Alchemical free energy calculations
using conventional molecular
dynamics and thermodynamic integration rely on simulations performed
at fixed values of the coupling parameter λ. When multiple conformers
in equilibrium are separated by high barriers in the space orthogonal
to λ, proper convergence may require extremely long simulations.
Four main strategies can be employed to address this orthogonal-sampling
problem: (a) λ-variations, where λ can change along the
simulations to circumvent barriers; (b) λ-extrapolations, where
statistical information is transferred between λ-points; (c)
specific biasing, where orthogonal barriers are reduced using a biasing
potential designed specifically for the system; and (d) generic biasing,
where orthogonal barriers are reduced using a generic approach. Here,
we investigate the relative merits of the first three strategies considering
two benchmark systems. The KXK system involves a mutation of the central
residue in a tripeptide to a glycine and the XTP system involves a
hydrogen-to-bromine mutation in the base of a nucleotide. Three sampling
methods are compared, the latter two involving λ-variations:
molecular dynamics simulations with fixed λ-points, Hamiltonian
replica exchange, and the recently introduced conveyor belt method.
Two free energy estimators are applied, the second one involving λ-extrapolations:
thermodynamic integration with Simpson quadrature and the multistate
Bennett acceptance ratio. Finally, three different seeding schemes
are considered for the generation of the initial configurations. For
both benchmark systems, λ-extrapolations are found to provide
little gain, whereas λ-variations can significantly enhance
the convergence. They are sufficient on their own if the orthogonal
barriers are low in at least one state (e.g., the glycine state in
KXK). However, if the orthogonal barriers are high over the entire
λ-range (e.g., the XTP system), λ-variations are only
effective when applied together with a specific biasing for introducing
such a low-barrier state.