[Paper Review] Intrinsic-Extrinsic Convolution and Pooling for Learning on 3D Protein Structures

Pedro Hermosilla, Marco Schäfer+7 more|arXiv (Cornell University)|Jul 13, 2020

Protein Structure and Dynamics52 references18 citations

TL;DR

This paper proposes a novel deep learning framework for 3D protein structure analysis using intrinsic-extrinsic convolution and hierarchical pooling. By modeling primary, secondary, and tertiary protein structures via covalent/hydrogen bonds and 3D atomic coordinates, the method captures multi-level invariances and outperforms state-of-the-art methods on protein fold and enzyme classification tasks with 46.5% and 85.3% accuracy, respectively.

ABSTRACT

Proteins perform a large variety of functions in living organisms, thus playing a key role in biology. As of now, available learning algorithms to process protein data do not consider several particularities of such data and/or do not scale well for large protein conformations. To fill this gap, we propose two new learning operations enabling deep 3D analysis of large-scale protein data. First, we introduce a novel convolution operator which considers both, the intrinsic (invariant under protein folding) as well as extrinsic (invariant under bonding) structure, by using $n$-D convolutions defined on both the Euclidean distance, as well as multiple geodesic distances between atoms in a multi-graph. Second, we enable a multi-scale protein analysis by introducing hierarchical pooling operators, exploiting the fact that proteins are a recombination of a finite set of amino acids, which can be pooled using shared pooling matrices. Lastly, we evaluate the accuracy of our algorithms on several large-scale data sets for common protein analysis tasks, where we outperform state-of-the-art methods.

Motivation & Objective

• To address the limitation of existing protein learning methods that fail to simultaneously model primary, secondary, and tertiary structural levels.
• To develop a deep learning architecture that explicitly incorporates protein-specific structural invariances across multiple levels.
• To enable multi-scale analysis of proteins through novel hierarchical pooling operations.
• To outperform existing state-of-the-art methods on downstream protein classification tasks.
• To provide an end-to-end framework that leverages both intrinsic (bond-based) and extrinsic (3D spatial) distances in a unified learning process.

Proposed method

• Proposes a multi-graph data structure to represent primary and secondary structures using covalent and hydrogen bonds, and tertiary structure via 3D atomic coordinates.
• Introduces an intrinsic-extrinsic convolution operator that applies n-D convolutions on both Euclidean distances and multiple geodesic distances derived from the multi-graph.
• Designs protein-specific hierarchical pooling operators to enable dimensionality reduction and multi-scale feature learning across variable protein sizes.
• Employs a siamese network architecture for one-shot fold classification to evaluate generalization to unseen folds.
• Uses a 3D coordinate-based representation combined with bond network features as input to the convolutional layers.
• Applies a learnable kernel that operates on both intrinsic (bond network) and extrinsic (3D spatial) distances to capture structural invariances.

Experimental results

Research questions

• RQ1 Can a deep learning model effectively integrate primary, secondary, and tertiary protein structural levels into a unified representation?
• RQ2 How does combining intrinsic (bond-based) and extrinsic (3D spatial) distances improve protein representation learning?
• RQ3 To what extent can hierarchical pooling operations enable multi-scale analysis of proteins with highly variable sizes?
• RQ4 Does the proposed method generalize to unseen protein folds in a one-shot learning setting?
• RQ5 Can the proposed architecture outperform existing state-of-the-art methods on protein fold and enzyme classification tasks?

Key findings

• The proposed method achieves 46.5% accuracy on protein fold classification, outperforming prior state-of-the-art methods.
• On enzyme-catalyzed reaction classification, the method attains 85.3% mean accuracy, surpassing previous SOTA results.
• Ablation studies confirm that all components—protein-specific representation, intrinsic-extrinsic convolution, and pooling—are essential for optimal performance.
• The model generalizes to unseen protein folds, achieving 31.9% accuracy on the unseen test set in one-shot fold classification.
• The method demonstrates robustness across diverse protein sizes and structural complexities due to its hierarchical pooling mechanism.
• The results indicate that explicit modeling of multi-level protein structure leads to more informative and generalizable representations than sequence-only or 3D-coordinate-only baselines.