Instability of Myelin Tubes under Dehydration: deswelling of layered cylindrical structures

We report experimental observations of an undulational instability of myelin figures. Motivated by this, we examine theoretically the deformation and possible instability of concentric, cylindrical, multi-lamellar membrane structures. Under conditions of osmotic stress (swelling or dehydration), we find a stable, deformed state in which the layer deformation is given by \delta R ~ r^{\sqrt{B_A/(hB)}}, where B_A is the area compression modulus, B is the inter-layer compression modulus, and h is the repeat distance of layers. Also, above a finite threshold of dehydration (or osmotic stress), we find that the system becomes unstable to undulations, first with a characteristic wavelength of order \sqrt{xi d_0}, where xi is the standard smectic penetration depth and d_0 is the thickness of dehydrated region.Comment: 5 pages + 3 figures [revtex 4

Influence of the Lamellar Phase Unbinding Energy on the Relative Stability of Lamellar and Inverted Cubic Phases

Based on curvature energy considerations, nonbilayer phase-forming phospholipids in excess water should form stable bicontinuous inverted cubic (QII) phases at temperatures between the lamellar (Lα) and inverted hexagonal (HII) phase regions. However, the phosphatidylethanolamines (PEs), which are a common class of biomembrane phospholipids, typically display direct Lα/HII phase transitions and may form intermediate QII phases only after the temperature is cycled repeatedly across the Lα/HII phase transition temperature, TH, or when the HII phases are cooled from T > TH. This raises the question of whether models of inverted phase stability, which are based on curvature energy alone, accurately predict the relative free energy of these phases. Here we demonstrate the important role of a noncurvature energy contribution, the unbinding energy of the Lα phase bilayers, gu, that serves to stabilize the Lα phase relative to the nonlamellar phases. The planar Lα phase bilayers must separate for a QII phase to form and it turns out that the work of their unbinding can be larger than the curvature energy reduction on formation of QII phase from Lα at temperatures near the Lα/QII transition temperature (TQ). Using gu and elastic constant values typical of unsaturated PEs, we show that gu is sufficient to make TQ > TH for the latter lipids. Such systems would display direct Lα → HII transitions, and a QII phase might only form as a metastable phase upon cooling of the HII phase. The gu values for methylated PEs and PE/phosphatidylcholine mixtures are significantly smaller than those for PEs and increase TQ by only a few degrees, consistent with observations of these systems. This influence of gu also rationalizes the effect of some aqueous solutes to increase the rate of QII formation during temperature cycling of lipid dispersions. Finally, the results are relevant to protocols for determining the Gaussian curvature modulus, which substantially affects the energy of intermediates in membrane fusion and fission. Recently, two such methods were proposed based on measuring TQ and on measuring QII phase unit cell dimensions, respectively. In view of the effect of gu on TQ that we describe here, the latter method, which does not depend on the value of gu, is preferable