Back

EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction

Hannes StärkOctavian GaneaLagnajit PattanaikRegina BarzilayTommi S. Jaakkola

article2022ICML354 citations

Introduces EquiBind, an SE(3)-equivariant neural network that achieves fast, direct-shot prediction of both receptor binding pockets and 3D ligand poses, replacing computationally heavy candidate sampling to accelerate virtual drug screening.

Listen

Early-stage drug discovery faces a massive search bottleneck, as evaluating how prospective drug molecules bind to target proteins across vast chemical and biological libraries requires immense time and financial resources. Conventional molecular docking tools rely on computationally heavy candidate sampling, scoring, and energy-based refinement, often taking minutes per molecule. The article introduces and evaluates EquiBind, an equivariant geometric deep learning framework designed to predict both the target protein's binding location and the bound structure and orientation of a flexible drug molecule directly in a single forward pass.

To demonstrate this method, the authors constructed a rigorous benchmarking framework using 19,119 protein-ligand complexes from the PDBbind database. They partitioned the data using a strict time-based split—training on older structures and testing on 363 diverse complexes discovered in 2019 or later—to mirror real-world virtual screening conditions. EquiBind treats the protein as a rigid receptor graph and models the flexible ligand by first predicting an atomic coordinate point cloud, followed by a fast mathematical optimization that adjusts rotatable bond angles into chemically valid structures without expensive iterative sampling.

Key findings show that EquiBind delivers substantial speed improvements while achieving superior structural accuracy across several standard metrics. When run on a graphics processing unit, EquiBind predicts binding poses in approximately 0.04 seconds per complex—roughly three to four orders of magnitude faster than leading physics-based and commercial tools, which require between 49 and 1,405 seconds per molecule. In flexible self-docking tests, EquiBind achieved an average ligand root-mean-square deviation of 8.2 Å and an average centroid distance of 5.6 Å, substantially outperforming traditional baselines such as Quick Vina-W, GNINA, and GLIDE, which averaged between 12.1–16.2 Å and 9.8–14.4 Å respectively. Furthermore, EquiBind's fast point-cloud fitting recovered rotatable bond angles in 0.04 seconds compared to over 3,000 seconds required by conventional differential evolution optimization.

These results demonstrate that direct-shot geometric deep learning can fundamentally accelerate high-throughput virtual screening, enabling researchers to computationally scan libraries of hundreds of millions of compounds against entire proteomes at a fraction of standard computing costs and timelines. The article notes that while standalone EquiBind accurately identifies global binding pockets and avoids catastrophic placement errors, traditional optimization remains better at fine atomic adjustments. Consequently, the authors recommend deploying EquiBind either as a standalone rapid-screening filter or within a hybrid pipeline coupled with localized classical fine-tuning tools, which achieved top-tier structural accuracy in under 15 seconds.

Decision-makers should consider key boundary conditions: the model currently assumes a rigid target protein and represents protein side chains implicitly rather than modeling full atomic detail. Nevertheless, the framework demonstrates strong consistency across diverse conformers, offering high confidence for organizations seeking to scale computational drug screening workflows.

Massachusetts Institute of Technologyclosed-form expressiondeep learningdifferential evolutionEquiBinddrug binding structure predictiongeometric deep learning
arXiv: 2202.05146
Cover for EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction

Abstract

Predicting how a drug-like molecule binds to a specific protein target is a core problem in drug discovery. An extremely fast computational binding method would enable key applications such as fast virtual screening or drug engineering. Existing methods are computationally expensive as they rely on heavy candidate sampling coupled with scoring, ranking, and fine-tuning steps. We challenge this paradigm with EquiBind, an SE(3)-equivariant geometric deep learning model performing direct-shot prediction of both i) the receptor binding location (blind docking) and ii) the ligand's bound pose and orientation. EquiBind achieves significant speed-ups and better quality compared to traditional and recent baselines. Further, we show extra improvements when coupling it with existing fine-tuning techniques at the cost of increased running time. Finally, we propose a novel and fast fine-tuning model that adjusts torsion angles of a ligand's rotatable bonds based on closed-form global minima of the von Mises angular distance to a given input atomic point cloud, avoiding previous expensive differential evolution strategies for energy minimization.

Topics

closed-form expressiondeep learningdifferential evolutionevolution strategiespoint cloudtuning methodvirtual spacesconvolutional neural networks

Keywords

EquiBinddrug binding structure predictiongeometric deep learningcomputational drug discoverycomputer-aided molecular designmolecular conformation generationligand RMSDaffinity predictionProtein Data Bank

Table of Contents

  • 1 Introduction
  • 2 Related Work
  • 3 EquiBind Model
  • 3.1 Rigid transformation through binding keypoints
  • 3.2 Modeling Chemically Plausible Ligand Flexibility
  • 3.2.1 Distance Geometric Constraints
  • 3.2.2 Fast Point Cloud Ligand Fitting
  • 4 Experiments
  • 4.1 Data
  • 4.2 Evaluation Setup
  • 4.3 Results
  • 5 Conclusion
  • 6 Acknowledgments
  • References
  • A Additional Results
  • B Dataset
  • C Implementation Details

Knowls

  1. Knowl 1 — EquiBind End-to-End Blind Docking Framework

    model/method

    EQUIBIND is a geometric deep learning framework designed to predict the bound 3D complex of a small-molecule ligand to a rigid protein receptor target in a single forward pass (blind docking), without requiring prior knowledge of the binding pocket or extensive spatial pose sampling.

    The model takes as input an initial unbound 3D ligand conformer (represented as a spatial kk-nearest neighbor graph G=(V,E)G = (V, E) with atom coordinates X hickspace ext{in} hickspace ield{R}^{3 imes n} and node features F hickspace ext{in} hickspace ield{R}^{d imes n}) and a rigid receptor structure (represented as an α\alpha-carbon residue graph G′=(V′,E′)G' = (V', E') with coordinates X' hickspace ext{in} hickspace ield{R}^{3 imes m} and node features F' hickspace ext{in} hickspace ield{R}^{d imes m}). The core architecture consists of stacked Independent E(3)\mathrm{E}(3)-Equivariant Graph Matching Network (IEGMN) layers that output transformed coordinate sets Z hickspace ext{in} hickspace ield{R}^{3 imes n}, Z' hickspace ext{in} hickspace ield{R}^{3 imes m} and node embeddings H hickspace ext{in} hickspace ield{R}^{d imes n}, H' hickspace ext{in} hickspace ield{R}^{d imes m}.

    The framework operates in two stages:

    1. Rigid Transformation via Keypoint Alignment: Equivariant multi-head attention computes KK binding keypoints Y hickspace ext{in} hickspace ield{R}^{3 imes K} and Y' hickspace ext{in} hickspace ield{R}^{3 imes K} on the ligand and receptor. Superimposing YY to Y′Y' recovers the global rotation UhickspaceextinhickspaceSO(3)U hickspace ext{in} hickspace \mathrm{SO}(3) and translation b hickspace ext{in} hickspace ield{R}^3 required to place the ligand into the binding pocket.
    2. Flexible Conformation Modeling: Ligand internal flexibility is modeled by training coordinate output ZZ to approximate the bound atomic point cloud, constrained during layer updates by a soft Local Atomic Structure (LAS) distance geometry projection Ψ\Psi, followed by an exact, closed-form von Mises dihedral angle fitting step that yields a chemically valid bound conformer C hickspace ext{in} hickspace ield{R}^{3 imes n}.

  2. Knowl 2 — Closed-Form von Mises Maximum Likelihood Fitting for Rotatable Bond Torsion Angles

    theoretical result

    To convert an uncorrected ligand coordinate point cloud Z∈R3×nZ \in \mathbb{R}^{3 \times n} into a chemically plausible bound conformer C∈R3×nC \in \mathbb{R}^{3 \times n} while keeping local atomic structures (LAS) such as bond lengths, bond angles, and rigid rings fixed to an initial conformer X∈R3×nX \in \mathbb{R}^{3 \times n}, EQUIBIND optimizes the dihedral angles of all rotatable bonds independently in closed form without iterative optimization.

    The objective maximizes the likelihood of von Mises distributions on dihedral angles, framed as:

    max⁡{∠(k,i,j,l)}∑(k,i),(i,j),(j,l)∈Ecos⁡(∠Z(k,i,j,l)−∠(k,i,j,l))\max_{\{\angle(k, i, j, l)\}} \sum_{(k,i),(i,j),(j,l) \in E} \cos\left(\angle_Z(k, i, j, l) - \angle(k, i, j, l)\right)

    where ∠Z(k,i,j,l)\angle_Z(k, i, j, l) denotes the dihedral angle in the predicted point cloud ZZ, and ∠(k,i,j,l)\angle(k, i, j, l) is the dihedral angle in the conformer CC. Dihedral angles around the same rotatable bond (i,j)∈E(i, j) \in E are constrained by the local geometry:

    ∠(k,i,j,l)=2π∠(k′,i,j,l′)+∠(k,i,j,k′)+∠(j,l′,j,l)\angle(k, i, j, l) =_{2\pi} \angle(k', i, j, l') + \angle(k, i, j, k') + \angle(j, l', j, l)

    For a fixed rotatable bond (i,j)(i, j), let Δkl=∠(k,i,j,l)\Delta_{kl} = \angle(k, i, j, l), βkk′l′l=∠(k,i,j,k′)+∠(j,l′,j,l)\beta_{k k' l' l} = \angle(k, i, j, k') + \angle(j, l', j, l), sα=[cos⁡(α),sin⁡(α)]Ts_\alpha = [\cos(\alpha), \sin(\alpha)]^T, and

    Aα=[cos⁡(α)−sin⁡(α)sin⁡(α)cos⁡(α)]A_\alpha = \begin{bmatrix} \cos(\alpha) & -\sin(\alpha) \\ \sin(\alpha) & \cos(\alpha) \end{bmatrix}

    Choosing arbitrary fixed reference neighbors k0∈Nik_0 \in \mathcal{N}_i and l0∈Njl_0 \in \mathcal{N}_j, the optimization reduces to max⁡Δk0l0sΔk0l0Tv\max_{\Delta_{k_0 l_0}} s_{\Delta_{k_0 l_0}}^T v, where:

    v=∑k∈Ni∑l∈NjAβkk0l0lTsΔkl∗v = \sum_{k \in \mathcal{N}_i} \sum_{l \in \mathcal{N}_j} A_{\beta_{k k_0 l_0 l}}^T s^*_{\Delta_{kl}}

    with sΔkl∗=[cos⁡(∠Z(k,i,j,l)),sin⁡(∠Z(k,i,j,l))]Ts^*_{\Delta_{kl}} = [\cos(\angle_Z(k, i, j, l)), \sin(\angle_Z(k, i, j, l))]^T. The global optimum is obtained in closed form as:

    sΔk0l0=v∥v∥2s_{\Delta_{k_0 l_0}} = \frac{v}{\|v\|_2}

    from which all dihedral angles Δkl\Delta_{kl} for bond (i,j)(i, j) are computed analytically.

  3. Knowl 3 — Independent E(3)-Equivariant Graph Matching Network Layer

    model/method

    The Independent E(3)\mathrm{E}(3)-Equivariant Graph Matching Network (IEGMN) processes pair molecular graphs (G,G′)(G, G') to guarantee independent roto-translational equivariance: for any U,U′∈SO(3)U, U' \in \mathrm{SO}(3) and b,b′∈R3b, b' \in \mathbb{R}^3, applying the transformation to inputs (UX+b,F,U′X′+b′,F′)(UX + b, F, U'X' + b', F') transforms output coordinates to (UZ+b,U′Z′+b′)(UZ + b, U'Z' + b') while node feature embeddings (H,H′)(H, H') remain invariant.

    Let VV and V′V' denote the node sets, and EE and E′E' denote the edge sets of the ligand graph GG and receptor graph G′G', respectively. For layer ll, the message passing and coordinate update equations are defined as follows:

    mj→i=ϕe(hi(l),hj(l),∥xi(l)−xj(l)∥2,fj→i),∀(i,j)∈E∪E′m_{j \to i} = \phi_e\left(h_i^{(l)}, h_j^{(l)}, \|x_i^{(l)} - x_j^{(l)}\|^2, f_{j \to i}\right), \quad \forall (i, j) \in E \cup E'

    μj′→i=aj′→iWhj′(l),∀i∈V,j′∈V′ or i∈V′,j′∈V\mu_{j' \to i} = a_{j' \to i} W h_{j'}^{(l)}, \quad \forall i \in V, j' \in V' \text{ or } i \in V', j' \in V

    mi=1∣N(i)∣∑j∈N(i)mj→i,∀i∈V∪V′m_i = \frac{1}{|\mathcal{N}(i)|} \sum_{j \in \mathcal{N}(i)} m_{j \to i}, \quad \forall i \in V \cup V'

    μi=∑j′∈V′μj′→i  (∀i∈V),μi′=∑j∈Vμj→i′  (∀i′∈V′)\mu_i = \sum_{j' \in V'} \mu_{j' \to i} \; (\forall i \in V), \quad \mu'_i = \sum_{j \in V} \mu_{j \to i'} \; (\forall i' \in V')

    xi(l+1)=Ψ(xi(l)+∑j∈N(i)xi(l)−xj(l)∥xi(l)−xj(l)∥ϕx(mj→i))x_i^{(l+1)} = \Psi\left(x_i^{(l)} + \sum_{j \in \mathcal{N}(i)} \frac{x_i^{(l)} - x_j^{(l)}}{\|x_i^{(l)} - x_j^{(l)}\|} \phi_x(m_{j \to i})\right)

    hi(l+1)=(1−β)hi(l)+βϕh(hi(l),mi,μi,fi),∀i∈V∪V′h_i^{(l+1)} = (1 - \beta) h_i^{(l)} + \beta \phi_h\left(h_i^{(l)}, m_i, \mu_i, f_i\right), \quad \forall i \in V \cup V'

    where ϕe,ϕh,ϕx\phi_e, \phi_h, \phi_x are shallow neural networks (with ϕx\phi_x outputting a scalar), WW is a parameter matrix, aj′→ia_{j' \to i} are SE(3)\mathrm{SE}(3)-invariant cross-graph attention coefficients derived from node features, β\beta is a weighting hyperparameter, and Ψ\Psi is the distance geometry constraint projection.

  4. Knowl 4 — Local Atomic Structure Distance Geometry Regularization

    model/method

    To preserve bond lengths, adjacent bond angles, and rigid ring structures during the E(3)\mathrm{E}(3)-equivariant coordinate updates of the ligand, EQUIBIND applies a differentiable Local Atomic Structure (LAS) distance geometry projection Ψ\Psi.

    For a fixed unbound conformer X∈R3×nX \in \mathbb{R}^{3 \times n} and transformed coordinates Z∈R3×nZ \in \mathbb{R}^{3 \times n}, the LAS constraint penalty function S(Z,X)S(Z, X) is defined as:

    S(Z,X)=∑(i,j)∈E(dX2(i,j)−dZ2(i,j))2+∑i,j:2-hops in G(dX2(i,j)−dZ2(i,j))2+∑i,j in aromatic ring(dX2(i,j)−dZ2(i,j))2S(Z, X) = \sum_{(i,j) \in E} \left(d_X^2(i, j) - d_Z^2(i, j)\right)^2 + \sum_{i,j: 2\text{-hops in } G} \left(d_X^2(i, j) - d_Z^2(i, j)\right)^2 + \sum_{i,j \text{ in aromatic ring}} \left(d_X^2(i, j) - d_Z^2(i, j)\right)^2

    where dX(i,j)=∥xi−xj∥2d_X(i, j) = \|x_i - x_j\|_2. The operator Ψ\Psi is implemented as a sequence of TT unrolled gradient descent steps with step size η\eta:

    Ψ(Z)=ΨT∘⋯∘Ψ1(Z),where Ψt(Z)=Z−η∇ZS(Z,X)\Psi(Z) = \Psi_T \circ \dots \circ \Psi_1(Z), \quad \text{where } \Psi_t(Z) = Z - \eta \nabla_Z S(Z, X)

    This projection softly guides the coordinates predicted by IEGMN layers toward chemically plausible local bond geometry before final conformer fitting.

  5. Knowl 5 — Equivariant Keypoint Multi-Head Attention for Rigid Pocket Docking

    model/method

    EQUIBIND predicts the rigid SE(3)\mathrm{SE}(3) transformation (rotation and translation) that docks the ligand into the receptor pocket by constructing KK corresponding keypoints in 3D space for each molecule via an SE(3)\mathrm{SE}(3)-equivariant multi-head attention mechanism.

    The predicted ligand keypoints Y=[y1,…,yK]∈R3×KY = [y_1, \dots, y_K] \in \mathbb{R}^{3 \times K} and receptor keypoints Y′=[y1′,…,yK′]∈R3×KY' = [y'_1, \dots, y'_K] \in \mathbb{R}^{3 \times K} are defined as weighted sums over transformed coordinates Z=[z1,…,zn]Z = [z_1, \dots, z_n] and Z′=[z1′,…,zm′]Z' = [z'_1, \dots, z'_m]:

    yk=∑i=1nαikzi,yk′=∑j=1mβjkzj′y_k = \sum_{i=1}^n \alpha_i^k z_i, \qquad y'_k = \sum_{j=1}^m \beta_j^k z'_j

    where attention coefficients αik\alpha_i^k and βjk\beta_j^k are computed from node embeddings, for example:

    αik=softmaxi(1dh1iTUμ(ϕ(H2)))\alpha_i^k = \text{softmax}_i\left(\frac{1}{\sqrt{d}} h_{1i}^T U \mu\left(\phi(H_2)\right)\right)

    with UU being a learnable matrix. Keypoints are trained using an optimal transport loss against ground truth pocket points (defined as ligand atoms within 4 A˚4\,\text{\AA} of any receptor atom in the bound complex). Superimposing the predicted keypoints YY onto Y′Y' via the Kabsch algorithm directly provides the rigid rotation and translation for docking.

  6. Knowl 6 — PDBBind Time-Split Benchmark for Blind Docking

    experimental setup

    To evaluate blind flexible self-docking and avoid optimistic performance estimates from curated benchmark sets like the PDBBind core set (which features smaller ligands and higher resolution), EQUIBIND introduces a time-based split on PDBBind v2020 (19,443 original complexes).

    Dataset Preprocessing:

    • Complexes that cannot be parsed by RDKit are removed, yielding 19,119 complexes.
    • Missing hydrogens are added and existing ones corrected using reduce and OpenBabel.
    • To address symmetric multimeric proteins where a ligand can bind to multiple equivalent pockets but is annotated in only one, connected components of the receptor without any atom within 10 A˚10\,\text{\AA} of the ligand are removed.

    Split Construction:

    • Test Set: 363 complexes comprising 125 unique proteins discovered strictly in 2019 or later.
    • Train and Validation Sets: Complexes older than 2019, removing any complex containing a ligand present in the test set. This yields 16,379 training complexes and 968 validation complexes with no shared ligands between splits.

    Evaluation Metrics:

    • Ligand RMSD (L-RMSD): Symmetry-corrected root-mean-square deviation between predicted and true bound ligand atomic positions (using obrms with hydrogens removed).
    • Centroid Distance: Distance between the mean atomic coordinates of predicted and ground truth ligands, measuring pocket identification accuracy.
    • Kabsch-RMSD: Minimum achievable RMSD after optimal rigid superimposition.

  7. Knowl 7 — Flexible Blind Self-Docking Performance and Inference Speed

    data/table

    The flexible blind self-docking task tests methods on predicting the binding pocket location, ligand pose, and bound conformation given a rigid receptor and a random initial RDKit conformer. EQUIBIND is compared against physics-based and CNN-based docking programs on 363 PDBBind time-split test complexes.

    Avg. Sec. Ligand RMSD ()Ä ↓\downarrow Centroid Distance ()Ä ↓\downarrow Kabsch
    Method CPU GPU Mean 25th 50th 75th % < 2Ä Mean 25th 50th 75th Mean
    QVina-W 49 - 13.6 2.5 7.7 23.7 20.9 11.9 0.9 3.7 22.9 2.1
    GNINA 247 146 13.3 2.8 8.7 22.1 21.2 11.5 1.0 4.5 21.2 2.2
    SMINA 146 - 12.1 3.8 8.1 17.9 13.5 9.8 1.3 3.7 16.2 2.2
    GLIDE (c.) 1405 - 16.2 2.6 9.3 28.1 21.8 14.4 0.8 5.6 26.9 2.2
    EQUIBIND 0.16 0.04 8.2 3.8 6.2 10.3 5.5 5.6 1.3 2.6 7.4 2.6
    EQUIBIND+Q 8 8 8.4 2.6 6.6 11.1 18.7 5.9 1.0 2.5 6.4 2.3
    EQUIBIND+Q2 15 15 8.7 2.6 6.8 11.1 21.6 6.0 1.0 2.4 6.6 2.2
    EQUIBIND+S 146 146 8.3 2.1 5.6 10.5 24.6 6.0 0.9 2.0 6.2 2.1
    EQUIBIND-U 0.14 0.02 7.8 3.3 5.7 9.7 7.2 5.6 1.3 2.6 7.4 2.1

    Vanilla EQUIBIND runs in 0.04 seconds on GPU (over 1000×1000\times faster than QVina-W and over 3500×3500\times faster than GNINA) and achieves superior median centroid distance (2.6 A˚2.6\,\text{\AA}) and 75th percentile RMSD (10.3 A˚10.3\,\text{\AA}), avoiding catastrophic pocket mispredictions. When coupled with local scoring fine-tuning (EQUIBIND+S), it outperforms all baselines across all metrics, achieving 24.6%24.6\% of predictions below 2 A˚2\,\text{\AA} L-RMSD and 50.6%50.6\% below 2 A˚2\,\text{\AA} centroid distance.

  8. Knowl 8 — Blind Rigid Re-Docking Performance

    data/table

    In the blind re-docking setting, the ground truth bound ligand structure is extracted from the complex, placed in a random location/orientation, and docked into the receptor. EQUIBIND-R treats the ligand as a rigid body and only predicts the global SE(3)\mathrm{SE}(3) transformation.

    Avg. Sec. Ligand RMSD ()Ä ↓\downarrow Centroid Distance ()Ä ↓\downarrow Kabsch
    Method CPU GPU Mean 25th 50th 75th % < 2Ä Mean 25th 50th 75th Mean
    QVina-W 49 - 13.4 1.6 7.9 24.1 27.7 11.8 0.9 3.8 23.2 1.8
    GNINA 247 146 12.2 1.3 6.1 22.9 32.2 10.9 0.7 2.8 22.1 1.7
    SMINA 146 - 10.3 1.4 6.2 15.2 30.1 8.5 0.8 2.6 12.7 1.7
    GLIDE 1405 - 15.7 0.5 8.3 29.5 43.4 14.8 0.3 4.9 28.5 0.0
    EQUIBIND-R 0.14 0.02 7.4 2.0 5.1 9.8 25.1 5.8 1.4 2.6 7.3 0.0
    EQUIBIND-R+S 146 146 7.0 1.0 3.4 9.6 41.1 5.3 0.7 1.4 4.7 1.5

    EQUIBIND-R docks the rigid conformer in 0.02 seconds on GPU, yielding a mean Ligand RMSD of 7.4 A˚7.4\,\text{\AA} compared to 13.4 A˚13.4\,\text{\AA} for QVina-W, 12.2 A˚12.2\,\text{\AA} for GNINA, and 15.7 A˚15.7\,\text{\AA} for GLIDE. Combining EQUIBIND-R with SMINA fine-tuning (EQUIBIND-R+S) yields a median RMSD of 3.4 A˚3.4\,\text{\AA} and places 59.2%59.2\% of predictions within 2 A˚2\,\text{\AA} centroid distance.

  9. Knowl 9 — Hybrid Workflows Combining EquiBind Pose Initialization with Physics-Based Fine-Tuning

    model/method

    To combine the global search speed of geometric deep learning with the fine-grained local atomic precision of force-field and grid scoring methods, EQUIBIND supports hybrid workflows:

    1. EQUIBIND + Q / Q2: EQUIBIND predicts the coarse ligand binding pose and orientation in a single forward pass (<0.16 s< 0.16\,\text{s}). A bounding box of side length 5 A˚5\,\text{\AA} is constructed around the predicted ligand coordinates, and QuickVina 2 is executed exclusively within this restricted volume. This restricts the global search space, completing the docking pipeline in 8 s8\,\text{s} (or 15 s15\,\text{s} for Q2 with double candidate sampling) while increasing the percentage of <2 A˚< 2\,\text{\AA} RMSD predictions from 5.5%5.5\% to 18.7%18.7\% (21.6%21.6\% for Q2).
    2. EQUIBIND + S / EQUIBIND-R + S: Uses SMINA to locally optimize the pose within the bounding box, achieving 24.6%24.6\% (41.1%41.1\% for rigid re-docking) of ligand RMSDs <2 A˚< 2\,\text{\AA} and 50.6%50.6\% (59.2%59.2\% for rigid re-docking) centroid distances <2 A˚< 2\,\text{\AA}.

  10. Knowl 10 — Structural Modeling Limitations: Coarse-Grained Receptor Representation and Rigid Target Assumption

    limitation

    EQUIBIND exhibits two primary structural modeling limitations:

    1. Coarse-Grained Receptor Representation: The receptor is represented exclusively using α\alpha-carbon coordinates and local frame orientation encodings, omitting explicit atomic coordinates of amino acid side chains. Experiments incorporating surface atoms (EQUIBIND-SA) or local all-atom subgraphs within 10 A˚10\,\text{\AA} (EQUIBIND-A) did not substantially improve dock accuracy (mean L-RMSD 8.6 A˚8.6\,\text{\AA} and 8.2 A˚8.2\,\text{\AA} vs. 7.8 A˚7.8\,\text{\AA} for EQUIBIND-U) while multiplying GPU memory consumption by 2–3×2\text{--}3\times.
    2. Rigid Receptor Assumption: The model assumes a static, rigid protein conformation during docking and does not model receptor conformational flexibility, induced fit, or allosteric rearrangements upon ligand binding.

Coverage note — None was omitted; all primary architectural components, mathematical derivations (closed-form von Mises fitting and IEGMN layers), empirical evaluation tables, and stated limitations are fully represented.

References

  1. 1.Aggarwal, R., Gupta, A., Chelur, V., Jawahar, C., and Priyakumar, U. Deeppocket: Ligand binding site detection and segmentation using 3d convolutional neural networks, 2021.
  2. 2.Baek, M., DiMaio, F., Anishchenko, I., Dauparas, J., Ovchinnikov, S., Lee, G. R., Wang, J., Cong, Q., Kinch, L. N., Schaeffer, R. D., et al. Accurate prediction of protein structures and interactions using a three-track neural network. Science, 373(6557):871–876, 2021.
  3. 3.Bao, J., He, X., and Zhang, J. Z. Deepbsp—a machine learning method for accurate prediction of protein–ligand docking structures. Journal of Chemical Information and Modeling, 2021.
  4. 4.Batzner, S., Musaelian, A., Sun, L., Geiger, M., Mailoa, J. P., Kornbluth, M., Molinari, N., Smidt, T. E., and Kozinsky, B. Se (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. arXiv preprint arXiv:2101.03164, 2021.
  5. 5.Berman, H., Henrick, K., and Nakamura, H. Announcing the worldwide Protein Data Bank. Nat Struct Biol, 10 (12):980, Dec 2003.
  6. 6.Brandstetter, J., Hesselink, R., van der Pol, E., Bekkers, E., and Welling, M. Geometric and physical quantities improve e (3) equivariant message passing. arXiv preprint arXiv:2110.02905, 2021.
  7. 7.Cohen, T. and Welling, M. Group equivariant convolutional networks. In International conference on machine learning, pp. 2990–2999. PMLR, 2016.
  8. 8.Dai, B. and Bailey-Kellogg, C. Protein interaction interface region prediction by geometric deep learning. Bioinformatics, 2021.
  9. 9.de Freitas, R. F. and Schapira, M. A systematic analysis of atomic protein–ligand interactions in the pdb. MedChemComm, 8(10):1970–1981, 2017.
  10. 10.Drotár, P., Jamasb, A. R., Day, B., Cangea, C., and Liò, P. Structure-aware generation of drug-like molecules. arXiv preprint arXiv:2111.04107, 2021.
  11. 11.Du, X., Li, Y., Xia, Y.-L., Ai, S.-M., Liang, J., Sang, P., Ji, X.-L., and Liu, S.-Q. Insights into protein–ligand interactions: mechanisms, models, and methods. International journal of molecular sciences, 2016.
  12. 12.Du, Y., Fu, T., Sun, J., and Liu, S. Molgensurvey: A systematic survey in machine learning models for molecule design. arxiv, 2022.
  13. 13.Eismann, S., Townshend, R. J., Thomas, N., Jagota, M., Jing, B., and Dror, R. O. Hierarchical, rotation-equivariant neural networks to select structural models of protein complexes. Proteins: Structure, Function, and Bioinformatics, 2020.
  14. 14.Evans, R., O’Neill, M., Pritzel, A., Antropova, N., Senior, A. W., Green, T., Žídek, A., Bates, R., Blackwell, S., Yim, J., Ronneberger, O., Bodenstein, S., Zielinski, M., Bridgland, A., Potapenko, A., Cowie, A., Tunyasuvunakool, K., Jain, R., Clancy, E., Kohli, P., Jumper, J., and Hassabis, D. Protein complex prediction with alphafold-multimer. birxiv, 2021.
  15. 15.Francoeur, P. G., Masuda, T., Sunseri, J., Jia, A., Iovanisci, R. B., Snyder, I., and Koes, D. R. Three-dimensional convolutional neural networks and a cross-docked data set for structure-based drug design. Journal of Chemical Information and Modeling, 60(9):4200–4215, 2020.
  16. 16.Fuchs, F. B., Worrall, D. E., Fischer, V., and Welling, M. Se(3)-transformers: 3d roto-translation equivariant attention networks. arXiv preprint arXiv:2006.10503, 2020.
  17. 17.Gainza, P., Sverrisson, F., Monti, F., Rodola, E., Boscaini, D., Bronstein, M., and Correia, B. Deciphering interaction fingerprints from protein molecular surfaces using geometric deep learning. Nature Methods, 17(2):184–192, 2020.
  18. 18.Ganea, O.-E., Huang, X., Bunne, C., Bian, Y., Barzilay, R., Jaakkola, T., and Krause, A. Independent se(3)-equivariant models for end-to-end rigid protein docking. arXiv preprint arXiv:2111.07786, 2021a.
  19. 19.Ganea, O.-E., Pattanaik, L., Coley, C. W., Barzilay, R., Jensen, K. F., Green, W. H., and Jaakkola, T. S. Geomol: Torsional geometric generation of molecular 3d conformer ensembles. arXiv preprint arXiv:2106.07802, 2021b.
  20. 20.Gao, K. Y., Fokoue, A., Luo, H., Iyengar, A., Dey, S., and Zhang, P. Interpretable drug target prediction using deep neural representation. In IJCAI, volume 2018, pp. 3371–3377, 2018.
  21. 21.Gligorijević, V., Renfrew, P. D., Kosciolek, T., Leman, J. K., Berenberg, D., Vatanen, T., Chandler, C., Taylor, B. C., Fisk, I. M., Vlamakis, H., et al. Structure-based protein function prediction using graph convolutional networks. Nature communications, 2021.
  22. 22.Gniewek, P., Worley, B., Stafford, K., Bedem, H. v. d., and Anderson, B. Learning physics confers pose-sensitivity in structure-based virtual screening. arXiv preprint arXiv:2110.15459, 2021.
  23. 23.Halgren, T. A., Murphy, R. B., Friesner, R. A., Beard, H. S., Frye, L. L., Pollard, W. T., and Banks, J. L. Glide: a new approach for rapid, accurate docking and scoring. 2. enrichment factors in database screening. Journal of medicinal chemistry, 2004.
  24. 24.Hassan, N. M., Alhossary, A. A., Mu, Y., and Kwoh, C.-K. Protein-ligand blind docking using quickvina-w with inter-process spatio-temporal integration. Scientific reports, 7(1):1–13, 2017.
  25. 25.Huang, S.-Y. Comprehensive assessment of flexible-ligand docking algorithms: current effectiveness and challenges. Briefings in bioinformatics, 19(5):982–994, 2018.
  26. 26.Imrie, F., Hadfield, T. E., Bradley, A. R., and Deane, C. M. Deep generative design with 3d pharmacophoric constraints. bioRxiv, 2021.
  27. 27.Jastrzebski, S., Szymczak, M., Pocha, A., Mordalski, S., Tabor, J., Bojarski, A. J., and Podlewska, S. Emulating docking results using a deep neural network: a new perspective for virtual screening. Journal of Chemical Information and Modeling, 2020.
  28. 28.Jiang, D., Hsieh, C.-Y., Wu, Z., Kang, Y., Wang, J., Wang, E., Liao, B., Shen, C., Xu, L., Wu, J., et al. Interactiongraphnet: A novel and efficient deep graph representation learning framework for accurate protein–ligand interaction predictions. Journal of medicinal chemistry, 2021.
  29. 29.Jiménez, J., Doerr, S., Martínez-Rosell, G., Rose, A. S., and De Fabritiis, G. Deepsite: protein-binding site predictor using 3d-convolutional neural networks. Bioinformatics, 2017.
  30. 30.Jindal, A., Kotelnikov, S., Padhorny, D., Kozakov, D., Zhu, Y., Chowdhury, R., and Vajda, S. Side-chain packing using se (3)-transformer. In PACIFIC SYMPOSIUM ON BIOCOMPUTING 2022, pp. 46–55, 2021.
  31. 31.Jing, B., Eismann, S., Suriana, P., Townshend, R. J. L., and Dror, R. Learning from protein structure with geometric vector perceptrons. In International Conference on Learning Representations, 2020.
  32. 32.Jumper, J., Evans, R., Pritzel, A., Green, T., Figurnov, M., Ronneberger, O., Tunyasuvunakool, K., Bates, R., Žídek, A., Potapenko, A., Bridgland, A., Meyer, C., Kohl, S. A. A., Ballard, A. J., Cowie, A., Romera-Paredes, B., Nikolov, S., Jain, R., Adler, J., Back, T., Petersen, S., Reiman, D., Clancy, E., Zielinski, M., Steinegger, M., Pacholska, M., Berghammer, T., Bodenstein, S., Silver, D., Vinyals, O., Senior, A. W., Kavukcuoglu, K., Kohli, P., and Hassabis, D. Highly accurate protein structure prediction with alphafold. Nature, 2021a.
  33. 33.Jumper, J., Evans, R., Pritzel, A., Green, T., Figurnov, M., Ronneberger, O., Tunyasuvunakool, K., Bates, R., Žídek, A., Potapenko, A., et al. Highly accurate protein structure prediction with alphafold. Nature, 596(7873):583–589, 2021b.
  34. 34.Karimi, M., Wu, D., Wang, Z., and Shen, Y. Deepaffinity: interpretable deep learning of compound–protein affinity through unified recurrent and convolutional neural networks. Bioinformatics, 35(18):3329–3338, 2019.
  35. 35.Kingma, D. P. and Ba, J. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
  36. 36.Koes, D. R., Baumgartner, M. P., and Camacho, C. J. Lessons learned in empirical scoring with smina from the csar 2011 benchmarking exercise. Journal of chemical information and modeling, 53(8):1893–1904, 2013.
  37. 37.Lam, P. C.-H., Abagyan, R., and Totrov, M. Ligandbiased ensemble receptor docking (ligbend): a hybrid ligand/receptor structure-based approach. Journal of Computer-Aided Molecular Design, 32(1):187–198, Jan 2018.
  38. 38.Lam, P. C.-H., Abagyan, R., and Totrov, M. Hybrid receptor structure/ligand-based docking and activity prediction in icm: development and evaluation in d3r grand challenge 3. Journal of Computer-Aided Molecular Design, Jan 2019.
  39. 39.Landrum, G. Rdkit: Open-source cheminformatics software, 2016.
  40. 40.Lang, P. T., Brozell, S. R., Mukherjee, S., Pettersen, E. F., Meng, E. C., Thomas, V., Rizzo, R. C., Case, D. A., James, T. L., and Kuntz, I. D. Dock 6: Combining techniques to model rna–small molecule complexes. Rna, 2009.
  41. 41.Li, S., Zhou, J., Xu, T., Huang, L., Wang, F., Xiong, H., Huang, W., Dou, D., and Xiong, H. Structure-aware interactive graph neural networks for the prediction of protein-ligand binding affinity. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, pp. 975–985, 2021.
  42. 42.Li, Y., Gu, C., Dullien, T., Vinyals, O., and Kohli, P. Graph matching networks for learning the similarity of graph structured objects. In International Conference on Machine Learning, pp. 3835–3845. PMLR, 2019.
  43. 43.Lim, J., Ryu, S., Park, K., Choe, Y. J., Ham, J., and Kim, W. Y. Predicting drug–target interaction using a novel graph neural network with 3d structure-embedded graph representation. Journal of chemical information and modeling, 59(9):3981–3988, 2019.
  44. 44.Liu, Z., Su, M., Han, L., Liu, J., Yang, Q., Li, Y., and Wang, R. Forging the basis for developing protein–ligand interaction scoring functions. Accounts of Chemical Research, 50(2):302–309, 2017.
  45. 45.Luo, S., Shi, C., Xu, M., and Tang, J. Predicting molecular conformation via dynamic graph score matching. NeurIPS, 2021.
  46. 46.Macari, G., Toti, D., and Polticelli, F. Computational methods and tools for binding site recognition between proteins and small molecules: from classical geometrical approaches to modern machine learning strategies. Journal of computer-aided molecular design, 2019.
  47. 47.Masuda, T., Ragoza, M., and Koes, D. R. Generating 3d molecular structures conditional on a receptor binding site with deep generative models. arXiv preprint arXiv:2010.14442, 2020.
  48. 48.McNutt, A. T., Francoeur, P., Aggarwal, R., Masuda, T., Meli, R., Ragoza, M., Sunseri, J., and Koes, D. R. Gnina 1.0: molecular docking with deep learning. Journal of cheminformatics, 13(1):1–20, 2021.
  49. 49.Méndez-Lucio, O., Ahmad, M., del Rio-Chanona, E. A., and Wegner, J. K. A geometric deep learning approach to predict binding conformations of bioactive molecules. Nature Machine Intelligence, 3(12):1033–1039, 2021.
  50. 50.Mohammad, T., Mathur, Y., and Hassan, M. I. Instadock: A single-click graphical user interface for molecular docking-based virtual high-throughput screening. Briefings in Bioinformatics, 22(4):bbaa279, 2021.
  51. 51.Morrone, J. A., Weber, J. K., Huynh, T., Luo, H., and Cornell, W. D. Combining docking pose rank and structure with deep learning improves protein–ligand binding mode prediction over a baseline docking approach. Journal of chemical information and modeling, 2020.
  52. 52.Open Babel development team. Open babel, 2005. URL http://openbabel.org/wiki/Main_Page.
  53. 53.Ragoza, M., Hochuli, J., Idrobo, E., Sunseri, J., and Koes, D. R. Protein–ligand scoring with convolutional neural networks. Journal of chemical information and modeling, 2017.
  54. 54.Reymond, J.-L. and Awale, M. Exploring chemical space for drug discovery using the chemical universe database. ACS chemical neuroscience, 2012.
  55. 55.Riniker, S. and Landrum, G. A. Better informed distance geometry: using what we know to improve conformation generation. Journal of chemical information and modeling, 2015.
  56. 56.Sankararaman, S., Sha, F., Kirsch, J. F., Jordan, M. I., and Sjölander, K. Active site prediction using evolutionary and structural information. Bioinformatics, 26(5):617–624, 2010.
  57. 57.Satorras, V. G., Hoogeboom, E., and Welling, M. E(n)-equivariant graph neural networks. arXiv preprint arXiv:2102.09844, 2021.
  58. 58.Shen, C., Hu, X., Gao, J., Zhang, X., Zhong, H., Wang, Z., Xu, L., Kang, Y., Cao, D., and Hou, T. The impact of cross-docked poses on performance of machine learning classifier for protein–ligand binding pose prediction. Journal of cheminformatics, 13(1):1–18, 2021.
  59. 59.Shi, C., Luo, S., Xu, M., and Tang, J. Learning gradient fields for molecular conformation generation. arXiv preprint arXiv:2105.03902, 2021.
  60. 60.Somnath, V. R., Bunne, C., and Krause, A. Multi-scale representation learning on proteins. NeurIPS, 34, 2021.
  61. 61.Sverrisson, F., Feydy, J., Correia, B. E., and Bronstein, M. M. Fast end-to-end learning on protein surfaces. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 15272–15281, 2021.
  62. 62.Thomas, N., Smidt, T., Kearnes, S., Yang, L., Li, L., Kohlhoff, K., and Riley, P. Tensor field networks: Rotation-and translation-equivariant neural networks for 3d point clouds. arXiv preprint arXiv:1802.08219, 2018.
  63. 63.Torng, W. and Altman, R. B. Graph convolutional neural networks for predicting drug-target interactions. Journal of chemical information and modeling, 2019a.
  64. 64.Torng, W. and Altman, R. B. High precision protein functional site detection using 3d convolutional neural networks. Bioinformatics, 2019b.
  65. 65.Townshend, R., Bedi, R., Suriana, P., and Dror, R. End-to-end learning on 3d protein structure for interface prediction. NeurIPS, 32:15642–15651, 2019.
  66. 66.Trott, O. and Olson, A. J. Autodock vina: improving the speed and accuracy of docking with a new scoring function, efficient optimization, and multithreading. Journal of computational chemistry, 2010.
  67. 67.Wallach, I., Dzamba, M., and Heifets, A. Atomnet: a deep convolutional neural network for bioactivity prediction in structure-based drug discovery. arXiv preprint arXiv:1510.02855, 2015.
  68. 68.Xu, M., Luo, S., Bengio, Y., Peng, J., and Tang, J. Learning neural generative dynamics for molecular conformation generation. In International Conference on Learning Representations, 2020.
  69. 69.Zhang, W., Bell, E. W., Yin, M., and Zhang, Y. Edock: blind protein–ligand docking by replica-exchange monte carlo simulation. Journal of cheminformatics, 12:1–17, 2020.
  70. 70.Zsoldos, Z., Reid, D., Simon, A., Sadjad, S. B., and Johnson, A. P. ehits: a new fast, exhaustive flexible ligand docking system. Journal of Molecular Graphics and Modelling, 26(1):198–212, 2007.

Citation

MLA
Stärk, H., et al. “EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction”. 39th International Conference on Machine Learning (ICML 2022), 2022, http://arxiv.org/abs/2202.05146v4.
APA
Stärk, H., Ganea, O.-E., Pattanaik, L., Barzilay, R., & Jaakkola, T. (2022). EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction. 39th International Conference on Machine Learning (ICML 2022). http://arxiv.org/abs/2202.05146v4
Chicago
Stärk, H., O.-E. Ganea, L. Pattanaik, R. Barzilay, and T. Jaakkola. 2022. “EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction”. 39th International Conference on Machine Learning (ICML 2022). http://arxiv.org/abs/2202.05146v4.
Harvard
Stärk, H. et al. (2022) “EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction”, 39th International Conference on Machine Learning (ICML 2022) [Preprint]. Available at: http://arxiv.org/abs/2202.05146v4.
Vancouver
1. Stärk H, Ganea O-E, Pattanaik L, Barzilay R, Jaakkola T (2022) EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction. 39th International Conference on Machine Learning (ICML 2022)

BibTeX

@article{stark2022equibind,
  title = {EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction},
  author = {Stärk, Hannes and Ganea, Octavian-Eugen and Pattanaik, Lagnajit and Barzilay, Regina and Jaakkola, Tommi},
  year = {2022},
  journal = {39th International Conference on Machine Learning (ICML 2022)},
  url = {http://arxiv.org/abs/2202.05146v4},
  eprint = {2202.05146}
}
Metadata:arXiv

Access the Paper

This paper is available from its original source. Click below to access the PDF.

Open PDF
License: https://creativecommons.org/licenses/by/4.0/