Metric Similarity and Manifold Learning of Circular Dichroism Spectra of Proteins

Abstract

We present a machine learning analysis of circular dichroism spectra of globular proteins from the SP175 database, using the optimal transport-based $1$-Wasserstein distance ${\mathcal{W}}_1$ (with order $p=1$) and the manifold learning algorithm $t$-SNE. Our results demonstrate that ${\mathcal{W}}_1$ is consistent with both Euclidean and Manhattan metrics while exhibiting robustness to noise. On the other hand, $t$-SNE uncovers meaningful structure in the high-dimensional data. The clustering in the $t$-SNE embedding is primarily determined by proteins with distinct secondary structure compositions: one cluster predominantly contains $\beta$-rich proteins, while the other consists mainly of proteins with mixed $\alpha /\beta$ and $\alpha$-helical content.