Diffusion coefficient of lipids

In the fluid state, the lateral diffusion coefficient of lipids in the bilayer structure is 0( 10 1 ) m2 s-1 (the symbol O is used to indicate order of magnitude). Interestingly, it has been shown that the diffusion coefficients of phospholipids may differ greatly from the inner to the outer leaflet of the biomembrane layer [4,5]. Again, this is related to the differences in chemical... 

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. 

Table 1 Translational diffusion coefficients of lipids and order parameters in some membrane phases...

Lipids diffuse freely in fluid model membranes. FRAP measurements show full recovery and diffusion coefficients on the order of magnitude of 10 cm /sec. Free diffusion with a similar rate is often observed for lipids in the biomembrane. However, many cell membrane proteins show lower diffusion rates and incomplete recovery after photobleaching. For membrane proteins, dramatically different behavior in model and biological membranes is a common case. In model membranes, membrane proteins also diffuse freely and their diffusion coefficients are often similar to the diffusion coefficients of lipids. On the contrary, in biomembranes, the diffusion of proteins is 2-3 orders of magnitude slower and the fluorescence recovery is often incomplete. This observation points to limitations of the fluid mosaic model as will be discussed below. 

The diffusion coefficient of lipids in a variety of membranes is about 1 p m s f Thus, a phospholipid molecule diffuses an average distance of 2 p m in 1 s. This rate means that a lipid molecule can travel from one end of a bacterium to the other in a second. The magnitude of the observed diffusion coefficient indicates that the viscosity of the membrane is about 100 times that of water, rather like that of olive oil. 

The diffusion coefficient of lipids in a variety of membranes is about... 

Interestingly, the lipid diffusion in the outer leaflet of each vesicle is typically enhanced over that in a flat bilayer, but the lipid mobility in the inner leaflet is suppressed. Moreover, the diffusion coefficient of lipid molecules in the outer leaflet is almost constant for any size vesicle, whereas that in the inner leaflet shows a strong size dependency. The outer leaflet of the inner bilayer of the MLV shows slightly lower mobility, due to the effect of the outer bilayer, although a similar effect on the inner leaflet of the opposing bilayer is not evident. 

The values for the lipid molecules compare well (althoughJgiey are still somewhat larger) with the experimental value of 1.5x10 cm /s as measured with the use of a nitroxide spin label. We note that the discrepancy of one order of magnitude, as found in the previous simulation with simplified head groups, is no longer observed. Hence we may safely conclude that the diffusion coefficient of the lipid molecules is determined by hydrodynamic interactions of the head groups with the aqueous layer rather than by the interactions within the lipid layer. The diffusion coefficient of water is about three times smaller than the value of the pure model water thus the water in the bilayer diffuses about three times slower than in the bulk. 

R. Fato, M. Battino, G. P. Castelli, and G. Lenaz, Measurement of the lateral diffusion coefficients of ubiquinones in lipid vesicles by fluorescence quenching of 12-(9-anthroyl) stearate, FEES Lett. 179, 238-242 (1985). 

The intercellular route is considered to be the predominantly used pathway in most cases, especially when steady-state conditions in the stratum corneum are reached. In case of intercellular absorption, substance transport occurs in the bilayer-structured, continuous, intercellular lipid domain within the stratum corneum. Although this pathway is very tortuous and therefore much longer in distance than the overall thickness of the stratum corneum, the intercellular route is considered to yield much faster absorption due to the high diffusion coefficient of most drugs within the lipid bilayer. Resulting from the bilayer structure, the intercellular pathway provides hydrophilic and lipophilic regions, allowing more hydrophilic substances to use the hydrophilic and more lipophilic substances to use the lipophilic route. In addition, it is possible to influence this pathway by certain excipients in the formulation. 

There is an abrupt decrease in the lateral diffusion coefficient of DPPC upon the phase transition from the GI phase to the Gi phase. This is because the acyl-chain region is being packed even more efficiently in the Gi phase than in the GI phase, and the hydrocarbon volume in the Gi phase is smaller than in the GI phase. Also, in the Gi phase, the lipid acyl-chains from the opposing bilayer leaflets interdigitate. In order for a phospholipid molecule to diffuse it has to circumvent the nearby interdigitated molecules which hinder diffusion. 

It should also be recalled that the diffusion coefficient of a molecule will decrease with increasing viscosity of the solvent. Thus, as might be expected with cytosols or lipid bilayers, a viscous medium will slow down the rate of encounters. Since viscosity is itself temperature dependent, such encounters in solution will have their own activation energy. 

Fluorescein-labeled proteins are also used to measure the translational mobility of proteins and lipids by the Fluorescence Recovery After Photo-bleaching technique [54-59]. The uniformly labeled fluorescent sample is flashed with an intense light source to bleach a spot, thus producing a concentration gradient. The rate of recovery of fluorescence in that bleached area is measured and used to calculate the diffusion coefficient of the probe dye into the bleached zone. Such diffusion coefficient measurements have been used to determine the association constants of proteins in cells [60], to measure the exchange of tubulin between the cytoplasm and the microtubules [61,62], to study the polymerization-depolymerization process of actin [63-65] and to monitor the changes that occur upon cell maturation [66,67]. 

To improve topical therapy, it is advantageous to use formulation additives (penetration enhancers) that will reversibly and safely modulate the barrier properties of the skin. Fick s first law of diffusion shows that two potential mechanisms are possible. The two constants that could be altered significantly are the diffusion coefficient in the stratum corneum and the concentration in the outer regions of the stratum corneum. Thus, one of mechanisms of action of an enhancer is for it to insert itself into the bilayer structures and disrupt the packing of the adjacent lipids, thereby, reducing the microviscosity. The diffusion coefficient of the permeant will increase This effect has been observed using ESR and fluorescence spectroscopy [16,17]. 

In contrast, proteins vary markedly in their lateral mobility. Some proteins are nearly as mobile as lipids, whereas others are virtually immobile. For example, the photoreceptor protein rhodopsin (Section 32.3.1). a very mobile protein, has a diffusion coefficient of 0.4 pm s f The rapid movement of rhodopsin is essential for fast signaling. At the other extreme is fibronectin, a peripheral glycoprotein that interacts with the extracellular matrix. For fibronectin, D is less than 10-4 pm2 s f Fibronectin has a very low mobility because it is anchored to actin filaments on the inside of the plasma membrane through integrin, a transmembrane protein that links the extracellular matrix to the cytoskeleton. 

Lipid diffusion. What is the average distance traversed by a membrane lipid in 1 is, 1 ms, and 1 s Assume a diffusion coefficient of 10 cm s i. 

In membranes, the motional anisotropies in the lateral plane of the membrane are sufficiently different from diffusion in the transverse plane that the two are separately measured and reported [4b, 20d,e]. Membrane ffip-ffop and transmembrane diffusion of molecules and ions across the bilayer were considered in a previous section. The lateral motion of surfactants and additives inserted into the lipid bilayer can be characterized by the two-dimensional diffusion coefficient (/)/). Lateral diffusion of molecules in the bilayer membrane is often an obligatory step in membrane electron-transfer reactions, e.g., when both reactants are adsorbed at the interface, that can be rate-limiting [41]. Values of D/ have been determined for surfactant monomers and probe molecules dissolved in the membrane bilayer typical values are given in Table 2. In general, lateral diffusion coefficients of molecules in vesicle... 

Occluded skin may absorb up to 5-6 times its dry weight of water. In the idealised model of the stratum corneum shown in Fig. 9.23, L represents the lipid-rich interstitial phase and P the proteinaceous phase. If p = P /Pp (the ratio of the partition coefficients of the drug between vehicle and the L and P phases), and Dl and Dp are the diffusion coefficients of the drug in these phases, the flux through stratum corneum of average thickness (that is, 40 pm) is found to reduce to... 

The diffusion coefficients and translational movements of proteins are important in considering the release of proteins from hydrogel matrix devices and other delivery vehicles, and in membrane transport, as far as this can be considered to be a passive diffusion process. Changes in shape during membrane transport in a lipid environment may also have to be considered. Table 11.6 gives some values of diffusion coefficient of a number of therapeutic peptides and proteins. 

Here, and // denote respectively the local mole fraction and local electrochemical potential of the charged lipid species in that particular leaflet, g is the metric tensor defined on the leaflet surface, and Di p represents the diffusion coefficient of charged lipids. Note that Diip should not affect the equilibrium state. The local electrochemical potentials, in turn, are derived from the free energy functional that itself depends on local lipid component densities membrane curvature. This property results in a self-consistent formulation, which remains as the main computational task. 

Figure 27. Dynamical scaling of DNA confined to the surface of a supported lipid membrane, (a) Time sequence (At = 30 s) of a DNA molecule diffusing on a cationic lipid membrane. The image on the right depicts an overlay of 16 images time average yields a smeared fluorescence distribution, (b) Scaling behavior of the self-diffusion coefficient of the center of mass D with the number of base pairs, (c) Scaling behavior of the rotational relaxation time r, with the number of base pairs.140...

Reactivity in aggregates may be used to get useful infonnation on mobility in these systems. Vesicles are particularly amenable to these studies because, as mentioned earlier, mobihty in these aggregates is lower than in micelles. For instance, it is estimated that above T, lateral diffusion of the lipids within the plane of the vesicle bilayer is very fast (diffusion coefficient of 10 cm s , in the fluid phase), though three orders of magnitude slower than in an aqueous medium. Accordingly, randomization of a hpid in a leaflet of the bilayer of a 500 A vesicle will occur in milliseconds, whereas the slow transverse (flip-flop) movement from one leaflet to another may take up to several days [1, 7, 60]. 

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