  Understanding how different classes of molecules move across biological
membranes is a prerequisite to predicting a solute's permeation rate, which is
a critical factor in the fields of drug design and pharmacology. We use biased
Molecular Dynamics computer simulations to calculate and compare the free
energy profiles of translocation of several small molecules across
1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayers as a first step
towards determining the most efficient method for free energy calculations. We
study the translocation of arginine, a sodium ion, alanine, and a single water
molecule using the Metadynamics, Umbrella Sampling, and Replica Exchange
Umbrella Sampling techniques. Within the fixed lengths of our simulations, we
find that all methods produce similar results for charge-neutral permeants, but
not for polar or positively charged molecules. We identify the long relaxation
timescale of electrostatic interactions between lipid headgroups and the solute
to be the principal cause of this difference, and show that this slow process
can lead to an erroneous dependence of computed free energy profiles on the
initial system configuration. We demonstrate the use of committor analysis to
validate the proper sampling of the presumed transition state, which in our
simulations is achieved only in replica exchange calculations. Based on these
results we provide some useful guidance to perform and evaluate free energy
calculations of membrane permeation.
