  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 Pearson's 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.
