How to Determine Lipid Interactions in Membranes from Experiment Through the Ising Model

The determination and the meaning of interactions in lipid bilayers are discussed and interpreted through the Ising model. Originally developed to understand phase transitions in ferromagnetic systems, the Ising model applies equally well to lipid bilayers. In the case of a membrane, the essence of the Ising model is that each lipid is represented by a site on a lattice and that the interaction of each site with its nearest neighbors is represented by an energy parameter ω. To calculate the thermodynamic properties of the system, such as the enthalpy, the Gibbs energy, and the heat capacity, the partition function is derived. The calculation of the configurational entropy factor in the partition function, however, requires approximations or the use of Monte Carlo (MC) simulations. Those approximations are described. Ultimately, MC simulations are used in combination with experiment to determine the interaction parameters ω in lipid bilayers. Several experimental approaches are described, which can be used to obtain interaction parameters. They include nearest-neighbor recognition, differential scanning calorimetry, and Förster resonance energy transfer. Those approaches are most powerful when used in combination of MC simulations of Ising models. Lipid membranes of different compositions are discussed, which have been studied with these approaches. They include mixtures of cholesterol, saturated (ordered) phospholipids, and unsaturated (disordered) phospholipids. The interactions between those lipid species are examined as a function of molecular properties such as the degree of unsaturation and the acyl chain length. The general rule that emerges is that interactions between different lipids are usually unfavorable. The exception is that cholesterol interacts favorably with saturated (ordered) phospholipids. However, the interaction of cholesterol with unsaturated phospholipids becomes extremely unfavorable as the degree of unsaturation increases.