The liquid crystalline lamellar (L ) to double-diamond inverse bicontinuous cubic (Q D II ) phase transition for the amphiphile monoelaidin in excess water exhibits a remarkable sequence of structural transformations for pressure or temperature jumps. Our data imply that the transition dynamics depends on a coupling between changes in molecular shape and the geometrical and topological constraints of domain size. We propose a qualitative model for this coupling based on theories of membrane fusion via stalks and existing knowledge of the structure and energetics of bicontinuous cubic phases. DOI: 10.1103/PhysRevLett.96.108102 PACS numbers: 87.16.Dg, 61.10.Eq, 87.17.Ee, 64.70.Md Lyotropic liquid crystalline phases form when amphiphilic molecules are mixed with a polar solvent [1,2]. The many structures they can adopt, their complex phase behavior and their energetics have received a great deal of attention over the past half century. Much is now understood about their equilibrium behavior and this has informed the development of surfactant technologies and our understanding of how amphiphiles in biological membranes can control biochemical activity [3,4]. By comparison the study of the nonequilibrium structure and dynamics of lyotropic liquid crystalline systems is in its infancy and little is understood about the mechanisms by which one phase transforms into another [5,6]. Understanding the dynamics of lyotropic phase transformations is of practical interest for applications where amphiphilic materials are processed and of relevance in biological systems where membrane fusion or division occurs.The present work focuses on a phase transition where membrane fusion occurs: the fluid lamellar to inverse bicontinuous cubic phase transition, Fig. 1. Models for the process of membrane fusion between apposed lipid bilayers have been proposed by a number of groups [7][8][9]. All rely on the formation of transient lipid contacts known as stalks, which subsequently break through to form the beginnings of the tubular connections that are the fundamental connecting element in the inverse bicontinuous cubic phases. Recent theoretical models of the structure and energy of the stalk have incorporated both elastic energy, accounting for the splay, saddle splay, and tilt deformations of the membrane, as well as hydration repulsion acting between the apposing membranes [10 -12]. The models have been used to estimate the energy of stalk formation and mesoscopic models have been used to simulate the entire fusion process [13]. However, very few measurements have been made to test these models. To date the most convincing evidence has been structural evidence that is consistent with the existence of fusion stalks [14]. As for the structural dynamics, a limited amount of experimental work has been carried out on the lamellar to inverse bicontinuous cubic phase transition [15][16][17][18][19]. The major problem to date with these dynamical studies is the lack of reproducibility in results [20,21]. FIG. 1 (color online). In these im...