Determining the ratio of the Gaussian curvature and bending elastic moduli of phospholipids from QII phase unit cell dimensions

A method is presented for measuring M, the ratio of the Gaussian (saddle splay) elastic modulus to the bending elastic modulus of a lipid monolayer. The ratio M is determined from measurements of the equilibrium bicontinuous inverted cubic (Q(II)) phase unit cell size in excess water as a function of temperature. The analysis includes the effect of a curvature elastic term that is second-order in the Gaussian curvature, K. Preliminary results using data on DOPE-Me validate the method. The fitted value of M is within 8% of the value estimated in an earlier treatment. The method can be used to measure changes in M due to addition of exogenous lipids and peptides to a host lipid system. The Gaussian elastic modulus has a substantial effect on the stability of fusion intermediates (stalks, hemifusion diaphragms, and fusion pores). Studying the effects of peptides and different lipids on M via this method may yield insights into how fusion protein moieties stabilize intermediates in membrane fusion in vivo. The contribution of the K-2 curvature elastic term to the free energy of Q(II) phase and fusion pores explains some features of fusion pore stability and dynamics, and some peculiar observations concerning the mechanism of L alpha/Q(II) phase transitions.