Interpretable machine learning of amino acid patterns in proteins: a statistical ensemble approach

Explainable and interpretable unsupervised machine learning helps understand the underlying structure of data. We introduce an ensemble analysis of machine learning models to consolidate their interpretation. Its application shows that restricted Boltzmann machines compress consistently into a few bits the information stored in a sequence of five amino acids at the start or end of $\alpha$-helices or $\beta$-sheets. The weights learned by the machines reveal unexpected properties of the amino acids and the secondary structure of proteins: (i) His and Thr have a negligible contribution to the amphiphilic pattern of $\alpha$-helices; (ii) there is a class of $\alpha$-helices particularly rich in Ala at their end; (iii) Pro occupies most often slots otherwise occupied by polar or charged amino acids, and its presence at the start of helices is relevant; (iv) Glu and especially Asp on one side, and Val, Leu, Iso, and Phe on the other, display the strongest tendency to mark amphiphilic patterns, i.e., extreme values of an "effective hydrophobicity", though they are not the most powerful (non) hydrophobic amino acids.