Alchemical Free-Energy Calculations by Multiple-Replica lambda-Dynamics: The Conveyor Belt Thermodynamic Integration Scheme

摘要

A new method is proposed to calculate alchemical free-energy differences based on molecular dynamics (MD) simulations, called the conveyor belt thermodynamic integration CBTI) scheme. As in thermodynamic integration (TI), K replicas of the system are simulated at different values of the alchemical coupling parameter lambda. The number K is taken to be even, and the replicas are equally spaced on a forward-turn- backward-turn path, akin to a conveyor belt (CB) between the two physical end-states; and as in lambda-dynamics (AD), the lambda-values associated with the individual systems evolve in time along the simulation. However, they do so in a concerted fashion, determined by the evolution of a single dynamical variable Lambda of period 2 pi controlling the advance of the entire CB. Thus, a change of Lambda is always associated with K/2 equispaced replicas moving forward and K/2 equispaced replicas moving backward along lambda. As a result, the effective free-energy profile of the replica system along Lambda is periodic of period 27 pi K-1, and the magnitude of its variations decreases rapidly upon increasing K, at least as K-1 in the limit of large K. When a sufficient number of replicas is used, these variations become small, which enables a complete and quasi-homogeneous coverage of the lambda-range by the replica system, without application of any biasing potential. If desired, a memory-based biasing potential can still be added to further homogenize the sampling, the preoptimization of which is computationally inexpensive. The final free-energy profile along lambda is calculated similarly to TI, by binning of the Hamiltonian lambda-derivative as a function of lambda considering all replicas simultaneously, followed by quadrature integration. The associated quadrature error can be kept very low owing to the continuous and quasi-homogeneous lambda-sampling. The CBTI scheme can be viewed as a continuous/deterministic/dynamical analog of the Hamiltonian replica-exchange/permutation (HRE/HRP) schemes or as a correlated multiple-replica analog of the lambda D or lambda-local elevation umbrella sampling (lambda-LEUS) schemes. Compared to TI, it shares the advantage of the latter schemes in terms of enhanced orthogonal sampling, i.e. the availability of variable-lambda paths to circumvent conformational barriers present at specific lambda-values. Compared to HRE/HRP, it permits a deterministic and continuous sampling of the lambda-range, is expected to be less sensitive to possible artifacts of the thermo- and barostating schemes, and bypasses the need to carefully preselect a lambda-ladder and a swapping-attempt frequency. Compared to lambda-LEUS, it eliminates (or drastically reduces) the dead time associated with the preoptimization of a biasing potential. The goal of this article is to provide the mathematical/physical formulation of the proposed CBTI scheme, along with an initial application of the method to the calculation of the hydration free energy of methanol.