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.精准预测蛋白质的性质与功能，需要紧凑且可解释的结构特征表征。本研究构建并评估了基于空间填充曲线（space-filling curves, SFCs）的蛋白质结构三维特征表征。本研究聚焦酶底物预测问题，选取两个广泛存在的酶家族作为案例研究：短链脱氢酶/还原酶（short-chain dehydrogenase/reductases, SDRs）与S-腺苷甲硫氨酸依赖型甲基转移酶（S-adenosylmethionine-dependent methyltransferases, SAM-MTases）。诸如希尔伯特曲线（Hilbert curve）与莫顿曲线（Morton curve）的空间填充曲线，可将离散化的三维结构可逆映射为一维表征，从而能够以系统无关的方式、仅通过少量可调参数对三维分子结构进行编码。本研究利用AlphaFold2预测得到的SDRs与SAM-MTases三维结构，在一个全新的酶分类任务基准数据库中评估了基于SFCs的特征表征的预测性能，该数据库涵盖酶的辅因子与底物选择性分类任务。针对上述分类任务，梯度提升树分类器的二分类预测准确率可达0.77~0.91，曲线下面积（area under curve, AUC）为0.83~0.92。本研究还探究了氨基酸编码方式、空间取向以及基于SFCs的编码的少量可调参数对预测准确率的影响。研究结果表明，诸如SFCs这类基于几何结构的方法在生成蛋白质结构表征方面颇具前景，且可与进化尺度建模（evolutionary scale modeling, ESM）序列嵌入等现有蛋白质特征表征方法形成互补。