The Conveyor Belt Umbrella Sampling (CBUS) Scheme:
Principle and Application to the Calculation of the Absolute Binding
Free Energies of Alkali Cations to Crown Ethers
posted on 2020-03-25, 15:39authored byDavid
F. Hahn, Rhiannon A. Zarotiadis, Philippe H. Hünenberger
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 λk. 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 from 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.