Equivariant Graph Neural Networks for Protein Interaction Modeling and Structure-Aware Molecular Design

1 Introduction andMotivation

Proteins serve as the primary functional units in biological systems, with their three-dimensional structures-ranging from complex proteins to organic compounds-fundamentally determining their biological functions and being crucial for drug discovery and molecular biology applications. However, computationally capturing these geometric features from non-Euclidean molecular data remains a significant challenge for traditional machine learning approaches. Graph Neural Networks (GNNs) have emerged as a natural framework for molecular representation, with Equivariant GNNs (EGNNs) specifically designed to preserve rotational and translational symmetries critical for 3-D molecular systems [Jing et al., 2020].

Despite progress, key gaps remain. First, existing EqGNNs for protein surfaces underutilize directional geometric information. Second, binding site prediction methods treat proteins as static, ignoring conformational dynamics. Third, generative molecular models often lack physics-based inductive biases, producing chemically implausible candidates. Fourth, specifying molecular design objectives remains inaccessible to domain experts without ML expertise.

This thesis addresses these gaps through the progressive research as shown in Figure 1. The overarching question is: How can geometric symmetry constraints be leveraged across the full drug discovery pipeline, from protein surface understanding to controllable 3D molecule generation?

2 Research Questions and Contributions

RQ1: How can attention mechanisms within equivariant GNNs leverage directional vector features to improve proteinprotein interaction site prediction?

Contribution: E(Q)AGNN-PPIS [Animesh et al., 2025]: In this work we hypothesize that incorporating geometric features of the amino acids into model architecture will enhance performance of protein-protein interaction site prediction. To validate this, in this study, we proposed E(Q)AGNNPPIS[Animesh et al., 2025], a method which takes geometric features into consideration. Our approach leverages equivariant GNNs, specifically augmenting the GVP-GNN architecture [Jing et al., 2020] through the integration of an attention mechanism. Our method preserves rotational and translational equivariance while incorporating both scalar and vector features through attention-enhanced message passing. We formally prove that attention integration maintains model equivariance. Empirical evaluation demonstrates 8.33% improvement in AUPRC (0.65) and 10% improvement in MCC (0.55) over the previous state-of-the-art on the standard benchmark datasets. Additionally, our method demonstrates 4× faster inference and robust generalization across proteins of varying lengths, with up to 32.15% F1-score improvement on large proteins.

RQ2: How can adaptive, variance-aware attention replace static dot-product attention in equivariant GNNs for ligand binding site prediction while offering superior computational efficiency and interpretability?

While dot-product attention mechanisms have proven effective, as we have shown in our earlier work [Animesh et al., 2025] in modelling protein data, their computational overhead and neighboring molecule understanding challenges motivate further exploration. In this work we built our mechanism based on the key insight that binding sites often appear as statistically distinct, tightly clustered regions compared to the rest of the protein surface.

Contribution: GDEGAN [Animesh et al., 2026]: We propose GDEGAN, a Gaussian Dynamic Equivariant Graph Attention Network built on the GotenNet [Aykent and Xia, 2025] backbone with higher-degree steerable features (Lmax = 2). Unlike standard dot-product attention that applies uniform similarity metrics, GDEGAN computes attention scores by measuring how statistically probable a neighboring atom's features are, given a Gaussian distribution defined by the target atom's local neighborhood. By dynamically computing local neighborhood statistics (µi, σ2 i ) of each atom's local environment at every layer, our attention mechanism becomes inherently adaptive, and we use the variance as an adaptive bandwidth parameter with learnable per-head temperatures. This adaptation to the emergent local geometry of the protein graphs provides a more powerful and physically grounded inductive bias, enabling the model to learn more robust representations of complex protein structures. We prove that binding sites exhibit significantly higher learned variance (σ2 = 1.41 ± 0.52) than non-binding regions (0.75 ± 0.35, p < 0.001, Cohen's d = 1.85). GDEGAN achieves 37-66% relative improvement in DCC and 7-19% in DCA success rates over state-of-the-art methods across COACH420, HOLO4K, and PDBBind2020, while being 19.5× faster at inference.

RQ3: How can physics-informed distance supervision and higher-order equivariant representations address the stability-affinity trade-off in structure-based drug design?

Contribution: PhysFlow (Under Submission): We uncover a critical limitation in existing SBDD methods: the state-ofthe-art PAFlow [Zhou et al., 2025] achieves strong binding affinity but only 2.7% molecular stability. We attribute this to position-level MSE losses that penalize all coordinate errors equally, ignoring chemical significance. PhysFlow replaces coordinate-level MSE with a novel pocket-aware energy loss that supervises pairwise interatomic distances with exponential decay weighting, combined with protein-ligand anchoring terms and clash-aware guided sampling. Using a higherorder equivariant backbone (ℓ = 2), PhysFlow achieves 6.3× higher molecular stability (18% vs. 2.9%), produces 6.6× more usable drug candidates (1,450 vs. 221), and is 2.8× more parameter-efficient, without sacrificing binding affinity on the CrossDocked2020 dataset.

RQ4: How can natural language instructions be integrated with pocket-conditioned equivariant flow matching for controllable 3D molecular generation?

Proposed Solution: TextSBDD (Work in progress): Existing text-guided molecular methods operate without pocket conditioning (generating SMILES, not 3D coordinates), while pocket-conditioned methods lack natural language control. We identify this as a genuine gap: no method combines text guidance + 3D pocket conditioning + 3D coordinate generation. We develop TextSBDD, which integrates text embeddings with equivariant flow matching to enable both de novo generation from text prompts (e.g., "increase solubility while maintaining binding") and editing of existing molecules, all conditioned on target pocket geometry.

3 Future Direction and Impact

Future work: Beyond RQ4 includes multi-target molecular optimization under geometric constraints and integration with experimental feedback loops. Scientific impact: This thesis advances geometric deep learning by demonstrating how symmetry-aware architectures can systematically address increasingly complex molecular tasks. Practical impact: The methods are directly applicable to early-stage drug discovery acceleration. TextSBDD (RQ4) has the potential to make generative drug design accessible to medicinal chemists without ML expertise.

Acknowledgments

I am thankful to my advisors, Prof. Plaban Kumar Bhowmick and Prof. Pralay Mitra, and to the TCS Research Fellowship (TCS Foundation) for supporting my PhD.