Can System Truncation Speed up Ligand-Binding Calculations with Periodic Free-Energy Simulations?

Abstract

We have investigated whether alchemical free-energy perturbation calculations of relative binding energies can be sped up by simulating a truncated protein. Previous studies with spherical nonperiodic systems showed that the number of simulated atoms could be reduced by a factor of 26 without affecting the calculated binding free energies by more than 0.5 kJ/mol on average ( Genheden, S.; Ryde, U. J. Chem. Theory Comput. 2012 , 8 , 1449 ), leading to a 63-fold decrease in the time consumption. However, such simulations are rather slow, owing to the need of a large cutoff radius for the nonbonded interactions. Periodic simulations with the electrostatics treated by Ewald summation are much faster. Therefore, we have investigated if a similar speed-up can be obtained also for periodic simulations. Unfortunately, our results show that it is harder to truncate periodic systems and that the truncation errors are larger for these systems. In particular, residues need to be removed from the calculations, which means that atoms have to be restrained to avoid that they move in an unrealistic manner. The results strongly depend on the strength on this restraint. For the binding of seven ligands to dihydrofolate reductase and ten inhibitors of blood-clotting factor Xa, the best results are obtained with a small restraining force constant. However, the truncation errors were still significant (e.g., 1.5-2.9 kJ/mol at a truncation radius of 10 Å). Moreover, the gain in computer time was only modest. On the other hand, if the snapshots are truncated after the MD simulations, the truncation errors are small (below 0.9 kJ/mol even for a truncation radius of 10 Å). This indicates that postprocessing with a more accurate energy function (e.g., with quantum chemistry) on truncated snapshots may be a viable approach.