BAR-Based Multi-Dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape

Construction of free energy landscapes at Quantum mechanics (QM) level is computationally demanding. By constructing a thermodynamic cycle connecting QM states via an alchemical pathway, we can obtain converged statistics with much less computational resources. The indirect scheme of QM/ molecular mechanics (MM) free energy simulation is often orders of magnitude faster than direct QM/MM simulations. Previous reports on indirect QM/MM simulations are mostly equilibrium sampling based and nonequilibrium methods are only exploited in one-dimensional alchemical QM/MM end-state correction at two end states. In the current work, we report a multi-dimensional nonequilibrium pulling scheme for indirect QM/MM free energy simulations, where the whole free energy simulation is performed only with nonequilibrium methods. The collective variable (CV) space we explore is the combination of one alchemical CV and one physically meaningful CV. The current nonequilibrium indirect QM/MM simulation method can be seen as the generalization of equilibrium perturbation based indirect QM/MM methods. The test systems include one backbone dihedral case and one distance case. The two cases are significantly different in size, enabling us to investigate the dependence of the speedup of the indirect scheme on the size of the system. It is shown that the speedup becomes larger when the size of the system becomes larger, which is consistent with the scaling behavior of QM Hamiltonian.