  Performing alchemical transformations, in which one molecular system is
nonphysically changed to another system, is a popular approach adopted in
performing free energy calculations associated with various biophysical
processes, such as protein-ligand binding or the transfer of a molecule between
environments. While the sampling of alchemical intermediate states in either
parallel (e.g. Hamiltonian replica exchange) or serial manner (e.g. expanded
ensemble) can bridge the high-probability regions in the configurational space
between two end states of interest, alchemical methods can fail in scenarios
where the most important slow degrees of freedom in the configurational space
are in large part orthogonal to the alchemical variable, or if the system gets
trapped in a deep basin extending in both the configurational and alchemical
space.
  To alleviate these issues, we propose to use alchemical variables as an
additional dimension in metadynamics, augmenting the ability both to sample
collective variables and to enhance sampling in free energy calculations. In
this study, we validate our implementation of alchemical metadynamics in PLUMED
with test systems and alchemical processes with varying complexities and
dimensions of collective variable space, including the interconversion between
the torsional metastable states of a toy system and the methylation of a
nucleoside both in the isolated form and in a duplex. We show that
multi-dimensional alchemical metadynamics can address the challenges mentioned
above and further accelerate sampling by introducing configurational collective
variables. The method can trivially be combined with other metadynamics-based
algorithms implemented in PLUMED. The necessary PLUMED code changes have
already been released for general use in PLUMED 2.8.
