Spherical cell approach

The spherical cell approach is based on a hypothetical subdivision of the colloidal solution into electroneutral subvolumes, each containing one macroion and corresponding amount of counterions and solvent. This boundary condition is most frequently used to examine the distribution of small ions near a macroion and to obtain approximate thermodynamic results. It is most often implemented by placing a single macroion concen-... 

In recent years a lot of attention has been devoted to the application of electroacoustics for the characterization of concentrated disperse systems. As pointed out by Dukhin [26,27], equation (V-51) is not valid in such systems because it does not account for hydrodynamic and electrostatic interactions between particles. These interactions can typically be accounted for by the introduction of the so-called cell model, which represents an approach used to model concentrated disperse systems. According to the cell model concept, each particle in the disperse system is inclosed in the spherical cell of surrounding liquid associated only with that individual particle. The particle-particle interactions are then accounted for by proper boundary conditions imposed on the outer boundary of the cell. The cell model provides a relationship between the macroscopic (experimentally measured) and local (i.e. within a cell) hydrodynamic and electric properties of the system. By employing a cell model it is also possible to account for polydispersity. Different cell models were described in the literature [26,27]. In each case different expressions for the CVP were obtained. It was argued that some models were more successful than the others for characterization of concentrated disperse systems. Nowadays further development of the theoretical description of electroacoustic phenomena is a rapidly growing area. 

Fig. 5.6 Theoretical concentration gradient of substrate molecules around a spherical cell at different radial distances from its center (R is the radius of the cell). The concentration of substrate in the bulk water is and concentration curves were calculated from Eq. 5.10 for a cell limited in its substrate uptake by external diffusion ( Diffusion limited ) or by the uptake capacity across its own cell membrane ( Uptake limited ). Note how the substrate concentration only gradually approaches the bulk concentration with increasing distance from the cell.

Gheorghiu, E., 1994. The dielectric behaviour of suspensions of spherical cells a unitary approach. J. Phys. A Math. Gen. 27, 3883-3893. 

In this approach a cell is held at the end of micropipette by a small amount of suction. The cell is then brought into contact with a test surface, adhesive contacts are allowed to form, and then suction is applied to break this contact (Figure 34.4). The underlying principle is that suction, AP, used to draw a spherical cell of radius Pq into the end of micropipette tip of radius Pp creates a membrane tension, Tm, at the... 

Microdosimetry technique is a quantitative evaluation of the electric field on the cell membrane, in the process of cell electroporation has received considerable interest [1], However, most of the work up to date is based on the spherical cell shape based on analytical approach [2],... 

This method has been applied to the prediction of the fractional occupancy of the large cavities of an S-II hydrate of hydrogen. Figure 6 compares the results of this simple approach using the spherical cell vdW-P model with those obtained from more elaborate grand canonical ensemble Monte Carlo calculations. The overall agreement is reasonable. 

This is a simpler model for spherical cells containing imiform cytoplasm and covered with membrane, which is applicable, for example, to nuclei-free cells such as red blood cells and platelets. More complex "double-shell" models requiring a computer-assisted approach should be considered for cells with nuclei, such as monocytes and endothelial cells. For nonspherical cellular shapes geometrical corrections can be introduced into the Clausius-Mossotti formula [9]. 

Another approach is to estimate cell properties based on typical values. First, we assume a typical bacterium is rod shaped with a cell size of 0.5 pm x 2.5 pm. Assuming a cylinder, the cell has a projected surface area of Aceii= 1-25 pm (i.e., what you would view through a microscope) and a volume (v = jtd L/4) of Vcen= 0.491 pm. For an equivalent spherical cell, based on the volume, this is equivalent to a cell diameter of dceti = 0.98 pm. Assuming that a cell has a density of 1.06 g/cm and that it is 70% water (i.e it has a dry weight that is 30% of the mass), the mass of a single cell is... 

The first part of the method involves sorting all the atoms into their appropriate cells. This sorting is rapid, and may be perfonned at every step. Then, within the force routine, pointers are used to scan tlirough the contents of cells, and calculate pair forces. This approach is very efficient for large systems with short-range forces. A certain amount of unnecessary work is done because the search region is cubic, not (as for the Verlet list) spherical. 

In addition to bulk liquid turbulence effects, suspended particles maybe involved in collisions with one another or with solid surfaces within the vessel. This phenomenon has been extensively studied in micro-carrier cultures [60] and appears to be significant at high concentrations [61]. Rosenberg [69] and Meijer [72] applied the approach of Cherry and Papoutsakis [60] to the study of collision phenomena involving spherical plant cell aggregates of 190 and 100 pm, respectively. In both cases it was concluded that for typical biomass concentrations, particle-particle interactions were of less significance than particle-impeller collisions. 

In the previous chapters it has been shown that stable cell membrane models can be realized via polymerization of appropriate lipids in planar monolayers at the gas-water interface as well as in spherical vesicles. Moreover, initial experiments demonstrate that polymeric liposomes carrying sugar moieties on their surface can be recognized by lectins, which is a first approach for a successful targeting of stabilized vesicles being one of the preconditions of their use as specific drug carriers in vivo. 

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