Relative Ligand-Binding Free Energies Calculated from Multiple Short QM/MM MD Simulations

Abstract

We have devised a new efficient approach to compute combined quantum mechanical (QM) and molecular mechanical (MM, i.e. QM/MM) ligand-binding relative free energies. Our method employs the reference-potential approach with free-energy perturbation both at the MM level (between the two ligands) and from MM to QM/MM (for each ligand). To ensure that converged results are obtained for the MM → QM/MM perturbations, explicit QM/MM molecular dynamics (MD) simulations are performed with two intermediate mixed states. To speed up the calculations, we utilize the fact that the phase space can be extensively sampled at the MM level. Therefore, we run many short QM/MM MD simulations started from snapshots of the MM simulations, instead of a single long simulation. As a test case, we study the binding of nine cyclic carboxylate ligands to the octa-acid deep cavitand. Only the ligand is in the QM system, treated with the semiempirical PM6-DH+ method. We show that for eight of the ligands, we obtain well converged results with short MD simulations (1-15 ps). However, in one case, the convergence is slower (∼50 ps) owing to a mismatch between the conformational preferences of the MM and QM/MM potentials. We test the effect of initial minimization, the need of equilibration, and how many independent simulations are needed to reach a certain precision. The results show that the present approach is about four times faster than using standard MM → QM/MM free-energy perturbations with the same accuracy and precision.

Binding free energies in the SAMPL6 octa-acid host–guest challenge calculated with MM and QM methods

“…This gave even better results with a precision of 0.5-0.9 kJ/mol, a MAD of 4.7 ± 0.2 and a R 2 correlation of 0.86 ± 0.04. Recently, we have shown that similar results can be obtained with approximately a fourth of the computational effort using multiple short QM/MM simulations [23] or by using non-equilibrium simulations and Jarzynski's equality [32][33][34].…”

“…Relative QM/MM binding affinities between two ligands, L 0 and L 1 , were estimated by the reference-potential method with QM/MM sampling (RPQS) [22,23]. In this approach, the ∆∆G bind free energies, calculated at the MM level, as described in the previous section, are corrected by a FEP calculation for each ligand in the method space, from the MM potential to the QM/MM potential, as is shown by the thermodynamic cycle in Fig.…”

“…Owing to the much larger computational cost of QM calculations, most such studies are based either on single-point QM calculations on structures obtained by MM sampling or on structures minimised by QM [14][15][16] or by combined QM and MM calculations (QM/MM) [17,18]. Only a few studies have involved sampling at the QM/MM level, typically using a semiempirical QM (SQM) method [19][20][21][22][23].…”

“…In a series of publications, we have studied the binding of nine cyclic carboxylate guest molecules to OAH with computational methods at both the MM and QM/MM level [15,22,23,[29][30][31]. In the SAMPL4 challenge, we used FEP to calculate the relative affinities of the nine guests at the MM level [15], which gave the best results in the competition [25], with a mean absolute deviation (MAD) of 3.6 ± 0.2 kJ/mol and a correlation (R 2 ) to experimental data of 0.84 ± 0.04.…”

Biomolecular simulations: From dynamics and mechanisms to computational assays of biological activity

“…While electronic structure calculations are now possible on quite large systems using low‐scaling methods and efficient codes, QM/MM methods offer a combination of flexibility and speed that makes them attractive and practical. QM/MM methods allow calculation of electronic properties of (a small region in) biomolecular systems and are finding application in many areas of biomolecular science (e.g., in the calculation of spectroscopic properties, photochemistry, p K a s, and predictions of ligand‐binding affinities) and beyond (e.g., chemistry of solid‐state materials), but is particularly popular for the study of reactions (and interactions) in enzymes . A QM/MM method was first applied to an enzyme‐catalyzed reaction by Warshel and Levitt in their seminal study of the reaction mechanism of hen egg white lysozyme .…”