Numerical Encodings of Amino Acids in Multivariate Gaussian Modeling of Protein Multiple Sequence Alignments

Enzyme Substrate Prediction from Three-Dimensional Feature Representations Using Space-Filling Curves

Compact and interpretable structural feature representations are required for accurately predicting properties and function of proteins. In this work, we construct and evaluate three-dimensional feature representations of protein structures based on space-filling curves (SFCs). 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 the 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 only a few adjustable 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 0.77-0.91 and area under curve (AUC) characteristics of 0.83-0.92 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 existing protein feature representations such as evolutionary scale modeling (ESM) sequence embeddings.