Vesicles radius

Figure 23. Radial segment density profile through a cross-section of a highly curved spherical vesicle. The origin is at r = 0, and the vesicle radius is very small, i.e. approximately r = 25 (in units of segment sizes). The head-group units, the hydrocarbons of the tails and the ends of the hydrocarbon tails are indicated. Calculations were done on a slightly more simplified system of DPPC molecules in the RIS scheme method (third-order Markov approximation), i.e. without the anisotropic field contributions...

Vesicles are, first of all, aesthetically pleasing, but are also of considerable technical value, as they enclose a voliune of solvent and separate it from the bulk solvent. Thus, they can be used as mini-reactors for different applications. The volume enclosed in vesicles can be custom-tailored to the application over more than nine orders of magnitude, as the vesicle radius can be varied from about 40 nm to 10 pm. 

If the vesicle radius is now increased to 500 nm, the internal aqueous volume becomes 512 x 10 jl1, the total internal volume of all liposomes in a 10 mM POPC solution becomes 355.9 ml, namely 35.59% of the total volume. 

Ve = electrostatic free energy of interaction Vw = VDW free energy of interaction VT = total or sum of Ve and Vw free energies v = vesicle volume a = vesicle radius... 

Zipfel et al. [55] observed a vesicle radius of 3 pm, which is clearly compatible with our calculation. We note that this estimate assumes that the experiments are done in the hydrodynamic regime. 

In a vesicle an aqueous volume (water pool) is entirely enclosed by a membrane that is basically a bilayer of lipid molecules [127-137]. In the case of the unilamellar dimyristoylphosphatidylcholine (DMPC) vesicles (radius = 250 nm) there is only one such bilayer, whereas a multilamellar vesicle (radius 1000 nm) consists of several concentric bilayers. Unilamellar vesicles can be produced from multilamellar vesicles by sonication. In such a system there are two kinds of... 

A very interesting case, not yet fully clarified, concerns the simultaneous entrapment of several (>80) macromolecular compounds (the whole transcription-translation machinery) inside submicrometric lipid vesicles (radius 100nm). ° In fact, under the conditions of the experiment, the Poisson probability to find a small vesicles containing more than 80 different compounds is 10 , i.e., critically close to zero. However, the experimental results indicate a low but well measurable yield of protein produced by the entrapped molecular machinery. Now, the calculated cumulative probability for the entrapment of ca. 80 molecules in a vesicle should be the product of 80 independent... 

Fig. 6.10. Time dependence of curvature fluctuations of a giant lipid vesicle with stress-sensitive alamethicin channels in its membrane. Inside the vesicle there is a ferricyanide solution undergoing a photochemical reaction under illumination, which produces a pH gradient and a photopotential across the membrane. The graph shows the second Legendre polynomial amplitude of the angular autocorrelation function of the vesicle radius as a function of time. Brief episodes (peaks) of extensive thermal fluctuations in a tension-free membrane are separated by long periods of a tensed, non-fluctuating vesicle membrane. (V. Vitkova, A.G. Petrov, unpublished.)...

Since the bending energy Fbend = 8tik is independent ofi , there is no distinguished equilibrium radius for i ves > Rmin- Afl er preparation one mostly obtains polydisperse vesicle samples. The increase in translational entropy will shghtly favor the formation of small vesicles. As will be outlined below, a control of the vesicle radius is possible by inducing an asymmetry between the outer and the inner monolayer. 

Sustained Release. Depending on permeation coefficient, vesicle radius, and bilayer thickness, encapsulated low molecular weight solutes will be released on timescales of minutes to days. This can be used for the controlled release of drugs, where the dose can be predicted from the encapsnlated volume and the initial drug concentration in the vesicle using eqnation 21. Large ionic solutes, in particular proteins, will have low release rates and are practically permanently encapsulated until the vesicle is ruptured. 

The difference in time scale, amplitude, and area of the artificial cell current spike is due to the fact that the vesicle is larger and contains more electroactive molecules than those in living cells. However, release from the smallest vesicles measured (approximately 4 pm diameter) is similar in time to events measured from the large vesicles of the beige mouse mast cell which average 700 nm in diameter (81). In Figure 17.1.6C, the relationship between vesicle radius and full width at half maximum (half-width) is shown for experiments with artificial cells. The fit is nearly perfectly cubic, meaning that release kinetics scale linearly with vesicle volume. 

Figure 17.1.6 Amperometric monitoring of repeated exocytosis events at artificial cells and cells. (A) Amperometric detection of continuous exocytosis of three vesicles from an artificial cell (scale bars are 40 pA and 3000 msec). (B) Amperometric detection of dopamine exocytosis from a PC12 cell (scale bars are 10 pA and 40 msec). (C) Plot of half-width vs. vesicle radius for vesicles fusing from an artificial cell where the vesicle radius has been the only parameter varied in the experiment. Reproduced with permission from (79).

Only 25% of the Cottrell equation is used in the final expression to correct for the diminished diffusion in the narrowing frustum. This model correctly predicts the shape of the percent coulometric efficiency vs. vesicle radius however, the predicted magnitude is 2.6 times larger than that observed. To correct this a factor of 0.38 has been applied to the theoretical prediction. Experimental data, predicted coulometric efficiency, and the best fit of the experimental data is shown in Figure 17.1.11. 

Figure 10 is a pictorial representation of the space between the cell and electrode surface (the drawing is not to scale) [31]. Following complete fusion of a spherical intracellular vesicle to the plasma membrane, the surface area of the vesicle creates a disk-shaped pore with a radius of 2r. The contents of the vesicle diffuse from this disk and spread at an angle, 9, until they reach the surface of the carbon fiber electrode positioned at a distance, h, away from the cell surface. The electrochemical reaction occurs at an area defined by r, which is representative of the size of each detected vesicle. This being the case, the quantity is related to the vesicle radius and the cell/electrode distance (h) by Eq. (3) [31]. 

Figure 10 Contents of a single vesicle after complete exocytosis. 0 is the angle at which diffusion of analyte occurs following release, h is the distance between the electrode and the cell surface, is the apparent vesicle radius that defines the electroactive area of the electrode for each release event, and is the radius of the membrane for a spherical vesicle after it has completely fused with the plasma membrane, where is the original radius of the intact vesicle. (Reproduced from J. Neurosci. Meth with permission [31].)...

Figure 11 Normalized histogram of calculated vesicle radius (open bars) overlaid with the known radius histogram (shaded bars) from Schubert et al. (1980) (14 bins, 10 nm/bin each). (Reproduced from/. Neurosci. Meth. with permission [31].)...

In 1981, Helfrich [7] studied the effect of the external osmotic pressure on egg yolk phosphatidylcholine (EPC) giant vesicles by adding 15 mM of salt or glucose in the external medium of the vesicles. The vesicle radius appears to decrease linearly with time according to the law d /dt = -aPAc, where P is the membrane permeability coefficient to water, a, is the water molar volume, and Ac, the difference of molar concentrations. The water permeability coefficient for EPC bilayers was found to be 41 pms . ... 

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