Diffusion model, biological membranes

Hydrated bilayers containing one or more lipid components are commonly employed as models for biological membranes. These model systems exhibit a multiplicity of structural phases that are not observed in biological membranes. In the state that is analogous to fluid biological membranes, the liquid crystal or La bilayer phase present above the main bilayer phase transition temperature, Ta, the lipid hydrocarbon chains are conforma-tionally disordered and fluid ( melted ), and the lipids diffuse in the plane of the bilayer. At temperatures well below Ta, hydrated bilayers exist in the gel, or Lp, state in which the mostly all-trans chains are collectively tilted and pack in a regular two-dimensional... 

Fig. 5. Tentative mixed potential model for the sodium-potassium pump in biological membranes the vertical lines symbolyze the surface of the ATP-ase and at the same time the ordinate of the virtual current-voltage curves on either side resulting in different Evans-diagrams. The scale of the absolute potential difference between the ATP-ase and the solution phase is indicated in the upper left comer of the figure. On each side of the enzyme a mixed potential (= circle) between Na+, K+ and also other ions (i.e. Ca2+ ) is established, resulting in a transmembrane potential of around — 60 mV. This number is not essential it is also possible that this value is established by a passive diffusion of mainly K+-ions out of the cell at a different location. This would mean that the electric field across the cell-membranes is not uniformly distributed.

Meanwhile, computational methods have reached a level of sophistication that makes them an important complement to experimental work. These methods take into account the inhomogeneities of the bilayer, and present molecular details contrary to the continuum models like the classical solubility-diffusion model. The first solutes for which permeation through (polymeric) membranes was described using MD simulations were small molecules like methane and helium [128]. Soon after this, the passage of biologically more interesting molecules like water and protons [129,130] and sodium and chloride ions [131] over lipid membranes was considered. We will come back to this later in this section. 

The vast majority of biological membranes are in the liquid-crystalline phase. There are many experimental studies on model bilayer phase behavior [3]. Briefly, at low temperatures lipid bilayers form a gel phase, characterized by high order and rigidity and slow lateral diffusion. There is a main phase transition, as the temperature is increased, to the liquid-crystalline phase. The liquid-crystalline phase has more fluidity and fast lateral diffusion. 

I can easily understand a thickness of the order of 50 to 100 ptm for the unstirred diffusion layers of the flat and thin macromembranes you discussed. In microsystems such as mitochondria with diameters around a few p.m these unstirred layers must, however, be considerably smaller. Would you please comment on this substantial difference between the model membranes you studied and actual biological membrane systems ... 

A very brief description of biological membrane models, and model membranes, is given. Studies of lateral diffusion in model membranes (phospholipid bilayers) and biological membranes are described, emphasizing magnetic resonance methods. The relationship of the rates of lateral diffusion to lipid phase equilibria is discussed. Experiments are reported in which a membrane-dependent immunochemical reaction, complement fixation, is shown to depend on the rates of diffusion of membrane-bound molecules. It is pointed out that the lateral mobilities and distributions of membrane-bound molecules may be important for cell surface recognition. 

Devaux et al. have described in some detail the use of the Bloch equations to relate electron spin-spin interactions between spin-labeled lipids to diffusion constants. This method was originally employed by Trauble and Sackmann,50 Scandella et al.,42 Devaux and McConnell,10 and Devaux et al.11 to measure diffusion constants in multibilayer model membranes and in biological membranes. In all cases diffusion constants of the order of those reported previously were obtained. 

The fluid-mosaic model for biological membranes as envisioned by Singer and Nicolson. Integral membrane proteins are embedded in the lipid bilayer peripheral proteins are attached more loosely to protruding regions of the integral proteins. The proteins are free to diffuse laterally or to rotate about an axis perpendicular to the plane of the membrane. For further information, see S. J. Singer and G. L. Nicolson, The fluid mosaic model of the structure of cell membranes, Science 175 720, 1972. 

The widespread interest in transport across membranes of living cells has led to studies of diffusion in lyotropic liquid crystals. Biological membranes are generally thought to contain single bimolecular leaflets of phospholipid material, leaflets which are like the large, flat micelles of lamellar liquid crystals. No effort is made here to review the literature on transport either across actual cell membranes or across single bimolecular leaflets (black lipid films) which have often been used recently as model systems for membrane studies. Instead, experiments where lamellar liquid crystals have been used as model systems are discussed. 

The modeling of membrane bioreactors is in the initial stage. There are not available more or less sophisticated mathematical tools to describe the complex biochemical processes. It is not known how the mass-transport parameters, diffusion coefficients, convective velocity, biological kinetic parameters might vary in function of the operating conditions, of the biolayer (enzyme/micro-organism membrane layer)... 

Many factors including partition characteristics, degree of ionization, molecular size etc. influence the transport of drugs across biological membranes. Permeation of intact mucosa may also involve passive diffusion, intercellular movement, transport through pores or other mechanisms. The objective of the studies reported here was to employ the dog model to investigate these factors in a systematic and experimentally well-controlled fashion. The non-steriodal anti-inflammatory drug, diclofenac sodium, was selected as a test compound in this evaluation process. 

In the 1970s, the fluid mosaic concept emerged as the most plausible model to account for the known structure and properties of biological membranes [41]. The fact that membranes exist as two-dimensional fluids (liquid disordered) rather than in a gel state (solid ordered) was clearly demonstrated by Frye and Ededin [42], who showed that the lipid and protein components of two separate membranes diffuse into each other when two different cells were fused. Since that time, numerous studies have measured the diffusion coefficient of lipids and proteins in membranes, and the diffusion rates were found to correspond to those expected of a fluid with the viscosity of olive oil rather than a gel phase resembling wax. 

Prognosis of a compounds permeability should be made stressing limitations of the model. There is no bioavailability prognosis from in vitro data - a cellular assay can provide only permeability potential through a biological membrane. The membrane, in most cases CACO-2 cells, is very similar to what we observe in vivo in the small intestine and resembles many characteristics to in vivo enterocytes. CACO-2 cells can be used for prediction of different pathways across intestinal cells. Best correlation occurs for passive transcellular route of diffusion. Passive paracellular pathway is less permeable in CACO-2 and correlations are rather qualitative than quantitative for that pathway. CACO-2 cells are an accepted model for identification of compounds with permeability problems, for ranking of compounds and selection of best compounds within a series. Carrier-mediated transport can be studied as well using careful characterization of transporters in the cell batch or clone as a prerequisite for transporter studies. 

Gas diffusion through NBF is of particular interest, since this film represents a model of biphilic bilayer the permeability of which is of principle importance for biological membranes. 

A very suitable method for measurement of the lateral diffusion of molecules adsorbed at the foam film surfaces is Fluorescence Recovery after Photobleaching (FRAP) ([491-496], see also Chapter 2). Measurements of the lateral diffusion in phospholipid microscopic foam films, including black foam films, are of particular interest as they provide an alternative model system for the study of molecular mobility in biological membranes in addition to phospholipid monolayers at the air/water interface, BLMs, single unilamellar vesicles, and multilamellar vesicles. 

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