Binding affinities by alchemical perturbation using QM/MM with a large QM system and polarizable MM model.
The most general way to improve the accuracy of binding-affinity calculations for protein-ligand systems is to use quantum-mechanical (QM) methods together with rigorous alchemical-perturbation (AP) methods. We explore this approach by calculating the relative binding free energy of two synthetic disaccharides binding to galectin-3 at a reasonably high QM level (dispersion-corrected density functional theory with a triple-zeta basis set) and with a sufficiently large QM system to include all short-range interactions with the ligand (744-748 atoms). The rest of the protein is treated as a collection of atomic multipoles (up to quadrupoles) and polarizabilities. Several methods for evaluating the binding free energy from the 3600 QM calculations are investigated in terms of stability and accuracy. In particular, methods using QM calculations only at the endpoints of the transformation are compared with the recently proposed non-Boltzmann Bennett acceptance ratio (NBB) method that uses QM calculations at several stages of the transformation. Unfortunately, none of the rigorous approaches give sufficient statistical precision. However, a novel approximate method, involving the direct use of QM energies in the Bennett acceptance ratio method, gives similar results as NBB but with better precision, ∼3 kJ/mol. The statistical error can be further reduced by performing a greater number of QM calculations.
School of Chemistry, University of Southampton, Highfield, Southampton, SO17 1BJ, United Kingdom.
Samuel
S
Genheden
Department of Theoretical Chemistry, Lund University, Chemical Centre, P. O. Box 124, Lund, SE-221 00, Sweden.
Ulf
U
Ryde
Department of Biophysical Chemistry, Lund University, Chemical Centre, P. O. Box 124, Lund, SE-221 00, Sweden.
Pär
P
Söderhjelm
D008024:Ligands; D015394:Molecular Structure; D011789:Quantum Theory; D013816:Thermodynamics
D008024:Ligands
Bennett acceptance ratio; alchemical transformation; binding affinity; dispersion-corrected density functional theory; free-energy perturbation; galectin-3; protein-ligand interaction; quantum chemistry; quantum-mechanical/molecular mechanics