Models of Lipid Bilayers

It will be rather obvious that models that satisfy these requirements will require the use of a computer to do the detailed work of dealing with all the molecules and the forces between them. Apart from this, there is usually a considerable amount of information that needs to go into the formulation of the problem before one can get something useful out. In this review, we will demonstrate that the break-even point has been passed convincingly by several but not all modelling approaches in recent years. To elaborate on this, we will discuss both the in- and output of these models. 

A further issue is the quality of the results. It will not come as a surprise that the quality of the information gain depends nonlinearly on the computation time that one is willing or able to spend on the problem. There are highly 

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Models of lipid bilayers have been employed widely to investigate diffusion properties across membranes through assisted and non-assisted mechanisms. Simple monovalent ions, e.g., Na+, K+, and Cl, have been shown to play a crucial role in intercellular communication. In order to enter the cell, the ion must preliminarily permeate the membrane that acts as an impervious wall towards the cytoplasm. Passive transport of Na+ and Cl ions across membranes has been investigated using a model lipid bilayer that undergoes severe deformations upon translocation of the ions across the aqueous interface [126]. This process is accompanied by thinning defects in the membrane and the formation of water fingers that ensure appropriate hydration of the ion as it permeates the hydrophobic environment. 

The implications of the existence of an enormous diversity of lipid species and fatty acid patterns in different membranes within one organism as well as the variations between different organisms have posed a allenge for a long time. Any model of lipid bilayer function has to take account of these variations. If we consider erythrocyte membrane phospholipids for example, the rat has about 50% phosphatidylcholine (PC) and only about 10% sphingomyelin (SM), whereas the sheep erythrocyte membrane contains more than 50% SM and no PC. By contrast the total membrane content of phosphatidylethanolamine (PE) + PC + PM in mammalian species is fairly constant, equal to about 15-20%, and the rest are charged lipids... 

There has been considerable interest in the simulation of lipid bilayers due to their biological importance. Early calculations on amphiphilic assemblies were limited by the computing power available, and so relatively simple models were employed. One of the most important of these is the mean field approach of Marcelja [Marcelja 1973, 1974], in which the interaction of a single hydrocarbon chain with its neighbours is represented by two additional contributions to the energy function. The energy of a chain in the mean field is given by ... 

Biological membranes provide the essential barrier between cells and the organelles of which cells are composed. Cellular membranes are complicated extensive biomolecular sheetlike structures, mostly fonned by lipid molecules held together by cooperative nonco-valent interactions. A membrane is not a static structure, but rather a complex dynamical two-dimensional liquid crystalline fluid mosaic of oriented proteins and lipids. A number of experimental approaches can be used to investigate and characterize biological membranes. However, the complexity of membranes is such that experimental data remain very difficult to interpret at the microscopic level. In recent years, computational studies of membranes based on detailed atomic models, as summarized in Chapter 21, have greatly increased the ability to interpret experimental data, yielding a much-improved picture of the structure and dynamics of lipid bilayers and the relationship of those properties to membrane function [21]. 

With the adequacy of lipid bilayer membranes as models for the basic structural motif and hence for the ion transport barrier of biological membranes, studies of channel and carrier ion transport mechanisms across such membranes become of central relevance to transport across cell membranes. The fundamental principles derived from these studies, however, have generality beyond the specific model systems. As noted above and as will be treated below, it is found that selective transport... 

Fig. 5 Membrane models for NMR structure analysis, (a) An isotropic detergent micelle (left) is compared to the dimensions of lipid bilayers (right), (b) Macroscopically oriented membrane samples can be prepared on solid support, as nanodiscs, or as magnetically oriented bicelles. (c) Nomenclature and variability of liposomes small (SUV, 20-40 nm), intermediate (IUV, 40-60 nm), large (LUV, 100-400 nm), and giant unilamellar vesicles (GUV, 1 pm) multi-lamellar (MLV), oligo-lamellar (OLV) and highly heterogeneous multi-oligo-lamellar vesicles (MOLV)...

The formalism sketched above has been used in the literature in more or less the same detail by many authors [87-92]. The predicted membrane structure that follows from this strategy has one essential problem the main gel-to-liquid phase transition known to occur in lipid membranes is not recovered. It is interesting to note that one of the first computer models of the bilayer membrane by Marcelja [93] did feature a first-order phase transition. This author included nematic-like interactions between the acyl tail, similar to that used in liquid crystals. This approach was abandoned for modelling membranes in later studies, because this transition was (unfortunately) lost when the molecules were described in more detail [87]. 

Natural biological membranes consist of lipid bilayers, which typically comprise a complex mixture of phospholipids and sterol, along with embedded or surface associated proteins. The sterol cholesterol is an important component of animal cell membranes, which may consist of up to 50 mol% cholesterol. As cholesterol can significantly modify the bilayer physical properties, such as acyl-chain orientational order, model membranes containing cholesterol have been studied extensively. Spectroscopic and diffraction experiments reveal that cholesterol in a lipid-crystalline bilayer increases the orientational order of the lipid acyl-chains without substantially restricting the mobility of the lipid molecules. Cholesterol thickens a liquid-crystalline bilayer and increases the packing density of lipid acyl-chains in the plane of the bilayer in a way that has been referred to as a condensing effect. 

Figure 5 A schematic model of the formation of lipid gel phase by hydration of the polar groups in crystalline regions of emulsifiers, d = interplanar Bragg spacing d, = thickness of lipid bilayer dw = thickness of water iayer. Redrawn from reference 15, courtesy of Marcel Dekker Inc.

A general model for the interaction of drags and anesthetics with lipid membranes has been developed by Jorgensen el al. [49], The situation is best described by a multistate lattice model for the main transition of lipid bilayers. The foreign mole-... 

Before detailed conclusions are presented with regard to the physical meaning of the present model more fundamental studies are needed. While it is clear that ethanol "induces" new pores or "activates" latent pores in hairless mouse stratum corneum at high ethanol concentrations (10), the role of ethanol at lower concentrations is less clear at this moment. It is well known (12 ) that ethanol at low concentrations, may "fluidize" bilayers, thus leading to changes in both partitioning and diffusivity. Thus a complete description for permeation through stratum corneum will have to consider the effects of adjuvants on the properties of lipid bilayers in addition to the pore model described here. 

Using liposomes for membrane affinity studies has the great advantage that liposomes are a nearly one-to-one model of biological bilayer membranes. Liposomes can be generated from a variability of lipids and mixtures of lipids in order to study the influence of the membrane constituents on the partition behaviour of drag candidates. 

Abstract The fluid mosaic model of membrane bilayers implies that proteins and lipids are homoge-... 

The importance of lipid bilayers, as, near natural environment for, e.g., protein studies by AFM and the model character of these systems for AFM liquid cell work... 

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