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We recently introduced a method called conveyor belt (CB) thermodynamic integration (TI) for the calculation of alchemical free-energy differences based on molecular dynamics simulations. In the present work, the CBTI approach is generalized to conformational free-energy changes, i.e. to the determination of the potential of mean force (PMF) along a conformational coordinate ξ of interest. The proposed conveyor belt umbrella sampling (CBUS) scheme relies on the parallel simulation of K replicas k = 0, 1, ..., K - 1 of the system, with K even. For each replica k, the instantaneous value of ξ is restrained to an anchor value λ. The latter anchor points are equally spaced along a forward-turn-backward-turn path (i.e. a CB) between two extreme values defining the ξ-range of interest. The rotation of the CB is controlled by a variable Λ (range 0 to 2π) which evolves dynamically along the simulation. The evolution of Λ results from the forces exerted by the restraining potentials on the anchor points, taken equal and opposite to those they exert on the replicas. Because these forces tend to cancel out along the CB, the dynamics of Λ is essentially diffusive, and the continuous distribution of ξ-values sampled by the replica system is automatically close to homogeneous. The latter feature represents an advantage over direct counting (DCNT) and traditional umbrella sampling (TRUS), shared to some extent with replica-exchange umbrella sampling (REUS). In this work, the CBUS scheme is introduced and compared to the three latter schemes in the calculation of 45 standard absolute binding free energies. These correspond to the binding of five alkali cations to three crown ethers in three solvents. Different free-energy estimators are considered for the PMF calculation, and the calculated values are also compared to those of a previous study relying on an alchemical path, as well as to experimental data.
This article was published in the following journal.
Name: Journal of chemical theory and computation
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An application that must be submitted to a regulatory agency (the FDA in the United States) before a drug can be studied in humans. This application includes results of previous experiments; how, where, and by whom the new studies will be conducted; the chemical structure of the compound; how it is thought to work in the body; any toxic effects found in animal studies; and how the compound is manufactured. (From the "New Medicines in Development" Series produced by the Pharmaceutical Manufacturers Association and published irregularly.)