Diffusion lateral rotational

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. 

Although phospholipids diffuse laterally in the plane of the bilayer and rotate more or less freely about an axis perpendicular to this plane, movements from one side of the bilayer to the other are a different matter. Diffusion across the membrane, a transverse, or flip-flop, motion, requires getting the polar head-group of the phospholipid through the... 

In the bilayer membrane model of the 1980s, cell membranes were based largely on a fluid lipid bilayer in which proteins were embedded [149,150]. The bilayer was highly dynamic lipids and proteins could flex, rotate, and diffuse laterally in a two-dimensional fluid. Based on this, the enhancing mechanisms of absorption enhancers on transcellular routes have been clarified. In summary, most of the mechanisms are strongly associated with membrane fluidity. The fluidity is likely to be changed by the following factors. 

The structure is not rigid. Because the hydrocarbon region is liquid, there is rapid lateral diffusion and rotational motion (about an axis perpendicular to the bilayer) of both lipid and protein components. 

In the two-dimensional plane of a bilayer, thermal motion permits lipid molecules to rotate freely around their long axes and to diffuse laterally within each leaflet. Because such movements are lateral or rotational, the fatty acyl chains remain in the hydrophobic interior of the bllayer. In both natural and ar-... 

The lipid layer exhibits a fluidity allowing molecules to diffuse laterally in the plane of the membrane but not to rotate from one surface of the membrane to the other. This fluidity is temperature dependent, diminishing at lower temperatures. Membranes vary in their protein, lipid, and carbohydrate content, and it appears that the protein content in particular increases as the specialization of the membranes increases (Guidotti, 1972). In general, the percentage of protein varies from 18%... 

In 1972 Singer and Nicolson (1) proposed that biological membranes are fluid-mosaic structures. Their model implied that the lipid bilayer acted as a two-dimensional fluid in which protein complexes and other hydrophobic components could freely diffuse, both rotationally and laterally. Evidence for such motions are numerous (2). Despite this it is also quite obvious that not all proteins in membranes are freely diffusing. Indeed the clustering of proteins to specific regions is necessary to form well known features, such as gap junctions, coated pits etc. 

The mechanism by which phospholipid inserts into the outer membrane is unclear. Pulse-chase experiments indicate that newly synthesised PE is first located in the inner leaflet of the outer membrane and later rotates ( flip-flops ) through the lipid bilayer to become part of the external lipid leaflet. Attempts to visualise discrete sites of PE insertion into the outer membrane have failed. This is not surprising since the lateral diffusion time... 

The lipids not only undergo rapid rotational motion, but also diffuse laterally within the plane of the membrane. This rapid... 

From a mathematical perspective either of the two cases (correlated or non-correlated) considerably simplifies the situation [26]. Thus, it is not surprising that all non-adiabatic theories of rotational and orientational relaxation in gases are subdivided into two classes according to the type of collisions. Sack s model A [26], referred to as Langevin model in subsequent papers, falls into the first class (correlated or weak collisions process) [29, 30, 12]. The second class includes Gordon s extended diffusion model [8], [22] and Sack s model B [26], later considered as a non-correlated or strong collision process [29, 31, 32],... 

Henis, Y. I., Lateral and rotational diffusion in biological membranes, in Shinitzky, M. (ed.), Biomembranes Physical Aspects, VCH, Weinheim, 1993, pp. 279-340. 

Phospholipids, which are one of the main structural components of the membrane, are present primarily as bilayers, as shown by molecular spectroscopy, electron microscopy and membrane transport studies (see Section 6.4.4). Phospholipid mobility in the membrane is limited. Rotational and vibrational motion is very rapid (the amplitude of the vibration of the alkyl chains increases with increasing distance from the polar head). Lateral diffusion is also fast (in the direction parallel to the membrane surface). In contrast, transport of the phospholipid from one side of the membrane to the other (flip-flop) is very slow. These properties are typical for the liquid-crystal type of membranes, characterized chiefly by ordering along a single coordinate. When decreasing the temperature (passing the transition or Kraft point, characteristic for various phospholipids), the liquid-crystalline bilayer is converted into the crystalline (gel) structure, where movement in the plane is impossible. 

To work out the time-dependence requires a specific model for the movement of the paramagnet, for example, Brownian motion, or lateral diffusion in a membrane, or axial rotation on a protein, or jumping between two conformers, etc. That theory is beyond the scope of this book the math can become quite hairy and can easily fill another book or two. We limit the treatment here to a few simple approximations that are frequently used in practice. 

The convective diffusion theory was developed by V.G. Levich to solve specific problems in electrochemistry encountered with the rotating disc electrode. Later, he applied the classical concept of the boundary layer to a variety of practical tasks and challenges, such as particle-liquid hydrodynamics and liquid-gas interfacial problems. The conceptual transfer of the hydrodynamic boundary layer is applicable to the hydrodynamics of dissolving particles if the Peclet number (Pe) is greater than unity (Pe > 1) (9). The dimensionless Peclet number describes the relationship between convection and diffusion-driven mass transfer ... 

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