Understanding the permeation of molecules through lipid membranes is fundamental for predicting the cellular uptake of solutes and drug delivery mechanisms. In molecular simulations the usual approach is to
compute the free energy (FE) profile of a molecule across a model lipid bilayer, which can then be used to
estimate the permeability of the molecule. Umbrella sampling (US), which involves carrying out a series of
biased simulations along a defined reaction coordinate (usually the bilayer normal direction), is a popular
method for the computation of such FE profiles. However, US can be challenging to implement because
the results are dependent on the strength of the biasing potential and the spacing of windows along the
reaction coordinate, which, in practice, are usually optimized by an inefficient trial and error approach. The
Steered Molecular Dynamics implementation of the Jarzynski Equality (JE-SMD) has been identified as an
alternative to equilibrium sampling methods for measuring the FE change across a reaction coordinate. In
the JE-SMD approach, equilibrium FE values are evaluated from the average of rapid non-equilibrium trajectories, thus avoiding the practical issues that come with US. Here, we use three different corrections of the
JE-SMD method to calculate the FE change for the translocation of two aromatic substrates, phenylalanine
and toluene, across a lipid bilayer, and compare the accuracy and computational efficiency of these approaches
to the results obtained using US. We show evidence that when computing the free energy profile, the JE-SMD
approach suffers from insufficient sampling convergence of the bilayer environment, and is dependent on the
characteristic of the aromatic substrate itself. We deduce that, despite its drawbacks, US remains the more
viable approach of the two for computing the FE profile.
Comparison of Umbrella Sampling and Steered Molecular Dynamics Methods for Computing Free Energy Profiles of Toluene Molecules through Phospholipid Bilayers