Protein Function Prediction from Three-Dimensional Feature Representations Using Space-Filling Curves

Compact and interpretable structural feature representations are required for accurately predicting properties and the function of proteins. In this work, we construct and evaluate three-dimensional feature representations of protein structures based on space-filling curves. We focus on the problem of enzyme substrate prediction, using two ubiquitous enzyme families as case studies: the short-chain dehydrogenase/reductases (SDRs) and the S-adenosylmethionine dependent methyltransferases (SAM-MTases). Space-filling curves such as Hilbert curve and the Morton curve generate a reversible mapping from discretized three-dimensional to one-dimensional representations and thus help to encode three-dimensional molecular structures in a system-independent way and with a minimal number of parameters. Using three-dimensional structures of SDRs and SAM-MTases generated using AlphaFold2, we assess the performance of the SFC-based feature representations in predictions on a new benchmark database of enzyme classification tasks including their cofactor and substrate selectivity. Gradient-boosted tree classifiers yield binary prediction accuracy of 0.766-0.906 and AUC (area under curve) parameters of 0.828-0.922 for the classification tasks. We investigate the effects of amino acid encoding, spatial orientation, and (the few) parameters of SFC-based encodings on the accuracy of the predictions. Our results suggest that geometry-based approaches such as SFCs are promising for generating protein structural representations and are complementary to the highly parametric methods, for example, convolutional neural networks (CNNs).