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Flux equations active transport

There is a local (Fickian transport) and a non-local (stress induced) term in this flux equation. In the local term, the stress acts in the same way as an activity coefficient does. It always increases local diffusion since V] is positive and independent of the sign of the partial molar volume of /. [Pg.340]

In order to be able to distinguish between active and passive transport through biological membranes, P. Meares and H. H. Ussing (95) likewise made a study of the fluxes through a membrane under the influence of diffusion together with an electric current. They studied the influxes and the outfluxes of sodium- and chloride ions at a cation exchange resin membrane. They started from the Nemst-Planck flux equations of the type ... [Pg.337]

This simple experiment was important in that it clearly established the key notion that cellular extrusion of sodium ions by the sodium pump was coupled to metabolism. Because in this and subsequent experiments of the same sort the electrochemical gradient for sodium was known precisely, and since the fluxes of sodium (and later potassium) both into and out of the cell could be measured independently, this study also laid the groundwork for a theoretical definition of active transport, a theory worked out independently by Ussing in the flux ratio equation for transepithelial active transport of ions (see below). [Pg.257]

We begin by showing how active transport can directly affect membrane potentials. We then compare the temperature dependencies of metabolic reactions with those for diffusion processes across a barrier to show that a marked enhancement of solute influx caused by increasing the temperature does not necessarily indicate that active transport is taking place. Next we will consider a more reliable criterion for deciding whether fluxes are passive or not — namely, the Ussing-Teorell, or flux ratio, equation. We will then examine a specific case in which active transport is involved, calculate the energy required, and finally speculate on why K+ and Cl- are actively transported into plant cells and Na+ is actively transported out. [Pg.130]

Similarly, the expected flux ratio is 0.20 for K+ and 0.000085 for Cl- (values given in Table 3-1, column 5). However, the observed influxes in the light equal the effluxes for each of these three ions (Table 3-1, columns 6 and 7). Equal influxes and effluxes are quite reasonable for mature cells of N. translucens, which are in a steady-state condition. On the other hand, if 7 n equals 7°ut, the flux ratios given by Equation 3.25 are not satisfied for K+, Na+, or Cl-. In fact, active transport of K+ and Cl- in and Na+ out accounts for the marked deviations from the Ussing-Teorell equation for N. translucens, as is summarized in Figure 3-13. [Pg.141]

Facilitated diffusion has certain general characteristics. As already mentioned, the net flux is toward a lower chemical potential. (According to the usual definition, active transport is in the energetically uphill direction active transport may use the same carriers as those used for facilitated diffusion.) Facilitated diffusion causes fluxes to be larger than those expected for ordinary diffusion. Furthermore, the transporters can exhibit selectivity (Fig. 3-17) that is, they can be specific for certain molecules solute and not bind closely related ones, similar to the properties of enzymes. In addition, carriers in facilitated diffusion become saturated when the external concentration of the solute transported is raised sufficiently, a behavior consistent with Equation 3.28. Finally, because carriers can exhibit competition, the flux density of a solute entering a cell by facilitated diffusion can be reduced when structurally similar molecules are added to the external solution. Such molecules compete for the same sites on the carriers and thereby reduce the binding and the subsequent transfer of the original solute into the cell. [Pg.152]

Both active and passive fluxes across the cellular membranes can occur simultaneously, but these movements depend on concentrations in different ways (Fig. 3-17). For passive diffusion, the unidirectional component 7jn is proportional to c°, as is indicated by Equation 1.8 for neutral solutes [Jj = Pj(cJ — cj)] and by Equation 3.16 for ions. This proportionality strictly applies only over the range of external concentrations for which the permeability coefficient is essentially independent of concentration, and the membrane potential must not change in the case of charged solutes. Nevertheless, ordinary passive influxes do tend to be proportional to the external concentration, whereas an active influx or the special passive influx known as facilitated diffusion—either of which can be described by a Michaelis-Menten type of formalism—shows saturation effects at higher concentrations. Moreover, facilitated diffusion and active transport exhibit selectivity and competition, whereas ordinary diffusion does not (Fig. 3-17). [Pg.153]

As applied to drug transfer from outside the cell (Co) to inside the cell (C,), the flux F) of drug into the cell (via facilitated diffusion or active transport) can be described by the following equation ... [Pg.123]

To explain these phenomena, it is necessary to consider the transient solutions of the ion flux equations for constant current. For simplicity we assume perfect solution laws (ion activity coefficients unity), a completely anion-selective membrane (transport number of anions in the membrane unity), and constant temperature, and neglect electro-osmotic water transport. We also assume linear geometry and a stationary diffusion layer of thickness 8 close to the membrane, beyond which the concentration remains essentially constant. Convection in the diffusion layer (2-4) is assumed to be negligible. [Pg.189]

Mass transfer, an important phenomenon in science and engineering, refers to the motion of molecules driven by some form of potential. In a majority of industrial applications, an activity or concentration gradient serves to drive the mass transfer between two phases across an interface. This is of particular importance in most separation processes and phase transfer catalyzed reactions. The flux equations are analogous to Ohm s law and the ratio of the chemical potential to the flux represents a resistance. Based on the stagnant-film model. Whitman and Lewis [25,26] first proposed the two-film theory, which stated that the overall resistance was the sum of the two individual resistances on the two sides. It was assumed in this theory that there was no resistance to transport at the actual interface, i.e., within the distance corresponding to molecular mean free paths in the two phases on either side of the interface. This argument was equivalent to assuming that two phases were in equilibrium at the actual points of contact at the interface. Two individual mass transfer coefficients (Ld and L(-n) and an overall mass transfer coefficient (k. ) could be defined by the steady-state flux equations ... [Pg.239]

The chapter emphasizes migrational effects and provides analytical expressions for the electric potential drop in the solution under different experimental conditions. The fundamental concepts are discussed in detail, and a number of important restrictions are introduced for the sake of clarity. First, diluted solutions are considered throughout and the flux equations incorporate neither cross terms nor activity coefficients [2-5]. Second, one-dimensional systems are considered, except when presenting the transport equations in Sect. 2.1.1. Third, except in... [Pg.622]

Another model that treats the ion transfer across ITIES as an activated transport process by applying classical transition state theory has been suggested by Girault and SchifFrin [55]. Also in this case the equation describing the ion flux across the interface is similar to that obtained by the Butler-Volmer approach. Naturally, the interpretation of the a values and k° is somewhat different in that case. Experimentally [85] and theoretically [79], the effect of solvent viscosity on the ion-transfer process has been confirmed indicating the importance of this parameter. [Pg.920]

The above derivation indicates that the flux equation (4.118) is strictly applicable only to dilute solutions for which the gradients of activity coefficients are negligible. The theory, based on the four equations summarized in Table 4.34, is therefore often referred to as dilute solution transport theory. Dilute solution transport theory is commonly used in practice to describe transport phenomena in electrolytes. [Pg.161]

We insert these into the flux equations for the species and utilise that the sum of all transport numbers equals unity. We furthermore use that dp = kTdlna kTdlnp, where a and p are activity and partial pressure, respectively, and obtain... [Pg.202]

This can now be integrated to obtain the voltage of a cell, or inserted into a flux equation of a species of interest in the usual manner. We now have a system with two chemical driving forces for electrochemical transport that of oxygen activity and that of hydrogen activity. [Pg.202]

The transport parameters of carrier 1-4 are summarized in Table 1. Transport parameters Dn, and (Table 1) are determined by describing the initial fluxes obtained from transport experiments as a ftmction of the initial salt activity with the initial flux model (Equation 16) according to the best fit of the model to the experimental data. [Pg.27]

Flux through microporous membranes incorporates both adsorption and diffusion characteristics and as such the equations developed are modified based on the membrane material and pore structure. For example, the following expression (Equation [8.8]) for permeating flux through microporous silica membranes is accepted as an appropriate description of molecular sieving or activated transport (de Lange et al, 1995c) ... [Pg.321]


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See also in sourсe #XX -- [ Pg.122 ]




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