An Explainable Model Using Graph-Wavelet for Predicting Biophysical Properties of Proteins and Measuring Mutational Effects

Proteins hold multispectral patterns of different kinds of physicochemical features of amino acids in their structures, which can help understand proteins' behavior. Here, we propose a method based on the graph-wavelet transform of signals of features of amino acids in protein residue networks derived from their structures to achieve their abstract numerical representations. Such abstract representations of protein structures hand in hand with amino-acid features can be used for different purposes, such as modelling the biophysical property of proteins. Our method outperformed graph-Fourier and convolutional neural-network-based methods in predicting the biophysical properties of proteins. Even though our method does not predict deleterious mutations, it can summarize the effect of an amino acid based on its location and neighbourhood in protein-structure using graph-wavelet to estimate its influence on the biophysical property of proteins. Such an estimate of the influence of amino-acid has the potential to explain the mechanism of the effect of deleterious non-synonymous mutations. Thus, our approach can reveal patterns of distribution of amino-acid properties in the structure of the protein in the context of a biophysical property for better classification and more insightful understanding.