  We apply well-established concepts of Langevin sampling to derive a new class
of algorithms for the efficient computation of free energy differences of
fluctuating particles embedded in a 'fast' membrane, i.e., a membrane that
instantaneously adapts to varying particle positions. A geometric potential
accounting for membrane-mediated particle interaction is derived in the
framework of variational hybrid models for particles in membranes. Recent
explicit representations of the gradient of the geometric interaction potential
allows to apply well-known gradient based Markov Chain Monte-Carlo (MCDC)
methods such as Langevin-based sampling.
