Solute Partitioning into Lipid Bilayers: An Implicit Model for Nonuniform and Ordered Environment

We have developed a theoretical and computational methodology to evaluate the coupled orientational-positional distribution of solutes in lipid bilayers. Four different contributions to the solute free energy are considered, which can be traced back to (i) electrostatic and (ii) dispersion interactions between the solute and environment, (iii) work for the formation of a solute-shaped cavity, and (iv) anisotropic interactions with the ordered acyl chains. An atomistic representation of the solute is adopted, which includes the conformational degrees of freedom, whereas an implicit model is used for the water/bilayer environment. The highly nonuniform and anisotropic nature of this is introduced through the profiles of density, dielectric permittivity, lateral pressure, and acyl chain order parameters, which can be derived from experiments or simulations. Effects of chemical composition and physical state of the bilayer can be accounted for by a proper form of these profiles. The methodology which we propose is suitable for the integrated calculation of spectroscopic observables for probes in membranes, for the estimate of partition and permeability coefficients of solutes, and for the implicit modeling of the membrane environment in molecular dynamics and Monte Carlo simulations. Here, the method is presented, and the underlying assumptions are discussed. Cholesterol in the liquid crystalline DPPC bilayer is taken as a case study, to illustrate the capabilities of the proposed approach. Free energy maps, distribution profiles, and orientational properties are shown; they compare well with those obtained from all-atom molecular dynamics simulations, as well as with available experimental data, suggesting that the model used is able to capture the subtle effects of the interplay between intermolecular interaction and nanoscale architecture of the lipid bilayer. The detailed picture provided by our calculations appears suitable to investigate the determinants of the behavior of solutes in lipid membranes, highlighting even nonstraightforward issues, which may have biophysical implications.