How To Tackle the Issues in Free Energy Simulations of Long Amphiphiles Interacting with Lipid Membranes: Convergence and Local Membrane Deformations

One of the great challenges in membrane biophysics is to find a means to foster the transport of drugs across complex membrane structures. In this spirit, we elucidate methodological challenges associated with free energy computations of complex chainlike molecules across lipid membranes. As an appropriate standard molecule to this end, we consider 7-nitrobenz-2-oxa-1,3-diazol-4-yl-labeled fatty amine, NBD-C-n, which is here dealt with as a homologous series with varying chain lengths. We found the membrane-water interface region to be highly sensitive to details in free energy computations. Despite considerable simulation times, we observed substantial hysteresis, the cause being the small frequency of insertion/desorption events of the amphiphile's alkyl chain in the membrane interface. The hysteresis was most pronounced when the amphiphile was pulled from water to the membrane and compromised the data that were not in line with experiments. The subtleties in umbrella sampling for computing distance along the transition path were also observed to be potential causes of artifacts. With the PGD (pull geometry distance) scheme, in which the distance from the molecule was computed to a reference plane determined by an average over all lipids in the membrane, we found marked deformations in membrane structure when the amphiphile was close to the membrane. The deformations were weaker with the PGC (pull geometry cylinder) method, where the reference plane is chosen based on lipids that are within a cylinder of radius 1.7 nm from the amphiphile. Importantly, the free energy results given by PGC were found to be qualitatively consistent with experimental data, while the PGD results were not. We conclude that with long amphiphiles there is reason for concern with regard to computations of their free energy profiles. The membrane-water interface is the region where the greatest care is warranted.