Electron density modeling and reconstruction of infinite periodic minimal surfaces (IPMS) based phases in lipid-water systems. II. Reconstruction of D surface based phases

Abstract

This is the second of two papers dealing with the structure of lipid-water phases based on Infinite Periodic Minimal Surfaces (IPMS). The first paper describes mathematical modeling of such phases. In this paper, a new reconstruction method, called the methyl trough search, is described and used to solve the structures based on powder pattern X-ray diffraction data. Structures are derived for both a single chain lipid-water system (mono-olein) and a diacyl phospholipid-water system (2-2 methyl butyl 16:0 phosphatidylcholine). The methyl trough search uses the low electron density of the lipid methyl tails to determine the correct phasing for the electron density reconstruction. The data are consistent with a structure based on the IPMS D surface. The results are compared to other methods used to solve the mono-olein structure; the structure of the diacyl lipid has never before been solved. We discuss the subtleties involved in reconstruction of D surface based phases and the substantial artifacts that arise in low-resolution reconstructions of hydrocarbon lipids lacking heavy-atom sites.PACS. 61.30.Cz Theory and models of liquid crystal structure -87.15.By Structure and bonding -83.70.Jr

Stalk structures in lipid bilayer fusion studied by x-ray diffraction

“…Bicontinuous cubic phases consist of two distinct interwoven water regions. Their topology can be described by infinitely periodic minimal surfaces [44]. The transition from a lamellar to a bicontinuous cubic phase resembles the formation of an array of fusion pores [29].…”

“…• Methyl trough search: This method has been introduced for cubic phases containing infinite periodic minimal surfaces (IPMS) [44].…”

Three-dimensional periodic complex structures in soft matter: investigation using scattering methods

“…We calculated the G-surface structure factors f G hkl using the exact G-surface IPMS [48] and their values are given in electronic supplementary material, table S1 along with more recent calculations [15,47]. Using the approximation of the G-surface by Von Schnering & Nesper [53] by a nodal surface of equation sinð2pxÞ cosð2pyÞ þ sinð2pyÞ cosð2pzÞ þ sinð2pzÞ cosð2pxÞ ¼ 0;…”

“…The cubic unit cell for the Ia 3d bi-continuous phase for the rods model and the G-surface model. Using the G-surface model, different methods can be used [14] to take into account the thickness of the film L (a) a linear profile along the normal at each point of the surface [47] (b) a convolution by an infinitely thin shell [48] (c) a lattice method with the calculation of the distance to the G-surface [49] (d ) the iso-density surfaces using the nodal surfaces approximation [50].…”

“…More refined models are available in the literature, but without a simple factorization of a spherical form factor. Garstecki & Holyst [15,[54][55][56][57], Harper et al [47], Enlow et al [49] took into account the thickness either by a segment of length L oriented at each point along the normal to the G-surface, or using a lattice model (figure 5). Using parallel nodal surfaces (see equation (6.4) and figure 5), Solovyov et al [50] obtained a very precise modelization of a mesoporous Ia 3d phase based on more than 25 Bragg reflections.…”