Currently, there is no effective antiviral drugs nor vaccine for coronavirus disease 2019 (COVID-19) caused by acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Due to its high conservativeness and low similarity with human genes, SARS-CoV-2 main protease (M$^{text{pro}}$) is one of the most favorable drug targets. However, the current understanding of the molecular mechanism of M$^{text{pro}}$ inhibition is limited by the lack of reliable binding affinity ranking and prediction of existing structures of M$^{text{pro}}$-inhibitor complexes. This work integrates mathematics and deep learning (MathDL) to provide a reliable ranking of the binding affinities of 92 SARS-CoV-2 M$^{text{pro}}$ inhibitor structures. We reveal that Gly143 residue in M$^{text{pro}}$ is the most attractive site to form hydrogen bonds, followed by Cys145, Glu166, and His163. We also identify 45 targeted covalent bonding inhibitors. Validation on the PDBbind v2016 core set benchmark shows the MathDL has achieved the top performance with Pearsons correlation coefficient ($R_p$) being 0.858. Most importantly, MathDL is validated on a carefully curated SARS-CoV-2 inhibitor dataset with the averaged $R_p$ as high as 0.751, which endows the reliability of the present binding affinity prediction. The present binding affinity ranking, interaction analysis, and fragment decomposition offer a foundation for future drug discovery efforts.
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