Influence of the lamellar phase unbinding energy on the relative stability of lamellar and inverted cubic phases

¹ Givaudan, Inc.
² Northwestern University

^* To whom correspondence should be addressed. E-mail: david.siegel{at}givaudan.com.

Submitted on July 24, 2007
Revised on September 7, 2007
Accepted on 3 January 2008

	Abstract

Based on curvature energy considerations, nonbilayer phase-forming phospholipids in excess water should form stable bicontinuous inverted cubic (Q_II) phases at temperatures between the lamellar (L) and inverted hexagonal (H_II) phase regions. However, the phosphatidylethanolamines (PEs), which are a common class of biomembrane phospholipids, typically display a direct L/H_II phase transition, and may form intermediate Q_II phases only after the temperature is cycled repeatedly across the L/H_II phase transition temperature, T_H, or when the H_II phases are cooled from T > T_H. 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 non-curvature energy contribution, the unbinding energy of the L phase bilayers, g_u, that serves to stabilize the L phase relative to the non-lamellar phases. The planar L phase bilayers must separate in order for a Q_II phase to form, and it turns out that the work of their unbinding can be larger than the curvature energy reduction on formation of Q_II phase from L at temperatures near the L/Q_II transition temperature (T_Q). Using g_u and elastic constant values typical of unsaturated-chain PEs, we show that g_u is sufficient to make T_Q T_H for the latter lipids. Such systems would display direct LH_II phase transitions, and a Q_II phase might form as a metastable phase upon cooling of the H_II phase. The g_u values for methylated PEs and PE/phosphatidylcholine (PC) mixtures are significantly smaller than those for PEs and increase T_Q by only a few degrees, consistent with observations on these systems. This influence of g_u also rationalizes the effect of some aqueous solutes to increase the rate of Q_II 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 protocols were proposed, based on measuring T_Q, and on measuring Q_II phase unit cell dimensions; respectively. In view of the effect of g_u on T_Q that we describe here, the latter method, which does not depend on the value of g_u, is preferable.

Key Words: Gaussian, bicontinuous, elastic modulus, saddle splay

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