Improving efficiency of protein–ligand binding free-energy calculations by system truncation

We have studied whether the efficiency of alchemical free-energy calculations with the Bennett acceptance ratio method of protein–ligand binding energies can be improved by simulating only a part of the protein. To this end, we solvated the full protein in a spherical droplet with a radius of 46 Å, surrounded by vacuum. Then, we systematically reduced the size of the droplet and at the same time ignored protein residues that were outside the droplet. Radii of 40 to 15 Å were tested. Ten inhibitors of the blood clotting factor Xa were studied and the results were compared to an earlier study in which the protein was solvated in a periodic box, showing complete agreement between the two set of calculations within statistical uncertainty. We then show that the simulated system can be truncated down to 15 Å, without changing the calculated affinities by more than 0.5 kJ/mol on average (maximum difference 1.4 kJ/mol). Moreover, we show that reducing the number of intermediate states in the calculations from eleven to three gave deviations that on average were only 0.5 kJ/mol (maximum 1.4 kJ/mol). Together this shows that truncation is an appropriate way to improve efficiency of free-energy calculations for small mutations that preserve the net charge of the ligand. In fact, each calculation of a relative binding affinity requires only 6 simulations, each of which takes ~15 CPU hours of computation on a single processor.