## 4 Lamellar Structures  
In addition to fibrous materials, lamellar structures are common in biological organisms. For instance, these thin, plate-like layers occur naturally in cell membranes. Other lamellar structures include bones, nacre, feathers, and wood [7; 100; 101; 102]. The hierarchical architecture of lamellae gives them distinct properties [103; 104]. Lipid bilayers are the most ubiquitous example of lamellar structures arising from a primary phospholipid (primary structure) containing a hydrophobic tail and hydrophilic head. These phospholipids form monolayers (secondary structure) that stack into bilayers and organize into domains (ternary structure), which exhibit coordinated behavior. The quaternary structure emerges from the interactions of nearby domains [105]. The lamellar organization of lipids in biological materials is often found in cell membranes. Cell membranes play vital roles in biological processes such as molecular transport, signaling, and structure maintenance. The lamellar structure provides a matrix for various proteins and controls the permeability of organic molecules, water, and ions. Lamellae also prevent nonspecific protein-protein aggregation, whereas they allow protein diffusion and conformational changes in the membrane [106]. An example of a non-lipid lamellar structure is collagen fibrils organized into stacks in the cornea [107]. Electron density differences between the layers give rise to distinct SAXS patterns that can be analyzed to determine the detailed organization and spacing between these layers. The observed Bragg peaks are used to calculate the electron density profiles across the layers from which the protein distribution and phase behavior can be determined. Cell membranes and single-walled liposomes contain just one lamellar bilayer. But multilamellar structures with stacks of lipids have various advantages over unilamellar membranes; e.g., they spatially organize processes and compartmentalize molecules. They are also quite common biologically. Multilayer liposomal membranes, also called multilamellar vesicles (MLVs), with multiple concentric lipid bilayers, are widely used in drug delivery. [PERSON] et al. used SAXS to show polymorphic transformation in bilayer thickness, inter-bilayer spacing, and lipid packing as temperature, humidity, and chemical conditions varied [108]. An analysis of the lamellar structure can be illustrated by using data from myelin, which has long been used as a model system for studying the structure of membranes. Myelin consists of a stack of lipid bilayers made by oligodendrocytes that form an insulating sheath around nerves, including those in the brain and spinal cord, to facilitate the transmission of electrical impulses. In the sciatic nerve, for example, a dense lipid bilayer from the cytoplasmic surfaces repeatedly alternates with a layer derived from compact outer membranes to form the myelin sheath [109]. Figure 9a shows the myelin structure characterized by its multilayered, compact nature [110]. An example of SAXS pattern for the multilayer structure of myelin can be seen in the SAXS from a dried frog sciatic nerve (Figure 9b). Reflections 146, 73, and 49A are the first, second, and third reflections of the double layer; also present is the 61A, the first-order reflection of the single bilayer [34]. Most interesting in this diffraction pattern is splitting the 44 A reflections into six diffraction spots. This is the evidence for the formation of the near-hjexagonal arrangment or ripple phase in lamellar structures. While dried nerve patterns are useful for understanding the lamellar structures, analysis of hydrated structures is clinically more relevant. Figure 9c shows the SAXS profiles of aqueous suspensions of phosphatidylglycerol (PG, scan a) and a PG-21% myelin basic protein (MBP) complex (scan b). These features are typical of membrane monolayers. Multilayers are formed at protein concentrations > 35%, as shown in Figure 9d.