The fast-switching decoupling method is a powerful nonequilibrium technique to compute absolute binding free energies of ligand-receptor complexes (Sandberg et al., J. Chem. Theory Comput. 2014, 11, 423-435). Inspired by the theory of noncovalent binding association of Gilson and co-workers (Biophys. J. 1997, 72, 1047-1069), we develop two approaches, termed binded-domain and single-point alchemical-path schemes (BiD-AP and SiP-AP), based on the possibility of performing alchemical trajectories during which the ligand is constrained to fixed positions relative to the receptor. The BiD-AP scheme exploits a recent generalization of nonequilibrium work theorems to estimate the free energy difference between the coupled and uncoupled states of the ligand-receptor complex. With respect to the fast-switching decoupling method without constraints, BiD-AP prevents the ligand from leaving the binding site, but still requires an estimate of the positional binding-site volume, which may not be a simple task. On the other side, the SiP-AP scheme allows avoidance of the calculation of the binding-site volume by introducing an additional equilibrium simulation of ligand and receptor in the bound state. In the companion article (DOI: 10.1021/acs.jctc.7b00595), we show that the extra computational effort required by SiP-AP leads to a significant improvement of accuracy in the free energy estimates.

We propose a path-breaking route to the enhancement of unidirectional nonequilibrium simulations for the calculation of free energy differences via Jarzynski's equality [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)]. One of the most important limitations of unidirectional nonequilibrium simulations is the amount of realizations necessary to reach suitable convergence of the work exponential average featuring the Jarzynski's relationship. In this respect, a significant improvement of the performances could be obtained by finding a way of stopping trajectories with negligible contribution to the work exponential average, before their normal end. This is achieved using path-breaking schemes which are essentially based on periodic checks of the work dissipated during the pulling trajectories. Such schemes can be based either on breaking trajectories whose dissipated work exceeds a given threshold or on breaking trajectories with a probability increasing with the dissipated work. In both cases, the computer time needed to carry out a series of nonequilibrium trajectories is reduced up to a factor ranging from 2 to more than 10, at least for the processes under consideration in the present study. The efficiency depends on several aspects, such as the type of process, the number of check-points along the pathway and the pulling rate as well. The method is illustrated through radically different processes, i.e., the helix-coil transition of deca-alanine and the pulling of the distance between two methane molecules in water solution.

In the companion article (Giovannelli et al., 10.1021/acs.jctc.7b00594), we presented an alchemical approach, based on nonequilibrium molecular dynamics simulations, to compute absolute binding free energies of a generic host-guest system. Two alternative computational routes, called binded-domain and single-point alchemical-path schemes, have been proposed. This study is addressed to furnish numerical validation and illustrative examples of the above-mentioned alchemical schemes. Validation is provided by comparing binding free-energy data relative to two poses of a Zn(II)·anion complex with those recovered from an alternative approach, based on steered molecular dynamics simulations. We illustrate important technical and theoretical aspects for a good practice in applying both alchemical schemes, not only through the calculations on the Zn(II)·anion complex, but also estimating absolute binding free energies of 1:1 complexes of β-cyclodextrin with aromatic compounds (benzene and naphthalene). Comparison with experimental data and previous molecular dynamics simulation studies further confirms the validity of the present nonequilibrium-alchemical methodology.

Nonequilibrium Candidate Monte Carlo simulation [Nilmeier et al., Proc. Natl. Acad. Sci. U.S.A. 2011, 108, E1009-E1018] is a tool devised to design Monte Carlo moves with high acceptance probabilities that connect uncorrelated configurations. Such moves are generated through nonequilibrium driven dynamics, producing candidate configurations accepted with a Monte Carlo-like criterion that preserves the equilibrium distribution. The probability of accepting a candidate configuration as the next sample in the Markov chain basically depends on the work performed on the system during the nonequilibrium trajectory and increases with decreasing such a work. It is thus strategically relevant to find ways of producing nonequilibrium moves with low work, namely moves where dissipation is as low as possible. This is the goal of our methodology, in which we combine Nonequilibrium Candidate Monte Carlo with Configurational Freezing schemes developed by Nicolini et al. (J. Chem. Theory Comput. 2011, 7, 582-593). The idea is to limit the configurational sampling to particles of a well-established region of the simulation sample, namely the region where dissipation occurs, while leaving fixed the other particles. This allows to make the system relaxation faster around the region perturbed by the finite-time switching move and hence to reduce the dissipated work, eventually enhancing the probability of accepting the generated move. Our combined approach enhances significantly configurational sampling, as shown by the case of a bistable dimer immersed in a dense fluid.

An important limitation of unidirectional nonequilibrium simulations is the amount of realizations of the process necessary to reach suitable convergence of free energy estimates via Jarzynski's relationship [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)]. To this regard, an improvement of the method has been achieved by means of path-breaking schemes [R. Chelli et al., J. Chem. Phys. 138, 214109 (2013)] based on stopping highly dissipative trajectories before their normal end, under the founded assumption that such trajectories contribute marginally to the work exponential averages. Here, we combine the path-breaking scheme, called probability threshold scheme, to bidirectional nonequilibrium methods for free energy calculations [G. E. Crooks, Phys. Rev. E 61, 2361 (2000); R. Chelli and P. Procacci, Phys. Chem. Chem. Phys. 11, 1152 (2009)]. The method is illustrated and tested on a benchmark system, i.e., the helix-coil transition of deca-alanine. By using path-breaking in our test system, the computer time needed to carry out a series of nonequilibrium trajectories can be reduced up to a factor 4, with marginal loss of accuracy in free energy estimates.