Free energy of hydrophilic and hydrophobic pores in lipid bilayers by free energy perturbation of a restraint.

The free energy of pore formation in lipid bilayers has been previously calculated using a variety of reaction coordinates. Here, we use free energy perturbation of a cylindrical lipid exclusion restraint to compute the free energy profile as a function of pore radius in dimyristoylphosphatidylcholine (DMPC) and dioleoylphosphatidylcholine (DOPC) bilayers. Additionally restraining the headgroups to lie on the membrane surface allows us to also calculate the free energy profile of hydrophobic pores, i.e., cylindrical pores lined by acyl chains. For certain pore radii, the free energy of wetting of hydrophobic pores is calculated using the density bias method. It is found that wetting of hydrophobic pores becomes thermodynamically favorable at 5.0 Å for DMPC and 6.5 Å for DOPC, although significant barriers prevent spontaneous wetting of the latter on a nanosecond time scale. The free energy of transformation of hydrophilic pores to hydrophobic ones is also calculated using free energy perturbation of headgroup restraints along the bilayer normal. This quantity, along with wetting and pore growth free energies, provides complete free energy profiles as a function of radius. Pore line tension values for the hydrophilic pores obtained from the slope of the free energy profiles are 37.6 pN for DMPC and 53.7 pN for DOPC. The free energy profiles for the hydrophobic pores are analyzed in terms of elementary interfacial tensions. It is found that a positive three-phase line tension is required to explain the results. The estimated value for this three-phase line tension (51.2 pN) lies within the expected range.