posted on 2015-06-09, 00:00authored byNoah S. Bieler, Jan P. Tschopp, Philippe H. Hünenberger
An extension of the λ-local-elevation
umbrella-sampling (λ-LEUS)
scheme [Bieler et al. J.
Chem. Theory Comput. 2014, 10, 3006] is proposed to handle the multistate
(MS) situation, i.e. the calculation of the relative free energies
of multiple physical states based on a single simulation. The key
element of the MS-λ-LEUS approach is to use a single coupling
variable Λ controlling successive pairwise mutations between
the states of interest in a cyclic fashion. The Λ variable is
propagated dynamically as an extended-system variable, using a coordinate
transformation with plateaus and a memory-based biasing potential
as in λ-LEUS. Compared to other available MS schemes (one-step
perturbation, enveloping distribution sampling and conventional λ-dynamics)
the proposed method presents a number of important advantages, namely:
(i) the physical states are visited explicitly and
over finite time periods; (ii) the extent of unphysical
space required to ensure transitions is kept minimal and, in particular,
one-dimensional; (iii) the setup protocol solely
requires the topologies of the physical states; and (iv) the method only requires limited modifications in a simulation
code capable of handling two-state mutations. As an initial application,
the absolute binding free energies of five alkali cations to three
crown ethers in three different solvents are calculated. The results
are found to reproduce qualitatively the main experimental trends
and, in particular, the experimental selectivity of 18C6 for K+ in water and methanol, which is interpreted in terms of opposing
trends along the cation series between the solvation free energy of
the cation and the direct electrostatic interactions within the complex.