Lipid shape theory

The technique of fluorescence spectral measurements has become very sensitive over the past decade. In order to obtain more information on the surface monolayers, a new method based on fluorescence was developed. It consisted of placing the monolayer trough on the stage of an epifluorescence microscope, with doped low concentration of fluorescent lipid probe. Later, ordered solid-liquid coexistence at the water-air interface and on solid substrates were reported. The theory of domain shapes has been extensively described by this method. 

Since frequencies for EPR spectroscopy are -100 times higher than those for NMR spectroscopy, correlation times (Chapter 3) must be less than 10-9 s if sharp spectra are to be obtained. Sharp bands may sometimes be obtained for solutions, but samples are often frozen to eliminate molecular motion spectra are taken at very low temperatures. For spin labels in lipid bilayers, both the bandwidth and shape are sensitively dependent upon molecular motion, which may be either random or restricted. Computer simulations are often used to match observed band shapes under varying conditions with those predicted by theories of motional broadening of lines. Among the many spin-labeled compounds that have been incorporated into lipid bilayers are the following ... 

New theory will be required to describe the phase diagram of block liposomes. In particular, theories have to break new ground in explaining why nanorods and nanotubes stay attached to spherical vesicles. All current theories of lipid self-assemblies (based on Helffich s theory of membranes [98]), in contrast, predict spherical, tubular, and micellar shaped liposomes but only as separate objects. In our experiments, not a single instance of an isolated rod- or tube-shaped liposome (i.e., not connected to a sphere- or pear-shaped vesicle) was found. 

But the point particles of physics ignore shape and size that are the axiomatic attributes of the subject of chemistry, be they atoms, molecules, proteins joined in a supposedly particular configuration by "chemical bonds", or transient lipid vesicles or micelles. And where one object ends and another begins is not so self-evident. The notion of a bond that emerges from a quantum mechanical theory of two interacting atoms is not so obvious if those objects are immersed in a sea of their neighbours, forming a solid or liquid. 

Research in olfaction hats been impeded by a lack of knowl-ege concerning the physicochemical properties of molecules which lead to specific olfactory qualities. A diverse range of theories exists which have related quality with physicochemical properties. Factors such as molecular size and shape ( f ) low energy molecular vibrations ( ), molecular cross-section and desorption from a lipid-water interface into water ( ), proton, electron, and apolar factors (, 6 ), profile functional groups... 

Bending elasticity is a long-standing concept of continuum mechanics and has been used mostly to deal with solid rods and plates. More recently, it has been applied to fluid membranes, especially the lipid bilayers of giant vesicles, to understand their equilibrium shapes and shape fluctuations. For continuum theory to be applicable, the membranes should be reasonably smooth or, in other words, not fluctuate too much. 

From the point of view of non-equilibrium statistical physics, understanding the behavior of such active membranes is challenging. Recent theoretical results [8,9] have shown that the shape fluctuations of active membranes should differ both qualitatively and quantitatively from those of passive membranes. The presence of active proteins imbedded in the membrane is expected to induce a magnification of shape fluctuations due to a modification of the fluctuation spectrum. In search of the simplest model to test the theory [8,9], the shape fluctuations of giant lipid vesicles have been studied with the active protein, bacteriorhodopsin (BR) incorporated inside the lipid bilayer. 

The shape of lipid vesicles often deviates from a sphere and, thus, cannot be determined by interfacial tension. Already 20 years ago, W. Helfrich developed a fluid shell theory in which this shape is controlled by the curvature and, thus, by the bending rigidity of the membrane. Meanwhile, this approach has led to a very fruitful interaction of experiment and theory and, thus, to a quantitative understanding of the vesicle shape. 

For large separations, the force between two solid surfaces in a liquid medium can usually be described by continuum theories such as the van der Waals and the electrostatic double-layer theories. The individual nature of the molecules involved, their discrete size, shape, and chemical nature can be neglected. At surface separations approaching molecular dimensions, continuum theory breaks down and the discrete molecular nature of the liquid molecules has to be taken into account. For this reason, it is not surprising that some phenomena cannot be explained by DLVO theory. For example, the swelling of clays in water and nonaqueous liquids and the swelling of lipid bilayers in water cannot be understood on the basis of DLVO theory alone. In this chapter, we consider surface forces that are caused by the discrete nature of the liquid molecules and their specific interactions. 

---