Theory of superstructures in lipid monolayer phase transitions

We present a theory which explains the thermodynamically controlled striplike shapes of two-dimensional solid "crystal" domains observed in phospholipid monolayers in the presence of trace amounts of cholesterol. In the theory, dipole-dipole repulsions between lipid molecules favor the elongation of the domains into long strips, but this elongation is opposed by increasing interfacial free energy (line tension) associated with the perimeter of the domains. The width of the striplike domains is determined by a balance of dipolar and line tension forces and is found to vary exponentially with the ratio X/A where X is the line tension and Δμ is the difference in dipole density between the solid and fluid phases. We then derive an expression for the dependence of the line tension on the concentration of cholesterol molecules in the monolayer and use this relation to compare the predictions of the theory to experimental measurements of the width of the domains as a function of monolayer compression. The theory is found to agree well at high compression but deviates from experiment at low compression, where the domains are short and end effects neglected in the theory become important.