of proteins
(e.g., sequences, evolutionary histories, 3-dimensional (3D) structures and/or
molecular surfaces) into abstract representations optimized for prediction or
design of interactions. This avoids the need to identify and manually
handcraft features of protein biophysics and evolution responsible for
binding, an exercise based on still incomplete domain knowledge. Instead,
well-established principles underlying molecular recognition can be
incorporated into neural network primitives that transform raw protein inputs
into learned representations. As a simple example, the arbitrary assignment of
‘receptor’ and ‘ligand’ labels to two globular proteins has no bearing on
their ability to interact, and this insensitivity to label permutations can be
incorporated into the network architecture by using order-invariant operations
to process the input representations of all proteins (Chen et al., 2019; Huang
et al., 2023; Sledzieski et al., 2021).

All aspects of a neural network model, from the choice of inputs and
biophysical priors to the training scheme used (Fig. 2), influence how the
underlying biological problem is posed and encoded within the model.

Figure 2: Components of deep learning models of protein interactions. Deep
neural networks learn to transform (A-C) raw protein inputs, $x$, using (D-E)
various network primitives into abstract representations optimized to achieve
(F-G) particular learning objectives, $\mathcal{L}$. (A) As input to the
model, proteins can be described by their primary amino acid sequences. (B)
Evolutionary information can be supplied in the form of a position specific
scoring matrix, which contains statistics of residue conservation at each
sequence position, or, for example, a paired multiple sequence alignment,
which contains statistics of residue conservation and correlation across all
positions within and between species-paired proteins. (C) Structural
information can be supplied in the form of a point cloud containing atomic
coordinates, a voxelized density map tabulating the volumetric density of
atoms on a discrete 3D grid, a residue graph encoding residue-level features
in nodes and inter-residue quantities such as distances and angles in edges,
or a molecular surface mapping atomic features onto a triangulated mesh that
outlines the protein’s solvent accessible surface. (D) Neural network
primitives are chosen with appropriate symmetries built into the architecture.
For example, combining representations of two proteins with permutation
invariant operations, such as element-wise addition and multiplication or
generalized outer products, ensures invariance to input ordering. Group
equivariant networks update representations of protein structures to ensure
equivariance to global translations and rotations. (E) Neural network
primitives are also chosen with inductive priors reflective of the underlying
biophysics. Convolutional networks process inputs with a regular grid
structure by translating the same filters over all patches of the input and
thus capture short-ranged, translationally-invariant multibody interactions.
Recurrent networks process sequentially-ordered, variable-length inputs by
iteratively applying the same transformations to each element and can be
stacked to processes inputs in both directions. Graph neural networks process
inputs that lack a regular grid-like structure or inherent ordering but have a
fixed topology defined based on known relationships between elements, such as
distances and angles between atoms in molecular structures. Representations of
each node (and edge) are updated based on their connections to neighboring
nodes. Attention-based networks explicitly consider all pairwise connections
between elements and infer relationships between them during training, thus
allowing for variable, flexible topologies and capturing of both short- and
long-ranged interactions. In a self-attention primitive, representations of
each element are updated by considering all other elements within the same
input. In a reciprocal cross-attention primitive specifically formulated for
protein–protein interactions, representations in one protein are updated based
on those in the other protein according to attention values computed from both
representations. To learn network parameters, models are trained through (F)
supervised learning, in which the model is optimized to predict a target
observable from the input, $\mathcal{O}(x)$, that matches its experimental
value, $\mathcal{O}_{\rm expt}$. (G) Alternatively, models can be trained
through self-supervised learning, in which a model is optimized to accomplish
a proxy task constructed from the input data itself using an objective
function defined over input data alone, $\mathcal{L}(x,\tilde{x})$. Among
self-supervised approaches, autoregressive models learn to predict the next
amino acid in a sequence given a truncated input, $\tilde{x}$. Models tasked
to reconstruct protein sequences or structures from corrupted inputs,
$\tilde{x}$, for instance with masked residues or perturbed side-chain
orientations, learn contextual residue- or atomic-level representations.
Contrastive learning optimizes the learned internal representations instead of
a target output function. This is often accomplished by maximizing the
similarity, such as measured by $\ell_{2}$ norm or cosine similarity, between
representations of interacting protein pairs and minimizing that of non-
interacting pairs.

For example, protein–peptide interactions, unlike dimeric protein–protein
interactions, naturally admit ‘receptor’ and ‘ligand’ labels, and this
asymmetry motivates the use of two distinct network components for encoding
protein and peptide inputs within a single model (Lei et al., 2021; Li et al.,
2023; Abdin et al., 2022). In a more complex setting, neural networks
developed for paired protein inputs cannot model higher-order oligomers, and,
when trained on complexes decomposed into direct and indirect pairwise
interactions (Mosca et al., 2013; Peng et al., 2017), will fail to capture
contextual effects that emerge from multiway interactions. Conversely, many
higher-order complexes, including ion channels, metabolic enzymes, and
membrane remodeling proteins, adopt symmetric structures belonging to cyclic,
dihedral, cubic, or helical point groups, and symmetry can be exploited to
model and design these large complexes without explicitly representing all
equivalent units, reducing computational cost (Li et al., 2022c; Watson et
al., 2023). Indeed, tailoring models to a particular type of protein
interaction, even if it imposes practical constraints, is often valuable. In
the following sections, we discuss the implications of some of the key choices
encountered when building deep learning models of protein interactions.

###  2.1 Deep learning models operate on protein sequences, structures, and
evolutionary histories

Proteins can be presented to models in multiple complementary ways (Fig.
2A-C). Their individual amino acid sequences provide minimal descriptions
amenable to modeling all types of interactions. Including evolutionary and
structural information can facilitate predictions by exposing patterns of co-
evolution among residues and potential surface complementarity, respectively.
The former is most useful for interactions under strong selective pressures,
including permanent, obligate interactions and protein hubs (Ghadie et al.,
2018), while the latter for interactions occurring with limited conformational
changes. In contrast, short peptidic motifs are both structurally and
evolutionary plastic; this makes them ideal for constructing and adapting
complex regulatory programs that involve multiple binding partners (Van Roey
et al., 2014) but potentially limits the utility of structural and
evolutionary information in modeling them. Indeed, both the availability of a
given data modality (or feasibility of acquiring it) and the prediction
objective inform the decision to explicitly provide this data or to task the
model with implicitly inferring it. For example, models can learn to transform
unbound monomeric (apo) structures into a structure of the bound complex
(Ganea et al., 2022; Ketata et al., 2023; Sverrisson et al., 2022), but
providing apo structures as inputs may bias predictions towards proteins that
maintain their unbound conformations; alternatively, complex structures can be
inferred directly from input protein sequences, implicitly modeling
conformational changes upon binding (Evans et al., 2022).

How particular information is provided to the model is a key question. For
evolutionary information, residue conservation can be supplied as a position-
specific scoring matrix (PSSM), which tabulates the empirical probabilities of
every amino acid independently occurring at each residue position (Fig. 2B).
Multiple sequence alignments (MSAs) relax position independence and provide a
comprehensive account of evolutionary variation, conservation, and correlation
across all residue positions. While powerful, constructing high-quality MSAs
and, especially, species-paired MSAs (Fig. 2B) that capture inter-protein
residue co-evolution (that may be indicative of a protein–protein interaction)
can be challenging (Bryant et al., 2022a). In both PSSMs and MSAs, the
evolutionary information encompassing a single protein family is presented
explicitly to the model. Protein language models provide an alternate approach
in which patterns observed across millions of (unrelated) protein sequences
are distilled into a single model that attempts to implicitly capture all of
known protein evolution (Alley et al., 2019; Rives et al., 2021; Lin et al.,
2023; Chen et al., 2023a). Using a protein language model to embed a sequence
also avoids incurring the computational costs of storing and searching large
sequence databases to construct explicit MSAs.

For structural information, atomic point clouds (Krapp et al., 2023), density
maps (Townshend et al., 2019; Kozlovskii and Popov, 2021), residue graphs
(Abdin et al., 2022; Fout et al., 2017; Li et al., 2023), or molecular
surfaces (Gainza et al., 2020; Dai and Bailey-Kellogg, 2021) can be provided
as input to the model (Fig. 2C). Point clouds describe the detailed
arrangement of atoms in 3D space, but do not explicitly account for excluded
volume, which leads to short-ranged repulsion between molecules. Density maps
provide a voxelized representation in which electron density, for example, can
be directly encoded, at the cost of expending memory and computations on
unoccupied regions of space. Residue graphs, in which nodes correspond to the
C$\alpha$ positions of residues, provide efficient coarse representations of
backbone configurations but typically lack explicit descriptions of side chain
positions, which may significantly reorient upon binding. Molecular surfaces
represent proteins exclusively by exterior residues that may engage in direct
physical contact with other molecules; however, as surface-based
representations have limited capacity to capture internal residues and their
impact on binding, they can struggle to capture collective conformational
changes, such as coordinated by distributed allosteric networks.

###  2.2 Deep learning models encode properties of protein interactions into
abstract representations

Neural network primitives with different inductive priors can be used,
individually or in combination, to encode protein input data (Fig. 2D-E).
These primitives are typically chosen based on their suitability for different
protein representations and ability to capture aspects of the underlying
biophysics. Convolutional networks specialize in processing inputs with
regular grid structures, including 1D sequences and voxelized 3D density maps,
by reusing the same set of parameters to process grid patches. They can
capture local, translationally-invariant patterns such as short peptide-
binding motifs within proteins (Wardah et al., 2020; Kozlovskii and Popov,
2021; Lei et al., 2021). By virtue of their densely connected filters,
convolutional networks also excel at capturing collective many-body
interactions between elements within a patch, but their reliance on fixed
receptive fields limits the length-scale of the interactions that they can
model in practice (larger receptive fields lead to rapid increases in
parameter count and computational cost). By comparison, recurrent networks,
which sequentially process elements in a 1D or higher-dimensional sequence, do
not have explicit length-scale constraints and can in principle operate on
arbitrarily long sequences. However, they have been empirically found to lose
associations between far away elements, thus exhibiting an implicit locality
bias. Furthermore, in contrast to most other neural network primitives which
comprise numerous independent operations and are thus highly parallelizable,
the sequentiality of recurrent networks makes them less suited to modern
computing hardware.

Structured data lacking a regular grid-like topology or an inherent ordering,
such as molecular structures (Fout et al., 2017) or protein interaction
networks (Gao et al., 2023), are more naturally modeled with graphs that
explicitly encode known relationships. For instance, by encoding protein
structures as graphs, neural networks can leverage existing biophysical
knowledge to identify protein–protein interaction sites (Xie and Xu, 2022) and
rigidly dock proteins (Sverrisson et al., 2022) based on their spatiochemical
complementarity. However, such networks cannot explicitly represent
protein–protein contacts learned during training or discovered at prediction
time since they maintain the fixed topology of their inputs (they may however
implicitly encode such information). Graph-based protein representations can
include nodes for each heavy atom and model spatial relationships between
atoms using binary or distance-weighted edges (Tubiana et al., 2022; Liu et
al., 2021). Information then flows through the network according to the
connectivity of the graph using permutation-invariant operations to update the
representations of each node and edge (Fig. 2E). As a result, like
convolutional and recurrent networks, graph neural networks exhibit a spatial
locality bias towards interactions between atoms or residues within the same
physical neighborhood over ones distant in a protein’s structure.

An advantage of graph-based representations, particularly for protein
structure, is their invariance to global rotations and translations (Fig. 2D);
in the language of group theory, these are known as SE(3) transformations.
SE(3)-invariance is a desirable property because how a protein is
computationally oriented in 3D space has no bearing on its behavior. Graph
neural networks achieve SE(3)-invariance by encoding geometrical aspects of
structure using exclusively relative quantities (e.g., inter-residue lengths
and angles) that do not vary with global position or orientation. By
comparison, standard convolutional networks operating on voxelized densities
are sensitive to SE(3) transformations unless trained using data augmented
with arbitrary rotations to teach the model to recognize patterns in any
orientation (Townshend et al., 2019; Kozlovskii and Popov, 2021). However,
graph neural networks are at a comparative disadvantage to convolutional
networks in capturing many-body interactions. To harness the strengths of
both, a parallel line of research has focused on directly endowing
convolutional networks with awareness of SE(3) transformations. One approach
is to parameterize the receptive fields of convolutional networks using
SE(3)-equivariant mathematical functions, such as spherical harmonics,
resulting in representations of atomic coordinates that deterministically and
predictably change under coordinate transformations (Smidt, 2021). Tailoring
architectures to respect symmetries inherent to geometric structures,
including graphs, point clouds, and surfaces, forms a subfield of deep
learning, geometric deep learning (Bronstein et al., 2021), that is
increasingly being used to model protein interactions (Gainza et al., 2020;
Ganea et al., 2022; Krapp et al., 2023; Dai and Bailey-Kellogg, 2021; Huang et
al., 2023; Si and Yan, 2023b). By incorporating strong geometrical priors,
SE(3)-equivariant networks (Geiger and Smidt, 2022) more faithfully represent
physical systems and molecular interactions; however, they can be technically
challenging to implement efficiently.

As previously stated, graph neural networks prescribe a specific structure to
the inputs, which can make them unsuitable when this structure is unknown or
changing. To avoid this limitation, attention-based networks learn the
relationships between input elements over the course of training (strictly-
speaking, an attention-based network is analogous to a fully-connected graph
in a graph neural network). Because all pairwise connections are considered
within an attention primitive, information deemed valuable for solving a
particular objective flows directly between input elements irrespective of
their distance (Fig. 2E). Although the required all-to-all computation is
expensive, attention-based networks, unlike the primitives described earlier,
have effectively unlimited receptive fields and can encode short- and long-
ranged interactions equally well. These capabilities, combined with the
minimal incorporation of inductive assumptions, allow the structure and
inherent properties of an input to emerge during model inference, for example,
to realize the dogma ‘sequence determines structure’ and predict atomistic
complex structures from protein sequences (although in practice, existing
models require MSAs, not just individual sequences (Jumper et al., 2021; Evans
et al., 2022)). Due to their expressivity, attention-based neural networks are
increasingly used to capture complex and long-ranged interdependencies between
residues within and across interacting proteins (Lei et al., 2021; Hosseini
and Ilie, 2022; Tsukiyama and Kurata, 2022; Wang et al., 2022c). Specific
formulations of attention have also been developed to explicitly encode the
inherently reciprocal relationships between two interacting proteins (Abdin et
al., 2022; Baranwal et al., 2022) and to encode spatial relationships between
residue pairs in a manner that emulates a defining property of distances in
Euclidean geometry, namely the triangle inequality (Jumper et al., 2021; Wu et
al., 2022a).

###  2.3 Deep learning models acquire meaningful protein representations
through supervised and self-supervised learning

Neural networks are typically optimized end-to-end, meaning that all model
parameters are tuned simultaneously to maximize the final objective function
of the model (output end). This induces the model to learn to encode raw data
(input end) into abstract representations tailored for its particular
objective function. In supervised learning, objective functions are defined
over quantities dependent on, but distinct from, model inputs (Fig. 2F); for
example, an objective could be defined to minimize the error between
experimentally measured affinities of protein–protein interactions and ones
predicted given input protein sequences. However, experimental determination
of target observables for all training examples can be costly and time-
consuming, whereas input data modalities are often more readily available.
Self-supervised learning is an alternative approach in which input data alone
is used to create proxy tasks and associated objective functions for the model
to optimize (Fig. 2G). With suitably chosen tasks, this process can lead the
model to learn abstract representations that are generically useful (i.e.,
that encode intrinsic properties of the data that facilitate reasoning for a
broad array of tasks). For protein interaction modeling, large, existing
databases of protein sequences or structures can be leveraged in this way to
learn useful representations even if their interaction partners are unknown.

One self-supervised objective tasks models with predicting the next amino acid
in a protein sequence (Fig. 2G). The resulting models acquire the ability to
generate novel protein sequences, implicitly learning principles that underlie
natural protein stability and function (Ferruz et al., 2022). Such
autoregressive models are valuable for de novo sequence design but assume that
the identity of each residue depends exclusively on ones upstream of it and,
thus, do not capture a residue’s full sequence context. An objective devised
to avoid this limitation instead tasks models with recovering the amino acid
identities of masked or corrupted residues based on the rest of the protein
sequence or structure (Lin et al., 2023; Liu et al., 2021; Mohseni Behbahani
et al., 2023; Mahajan et al., 2023). Through such a masked language modeling
objective, protein language models acquire contextual representations of
protein sequences that capture evolutionary, physicochemical, and structural
information (Rives et al., 2021) applicable for solving downstream tasks
ranging from protein interaction (Hallee and Gleghorn, 2023; Sledzieski et
al., 2021; Chen et al., 2023a) and variant effect prediction (Unsal et al.,
2022) to complex structure prediction (Lin et al., 2023) and binder design
(Hie et al., 2022; Bhat et al., 2023). To learn contextual representations of
protein structures that capture atomistic details pertinent to molecular
recognition mechanisms, one data corruption approach leverages the insight
that side chain rearrangements at protein complex interfaces can disrupt key
stabilizing interactions by tasking models with reconstructing perturbed side
chain orientations. The resulting learned representations encode geometric and
physicochemical information predictive of mutational effects on binding
affinity (Liu et al., 2021).

While the above approaches encourage models to encode fundamental properties
of protein sequences or structures, they do not explicitly require a
sophisticated understanding of inter-protein relationships that determine, for
example, homology and interaction specificity. To capture characteristic
commonalities and differences between data points, a third type of self-
supervised objective tasks models with maximizing the similarity of
representations for related inputs over unrelated ones (Fig. 2G). Such
contrastive learning objectives have been used to encourage separation between
the abstract representations of interacting versus non-interacting protein
pairs and facilitate protein interaction prediction (Wang et al., 2022c;
Palepu et al., 2022; Gainza et al., 2020). Furthermore, by combining
objectives that require distinct but complementary methods of reasoning over
inputs, models can acquire more holistic representations of proteins that are
generally useful for solving complex, varied tasks (Chen et al., 2023a; Zhang
et al., 2023b). For this reason, self-supervised objectives have also been
integrated within supervised training schemes to fully leverage all types of
data available for modeling protein interactions and complex structures
(Jumper et al., 2021; Evans et al., 2022; Mohseni Behbahani et al., 2023; Wang
et al., 2022c).

##  3 Efforts to discover, elucidate, and design protein interactions using
deep learning

Deep learning models have been developed to predict the probability of
experimentally detecting an interaction between two proteins, the residues and
molecular surfaces that mediate an interaction, and the atomistic structure of
a bound complex. These models form the foundation of a growing ecosystem of
deep learning methods for discovering novel protein interactions, elucidating
their physical mechanisms, and designing binders to precisely modulate their
function. In the following sections, we describe the main types of approaches
that have been employed to address each of these biological questions, while a
comprehensive list of models is provided in Fig. 3.

Figure 3: Ecosystem of deep learning methods for modeling protein
interactions. Deep learning models have been developed to predict (1)
interactions, (2) interaction sites, and (3) atomistic complex structures and
to (4) design both direct physical interactions for (i) protein–peptide and
(ii) protein–protein dimers as well as (iii) high-order complexes, including
their complete pairwise decompositions into direct physical interactions
(solid black lines) and indirect interactions (dashed gray lines). Boxed and
colored models are applicable to multiple tasks and/or types of protein
interactions and labeled accordingly (e.g., models labeled (1-2.i) predict
interactions and interaction sites for protein–peptide interactions). All
models for complex structure prediction implicitly predict interaction sites
as well. References for all models are provided in the appendix. † Models for
protein docking. ‡ Models for designing protein sequences given a complex
structure. $\mathparagraph$ Models for predicting binding affinity.
$\mathsection$ Models for predicting changes in binding affinity upon
mutation. * Models based on AlphaFold2.

###  3.1 Discovering interactions

Scalable computational models suitable for screening large sets of possible
protein interactions have been developed to identify novel interacting protein
pairs. Methods for this task have typically been devised to complement high-
throughput experimental efforts to fully map protein interactomes (Luck et
al., 2020; Huttlin et al., 2021). Analogous to the qualitative readouts
obtained from these experiments, which indicate only the detection of an
interaction and not its affinity, these models almost universally formulate
interaction prediction as a binary classification problem: two proteins either
interact or do not based on a predicted interaction score (Fig. 4A).

Figure 4: Efforts to discover protein interactions employ deep learning
methods to accomplish multiple tasks. (A) Most methods classify a pair of
proteins as interacting or non-interacting based on a predicted interaction
score ($S_{\rm inter}$). If $S_{\rm inter}$ is greater than a chosen threshold
$S^{*}$, the pair is labeled as interacting, otherwise it is labeled non-
interacting. (B) Other methods quantify the affinity of an interaction between
two proteins, specifically the dissociation constant ($K_{\rm D}$), which
quantifies the relative probability of observing two proteins in their unbound
monomeric state versus bound state. (C) Models are evaluated for their ability
to generalize to proteins dissimilar from ones in their training sets (based
on sequence or structural homology) in order to (I) impute new interactions
among a set of known interacting proteins; (II) identify interactions between
a protein unseen in the training set and known PPI network; and (III)
extrapolate to interactions between pairs of unseen proteins.

In the case of purely bioinformatic methods, predicted interaction scores
derive from homology (based on sequence or structural similarity) to an
experimentally-validated interacting pair (Petrey et al., 2023; Zhang et al.,
2012; Peng et al., 2017; Kelly and Stumpf, 2008). As such, these methods
depend on the availability of homologous templates to make reliable
inferences. The increase in high-confidence structural models predicted by
deep learning models, whose application to complex structure prediction is
discussed in a latter section, has enabled homology-based approaches to expand
their applicability while maintaining their capacity for rapid screening
(Petrey et al., 2023).

Deep learning interaction predictors avoid the need for input homologous
templates altogether, and instead make inferences based on raw input
representations of individual proteins. They may, nevertheless, learn to
implicitly encode homology to known protein interactors used for training
(Bernett et al., 2023; Yang et al., 2023b). Training models for binary
interaction prediction requires experimentally-validated positive
(interacting) and negative (non-interacting) examples. While high-throughput
experimental methods have detected over 100,000 positive interactions to-date
(Luck et al., 2020; Huttlin et al., 2021), analogous methods to confirm
negatives at scale are lacking. As a result, there is a relative paucity of
experimentally-validated negative examples, of which we estimate there are
roughly 6,000 curated instances within databases (Blohm et al., 2014; Trabuco
et al., 2012). This is in stark contrast to estimates that, among human and
yeast proteomes, negatives exceed positive interactions by 1,000 fold (Trabuco
et al., 2012; Luck et al., 2020). One standard approach to circumvent the
scarcity of experimentally-validated negatives and better match the expected
sparsity of interaction networks is to train models with synthetically
generated negative examples: Assuming that all protein pairs not observed in
experimental datasets are negatives, they can be uniformly sampled to generate
a much larger number of negatives than positives (Hamp and Rost, 2015a;
Hashemifar et al., 2018; Sledzieski et al., 2021; Szymborski and Emad, 2022;
Volzhenin et al., 2023; Lei et al., 2021). Another approach to generate
synthetic negatives assumes that proteins localized to different cellular
compartments are unlikely to interact (Ben-Hur and Noble, 2006; Du et al.,
2017; Zhang and Kabuka, 2019; Yang et al., 2020a; Hallee and Gleghorn, 2023).
Other approaches do exist with different inductive priors (Hallee and
Gleghorn, 2023; Ben-Hur and Noble, 2006), and this remains an active area of
research.

Under the umbrella of ‘interaction prediction’ exist three specific tasks for
which models have been developed (Fig. 4C): (I) imputation of novel
interactions within a known, experimentally-validated protein interaction
network, (II) addition of new proteins, which currently lack experimentally-
validated interactions, to a known network, and (III) construction of novel
interaction networks composed of new proteins. A model’s suitability for each
of these tasks is determined through assessment on a test set of
experimentally-validated interactions constructed to differ from the training
set in a manner that mimics the desired use case: (I) interactions (edges in
the network) are split such that individual proteins may occur in both
training and test sets, (II) individual proteins are split into training and
test sets such that all test interactions involve at least one test protein
absent from the training set, and (III) individual proteins are split such
that all test interactions involve only test proteins (Park and Marcotte,
2012; Hamp and Rost, 2015b; Szymborski and Emad, 2022). Models consistently
excel at imputing interactions (task I), achieving accuracies above 95%
(Bernett et al., 2023). Although including structural information as input in
addition to raw sequences can slightly improve accuracies by roughly $1-4$%
(Yang et al., 2020a; Jha and Saha, 2020; Song et al., 2022; Huang et al.,
2023; Jha and Saha, 2023; Jha et al., 2023), sequence-based models using
representations obtained through self-supervised pre-training (Chen et al.,
2019; Yao et al., 2019; Dong et al., 2021; Sledzieski et al., 2021; Hallee and
Gleghorn, 2023; Palepu et al., 2022; Anteghini et al., 2023) match or
outperform structure-based models in recent evaluations (Gurvich et al., 2023;
Yang et al., 2023b). This may be because representations obtained through
self-supervised learning implicitly capture structural information (in
addition to evolutionary information). Indeed, large protein language models
have been shown capable of directly encoding atomic-level structural
information, such as intra-protein residue contacts (Lin et al., 2023; Rao et
al., 2020).

Predicting interactions involving novel protein(s) (tasks II and III) requires
models to generalize to proteins outside their training sets. Such
capabilities are especially key for constructing interaction networks that
include understudied or low-abundance proteins and those of non-model
organisms (Volzhenin et al., 2023). When evaluated on these more challenging
tasks, classifier effectiveness, as measured by the areas under the receiver
operating characteristics curve (AUROC) and precision-recall curve (AUPR),
drops by roughly 10% and 20% on interactions involving one (task II) or both
proteins (task III) being absent from the training set, respectively,
(Szymborski and Emad, 2022; Lei et al., 2021; Yang et al., 2023b; Volzhenin et
al., 2023), with models recalling around 70% of known interactions (Yang et
al., 2023b). Furthermore, because protein interaction surfaces are
evolutionarily conserved (Ghadie et al., 2018), proteins with unique but
related sequences may nevertheless engage similar binding partners, which can
be readily predicted by homology alone. To assess how well models generalize
to evolutionary distant proteins, within both these evaluation schemes, models
have been assessed on test proteins with varying levels of homology to
proteins in the training set based on sequence identity (Szymborski and Emad,
2022; Lei et al., 2021) or the species in which interactions occur (Yang et
al., 2023b; Volzhenin et al., 2023; Huang et al., 2023; Hashemifar et al.,
2018). Models perform nearly equally well on interactions involving proteins
that range in sequence identity from 100% to 40% to a training example and,
concordantly, test species with median sequence identities greater than 40% to
a training species (Szymborski and Emad, 2022; Lei et al., 2021; Yang et al.,
2023b; Volzhenin et al., 2023), but performance drops drastically on protein
pairs less than 30% sequence identical to all proteins in the training set
(Yang et al., 2023b; Volzhenin et al., 2023). The most successful methods for
these two tasks employ representations from large protein language models
(Yang et al., 2023b; Volzhenin et al., 2023), enhanced regularization
techniques (Szymborski and Emad, 2022), or multitask learning strategies (Lei
et al., 2021) to reduce overfitting on the training set and improve model
generalizability; if such techniques are not used, models have been shown to
randomly classify protein pairs absent from training sets as interacting or
non-interacting (Szymborski and Emad, 2022; Yang et al., 2023b; Volzhenin et
al., 2023; Bennett et al., 2023).

While extrapolating outside the training set is crucial for discovering novel
interactions, the capability to quantitatively predict interaction affinities
(Fig. 4B) with high sensitivity to single residue mutations is key to
unraveling variant effects. Scores predicted by binary classifiers can show
modest correlation with affinity (Pearson $R\approx 0.7$) but vary from
experimental values by roughly a factor of three (Hashemifar et al., 2018; Lei
et al., 2021; Motmaen et al., 2023). Such error is greater than that typically
reported for low-throughput experimental measurements, which commonly differ
by only a factor of two across technical replicates, methods, or labs
(Jankauskaitė et al., 2019). Training quantitative regression models has been
challenged by the limited number of curated affinity measurements compared to
qualitative measurements: Only about $7,000$ affinities are available in the
SKEMPI database for 345 complexes and their point mutants (Jankauskaitė et
al., 2019). To date, only two deep learning models (Chen et al., 2019; Unsal
et al., 2022) have been trained to quantify interaction affinities. Regression
models that leverage protein language models, which can directly encode
variant effects on individual protein’s functions (Rives et al., 2021; Meier
et al., 2021), exhibit substantially increased correlation with experimental
affinities (Pearson $R=0.9$) than binary classifiers but their errors still
exceed experimental ones (Unsal et al., 2022).

Across all problem formulations, models predict different types of
interactions (Fig. 1), and which types are predicted by a given model are
largely determined by the choice of training data. In the case of
protein–peptide interactions, models have been trained specifically on direct
physical interactions (Lei et al., 2021; Gurvich et al., 2023; Palepu et al.,
2022), almost exclusively derived from experimental structures in the Protein
Data Bank (PDB) and curated into the PepBDB (Wen et al., 2019) and Propedia
(Martins et al., 2021) databases. In the more general case of protein–protein
interactions, training datasets have been derived from a variety of assays,
ranging from in vitro biophysical assays to in vivo assays and ones based on
cell extracts such as affinity purification mass spectrometry, with each
providing evidence for a different interaction type(s). Many high-throughput
assays, in fact, do not differentiate between direct physical interactions
(Fig. 1A) and indirect interactions mediated by intermediary proteins (Fig.
1B) (Acuner Ozbabacan et al., 2011), nor do they distinguish between true
dimers, whose stability does not require any additional binders, and pairs of
proteins that are in direct physical contact only as part of a larger complex.
Models trained on amalgamations of these experimental sources will invariably
conflate different types of interactions. In instances where ambiguity is
undesirable, datasets can be limited to experimental methods that provide
unequivocal evidence for the sought interaction type, a curation step already
performed by some databases. For example, the IntAct database (del Toro et
al., 2022) provides a filter for true dimers and has been used to create
training and evaluation datasets for the MTT model (Dong et al., 2021); and
the HINT database (Das and Yu, 2012) provides a filter for direct physical
interactions, including true dimers and more generally direct interactions
derived from yeast two-hybrid assays.

Faithfully predicting higher-order complexes, on the other hand, remains
challenged both by standard data curation procedures, which record known
interactions in a pairwise manner, and by constraints imposed by current model
architectures, which exclusively process pairs of proteins as input. These
practices are suitable for dimers but require pairwise decomposition of
complexes with three or more proteins. Such a decomposition may be physically
appropriate for higher-order complexes that assemble from independent dimers
but would be inaccurate for obligate trimers, for example. Notable exceptions
to these practices, include, on the data side, the cataloguing of over 5,000
complexes and their subunit stoichiometries within the CORUM (Tsitsiridis et
al., 2022) and Complex Portal (Meldal et al., 2022) databases. On the model
side, deep learning methods for complex structure prediction, described in a
latter section, can accommodate a variable number of input monomer sequences
(Evans et al., 2022; Baek et al., 2021; Mirdita et al., 2022; Bryant et al.,
2022a, b; Gao et al., 2022). However, they require a priori knowledge of
complex stoichiometry, and this, in combination with the increased
computational costs and memory requirements associated with modeling the
structure of an increasing number of subunits, makes existing methods
impracticable for screening putative higher-order complexes at scale. One deep
learning method takes an entirely different approach and predicts which
protein nodes in an existing interaction network assemble into a higher-order
complex (Pan et al., 2023); such an approach could be applied to interaction
networks predicted using binary interaction classifiers in order to discover
novel higher-order complexes.

###  3.2 Elucidating interaction mechanisms

####  3.2.1 Predicting interaction sites

Identifying protein patches that physically contact other proteins is both
practically useful for rationally designing interaction modulators and helps
improve our understanding of the physicochemical and structural principles
that underpin interaction specificity and affinity. Methods for this task fall
into two broad categories: partner-agnostic ones that predict protein sites
engaging one of possibly many partners (including drugs) (Fig. 5A), and
partner-specific methods that predict sites engaging a particular partner
(Fig. 5B).

Figure 5: Efforts to elucidate the molecular surfaces that mediate protein
interactions employ deep learning methods to accomplish multiple tasks. Most
methods for interaction site prediction classify residues ($r$) of proteins as
interacting or non-interacting based on a predicted interaction score ($S_{\rm
inter}$). (A) Partner-agnostic models predict scores that are independent of a
specific binding partner, whereas (B) partner-specific models predict scores
conditioned on a particular interaction. (C) Interacting residues on an
individual protein are predicted by all partner-agnostic models and partner-
specific protein–peptide models, whereas (D) inter-protein residue contacts
between a specific pair of residues are predicted by most partner-specific
protein–protein models.

The definition of what constitutes an interaction site can vary but is
generally based on inter-protein atomic distances (Xue et al., 2015), derived
from experimental protein complex structures. Labels are typically assigned on
a per-residue basis, even though a set of residues within a contiguous surface
patch collectively determines interaction affinity and specificity (Kastritis
and Bonvin, 2013; Acuner Ozbabacan et al., 2011). As one way to account for
such correlations between residues within a patch, some residue-level
predictors spatially smooth predicted interaction propensities (Tubiana et
al., 2022). Since interacting residues provide evidence of a direct physical
interaction, multitask learning approaches have also been deployed for these
two synergistic tasks (Lei et al., 2021).

Most interaction site predictors are not developed to delineate how different
residues or regions contribute to binding affinity and, thus, neither directly
distinguish hot spot residues from others nor assess mutational effects on
binding affinity. Indeed, when evaluated for in silico alanine scanning, a
standard approach to identify hot spot residues, per-residue scores derived
from a binary classifier show minimal correlation with experimental changes in
affinity (Pearson $R=0.2$) (Tubiana et al., 2022). Models that do predict the
effects of point mutations on binding affinity often leverage residue-level
representations of complex structures extracted from self-supervised models,
which are trained on $\sim$100 times more complex structures than available
matching affinity measurements (Liu et al., 2021; Mohseni Behbahani et al.,
2023). These models achieve root-mean-squared-errors less than the threshold
typically used to define hot spots (binding free energy changes greater than 2
kcal/mol), but their correlation with experimental values remains modest
(Pearson $R\approx 0.6$) and drops substantially on complexes with reduced
sequence or structural similarity to those in their training sets ($R\approx
0.4$) (Liu et al., 2021; Mohseni Behbahani et al., 2023). Developing
generalizable models to quantify variant effects at scale remains a challenge
(Tsishyn et al., 2023), exacerbated by the limited amount of experimental data
available for both training and evaluating models.

Previous studies have found that partner-specific methods are generally more
accurate than partner-agnostic ones, especially for identifying sites that
mediate transient interactions (Xue et al., 2015; Abdin et al., 2022; Dai and
Bailey-Kellogg, 2021). Among partner-specific methods, protein–peptide models
tend to predict interacting residues on either the protein (Abdin et al.,
2022; Wang et al., 2022c) or the peptide (Lei et al., 2021), but not both
(Fig. 5C). On the other hand, protein–protein models not only identify the
residues that comprise interacting surfaces on both proteins (Dai and Bailey-
Kellogg, 2021), but also typically predict the specific residue pairs that
form inter-protein contacts (Fig. 5D), which altogether characterize how the
proteins are oriented relative to each other within the complex (Townshend et
al., 2019; Fout et al., 2017; Zeng et al., 2018; Xie et al., 2020; Sledzieski
et al., 2021; Xie and Xu, 2022; Hosseini et al., 2023; Si and Yan, 2023a, b).
This simultaneous prediction of residues on both interaction surfaces appears
to improve prediction accuracy for both protein–protein (Liu et al., 2020b;
Xue et al., 2015) and protein–peptide (Li et al., 2023) interaction sites,
when it is done. The improvement may be due to collective effects only being
evident when the entirety of the interfacial region(s) is considered.

Within both categories of methods, models using structural information
generally outperform those using only protein sequences (Li et al., 2023;
Abdin et al., 2022). While not a concern for sequence-based models, the
suitability of structure-based models for identifying novel interaction sites
rests on their success in using unbound monomer structures as input; knowledge
of a complex structure abrogates the need to predict interaction sites
altogether. Complexes with experimental structures for which the corresponding
apo structures are unavailable outnumber those for which they are available by
over one hundred to one (Townshend et al., 2019). As a result, many models
have been trained on bound monomer structures extracted from complex
structures, either alone or in combination with apo structures (Townshend et
al., 2019; Gainza et al., 2020; Dai and Bailey-Kellogg, 2021; Li et al., 2023;
Abdin et al., 2022; Kozlovskii and Popov, 2021; Tubiana et al., 2022; Krapp et
al., 2023; Si and Yan, 2023b). These models can reliably describe interactions
between proteins that maintain ‘near-rigid’ structures upon binding: For
proteins that undergo minimal conformational changes, amounting to only a few
angstrom root-mean-square-deviation between bound and unbound structures,
models identify interacting residues on apo structures with only minimally
reduced accuracy compared to bound ones (Tubiana et al., 2022; Krapp et al.,
2023). However, they typically report reduced performance on unbound
structures, overall, and those of proteins involved in transient interactions,
in particular, with classifier effectiveness, as measured by AUROC, dropping
by $5-10\%$ (Gainza et al., 2020; Dai and Bailey-Kellogg, 2021; Krapp et al.,
2023). Thus, they remain less suited for modeling interactions in which
monomers undergo significant conformational changes upon binding (Gainza et
al., 2020; Dai and Bailey-Kellogg, 2021). Such interactions may be better
described by models that instead predict complex structures directly from
sequence, avoiding the need for monomer structures altogether and implicitly
accounting for conformational changes.

####  3.2.2 Predicting complex structures

Further mechanistic information about a protein interaction can be gleaned
from its atomistic complex structure. When monomeric structures of each
binding partner are available, docking algorithms can produce complex
structures, conventionally through a search phase to sample different bound
configurations (in addition to varied monomer conformations in flexible
docking approaches) followed by scoring of each complex to select the optimal
one (Fig. 6A) (Li et al., 2022a; Tsuchiya et al., 2022; Wodak et al., 2023).

Figure 6: Efforts to elucidate the atomistic structure of a protein complex
using deep learning employ different strategies. (A) Atomistic complex
structures can be predicted by docking input monomer structures. Most
commonly, rigid docking approaches are employed to translate and rotate one
interactor into its bound position. Flexible docking approaches allow for
additional conformational changes in each monomer. (B) Alternatively,
atomistic complex structures can be predicted from the sequences of each
constituent monomer and their stoichiometries in the assembly.

When interaction site information is unknown, the requisite global search and
its computational expense often hinders successful docking. Focusing the
search using deep learning methods for interaction site prediction, even when
they are not perfectly accurate, can increase the success rate of conventional
docking methods (Li et al., 2023; Si and Yan, 2023a, b). End-to-end deep
learning methods that avoid the search phase altogether offer more significant
speedups over conventional docking methods (Ganea et al., 2022; Ketata et al.,
2023; Sverrisson et al., 2022; McPartlon and Xu, 2023; Chu et al., 2023).
Ultimately, the success of docking methods depends on accurately scoring
sampled complexes to identify the native pose among potentially many incorrect
ones (Lensink et al., 2021), and deep learning methods have been developed for
this task as well (Renaud et al., 2021; Mohseni Behbahani et al., 2022; Wang
et al., 2021, 2020b; Eismann et al., 2021; Han et al., 2023; Chen et al.,
2023b; Cao and Shen, 2020; Johansson-Åkhe et al., 2021).

Deep learning methods that predict atomistic complex structures from monomer
sequences and their stoichiometries (Fig. 6B) circumvent the need for input
monomer structures. The unprecedented accuracy of AlphaFold2 (AF2) at
predicting structures of individual protein chains (Jumper et al., 2021)
prompted the development of approaches that use AF2 to predict complex
structures. AF2 predicts atomistic structures by processing a protein’s amino
acid sequence, evolutionary history (in the form of an MSA), and, if
available, structural templates of homologous proteins through a series of
attention-based neural networks. Provided with monomer inputs connected either
with a residue insertion gap (Baek et al., 2021; Bryant et al., 2022a; Mirdita
et al., 2022) or flexible glycine linker (Ko and Lee, 2021; Tsaban et al.,
2022), AF2 often successfully predicts complex structures, and an AF2 model
developed specifically for complex structure prediction (AF2-Multimer) (Evans
et al., 2022) exhibits superior accuracy (Evans et al., 2022; Bryant et al.,
2022a; Gao et al., 2022): Out of 2,609 unique interfaces derived from over
4,000 complexes, 70% of heteromeric and 72% of homomeric interfaces are
correctly predicted (as defined by DockQ score $\geq 0.23$ (Basu and Wallner,
2016)) by AF2-Multimer compared to only 43% and 64% by AF2 supplied with
monomers connected with a flexible linker (Evans et al., 2022). AF2-based
approaches outperform conventional protein–protein and protein–peptide docking
methods and exhibit almost three-fold higher success rates (Ghani et al.,
2022; Yin et al., 2022; Akdel et al., 2022; Bryant et al., 2022a; Johansson-
Åkhe and Wallner, 2022; Shanker and Sanner, 2023), although further gains are
possible with consensus approaches that combine AF2 with traditional, physics-
inspired docking methods (Shanker and Sanner, 2023; Johansson-Åkhe and
Wallner, 2022; Ghani et al., 2022)).

Additionally, AF2 provides confidence metrics that can distinguish more
accurately modeled complex structures from less accurate ones (Yin et al.,
2022; Bryant et al., 2022a; Gao et al., 2022; Johansson-Åkhe and Wallner,
2022; Zhu et al., 2023), where accuracy is typically defined based on DockQ
scores or metrics defined by the Critical Assessment of Predicted Interactions
(CAPRI) (Lensink et al., 2021). Moreover, AF2 confidence metrics can be used
to distinguish directly interacting from non-interacting protein–protein (Gao
et al., 2022) and protein–peptide pairs (Johansson-Åkhe and Wallner, 2022;
Bret et al., 2023; Gurvich et al., 2023; Bryant and Elofsson, 2022; Teufel et
al., 2023; Lee et al., 2023). Evaluated on a classification benchmark of 672
protein–peptide interactions derived from experimental structures in the PDB,
AF2-Multimer recalls 26% at a false positive rate of 1% (Johansson-Åkhe and
Wallner, 2022) and, in fact, is matched only by one model developed
specifically for this task—Peptriever (Gurvich et al., 2023), which leverages
self-supervised pre-training to jointly learn representations of proteins and
peptides.

Despite the wide margin in accuracy between AF2-Multimer and state-of-the-art
docking methods, AF2-Multimer predicted acceptable structures, defined based
on metrics quantifying both overall fold and interface accuracy, for only 22
out of 41 complexes (54%) in the blind, community-wide assessment conducted
during the most recent Critical Assessment of protein Structure Prediction
(CASP15) (Ozden et al., 2023). Complexes with weak evolutionary signals,
lacking structural templates, or assembled from many heterogeneous subunits
and containing over 1,800 residues proved particularly challenging (Ozden et
al., 2023; Zhu et al., 2023; Akdel et al., 2022). These shortcomings were in
part alleviated by optimizing MSA construction (Ozden et al., 2023; Bryant and
Noé, 2023; Mirdita et al., 2022; Chen et al., 2022); increasing the number and
diversity of predicted complex structures, for example, by increasing the
number of iterations through the AF2-Multimer network (recycles) or randomly
disabling neurons (dropout) (Johansson-Åkhe and Wallner, 2022; Wallner, 2023);
and assembling higher-order complexes from smaller interacting subcomponents
individually predicted by AF2-Multimer (Bryant et al., 2022b; Shor and
Schneidman-Duhovny, 2023; Jeppesen and André, 2023). However, none of these
strategies individually yielded acceptable structures for all test complexes.
The top ranking approach, which leveraged methods for constructing diverse and
sensitive MSAs, successfully predicted 30 complexes (73%) and was complemented
by an approach employing increased sampling (Ozden et al., 2023). Integrating
available experimental information, specifically distance restraints obtained
from methods such as cross-linking mass spectrometry, either to select and
validate an optimal complex structure among those predicted (O’Reilly et al.,
2023; Shor and Schneidman-Duhovny, 2023; Burke et al., 2023) or to directly
bias the network’s predictions (Stahl et al., 2023a) promises further
improvements.

Indeed, different types of protein interactions pose their own modeling
challenges and motivate a variety of approaches to tackle them. Characteristic
differences in the physical and evolutionary properties of protein–protein
versus protein–peptide interactions warrant the use of different inputs or
variations of AF2. For protein–protein interactions, combining paired MSAs
(Fig. 2B) with unpaired ones improves predictions with AF2-Multimer (Yin et
al., 2022; Bryant et al., 2022a), but is often unnecessary to predict accurate
complex structures when templates are used (Yin et al., 2022; Gao et al.,
2022). In contrast, MSAs for peptide interactors, being difficult to construct
due to their short lengths, are typically not used (Ko and Lee, 2021; Tsaban
et al., 2022; Johansson-Åkhe and Wallner, 2022; Chang and Perez, 2023; Shanker
and Sanner, 2023), and using MSAs derived from their cognate proteins can even
be detrimental (Bret et al., 2023). In fact, including the full protein
context surrounding peptidic binding motifs, which often reside within
intrinsically disordered regions, substantially decreases prediction
sensitivity and accuracy (Lee et al., 2023; Bret et al., 2023). To address
this limitation, a fragmentation approach, which decomposes full length
proteins into constituent globular domains and peptidic motifs and removes
disordered linker regions, has been devised to predict multidentate
protein–protein interactions mediated by modular peptide-binding domains (Lee
et al., 2023). Interactions with limited evolutionary history, including
rapidly evolving peptidic sites and antibody–antigen interactions, may be more
suitably modeled with deep learning methods that predict structure directly
from single sequences and avoid MSAs entirely; however, attempts using such
methods with monomer inputs connected with a residue insertion gap or flexible
linker have so far proven unsatisfactory compared to AF2-based approaches
(Tsuchiya et al., 2022; Shanker and Sanner, 2023; Zhu et al., 2023; Lin et
al., 2023).

By combining high-throughput experimental measurements of protein interactions
with AF2 predictions, structurally resolved protein interaction networks can
be constructed at proteome-scale. To-date, initial networks have been
constructed for Saccharomyces cerevisiae (Humphreys et al., 2021), Escherichia
coli (Gao et al., 2022), Bacillus subtilis (O’Reilly et al., 2023), and humans
(Burke et al., 2023). These structural models provide new insights into how
proteins assemble into functional complexes responsible for processes ranging
from transcription, translation and DNA repair to metabolism, biomolecular
transport, and protein modification, and offer novel structural hypotheses for
how interfacial mutations contribute to disease pathophysiologies.

###  3.3 Designing binders

Mechanistic knowledge of protein interactions ultimately enables the design of
novel binders and ways to precisely modulate interaction networks.
Computational methods to de novo design proteins that specifically bind
protein targets with high affinity have immense potential for engineering
biosensors, therapeutics, synthetic biology tools, and biomaterials with broad
basic and translational applications (Marchand et al., 2022; Lu et al., 2020).
One approach leverages knowledge of existing protein–protein interactions and
their binding motifs to graft an existing interface onto a new protein
scaffold, which is then optimized to ensure the structural integrity of the
grafted binding motif and increase interaction affinity (Fig. 7A) (Marchand et
al., 2022).

Figure 7: Efforts to design binders using deep learning employ different
strategies. (A) One approach leverages knowledge of known (or predicted)
binders of a given target protein and grafts their interaction motifs onto a
scaffold to design a novel binder. (B) Another approach uses a generative
model to de novo design a binder, conditioned on its ability to bind the
target. Because the design is not constrained to a particular interaction
motif, novel interaction interfaces that maximize surface area and
complementarity to the target can be potentially designed.

Deep learning methods for protein interaction and interaction site prediction
can aid these efforts by expanding the pool of known interactions and guiding
the initial choice of binding motif to seed designs, respectively (Gainza et
al., 2023; Brixi et al., 2023). For example, molecular surface fingerprint
representations provided by the geometric deep learning framework MaSIF
(Gainza et al., 2020; Sverrisson et al., 2020) have been used to construct a
diverse set of initial designs by first identifying putative binding sites on
a target protein and then efficiently selecting interacting motifs from a
large database based on their fingerprint complementarity to the target site.
Subsequent optimization, either experimentally or purely in silico, yielded de
novo binders to the SARS-CoV-2 spike protein and immuno-oncology targets PD-1,
PD-L1, and CTLA-4 with high affinity and/or specificity for the
computationally designed interface (Gainza et al., 2023).

However, such approaches have low success rates, with thousands of
computational designs having to be experimentally screened to identify even a
single low affinity binder in many cases (Gainza et al., 2023; Marchand et
al., 2022). This is largely attributed to designed sequences failing to either
adopt the intended monomer structure or bind the intended surface (Bennett et
al., 2023). Since deep learning methods for structure prediction implicitly
assess the probability that a sequence adopts some (potentially a priori
unknown) structure and forms a complex, these models can help mitigate these
issues. One approach uses them to hallucinate novel binders: An initial amino
acid sequence is iteratively updated to maximize the structure prediction
model’s confidence and optimize additionally desired properties, such as
binding motif reconstruction, interaction quality, or complex symmetry (Wang
et al., 2022b; Wicky et al., 2022; Goudy et al., 2023; Wang et al., 2023;
Jendrusch et al., 2021; Bryant and Elofsson, 2022; Yang et al., 2022; Hie et
al., 2022). Using deep network hallucination, experimentally validated protein
and peptide binders (Wang et al., 2022b; Goudy et al., 2023; Wang et al.,
2023), viral receptor traps (Wang et al., 2022b), and giant oligomeric
assemblies (Wicky et al., 2022) distinct from natural proteins have been
designed. Integrating a deep learning model for structure-conditioned protein
sequence generation, specifically ProteinMPNN (Dauparas et al., 2022), into
the optimization scheme further increases success rates by generating
sequences with higher expression levels, solubilities, cyrstallization
propensities, and thermostabilities (Wicky et al., 2022; Goudy et al., 2023).

Most recently, deep generative models have shown even superior de novo design
capabilities (Fig. 7B). By faithfully recapitulating the distribution of
protein sequences or structures provided by training data, generative models
enable facile sampling of realistic new proteins whose stability and
expression matches that of natural ones. One especially successful class of
generative model deployed presently is a diffusion model (Watson et al., 2023;
Ingraham et al., 2022; Lin and AlQuraishi, 2023): Diffusion models transform
complex data distributions into simple ones by gradually adding noise to
training samples and learning to stochastically reverse this process in order
to generate new data. By conditioning each step of reverse diffusion on
specified design objectives, such as binding propensity, the model generates
diverse, authentic proteins with desired properties from random noise. One
protein diffusion model, RFdiffusion (Watson et al., 2023), leverages the
extensive knowledge of protein structure and complex assembly implicitly
embedded in deep learning structure prediction models by repurposing the
RoseTTAFold structure prediction network for reverse diffusion. Outperforming
other de novo design methods, RFdiffusion generates higher-order symmetric
oligomers, protein scaffolds for binding motifs, and picomolar affinity
peptide-binders without any subsequent optimization while requiring
experimental testing of only tens of computational designs to identify
successful ones (Watson et al., 2023; Vázquez Torres et al., 2022).

##  4 Successes, limitations, and promising directions

The challenge of understanding how molecularly diverse protein interactions
collectively coordinate biological processes has spawned a growing suite of
deep learning approaches (Fig. 3). Of the methods reviewed here, deep neural
networks for complex structure prediction (Jumper et al., 2021; Evans et al.,
2022) and de novo binder design (Watson et al., 2023; Vázquez Torres et al.,
2022) are preeminent examples of how synergistic use of data and biophysical
priors yields highly accurate and general models (Ahdritz et al., 2023). Based
on the observation that physicochemical complementarity consistently
distinguishes interacting proteins, structural information is increasingly
leveraged to accomplish varied modeling tasks (Abdin et al., 2022; Jha et al.,
2022; Krapp et al., 2023; Gainza et al., 2023; Gao et al., 2023). Structure-
based approaches accurately model stable, obligate interactions exhibiting
limited conformation changes upon binding and under strong evolutionary
pressures. However, they remain challenged by weak, transient interactions and
protein interactors with extensive disordered regions that do not readily
admit to experimental structure determination required for training and/or
inference (Akdel et al., 2022; Yin et al., 2022; Burke et al., 2023; Lee et
al., 2023; Gainza et al., 2020). We anticipate that advancements across
modeling tasks will continue to benefit from biologically-informed approaches
that effectively utilize all available data and tailor network architectures
and training regiments to suit different types of protein interactions.

###  4.1 Expanding training datasets

Depending on their biophysical properties, different classes of protein
interactions are each amenable to different experimental characterization
techniques. However, except for protein–protein interaction classifiers, the
full breadth of available experimental data remains underutilized. Existing
models for protein–peptide interaction prediction almost exclusively use
training datasets derived from complex structures, limiting them to tens of
thousands of interactions with well-defined bound structures (Lei et al.,
2021; Palepu et al., 2022; Gurvich et al., 2023). Retraining or fine-tuning
them on the millions of qualitative binding measurements previously curated to
construct (less performative) shallow machine learning models (Cunningham et
al., 2020; AlQuraishi et al., 2014; Miller et al., 2008; Kundu et al., 2014)
offers a straightforward route to improving them. Modern experimental methods
for proteome-scale mapping of motif-mediated interactions (Benz et al., 2022;
Davey et al., 2023) provide another, yet untapped, and continually growing
source of data for training and evaluating models, with methods scaling to
millions of peptides. A paucity of data has also stymied the development of
deep learning models for interaction affinity prediction. This stands to
change owing to recent experimental innovations that allow quantification of
binding affinities at scale (tens of thousands of measurements in a day) with
sensitivity for both strong (nanomolar) and weak (micromolar) interactions
(Gogl et al., 2022). These experimental methods provide data sorely needed to
construct quantitative models that can account for differences in binding
affinity that underlie interaction specificity, cooperativity, and
competition; it is precisely these differences that enable systems of protein
interactions to physically execute complex signaling logic and that explain
how specific disease variants alter functional protein interaction networks
(AlQuraishi et al., 2014).

Efforts to build quantitative models of protein interactions may further
benefit from approaches that harmonize small-scale, highly accurate
measurements with large-scale, noisy experimental data to extract
biophysically meaningful signals of binding that cover broad swaths of
interaction space. Multitask learning provides one way to integrate
heterogeneous data. For example, adding a classifier on top of AlphaFold2 and
fine-tuning the combined network parameters for simultaneous binary
classification of qualitative protein–peptide binding and complex structure
prediction further improves the resulting model’s discriminative capabilities
on transient interactions (Motmaen et al., 2023). Similar approaches could be
devised to synthesize data from varied types of experimental assays (Yan et
al., 2023), ranging from in vitro biophysical methods and those detecting
complexes present in cell extracts or in vivo to functional assays reporting
on the cellular consequences of an interaction but not the physical
interaction itself (Peng et al., 2017; Davey et al., 2023; Luck et al., 2020;
Huttlin et al., 2021). Directly accounting for known differences in readout,
detection limits, sensitivities, and sources of uncertainty within the loss
function (Lim et al., 2022), for instance, or even explicitly modeling the
steps of an experimental protocol (Rube et al., 2022) would provide a
principled way to combine heterogeneous data that has been simplistically
pooled to train many existing protein–protein interaction classifiers.

###  4.2 Leveraging self-supervised representation learning

Self-supervised representation learning offers another promising approach,
pursuable in parallel with efforts to expand labeled training datasets, to
improve the ability of deep learning models to reason about diverse protein
interactions. For instance, sequence-based models using representations
extracted from protein language models can match or even outperform structure-
based models for predicting both protein interactions (Gurvich et al., 2023;
Yang et al., 2023b) and interaction sites (Wang et al., 2022c; Hosseini et
al., 2023; Si and Yan, 2023a). Crucially, they are applicable to proteins that
have resisted experimental structure determination. One limitation of current
protein language models, whose vocabularies comprise canonical amino acids, is
their inability to account for post-translational modifications, which
dynamically regulate protein interactions and whose misregulation is
frequently associated with disease (Conibear, 2020). In principle, post-
translational modifications can be accounted for in structure-based models
using atomistic representations. An emerging area of protein representation
learning aims to better capture detailed spatiochemical information by
directly learning from both sequences and structures (Zhang et al., 2023b, a;
Yang et al., 2023a; Sun et al., 2023). Such approaches have been used to
distill geometric and physicochemical properties common among protein complex
interfaces at the atomic level (Mohseni Behbahani et al., 2023; Liu et al.,
2021); however, more general-purpose representations provided by models
trained on over an order-of-magnitude more monomer structures (Zhang et al.,
2023b, a) have yet to be incorporated within models of protein interactions.
Furthermore, while current self-supervised approaches for learning
representations of protein structure are quite promising, most directly borrow
methods from natural language processing or computer vision (Mohseni Behbahani
et al., 2023; Zhang et al., 2023b; Sun et al., 2023) and have not exploited
domain-specific knowledge to craft learning objectives tailored to
biomolecular structures (Liu et al., 2021).

###  4.3 Incorporating biophysical priors

Incorporating physical inductive biases can result in deep learning models
that efficiently learn from limited data, better generalize to proteins
outside their training distributions, and exhibit increased interpretability.
For example, one geometric deep learning model for interaction site prediction
builds on the concept of pharmacophores to construct local, atomic-scale
representations of amino acids that can be interpreted in terms of common
chemical motifs, including hydrogen-bond networks and solvent-exposed basic
residues; thus, the model provides testable hypotheses about molecular
recognition mechanisms (Tubiana et al., 2022). The continued development of
geometric deep learning architectures that account for inherent physical
properties of molecular systems (e.g., SE(3)-equivariance) has yielded a
number of successful approaches for encoding input monomer structures to model
interactions in which proteins maintain ‘near-rigid’ structures (Tubiana et
al., 2022; Gainza et al., 2020; Sverrisson et al., 2020; Ganea et al., 2022;
Krapp et al., 2023; Dai and Bailey-Kellogg, 2021; Huang et al., 2023). More
nascent efforts have focused on developing neural network architectures that
effectively utilize monomer structures while simultaneously allowing for
conformational changes upon binding (Chu et al., 2023; McPartlon and Xu, 2023;
Abdin et al., 2022). Such architectures may facilitate the development of
methods that enable explicit encoding of conformational ensembles, perhaps
through generative models. This promises advancements in modeling interactions
that involve substantial structural changes and interactions mediated by
intrinsically disordered proteins (Janson et al., 2023; Tesei et al., 2023),
both of which remain challenging for current methods. Key to training deep
learning models that predict equilibrium conformational ensembles has been the
use of data from physics-based molecular simulations (Noé et al., 2019; Zheng
et al., 2023; Tesei et al., 2023), which resolve equilibrium ensembles with
substantially higher resolution and efficiency than current experimental
approaches.

More broadly, physics-informed machine learning encompasses a variety of
approaches that integrate experimental observations with physical models to
facilitate learning of solutions that respect underlying physical constraints
(e.g., symmetries, conservation laws, thermodynamic equilibrium, monotonicity)
(Karniadakis et al., 2021). Such methods promise to be valuable for building
predictors of protein interaction thermodynamics and kinetics. One approach,
complementary to strategies described previously, incorporates known physical
functional forms to learn binding energy functions in which intermolecular
interactions scale with distance, as expected from quantum mechanical
arguments (Sverrisson et al., 2022). Another learns approximate steady-state
solutions to ordinary differential equations customarily employed within
dynamical models of interaction networks that saturate at physiological
concentrations (Nilsson et al., 2022). One flexible framework for learning
models that approximately satisfy generic physical constraints introduces
biases through the choice of optimization objectives and inference algorithms.
This has been used to learn generative models of protein conformational
ensembles that recapitulate the Boltzmann distribution (Noé et al., 2019;
Zheng et al., 2023) and neural network time-series models of transition path
ensembles linking different protein conformational states (Tsai et al., 2022).
Applying such approaches to protein interactions, and not just individual
proteins, may provide insights into binding mechanisms.

Integrated modeling frameworks also provide a promising path to expand models
beyond individual protein complexes to ultimately encompass entire networks
embedded with their cellular context. Formulating deep learning models in
terms of an appropriate statistical mechanical ensemble (Cunningham et al.,
2020; AlQuraishi et al., 2014), standard practice in physics-based modeling,
provides a natural way to account for variations in physical conditions (e.g.,
temperature, pH) or protein abundances characteristic of different
environmental conditions or cellular states. Predicting how proteome-scale
interaction networks coordinate cellular responses to environmental changes or
therapeutic interventions additionally serves to benefit from approaches that
integrate deep learning techniques with existing dynamical systems models
(Yuan et al., 2021; Stapor et al., 2022) or that directly exploit mathematical
correspondences between the two types of models (Chen et al., 2018; Rackauckas
et al., 2021). In the quest for a comprehensive understanding of protein
interaction networks and their roles in complex cellular behaviors, a variety
of innovations will likely be needed. One aspect nevertheless seems certain:
Given their demonstrated value for discovering novel interactions, elucidating
molecular recognition mechanisms, and designing functional assemblies, deep
learning methods will remain a flourishing component of the larger ecosystem
of quantitative biology models of protein interactions.

##  5 Appendix: Ecosystem of deep learning methods for modeling protein
interactions

  * •

(1.i) Predictors of direct protein–peptide interactions: Peptriever (Gurvich
et al., 2023)

  * •

(1.ii) Predictors of direct protein–protein interactions: Unsal et al. (2022)

  * •

(1.iii) Predictors of higher-order complexes: PCGAN (Pan et al., 2023)

  * •

(1.ii-iii) Predictors of direct protein–protein interactions and higher-order
complexes: DeepPPI (Du et al., 2017), DeepSequencePPI (Gonzalez-Lopez et al.,
2018), DPPI (Hashemifar et al., 2018), DNN-PPI (Li et al., 2018), PIPR (Chen
et al., 2019), Richoux et al. (2019), DeepFE-PPI (Yao et al., 2019),
Multimodal SAE (Zhang and Kabuka, 2019), Jha and Saha (2020), Liu et al.
(2020a), Yang et al. (2020b), S-VGAE (Yang et al., 2020a), MTT (Dong et al.,
2021), DeepViral (Liu-Wei et al., 2021), FSNN-LGBM (Mahapatra and Sahu, 2021),
FSFDW (Nasiri et al., 2021), D-SCRIPT (Sledzieski et al., 2021), S2F (Xue et
al., 2021), TransPPI (Yang et al., 2021), DeepTrio (Hu et al., 2022), Jha et
al. (2022), SDNN-PPI (Li et al., 2022b), Topsy-Turvy (Singh et al., 2022),
TAGPPI (Song et al., 2022), RAPPPID (Szymborski and Emad, 2022), P-PPI
(Anteghini et al., 2023), HIGH-PPI (Gao et al., 2023), SYNTERACT (Hallee and
Gleghorn, 2023), SGPPI (Huang et al., 2023), Jha and Saha (2023) CNN, Jha et
al. (2023) GNN, SENSE-PPI (Volzhenin et al., 2023), PPITrans (Yang et al.,
2023b), SemiGNN-PPI (Zhao et al., 2023)

  * •

(1-2.i) Predictors of protein–peptide interactions and interaction sites: CAMP
(Lei et al., 2021), Cut&CLIP (Palepu et al., 2022)

  * •

(1-2.ii) Predictors of direct protein–protein interactions and interaction
sites: MaSIF (Gainza et al., 2020), dMaSIF (Sverrisson et al., 2020)

  * •

(2.i) Predictors of protein–peptide interaction sites: Visual (Wardah et al.,
2020), BiteNetPP (Kozlovskii and Popov, 2021), PepNN (Abdin et al., 2022),
PepBCL (Wang et al., 2022c), GraphPPepIS (Li et al., 2023)

  * •

(2.ii) Predictors of direct protein–protein interaction sites: Fout et al.
(2017), ComplexContact (Zeng et al., 2018), SASNet (Townshend et al., 2019),
DLPred (Zhang et al., 2019), Liu et al. (2020b), TopNetTree (Wang et al.,
2020a), Xie et al. (2020), MuPIPR (Zhao et al., 2020), PInet (Dai and Bailey-
Kellogg, 2021), DELPHI (Li et al., 2021), GeoPPI (Liu et al., 2021),
DNCON2_Inter (Quadir et al., 2021), DeepHomo (Yan and Huang, 2021), DLA
(Mohseni Behbahani et al., 2023), PITHIA (Hosseini and Ilie, 2022), DRCon (Roy
et al., 2022), PIPENN (Stringer et al., 2022), ScanNet (Tubiana et al., 2022),
PGT (Wu et al., 2022b), GLINTER (Xie and Xu, 2022), SaLT&PepPer (Brixi et al.,
2023) Seq-InSite (Hosseini et al., 2023), EDLMPPI (Hou et al., 2023), PeSTo
(Krapp et al., 2023), ISPRED-SEQ (Manfredi et al., 2023), DRN-1D2D_Inter (Si
and Yan, 2023a), PLMGraph-Inter (Si and Yan, 2023b)

  * •

(3.ii) Predictors of direct protein–protein complex structures (and
interaction sites): ESMPair (Chen et al., 2022), EquiDock (Ganea et al.,
2022), Sverrisson et al. (2022), GeoDock (Chu et al., 2023), RoseTTAFold2
(Baek et al., 2023), AFProfile (Bryant and Noé, 2023), AlphaRED (Harmalkar et
al., 2023), DiffDock-PP (Ketata et al., 2023), AFsample (Wallner, 2023)

  * •

(3.i-ii) Predictors of protein–peptide and direct protein–protein complex
structures (and interaction sites): AF-linker (Tsaban et al., 2022; Ko and
Lee, 2021), Lee et al. (2023)

  * •

(1-3.i) Predictors of protein–peptide interactions and complex structures (and
interaction sites): Motmaen et al. (2023), Chang and Perez (2023), Teufel et
al. (2023)

  * •

(3.ii-iii) Predictors of direct protein–protein interactions and higher-order
complexes structures (and interaction sites): AF2Complex (Gao et al., 2022),
AFLink (Stahl et al., 2023b, a), ESMFold-linker (Lin et al., 2023)

  * •

(3.iii) Predictors of higher-order complex structures: MolPC (Bryant et al.,
2022b), Uni-Fold Symmetry (Li et al., 2022c), Jeppesen and André (2023),
CombFold (Shor and Schneidman-Duhovny, 2023)

  * •

(1-3.i-iii) Predictors of protein–peptide, direct protein–protein, and higher-
order complex interactions, interaction sites, and complex structures:
RosseTTAFold-gap (Baek et al., 2021; Tsaban et al., 2022), AF2-gap (Bryant et
al., 2022a), AF2-Multimer (Evans et al., 2022), ColabFold (Mirdita et al.,
2022), AlphaPulldown (Yu et al., 2023), OmegaFold-linker (Tsuchiya et al.,
2022; Shanker and Sanner, 2023)

  * •

(3-4.ii) Predictors of direct protein–protein complex structures (and
interaction sites) and models to design protein binders: DockGPT (McPartlon
and Xu, 2023)

  * •

(4.i) Models to design peptide binders: EvoBind (Bryant and Elofsson, 2022),
GANDALF (Rossetto and Zhou, 2020), Yang et al. (2022), PepPrCLIP (Bhat et al.,
2023)

  * •

(4.ii) Models to design protein binders: Gainza et al. (2023), EvoPro (Goudy
et al., 2023), ProteinEnT (Mahajan et al., 2023), EvoPlay (Wang et al., 2023)

  * •

(4.iii) Models to design higher-order complexes: Chroma (Ingraham et al.,
2022)

  * •

(4.i-ii) Models to design peptide and protein binders: RFjoint (Wang et al.,
2022b)

  * •

(4.ii-iii) Models to design protein binders and higher-order complexes:
AlphaDesign (Jendrusch et al., 2021), Hie et al. (2022), ESM-IF1 (Hsu et al.,
2022)

  * •

(4.i-iii) Models to design peptide and protein binders and higher-order
complexes: Hallucination with structure prediction models (RoseTTAFold,
trRosetta (Wang et al., 2022b), or AF2 (Wicky et al., 2022)), RFDiffusion
(Watson et al., 2023; Vázquez Torres et al., 2022)

##  6 Competing interests

M.A. is a member of the Scientific Advisory Boards of Cyrus Biotechnology,
Deep Forest Sciences, Nabla Bio, Oracle Therapeutics, and FL2021-002, a
Foresite Labs company.

##  7 Author contributions statement

J.R.R., G.N., and M.A. conceived, designed, wrote, and edited the manuscript.

##  8 Acknowledgments

J.R.R. acknowledges a Fellowship of The Jane Coffin Childs Memorial Fund for
Medical Research. We thank Eric Wong, Tony Culos, Martin Culka, Christina
Floristean, Lukas Jarosch, Yeqing Lin, Harry Lee, Pavan Ravindra, Charlotte
Rochereau, Toni Sagayaraj, Jae Shin, Wojtek Treyde, Arthur Valentin, and the
rest of the AlQuraishi group for valuable discussions about modeling
biomolecules using deep learning.

## References

  * Abdin et al. (2022) Abdin, O., Nim, S., Wen, H., and Kim, P. M. (2022) _Commun. Biol._ , 5, 503.
  * Acuner Ozbabacan et al. (2011) Acuner Ozbabacan, S. E., Engin, H. B., Gursoy, A., and Keskin, O. (2011) _Protein Eng. Des. Sel._ , 24, 635–648.
  * Ahdritz et al. (2023) Ahdritz, G., Bouatta, N., Floristean, C., et al. (2023) _bioRxiv_ , doi: 10.1101/2022.11.20.517210.
  * Akdel et al. (2022) Akdel, M., Pires, D. E. V., Pardo, E. P., et al. (2022) _Nat. Struct. Mol. Biol._ , 29, 1056–1067.
  * Alley et al. (2019) Alley, E. C., Khimulya, G., Biswas, S., et al. (2019) _Nat. Methods_ , 16, 1315–1322.
  * AlQuraishi et al. (2014) AlQuraishi, M., Koytiger, G., Jenney, A., et al. (2014) _Nat. Genet._ , 46, 1363–1371.
  * Anteghini et al. (2023) Anteghini, M., Martins dos Santos, V. A. P., and Saccenti, E. (2023) _bioRxiv_ , doi: 10.1101/2023.06.30.547177.
  * Baek et al. (2021) Baek, M., DiMaio, F., Anishchenko, I., et al. (2021) _Science_ , 373, 871–876.
  * Baek et al. (2023) Baek, M., Anishchenko, I., Humphreys, I. R., et al. (2023) _bioRxiv_ , doi: 10.1101/2023.05.24.542179.
  * Baranwal et al. (2022) Baranwal, M., Magner, A., Saldinger, J., et al. (2022) _BMC Bioinform._ , 23, 370.
  * Basu and Wallner (2016) Basu, S. and Wallner, B. (2016) _PLoS One_ , 11, e0161879.
  * Ben-Hur and Noble (2006) Ben-Hur, A. and Noble, W. S. (2006) _BMC Bioinform._ , 7, S2.
  * Bennett et al. (2023) Bennett, N. R., Coventry, B., Goreshnik, I., et al. (2023) _Nat. Commun._ , 14, 2625.
  * Benz et al. (2022) Benz, C., Ali, M., Krystkowiak, I., et al. (2022) _Mol. Syst. Biol._ , 18, e10584.
  * Bernett et al. (2023) Bernett, J., Blumenthal, D. B., and List, M. (2023) _bioRxiv_ , doi: 10.1101/2023.01.18.524543.
  * Bhat et al. (2023) Bhat, S., Palepu, K., Yudistyra, V., et al. (2023) _bioRxiv_ , doi: 10.1101/2023.06.26.546591.
  * Blohm et al. (2014) Blohm, P., Frishman, G., Smialowski, P., et al. (2014) _Nucleic Acids Res._ , 42, D396–D400.
  * Bret et al. (2023) Bret, H., Andreani, J., and Guerois, R. (2023) _bioRxiv_ , doi: 10.1101/2023.05.25.542287.
  * Brixi et al. (2023) Brixi, G., Ye, T., Palepu, K., et al. (2023) _Research Square_ , doi: 10.21203/rs.3.rs-1694183.
  * Bronstein et al. (2021) Bronstein, M. M., Bruna, J., Cohen, T., and Veličković, P. (2021) _arXiv_ , doi: 10.48550/arXiv.2104.13478.
  * Bryant and Elofsson (2022) Bryant, P. and Elofsson, A. (2022) _bioRxiv_ , doi: 10.1101/2022.07.23.501214.
  * Bryant and Noé (2023) Bryant, P. and Noé, F. (2023) _bioRxiv_ , doi: 10.1101/2023.07.04.547638.
  * Bryant et al. (2022a) Bryant, P., Pozzati, G., and Elofsson, A. (2022a) _Nat. Commun._ , 13, 1265.
  * Bryant et al. (2022b) Bryant, P., Pozzati, G., Zhu, W., et al. (2022b) _Nat. Commun._ , 13, 6028.
  * Burke et al. (2023) Burke, D. F., Bryant, P., Barrio-Hernandez, I., et al. (2023) _Nat. Struct. Mol. Biol._ , 30, 216–225.
  * Cao and Shen (2020) Cao, Y. and Shen, Y. (2020) _Proteins: Struct., Funct., Bioinf._ , 88, 1091–1099.
  * Chang and Perez (2023) Chang, L. W. and Perez, A. (2023) _Angew. Chem. Int. Ed._ , 62, e202213362.
  * Chen et al. (2022) Chen, B., Xie, Z., Qiu, J., et al. (2022) _bioRxiv_ , doi: 10.1101/2022.09.15.508065.
  * Chen et al. (2023a) Chen, B., Cheng, X., Geng, Y.-a., et al. (2023a) _bioRxiv_ , doi: 10.1101/2023.07.05.547496.
  * Chen et al. (2019) Chen, M. H., Ju, C. J. T., Zhou, G. Y., et al. (2019) _Bioinformatics_ , 35, i305–i314.
  * Chen et al. (2018) Chen, R. T. Q., Rubanova, Y., Bettencourt, J., and Duvenaud, D. (2018) _arXiv_ , doi: 10.48550/arXiv.1806.07366.
  * Chen et al. (2023b) Chen, X., Morehead, A., Liu, J., and Cheng, J. (2023b) _Bioinformatics_ , 39, i308–i317.
  * Cheng et al. (2021) Cheng, F., Zhao, J., Wang, Y., et al. (2021) _Nat. Genet._ , 53, 342–353.
  * Chu et al. (2023) Chu, L.-S., Ruffolo, J. A., Harmalkar, A., and Gray, J. J. (2023) _bioRxiv_ , doi: 10.1101/2023.06.29.547134.
  * Conibear (2020) Conibear, A. C. (2020) _Nat. Rev. Chem._ , 4, 674–695.
  * Cunningham et al. (2020) Cunningham, J. M., Koytiger, G., Sorger, P. K., and AlQuraishi, M. (2020) _Nat. Methods_ , 17, 175–183.
  * Dai and Bailey-Kellogg (2021) Dai, B. and Bailey-Kellogg, C. (2021) _Bioinformatics_ , 37, 2580–2588.
  * Das and Yu (2012) Das, J. and Yu, H. (2012) _BMC Syst. Biol._ , 6, 92\.
  * Dauparas et al. (2022) Dauparas, J., Anishchenko, I., Bennett, N., et al. (2022) _Science_ , 378, 49–56.
  * Davey et al. (2023) Davey, N. E., Simonetti, L., and Ivarsson, Y. (2023) _Curr. Opin. Struct. Biol._ , 80, 102593.
  * del Toro et al. (2022) del Toro, N., Shrivastava, A., Ragueneau, E., et al. (2022) _Nucleic Acids Res._ , 50, D648–D653.
  * Dong et al. (2021) Dong, T. N., Brogden, G., Gerold, G., and Khosla, M. (2021) _BMC Bioinform._ , 22, 572.
  * Du et al. (2017) Du, X. Q., Sun, S. W., Hu, C. L., et al. (2017) _J. Chem. Inf. Model._ , 57, 1499–1510.
  * Eismann et al. (2021) Eismann, S., Townshend, R. J. L., Thomas, N., et al. (2021) _Proteins: Struct., Funct., Bioinf._ , 89, 493–501.
  * Evans et al. (2022) Evans, R., O’Neill, M., Pritzel, A., et al. (2022) _bioRxiv_ , doi: 10.1101/2021.10.04.463034.
  * Ferruz et al. (2022) Ferruz, N., Schmidt, S., and Höcker, B. (2022) _Nat. Commun._ , 13, 4348.
  * Fout et al. (2017) Fout, A., Byrd, J., Shariat, B., and Ben-Hur, A. (2017) In _Proceedings of the 31st International Conference on Neural Information Processing Systems_. Long Beach, CA, USA, pp. 6533–6542.
  * Gainza et al. (2020) Gainza, P., Sverrisson, F., Monti, F., et al. (2020) _Nat. Methods_ , 17, 184–192.
  * Gainza et al. (2023) Gainza, P., Wehrle, S., Van Hall-Beauvais, A., et al. (2023) _Nature_ , 617, 176–184.
  * Ganea et al. (2022) Ganea, O.-E., Huang, X., Bunne, C., et al. (2022) _arXiv_ , doi: 10.48550/arXiv.2111.07786.
  * Gao et al. (2022) Gao, M., Nakajima An, D., Parks, J. M., and Skolnick, J. (2022) _Nat. Commun._ , 13, 1744.
  * Gao et al. (2023) Gao, Z., Jiang, C., Zhang, J., et al. (2023) _Nat. Commun._ , 14, 1093.
  * Geiger and Smidt (2022) Geiger, M. and Smidt, T. (2022) _arXiv_ , doi: 10.48550/arXiv.2207.09453.
  * Ghadie et al. (2018) Ghadie, M. A., Coulombe-Huntington, J., and Xia, Y. (2018) _Curr. Opin. Struct. Biol._ , 50, 42–48.
  * Ghani et al. (2022) Ghani, U., Desta, I., Jindal, A., et al. (2022) _bioRxiv_ , doi: 10.1101/2021.09.07.459290.
  * Gogl et al. (2022) Gogl, G., Zambo, B., Kostmann, C., et al. (2022) _Nat. Commun._ , 13, 5472.
  * Gonzalez-Lopez et al. (2018) Gonzalez-Lopez, F., Morales-Cordovilla, J. A., Villegas-Morcillo, A., et al. (2018) In _2018 IEEE International Conference on Bioinformatics and Biomedicine_. Madrid, Spain, pp. 2344–2350.
  * Goudy et al. (2023) Goudy, O. J., Nallathambi, A., Kinjo, T., et al. (2023) _bioRxiv_ , doi: 10.1101/2023.05.03.539278.
  * Guo et al. (2019) Guo, H., Suzuki, T., and Rubinstein, J. L. (2019) _eLife_ , 8, e43128.
  * Gurvich et al. (2023) Gurvich, R., Markel, G., Tanoli, Z., and Meirson, T. (2023) _bioRxiv_ , doi: 10.1101/2023.07.13.548811.
  * Hallee and Gleghorn (2023) Hallee, L. and Gleghorn, J. P. (2023) _bioRxiv_ , doi: 10.1101/2023.06.07.544109.
  * Hamp and Rost (2015a) Hamp, T. and Rost, B. (2015a) _Bioinformatics_ , 31, 1945–1950.
  * Hamp and Rost (2015b) Hamp, T. and Rost, B. (2015b) _Bioinformatics_ , 31, 1521–1525.
  * Han et al. (2023) Han, Y., Zhang, S., and He, F. (2023) _Mathematics_ , 11, 1817.
  * Harmalkar et al. (2023) Harmalkar, A., Lyskov, S., and Gray, J. J. (2023) _bioRxiv_ , doi: 10.1101/2023.07.28.551063.
  * Hashemifar et al. (2018) Hashemifar, S., Neyshabur, B., Khan, A. A., and Xu, J. B. (2018) _Bioinformatics_ , 34, 802–810.
  * Hie et al. (2022) Hie, B., Candido, S., Lin, Z., et al. (2022) _bioRxiv_ , doi: 10.1101/2022.12.21.521526.
  * Hosseini and Ilie (2022) Hosseini, S. and Ilie, L. (2022) _Int. J. Mol. Sci._ , 23, 12814.
  * Hosseini et al. (2023) Hosseini, S., Golding, G. B., and Ilie, L. (2023) _bioRxiv_ , doi: 10.1101/2023.06.19.545575.
  * Hou et al. (2023) Hou, Z., Yang, Y., Ma, Z., et al. (2023) _Commun. Biol._ , 6, 73.
  * Hsu et al. (2022) Hsu, C., Verkuil, R., Liu, J., et al. (2022) _bioRxiv_ , doi: 10.1101/2022.04.10.487779.
  * Hu et al. (2022) Hu, X. T., Feng, C., Zhou, Y. C., et al. (2022) _Bioinformatics_ , 38, 694–702.
  * Huang et al. (2023) Huang, Y., Wuchty, S., Zhou, Y., and Zhang, Z. (2023) _Brief. Bioinform._ , 24, bbad020.
  * Humphreys et al. (2021) Humphreys, I. R., Pei, J. M., Baek, M., et al. (2021) _Science_ , 374, eabm4805.
  * Huttlin et al. (2021) Huttlin, E. L., Bruckner, R. J., Navarrete-Perea, J., et al. (2021) _Cell_ , 184, 3022–3040.
  * Ingraham et al. (2022) Ingraham, J., Baranov, M., Costello, Z., et al. (2022) _bioRxiv_ , doi: 10.1101/2022.12.01.518682.
  * Jankauskaitė et al. (2019) Jankauskaitė, J., Jiménez-García, B., Dapkūnas, J., et al. (2019) _Bioinformatics_ , 35, 462–469.
  * Janson et al. (2023) Janson, G., Valdes-Garcia, G., Heo, L., and Feig, M. (2023) _Nat. Commun._ , 14, 774.
  * Jendrusch et al. (2021) Jendrusch, M., Korbel, J. O., and Sadiq, S. K. (2021) _bioRxiv_ , doi: 10.1101/2021.10.11.463937.
  * Jeppesen and André (2023) Jeppesen, M. and André, I. (2023) _bioRxiv_ , doi: 10.1101/2023.06.22.546069.
  * Jha and Saha (2020) Jha, K. and Saha, S. (2020) _Sci. Rep._ , 10, 14\.
  * Jha and Saha (2023) Jha, K. and Saha, S. (2023) _IEEE/ACM Trans. Comput. Biol. Bioinform._ , 20, 162–173.
  * Jha et al. (2022) Jha, K., Saha, S., and Singh, H. (2022) _Sci. Rep._ , 12, 8360.
  * Jha et al. (2023) Jha, K., Karmakar, S., and Saha, S. (2023) _Sci. Rep._ , 13, 5663.
  * Johansson-Åkhe and Wallner (2022) Johansson-Åkhe, I. and Wallner, B. (2022) _Front. Bioinform._ , 2, 959160.
  * Johansson-Åkhe et al. (2021) Johansson-Åkhe, I., Mirabello, C., and Wallner, B. (2021) _Front. Bioinform._ , 1, 763102.
  * Jumper et al. (2021) Jumper, J., Evans, R., Pritzel, A., et al. (2021) _Nature_ , 596, 583–589.
  * Karniadakis et al. (2021) Karniadakis, G. E., Kevrekidis, I. G., Lu, L., et al. (2021) _Nat. Rev. Phys._ , 3, 422–440.
  * Kastritis and Bonvin (2013) Kastritis, P. L. and Bonvin, A. M. J. J. (2013) _Curr. Opin. Struct. Biol._ , 23, 868–877.
  * Kelly and Stumpf (2008) Kelly, W. P. and Stumpf, M. P. H. (2008) _Curr. Opin. Biotechnol._ , 19, 396–403.
  * Ketata et al. (2023) Ketata, M. A., Laue, C., Mammadov, R., et al. (2023) _arXiv_ , doi: 10.48550/arXiv.2304.03889.
  * Ko and Lee (2021) Ko, J. and Lee, J. (2021) _bioRxiv_ , doi: 10.1101/2021.07.27.453972.
  * Kozlovskii and Popov (2021) Kozlovskii, I. and Popov, P. (2021) _J. Chem. Inf. Model._ , 61, 3814–3823.
  * Krapp et al. (2023) Krapp, L. F., Abriata, L. A., Cortés Rodriguez, F., and Dal Peraro, M. (2023) _Nat. Commun._ , 14, 2175.
  * Kundu et al. (2014) Kundu, K., Mann, M., Costa, F., and Backofen, R. (2014) _Bioinformatics_ , 30, 2668–2669.
  * Lee et al. (2023) Lee, C. Y., Hubrich, D., Varga, J. K., et al. (2023) _bioRxiv_ , doi: 10.1101/2023.08.07.552219.
  * Lei et al. (2021) Lei, Y. P., Li, S. Y., Liu, Z. Y., et al. (2021) _Nat. Commun._ , 12, 5465.
  * Lensink et al. (2021) Lensink, M. F., Brysbaert, G., Mauri, T., et al. (2021) _Proteins: Struct., Funct., Bioinf._ , 89, 1800–1823.
  * Li et al. (2018) Li, H., Gong, X.-J., Yu, H., and Zhou, C. (2018) _Molecules_ , 23, 1923.
  * Li et al. (2023) Li, K. L., Quan, L. J., Jiang, Y. L., et al. (2023) _J. Chem. Inf. Model._ , 63, 2251–2262.
  * Li et al. (2022a) Li, S. W., Wu, S. N., Wang, L., et al. (2022a) _Curr. Opin. Struct. Biol._ , 73, 18.
  * Li et al. (2022b) Li, X., Han, P., Wang, G., et al. (2022b) _BMC Genom._ , 23, 474.
  * Li et al. (2021) Li, Y. W., Golding, G. B., and Ilie, L. (2021) _Bioinformatics_ , 37, 896–904.
  * Li et al. (2022c) Li, Z., Yang, S., Liu, X., et al. (2022c) _bioRxiv_ , doi: 10.1101/2022.08.30.505833.
  * Lim et al. (2022) Lim, K. S., Reidenbach, A. G., Hua, B. K., et al. (2022) _J. Chem. Inf. Model._ , 62, 2316–2331.
  * Lin and AlQuraishi (2023) Lin, Y. and AlQuraishi, M. (2023) _arXiv_ , doi: 10.48550/arXiv.2301.12485.
  * Lin et al. (2023) Lin, Z., Akin, H., Rao, R., et al. (2023) _Science_ , 379, 1123–1130.
  * Liu et al. (2020a) Liu, L., Zhu, X., Ma, Y., et al. (2020a) _BMC Bioinform._ , 21, 537.
  * Liu et al. (2021) Liu, X., Luo, Y., Li, P., et al. (2021) _PLoS Comput. Biol._ , 17, e1009284.
  * Liu et al. (2020b) Liu, Y., Yuan, H., Cai, L., and Ji, S. (2020b) _arXiv_ , doi: 10.48550/arXiv.2007.09334.
  * Liu-Wei et al. (2021) Liu-Wei, W., Kafkas, Ş., Chen, J., et al. (2021) _Bioinformatics_ , 37, 2722–2729.
  * Lu et al. (2020) Lu, H., Zhou, Q., He, J., et al. (2020) _Signal Transduct. Target. Ther._ , 5, 213.
  * Luck et al. (2020) Luck, K., Kim, D.-K., Lambourne, L., et al. (2020) _Nature_ , 580, 402–408.
  * Mahajan et al. (2023) Mahajan, S. P., Ruffolo, J. A., and Gray, J. J. (2023) _bioRxiv_ , doi: 10.1101/2023.07.15.549154.
  * Mahapatra and Sahu (2021) Mahapatra, S. and Sahu, S. S. (2021) _Brief. Bioinform._ , 22, bbab255.
  * Manfredi et al. (2023) Manfredi, M., Savojardo, C., Martelli, P. L., and Casadio, R. (2023) _J. Mol. Biol._ , 435, 167963.
  * Marchand et al. (2022) Marchand, A., Van Hall-Beauvais, A. K., and Correia, B. E. (2022) _Curr. Opin. Struct. Biol._ , 74, 102370.
  * Martins et al. (2021) Martins, P. M., Santos, L. H., Mariano, D., et al. (2021) _BMC Bioinform._ , 22, 1.
  * McPartlon and Xu (2023) McPartlon, M. and Xu, J. (2023) _bioRxiv_ , doi: 10.1101/2023.04.01.535079.
  * Meier et al. (2021) Meier, J., Rao, R., Verkuil, R., et al. (2021) _bioRxiv_ , doi: 10.1101/2021.07.09.450648.
  * Meldal et al. (2022) Meldal, B. H. M., Perfetto, L., Combe, C., et al. (2022) _Nucleic Acids Res._ , 50, D578–D586.
  * Miller et al. (2008) Miller, M. L., Jensen, L. J., Diella, F., et al. (2008) _Sci. Signal._ , 1, ra2.
  * Mirdita et al. (2022) Mirdita, M., Schütze, K., Moriwaki, Y., et al. (2022) _Nat. Methods_ , 19, 679–682.
  * Mohseni Behbahani et al. (2022) Mohseni Behbahani, Y., Crouzet, S., Laine, E., and Carbone, A. (2022) _Bioinformatics_ , 38, 4505–4512.
  * Mohseni Behbahani et al. (2023) Mohseni Behbahani, Y., Laine, E., and Carbone, A. (2023) _Bioinformatics_ , 39, i544–i552.
  * Mosalaganti et al. (2021) Mosalaganti, S., Obarska-Kosinska, A., Siggel, M., et al. (2021) _Science_ , 376, eabm9506.
  * Mosca et al. (2013) Mosca, R., Céol, A., and Aloy, P. (2013) _Nat. Methods_ , 10, 47–53.
  * Motmaen et al. (2023) Motmaen, A., Dauparas, J., Baek, M., et al. (2023) _Proc. Natl. Acad. Sci. U. S. A._ , 120, e2216697120.
  * Nasiri et al. (2021) Nasiri, E., Berahmand, K., Rostami, M., and Dabiri, M. (2021) _Comput. Biol. Med._ , 137, 104772.
  * Nilsson et al. (2022) Nilsson, A., Peters, J. M., Meimetis, N., et al. (2022) _Nat. Commun._ , 13, 3069.
  * Noé et al. (2019) Noé, F., Olsson, S., Köhler, J., and Wu, H. (2019) _Science_ , 365, eaaw1147.
  * O’Reilly et al. (2023) O’Reilly, F. J., Graziadei, A., Forbrig, C., et al. (2023) _Mol. Syst. Biol._ , 19, e11544.
  * Ozden et al. (2023) Ozden, B., Kryshtafovych, A., and Karaca, E. (2023) _bioRxiv_ , doi: 10.1101/2023.07.10.548341.
  * Palepu et al. (2022) Palepu, K., Ponnapati, M., Bhat, S., et al. (2022) _bioRxiv_ , doi: 10.1101/2022.05.23.493169.
  * Pan et al. (2023) Pan, Y., Wang, Y., Guan, J., and Zhou, S. (2023) _Bioinformatics_ , 39, btad473.
  * Park and Marcotte (2012) Park, Y. and Marcotte, E. M. (2012) _Nat. Methods_ , 9, 1134–1136.
  * Peng et al. (2017) Peng, X. Q., Wang, J. X., Peng, W., et al. (2017) _Brief. Bioinform._ , 18, 798–819.
  * Petrey et al. (2023) Petrey, D., Zhao, H., Trudeau, S. J., et al. (2023) _J. Mol. Biol._ , 435, 168052.
  * Quadir et al. (2021) Quadir, F., Roy, R. S., Halfmann, R., and Cheng, J. (2021) _Sci. Rep._ , 11, 12295.
  * Rackauckas et al. (2021) Rackauckas, C., Ma, Y., Martensen, J., et al. (2021) _arXiv_ , doi: 10.48550/arXiv.2001.04385.
  * Rao et al. (2020) Rao, R., Meier, J., Sercu, T., et al. (2020) _bioRxiv_ , doi: 10.1101/2020.12.15.422761.
  * Renaud et al. (2021) Renaud, N., Geng, C., Georgievska, S., et al. (2021) _Nat. Commun._ , 12, 7068.
  * Reynolds et al. (2022) Reynolds, M. J., Hachicho, C., Carl, A. G., et al. (2022) _Nature_ , 611, 380–386.
  * Richoux et al. (2019) Richoux, F., Servantie, C., Borès, C., and Téletchéa, S. (2019) _arXiv_ , doi: 10.48550/arXiv.1901.06268.
  * Rives et al. (2021) Rives, A., Meier, J., Sercu, T., et al. (2021) _Proc. Natl. Acad. Sci. U. S. A._ , 118, e2016239118.
  * Rossetto and Zhou (2020) Rossetto, A. and Zhou, W. (2020) In _Proceedings of the 11th ACM International Conference on Bioinformatics, Computational Biology and Health Informatics_. Virtual Event, USA, pp. 45.
  * Roy et al. (2022) Roy, R. S., Quadir, F., Soltanikazemi, E., and Cheng, J. (2022) _Bioinformatics_ , 38, 1904–1910.
  * Rube et al. (2022) Rube, H. T., Rastogi, C., Feng, S., et al. (2022) _Nat. Biotechnol._ , 40, 1520–1527.
  * Shanker and Sanner (2023) Shanker, S. and Sanner, M. F. (2023) _J. Chem. Inf. Model._ , 63, 3158–3170.
  * Shor and Schneidman-Duhovny (2023) Shor, B. and Schneidman-Duhovny, D. (2023) _bioRxiv_ , doi: 10.1101/2023.05.16.541003.
  * Si and Yan (2023a) Si, Y. and Yan, C. (2023a) _Brief. Bioinform._ , 24, bbad039.
  * Si and Yan (2023b) Si, Y. and Yan, C. (2023b) _bioRxiv_ , doi: 10.1101/2023.01.07.523121.
  * Singh et al. (2022) Singh, R., Devkota, K., Sledzieski, S., et al. (2022) _Bioinformatics_ , 38, i264–i272.
  * Sledzieski et al. (2021) Sledzieski, S., Singh, R., Cowen, L., and Berger, B. (2021) _Cell Syst._ , 12, 969–982.
  * Smidt (2021) Smidt, T. E. (2021) _Trends Chem._ , 3, 82–85.
  * Song et al. (2022) Song, B., Luo, X., Luo, X., et al. (2022) _Brief. Bioinform._ , 23, bbab558.
  * Spiga et al. (2014) Spiga, E., Degiacomi, M. T., and Dal Peraro, M. (2014) _Adv. Protein Chem. Struct. Biol._ , 96, 77–111.
  * Stahl et al. (2023a) Stahl, K., Brock, O., and Rappsilber, J. (2023a) _bioRxiv_ , doi: 10.1101/2023.06.07.544059.
  * Stahl et al. (2023b) Stahl, K., Graziadei, A., Dau, T., et al. (2023b) _Nat. Biotechnol._ , doi: 10.1038/s41587-023-01704-z.
  * Stapor et al. (2022) Stapor, P., Schmiester, L., Wierling, C., et al. (2022) _Nat. Commun._ , 13, 34.
  * Stringer et al. (2022) Stringer, B., de Ferrante, H., Abeln, S., et al. (2022) _Bioinformatics_ , 38, 2111–2118.
  * Sun et al. (2023) Sun, J., Zhu, T., Cui, Y., and Wu, B. (2023) _bioRxiv_ , doi: 10.1101/2023.08.09.552725.
  * Sverrisson et al. (2020) Sverrisson, F., Feydy, J., Correia, B. E., and Bronstein, M. M. (2020) _bioRxiv_ , doi: 10.1101/2020.12.28.424589.
  * Sverrisson et al. (2022) Sverrisson, F., Feydy, J., Southern, J., et al. (2022) In _ICLR2022 Machine Learning for Drug Discovery_. Virtual Event, USA.
  * Szymborski and Emad (2022) Szymborski, J. and Emad, A. (2022) _Bioinformatics_ , 38, 3958–3967.
  * Tesei et al. (2023) Tesei, G., Trolle, A. I., Jonsson, N., et al. (2023) _bioRxiv_ , doi: 10.1101/2023.05.08.539815.
  * Teufel et al. (2023) Teufel, F., Refsgaard, J. C., Kasimova, M. A., et al. (2023) _J. Chem. Inf. Model._ , 63, 2651–2655.
  * Townshend et al. (2019) Townshend, R. J. L., Bedi, R., Suriana, P. A., and Dror, R. O. (2019) In _Proceedings of the 33rd International Conference on Neural Information Processing Systems_. Vancouver, Canada, pp. 1401.
  * Trabuco et al. (2012) Trabuco, L. G., Betts, M. J., and Russell, R. B. (2012) _Methods_ , 58, 343–348.
  * Tsaban et al. (2022) Tsaban, T., Varga, J. K., Avraham, O., et al. (2022) _Nat. Commun._ , 13, 176.
  * Tsai et al. (2022) Tsai, S.-T., Fields, E., Xu, Y., et al. (2022) _Nat. Commun._ , 13, 7231.
  * Tsishyn et al. (2023) Tsishyn, M., Pucci, F., and Rooman, M. (2023) _bioRxiv_ , doi: 10.1101/2023.08.04.551687.
  * Tsitsiridis et al. (2022) Tsitsiridis, G., Steinkamp, R., Giurgiu, M., et al. (2022) _Nucleic Acids Res._ , 51, D539–D545.
  * Tsuchiya et al. (2022) Tsuchiya, Y., Yamamori, Y., and Tomii, K. (2022) _Biophys. Rev._ , 14, 1341–1348.
  * Tsukiyama and Kurata (2022) Tsukiyama, S. and Kurata, H. (2022) _Comp. Struct. Biotechnol. J._ , 20, 5564–5573.
  * Tubiana et al. (2022) Tubiana, J., Schneidman-Duhovny, D., and Wolfson, H. J. (2022) _Nat. Methods_ , 19, 730–739.
  * Unsal et al. (2022) Unsal, S., Atas, H., Albayrak, M., et al. (2022) _Nat. Mach. Intell._ , 4, 227–245.
  * Van Roey et al. (2014) Van Roey, K., Uyar, B., Weatheritt, R. J., et al. (2014) _Chem. Rev._ , 114, 6733–6778.
  * Volzhenin et al. (2023) Volzhenin, K., Bittner, L., and Carbone, A. (2023) _bioRxiv_ , doi: 10.1101/2023.09.19.558413.
  * Vázquez Torres et al. (2022) Vázquez Torres, S., Leung, P. J. Y., Lutz, I. D., et al. (2022) _bioRxiv_ , doi: 10.1101/2022.12.10.519862.
  * Wallner (2023) Wallner, B. (2023) _bioRxiv_ , doi: 10.1101/2022.12.20.521205.
  * Wang et al. (2022a) Wang, J., Bhattarai, A., Do, H. N., and Miao, Y. (2022a) _QRB Discov._ , 3, e13.
  * Wang et al. (2022b) Wang, J., Lisanza, S., Juergens, D., et al. (2022b) _Science_ , 377, 387–394.
  * Wang et al. (2020a) Wang, M., Cang, Z., and Wei, G.-W. (2020a) _Nat. Mach. Intell._ , 2, 116–123.
  * Wang et al. (2022c) Wang, R. H., Jin, J. R., Zou, Q., et al. (2022c) _Bioinformatics_ , 38, 3351–3360.
  * Wang et al. (2020b) Wang, X., Terashi, G., Christoffer, C. W., et al. (2020b) _Bioinformatics_ , 36, 2113–2118.
  * Wang et al. (2021) Wang, X., Flannery, S. T., and Kihara, D. (2021) _Front. Mol. Biosci._ , 8.
  * Wang et al. (2023) Wang, Y., Tang, H., Huang, L., et al. (2023) _Nat. Mach. Intell._ , 5, 845–860.
  * Wardah et al. (2020) Wardah, W., Dehzangi, A., Taherzadeh, G., et al. (2020) _J. Theor. Biol._ , 496, 110278.
  * Watson et al. (2023) Watson, J. L., Juergens, D., Bennett, N. R., et al. (2023) _Nature_ , 620, 1089–1100.
  * Wen et al. (2019) Wen, Z., He, J., Tao, H., and Huang, S.-Y. (2019) _Bioinformatics_ , 35, 175–177.
  * Wicky et al. (2022) Wicky, B. I. M., Milles, L. F., Courbet, A., et al. (2022) _Science_ , 378, 56–61.
  * Wodak et al. (2023) Wodak, S. J., Vajda, S., Lensink, M. F., et al. (2023) _Annu. Rev. Biophys._ , 52, 183–206.
  * Wu et al. (2022a) Wu, R., Ding, F., Wang, R., et al. (2022a) _bioRxiv_ , doi: 10.1101/2022.07.21.500999.
  * Wu et al. (2022b) Wu, T., Huang, H., Li, J., et al. (2022b) In _2022 IEEE International Conference on Bioinformatics and Biomedicine_. Las Vegas, NV, USA, pp. 2143–2148.
  * Xie and Xu (2022) Xie, Z. W. and Xu, J. B. (2022) _Bioinformatics_ , 38, 947–953.
  * Xie et al. (2020) Xie, Z. Y., Deng, X. Y., and Shu, K. X. (2020) _Int. J. Mol. Sci._ , 21, 467.
  * Xue et al. (2015) Xue, L. C., Dobbs, D., Bonvin, A. M. J. J., and Honavar, V. (2015) _FEBS Lett._ , 589, 3516–3526.
  * Xue et al. (2021) Xue, Y., Liu, Z., Fang, X., and Wang, F. (2021) _arXiv_ , doi: 10.48550/arXiv.2112.04814.
  * Yan et al. (2023) Yan, J., Ye, Z., Yang, Z., et al. (2023) _arXiv_ , doi: 10.48550/arXiv.2306.04886.
  * Yan and Huang (2021) Yan, Y. and Huang, S.-Y. (2021) _Brief. Bioinform._ , 22, bbab038.
  * Yang et al. (2020a) Yang, F., Fan, K. J., Song, D. N., and Lin, H. K. (2020a) _BMC Bioinform._ , 21, 16.
  * Yang et al. (2023a) Yang, K. K., Yeh, H., and Zanichelli, N. (2023a) _bioRxiv_ , doi: 10.1101/2022.05.25.493516.
  * Yang et al. (2020b) Yang, L., Han, Y. K., Zhang, H. X., et al. (2020b) _Biomed Res. Int._ , 2020, 5072520.
  * Yang et al. (2023b) Yang, S., Feng, D., Cheng, P., et al. (2023b) _bioRxiv_ , doi: 10.1101/2023.02.09.527848.
  * Yang et al. (2021) Yang, X., Yang, S., Lian, X., et al. (2021) _Bioinformatics_ , 37, 4771–4778.
  * Yang et al. (2022) Yang, Z., Milas, K. A., and White, A. D. (2022) _bioRxiv_ , doi: 10.1101/2022.08.05.502972.
  * Yao et al. (2019) Yao, Y., Du, X. Q., Diao, Y. Y., and Zhu, H. X. (2019) _PeerJ_ , 7, e7126.
  * Yin et al. (2022) Yin, R., Feng, B. Y., Varshney, A., and Pierce, B. G. (2022) _Protein Sci._ , 31, e4379.
  * Yu et al. (2023) Yu, D., Chojnowski, G., Rosenthal, M., and Kosinski, J. (2023) _Bioinformatics_ , 39, btac749.
  * Yuan et al. (2021) Yuan, B., Shen, C., Luna, A., et al. (2021) _Cell Syst._ , 12, 128–140.
  * Zeng et al. (2018) Zeng, H., Wang, S., Zhou, T., et al. (2018) _Nucleic Acids Res._ , 46, W432–W437.
  * Zhang et al. (2019) Zhang, B. Z., Li, J. Y., Quan, L. J., et al. (2019) _Neurocomputing_ , 357, 86–100.
  * Zhang and Kabuka (2019) Zhang, D. and Kabuka, M. (2019) _BMC Bioinform._ , 20, 531.
  * Zhang et al. (2012) Zhang, Q. C., Petrey, D., Deng, L., et al. (2012) _Nature_ , 490, 556–560.
  * Zhang et al. (2023a) Zhang, Z., Xu, M., Chenthamarakshan, V., et al. (2023a) _arXiv_ , doi: 10.48550/arXiv.2303.06275.
  * Zhang et al. (2023b) Zhang, Z., Xu, M., Jamasb, A., et al. (2023b) _arXiv_ , doi: 10.48550/arXiv.2203.06125.
  * Zhao et al. (2020) Zhao, L. L., Wang, J. J., Hu, Y., and Cheng, L. (2020) _Mol. Ther.-Nucl. Acids_ , 22, 198–208.
  * Zhao et al. (2023) Zhao, Z., Qian, P., Yang, X., et al. (2023) _arXiv_ , doi: 10.48550/arXiv.2305.08316.
  * Zheng et al. (2023) Zheng, S., He, J., Liu, C., et al. (2023) _arXiv_ , doi: 10.48550/arXiv.2306.05445.
  * Zhu et al. (2023) Zhu, W., Shenoy, A., Kundrotas, P., and Elofsson, A. (2023) _bioRxiv_ , doi: 10.1101/2022.12.08.519586.