Lateral diffusion coefficients

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

Lateral diffusion coefficients were determined by monitoring mean-square displacements in the xy-plane, vdiich are proportional to MDt, where D is the diffusion coefficient and t the time. The following values were found ... 

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... 

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). 

M. F. Blackwell, K. Gounaris, S. J. Zara, and J. Barber, A method for estimating lateral diffusion coefficients in membranes from steady-state fluorescence quenching studies, Biophys. J. 51, 735-744 (1987). 

Substituting hx = 3.6 cm and K ip/w = K - into Eq. 28 Johnson et al. calculated solute lateral diffusion coefficients in stratum corneum bilayers from macroscopic permeability coefficients. Measurements with highly ionized or very hydrophilic compounds were not performed because of the possible transport along a nonlipoidal pathway. Comparison of the computed Aat values with experimentally determined data for fluorescent probes in extracted stratum corneum lipids [47] showed a highly similar curve shape. The diffusion coefficient for the lateral transport showed a bifunctional size dependence with a weaker size dependence for larger, lipophilic compounds (> 350 Da), than... 

Lateral diffusion of phospholipids in model membranes at ambient pressure has been studied over the years by a variety of techniques including fluorescence recovery after photobleaching (FRAP), spin-label ESR, pulse field gradient NMR (PFG-NMR), quasielastic neutron scattering (QENS), excimer fluorescence and others.In general, the values reported for the lateral diffusion coefficient (D) range from 10 to 10 cm /s in the... 

Figure 19 shows the pressure effeets on the lateral self diffusion eoeffieient of sonicated DPPC and POPC vesicles. The lateral diffusion coefficient of DPPC in the LC phase decreases with increasing pressure from 1 to 300 bar at 50 °C. A sharp decrease in the D-value occurs at the LC to GI phase transition pressure. From 500 bar to 800 bar in the GI phase, the values of the lateral diffusion coefficient 1 x 10 cm /s) are approximately constant. There is another sharp decrease in the value of the lateral diffusion coefficient at the... 

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. 

The above data suggest that a crosslinked bilayer vesicle is essentially a single polymer molecule (really two, one in each half of the bilayer). In other words the polymerization of the lipid monomers exceeded a gel-point. This concept raises the question of what mole fraction of bis-substituted lipid is necessary to achieve a gel-point for a bilayer composed of a crosslinker lipid, i.e. bis-lipid, and a mono-substituted lipid. Approximately 30% of the lipids in a bilayer vesicle of SorbPCs must be bis-SorbPC (4) in order to produce a polymerized vesicle that could not be dissolved by detergent or organic solvent [29], A complementary study of Kolchens et al. found that the lateral diffusion coefficient, D, of a small nonreactive lipid probe in a polymerized bilayer of mono- and bis-AcrylPC was dramatically reduced when the mole fraction of the bis-AcrylPC, was increased from 0.3 to 0.4 [24]. The decreased freedom of motion of the probe molecule indicates the onset of a crosslinked bilayer in a manner consistent with a 2-dimensional gel-point. 

Figure 23. The lateral diffusion coefficient of adsorbed FITC-/8-lg in thin films as a function of added Tween 20. (a), o/w thin films formed from aqueous non-homogenized solutions of /3-lg at 3 mg/ml ( ), o/w thin films formed from 10% v/v n-tetradecane emulsion or emulsion subnatant samples of FITC-/3-lg, initial protein concentration 3 mg/ml ( ), a/w thin films formed from aqueous non-homogenized solutions of /3-lg at 0.2 mg/ml.

Devaux and McConnell (39) measured a lateral diffusion coefficient of about 2 X 10"8 cm2/sec at 25°C for phosphatidylcholine (PC) diffusing along bimolecular leaflets in an oriented water-PC lamellar phase. Spin-labeled PC was used in this work. 

Note that in the Eqs. (147) and (148), the surface concentration cRs is different from the solution concentration cR in the second derivative on the left and in Eqs. (115) and (116) due to convection. Furthermore A is the lateral dispersion coefficient instead of a lateral diffusion coefficient De in the porous electrode case. 

The lateral diffusion coefficient (Dj) of Dil was calculated using the equation ... 

Several studies show that the values of the lateral diffusion coefficient (D, cm2 s 1) in foam films stabilised by phospholipid(s) depend on two main groups of factors. The first is related to the type of the film, its thickness and radius, and the lipid composition of film monolayers. The second is related to the dependence of the surface diffusion within the limits of given film type and composition on the molecular characteristics of the lipid(s) building the film (molecular charge, length, lipid phase, etc.). 

Lalchev et. al. [491-493] have reported results employing the FRAP method for the recovery half times (tm) and the lateral diffusion coefficients (D) of fluorophore molecules in lecithin foam films of different type. Significant differences between the values of D were obtained for very thick foam films (h 100 nm) and for grey foam films (h 30 nm) showing D values of 2210 8 and 8-10 8 cm2 s 1, respectively. A further decrease in D was observed in CBF (D = 51 O 8 cm2 s 1) and in NBF (D = 2.2-10 8 cm2 s 1) (Fig. 3.111). The CBFs have an equivalent water thickness of approximately 13 nm and consist of a free water layer between the two adsorbed layers according the three-layer model (see Chapter 2). The value of the lateral diffusion coefficient in NBF, characterised by an equivalent water thickness of approximately 7 to 8 nm (the thinnest foam bilayers in this case) and which contains no free water layer between the monolayers, was twice lower (D 210 8 cm2 s 1), than in the CBF (Fig. 3.111). Since the decrease of the film thickness reflects the decrease of the free-water... 

Fig. 3.111. Dependence of lateral diffusion coefficient (D, cm2 s 1) of surface adsorbed fluorophore molecules on phospholipid foam film thickness (h, nm) r = 100 - 500 pm t = 24°C [493].

TABLE 10.1. Effects of surfactants on the lateral diffusion coefficient (Di) of single Dil molecules, apparent viscosity (rji) and intrinsic viscosity (jji) at the dodecane/water interface. 

Diffusion is the random movement of a particle because of an exchange of thermal energy with its environment. Membrane lipids and proteins participate in highly anisotropic translational and rotational diffusion motion. Translational diffusion in the plane of the membrane is described by the mean square lateral displacement after a time At (r ) = TD At. Lipid lateral diffusion coefficients in fluid phase bilayers are typically in the range Dj 10 to 10 cm /s (3). 

The above estimates are for fluid-like systems. In gel-like systems with features of frozen order, the time scales are much longer. For example, the lateral diffusion coefficient in a gel-like one-component membrane is about 10 -10 cm /s (43), whereas in a fluid membrane it is usually 10 cm /s. In a similar maimer, the diffusion of matter inside lipid droplets is a much slower process compared with lipid interfaces caused by entanglement effects, as the situation is largely similar to a polymer melt. This effect is the case inside LDL. It has been estimated that the diffusion coefficient for cholesterol esters inside LDL particles is roughly 10 cm /s (44) and is intermediate to diffusion in fluid- and gel-like membranes. 

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... 

Table 2. Lateral diffusion coefficients measured for a variety of probes in vesicles and membranes.

Figure 3.93. Lateral diffusion coefficient of cholesterol in a monolayer spread at an air/water interface, as a function of the molecular area in the interface. The numbers in the figure indicate the number of measurements.

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