Interspace models

One may gain a sense of the performance of these more comprehensive interspace models by considering again the model depicted in Fig. 6. This time we make no a priori assumptions about the parameters of the component membranes. The equations for volume flow are... 

Thus, this interspace model has been cast in the form of the general phenomenological model of Section 2b (Eqns. 33 and 35), and the relevant parameters of coupled water transport may be calculated as outlined there. 

Since there is little reason to suppose the basement membrane reflection coefficient to be any value other than zero [41], the strength of transport for a realistic interspace model will be... 

The change of electronic conductivity G(r) over diameter of such two-sphere model composition as element in a system of contacting particles is shown in a Figure 10.6b. The transfer of electron across this composition consists of three stages electron tunneling over the interspace — Rq is replaced by the M/SC conductivity across a particle with subsequent electron tunneling over the further interspace R — Rq. The probability of electron tunneling falls down exponentially with increase in distance from the surface of particle. 

Simple diffusion from a flat surface through an unstirred layer 0.025 cm thick would result in a solute permeability 20-10 cm/s. Thus, the value of computed for this model, 5.5-10 cm/s, signifies that solute transport into an interspace bounded by a basement membrane retards its diffusion from the region adjacent to the cell membrane by a factor of four. The permeability can also be translated into an electrical resistance, R, by use of the formula... 

Distance along the channel, x, is measured from the tight junction (x = 0) to the channel mouth x = L). The cell is at the mucosal bath osmolality, Cq + and the serosal bath is at Q + Cg. The lateral cell membrane has unit water permeabUity RTLp and transports solute into the interspace at rate N(x) (mosm/cm. s). The solute transport rate is written as a function of position because in their model, solute transport was assumed to occur only in an apical segment of the channel. In this apical segment transport, N, is constant. If is the fraction of chaimel length over which solute transport occurs, then... 

Thus, recent models of the lateral intercellular space have included a permeable apical membrane for the channel, designed to reflect the properties of the tight junction. Hill [66] has used such a model to discuss the possible role of the junction in determining transport tonicity. Sackin and Boulpaep [55] have presented a detailed simulation of Necturus proximal tubule in the control and volume expanded state to illustrate the effects of altered junctional permeability. The proximal tubule model of Huss and Marsh [56] included a compliance relation for the interspace that permitted study of hypothesized relations between channel pressure and junctional permeability. 

Models of the lateral interspace have been developed that include diffusion within the channel as well as bounding membranes of finite permeability [55,56]. The model of Weinstein and Stephenson [57] extended these efforts by incorporating the three ionic species Na, and Cl into a model of the whole epitheUum. Within both cell and channel the ions move in response to both chemical gradients and electric fields according to the Nemst-Planck equation... 

A popular model since 1967 has been that of Diamond and Bossert [145]. According to this model, sodium enters the cell and is pumped into the interspace at its apical end by sodium pumps particularly concentrated at the apical ends of the baso-lateral membranes. A local hypertonicity is then created at the blind end of the interspace so that water moving through the cell osmotically increases the volume and pushes the fluid out of the interspace as isotonic fluid. In this way, a standing gradient is set up causing isotonic fluid flow. However, it is now known that in leaky epithelia the tight junctions are permeable to ions and probably to water molecules too. Also, there is no histochemical evidence for a concentration of pump sites at the apical end of the interspaces. 

FIGURE 15.2 Graphical interpretation of the structural model (a) electrical and mechanical analog of the microcollective or cluster (b) equivalent circuit for the emitter-coupled oscillator (c) the macrocollective a schematic cross-section of the droplet and its characteristics Vj, structural volumes or clusters 14, excluded surface volumes or interspaces 14, excluded bulk volumes or interspaces Si, internal separation external separation R, rigidity droplet boundary E, elasticity droplet boundary). 

VASP is also able to simulate the Daniell battery [106]. The model is a bimetallic slab consisting of two parts in epitaxy, one made of copper and the other of zinc. The interspace between the successive slabs is filled by four layers of water, originally in a hexagonal ice arrangement, and the optimization is run. One layer of water decomposes, the OH being adsorbed on Cu and the ff" on the Zn. There is a relaxation of the metal surfaces at the interfaces, some Zn atoms moving significantly outward. A limited periodic model accounts then for a typical electrochemical reaction. 

Model of defect structure of wiistite. The defect structures of wiistite were well studied by many researchers and it is commonly considered that the basic unit of that is as shown in Fig. 3.6, and the defect cluster structure of that is as shown in Fig. 3.7. It will be seen from Fig. 3.7(a) that one of Fe + cation located in the interspace of tetrahedron is surrounded by four Fe + located in interstitial of octahedron. This structure is called as 4 1 defect clusters, 4 indicates the defect amount of cations and 1 indicates the interstitial amount of tetrahedron. The defect unit possesses five units with negative charges. It was proved for the existence of the mentioned defect structures by theoretical calculation in the works of Catlow, Grimes and Press. 

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