Free Energy Calculations of Membrane Permeation: Challenges Due to Strong Headgroup–Solute Interactions

Abstract

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 toward 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 time scale 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. On the basis of these results we provide some useful guidance to perform and evaluate free energy calculations of membrane permeation.

Calculating Kinetic Rates and Membrane Permeability from Biased Simulations

“…For a fully quantitative description, it has become fundamental to predict the kinetic behaviour of drugs addressing membrane interaction and permeation. 1,[5][6][7][8] Studies related to the transport of small ligands crossing various phospholipid membranes are the subject of increased interest in recent years 5, [9][10][11][12][13] . There are also significant challenges to investigating this behaviour experimentally.…”

“…In fact, MSMs allow for the convenient combination of multiple MD trajectories into a single kinetic network model from which experimental observables and kinetic rates can be computed. 6,13,[26][27][28] Using experimentally obtained permeabilities by Eyer et al 14 across a lipid membrane for seven structurally unrelated drugs (Fig. 2), Dickson et al 29 recently demonstrated that accurate results for the permeability rates can be obtained by running long unbiased MD simulations 29 .…”

pVEC hydrophobic N‐terminus is critical for antibacterial activity

“…However, our calculations suggest that the PMF trends are similar for pVEC and del5 pVEC systems (Figure ). Both peptides exhibit a local free energy minimum when they are at the lipid‐water interface, which is a common property observed for hydrophilic solutes that prefer to reside either in bulk water or the water‐lipid interface, a highly sensitive region in the free energy calculation studies of peptide insertion . The energetic cost of carrying a single pVEC into the bilayer core is around 92 kcal/mol, while this value is 62 kcal/mol (Figure ) for del5 pVEC.…”

“…During these SMD simulations, pulling of the peptide may have induced the formation of the water pore, which is stable for tens or hundreds of nanoseconds, and this in turn makes it challenging to converge to an equilibrium PMF, as discussed in previous peptide translocation studies . The convergence of free energy profiles can be verified by checking the symmetry of the free energy profiles (with respect to the bilayer center), and the exhibition of a plateau region around the center of the bilayer . Furthermore, it was reported that even with sampling times that exceeded 20 microseconds, it was still not possible to obtain a fully converged free energy profile for CPP insertion .…”

“…47 The convergence of free energy profiles can be verified by checking the symmetry of the free energy profiles (with respect to the bilayer center), and the exhibition of a plateau region around the center of the bilayer. 52 Furthermore, it was reported that even with sampling times that exceeded 20 microseconds, it was still not possible to obtain a fully converged free energy profile for CPP insertion. 47 For the peptide to find the best path to move through the lipids without deforming it, very long simulations should be carried out.…”