Assessing how multiple mutations affect protein stability using rigid cluster size distributions

Predicting how amino acid substitutions affect the stability of a protein has relevance to drug design and may help elucidate the mechanisms of disease-causing protein variants. Unfortunately, wet-lab experiments are time intensive, and to the best of our knowledge there are no efficient computational techniques to asses the effect of multiple mutations. In this work we present a new approach for inferring the effects of single and multiple mutations on a protein's structure. Our rMutant algorithm generates in silico mutants with single or multiple amino acid substitutions. We use a graph-theoretic rigidity analysis approach to compute the distributions of rigid cluster sizes of the wild type and mutant structures which we then analyze to infer the effect of the amino acid substitutions. We successfully predict the effects of multiple mutations for which our previous methods were unsuccessful. We validate the predictions of our computational approach against experimental ΔΔG data. To demonstrate the utility of using rigid cluster size distributions to infer the effects of mutations, we also present a Random Forest Machine Learning approach that relies on rigidity data to predict which residues are critical to the stability of a protein. We predict the destabilizing effects of a single or multiple mutations with over 86% accuracy.