Calculating the free energy of transfer of small solutes into a model lipid membrane: comparison between Metadynamics and Umbrella Sampling

We compare the performance of two well-established computational algorithms for the calculation of free-energy landscapes of biomolecular systems, umbrella sampling and metadynamics. We look at benchmark systems composed of polyethylene and polypropylene oligomers interacting with lipid (phosphatidylcholine) membranes, aiming at the calculation of the oligomer water-membrane free energy of transfer. We model our test systems at two different levels of description, united-atom and coarse-grained. We provide optimized parameters for the two methods at both resolutions. We devote special attention to the analysis of statistical errors in the two different methods and propose a general procedure for the error estimation in metadynamics simulations. Metadynamics and umbrella sampling yield the same estimates for the water-membrane free energy profile, but metadynamics can be more efficient, providing lower statistical uncertainties within the same simulation time.