Fourth-Order Curvature Energy Model for the Stability of Bicontinuous Inverted Cubic Phases in Amphiphile−Water Systems

Abstract

The bicontinuous inverted cubic (Q(II)) phases of amphiphiles in water have many practical applications. It is necessary to understand the stability of these phases as a function of composition and ambient conditions in order to make the best use of them. Moreover, many biomembrane lipids and some biomembrane lipid extracts form Q(II) phases. The stability of Q(II) phases in a given lipid composition is closely related to the susceptibility of that composition to membrane fusion: changes in composition that stabilize Q(II) phases usually increase the rate of membrane fusion. However, the factors determining Q(II) phase stability are not fully understood. Previously, an expression was derived for the curvature free energy of Q(II) phases with respect to that of the lamellar (L(alpha)) phase using a model for the curvature energy with terms up to fourth order in curvature as formulated by Mitov. Here this model is extended to account for the effects of water content on Q(II) phase stability. It is shown that the observed L(alpha)/Q(II) phase-transition temperature, transition enthalpy, and transition kinetics are all sensitive to water content. The same observables also become sensitive to small noncurvature energy contributions to the total free-energy difference between the Q(II) and L(alpha) phases, especially the unbinding energy in the L(alpha) phase. These predictions rationalize earlier observations of Q(II) phase formation in N-monomethylated dioleoylphosphatidylethanolamine that otherwise appear to be inconsistent. The model also provides a fundamental explanation of the hysteresis typically observed in transitions between the L(alpha) and Q(II) phases. It is an accurate model of Q(II) phase stability when the ratio of the volume fraction of the lipid in the Q(II) phase unit cell is < or = 0.5.