Bending stiffness of lipid bilayers. V. Comparison of two formulations

(Received 30 July 1993, Received in final form 23 August 1993, accepted 30 August 1993)

Abstract
Two formulations of the intrinsic bending elasticity of lipid bilayers are compared which are based on (A) the mean and the Gaussian curvature and (B) the mean and the deviatoric curvature. It is shown that (i) formulation A contains implicitly the elasticity associated with the deviatoric curvature even if the topology of the membrane does not change, (ii) the deviatoric elasticity is responsible for the change in elastic energy that comes with a change in membrane topology, (iii) the elastic constant associated with the Gaussian curvature is negative, and (iv) the spontaneous-curvature model may be extended by a curvature-independent term which becomes relevant when the membrane surface area changes. Formulation B is then (for the special case of symmetric bilayers) refined in that the curvatures of the two monolayers are accounted for separately. This leads to a curvature independent term and a correction of the elastic constants of the bilayer which both depend on the value of the monolayer-curvature. A continuum mechanical model for the bending elasticity of a lipid monolayer is developed. By comparison of this model to experimental data (i) the elastic constant associated with the deviatoric curvature is estimated and (ii) the decrease in experimentally determined elastic constants with increasing lipid unsaturation is traced back to the change in area compressibility and a trend in the spontaneous curvature of the monolayers. Finally it is shown that upon a change in temperature the change in elastic energy of a lipid vesicle due to the curvature-independent term is much larger than the concomitant change in elastic energy due to the shape change but only a small fraction of the total change in internal energy.