Multiscale Topological Indices for the Quantitative Prediction of SARS CoV-2 Binding Affinity Change upon Mutations

The Coronavirus disease 2019 (COVID-19) has affected people's lives and the development of the global economy. Biologically, protein-protein interactions between SARS-CoV-2 surface spike (S) protein and human ACE2 protein are the key mechanism behind the COVID-19 disease. In this study, we provide insights into interactions between the SARS-CoV-2 S-protein and ACE2, and propose topological indices to quantitatively characterize the impact of mutations on binding affinity changes (ΔΔG). In our model, a series of nested simplicial complexes and their related adjacency matrices at various different scales are generated from a specially designed filtration process, based on the 3D structures of spike-ACE2 protein complexes. We develop a set of multiscale simplicial complexes-based topological indices, for the first time. Unlike previous graph network models, which give only a qualitative analysis, our topological indices can provide a quantitative prediction of the binding affinity change caused by mutations and achieve great accuracy. In particular, for mutations that happened at specifical amino acids, such as Polar amino acids or Arginine amino acids, the correlation between our topological gravity model index and binding affinity change, in terms of Pearson correlation coefficient, can be higher than 0.8. As far as we know, this is the first time multiscale topological indices have been used in the quantitative analysis of protein-protein interactions.