Potential of mean force and pKa profile calculation for a lipid membrane-exposed arginine side chain

The issue of ionizable protein side chains interacting with lipid membranes has been the focus of much attention since the proposal of the paddle model of voltage-gated ion channels, which suggested multiple arginine (Arg) side chains may move through the hydrocarbon core of a lipid membrane. Recent cell biology experiments have also been interpreted to suggest that these side chains would face only small free energy penalties to cross membranes, challenging a long-standing view in membrane biophysics. Here, we employ side chain analog and transmembrane helix models to determine the free energy of an Arg side chain, as a function of protonation state, across a membrane. We observe high free energy barriers for both the charged and neutral states that would prohibit lipid-exposed movement. The mechanisms for charged and neutral Arg transport are, however, very different, with the neutral state experiencing simple dehydration, whereas the charged state experiences a complex mechanism involving connections to the bilayer interfaces that deform the local membrane structure. We employ special methods to ensure sampling of these interfacial connections and decompose the free energy to shed light on the mechanisms. These deformations are found to preferentially stabilize the protonated form, such that the Arg side chain remains almost exclusively charged inside the membrane, with a pKa shift of <4.5 units. In contrast, the analog models are found to exaggerate the variations in energetics across the membrane and have larger pKa shifts. These results have implications for models of voltage gated ion channels, suggesting that although Arg side chains are ideally suited for carrying charge, the thermodynamics dictate that they must remain sequestered from the lipid bilayer environment.