Long timescale ensemble methods in molecular dynamics: Ligand-protein interactions and allostery in SARS-CoV-2 targets

We subject a series of five protein-ligand systems which contain important SARS-CoV-2 targets - 3-chymotrypsin-like protease, papain-like protease and adenosine ribose phosphatase - to long- timescale and adaptive sampling molecular dynamics simulations. By performing ensembles of ten or twelve 10-microsecond simulations for each system, we accurately and reproducibly determine ligand binding sites, both crystallographically resolved and otherwise, thereby discovering binding sites that can be exploited for drug discovery. We also report robust, ensemble-based observation of conformational changes that occur at the main binding site of 3CLPro due to the presence of another ligand at an allosteric binding site. We investigate the reliability and accuracy of long-timescale trajectories. Due to the chaotic nature of molecular dynamics trajectories, individual trajectories do not allow for accurate or reproducible elucidation of macroscopic expectation values. Upon comparing the statistical distribution of protein-ligand contact frequencies for these ten/twelve 10- microsecond trajectories, we find that over 90% of trajectories have significantly different contact frequency distributions. Furthermore, using a direct binding free energy calculation protocol, we determine the ligand binding free energies for each of the identified sites using the long-timescale simulations. The free energies differ by 0.77 to 7.26 kcal/mol across individual trajectories depending on the binding site and the system. We show that although this is the standard way such quantities are currently reported at long-timescale, individual simulation does not yield reliable free energy. Ensembles of independent trajectories are necessary to overcome the aleatoric uncertainty in order to obtain statistically meaningful and reproducible results. Our findings here are generally applicable to all molecular dynamics based applications and not just confined to free energy methods used in this study. Finally, we compare the application of different free energy methods to these systems and discuss their advantages and disadvantages.