Active transport formalism

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). 

Fig. 11. Active transport using the simple carrier. Formal kinetic schemes for (a) countertransport and (b) co-transport. A and B are the two substrates of the carrier E either of which (in countertramsport) or both which (in co-transport) combine with E to form EA, EB or EAB. Subscripts 1 or 2 refers to substrate at side 1 or 2 of the membrane. The rate constants b, d, f, g, k are defined in the figure. AT" is the equilibrium constant of the chemical reaction /I =4.42 in primary active transport (and is equal to unity in the case of secondary active transport). Af=A /A 2 in co-transport. The square brackets denote concentrations and terms such as /4, =[/l,]/Arj, where is the relevant dissociation constant, here = dj/gi. J is the net flux in the 1 ->2 direction. (Figure taken, with permission, from [30].)...

Not all active transport is brought about by the coupling of two transport flows. It can also be the case that a transport flow is coupled to the progress of a chemical reaction, as we shall now discuss. We saw in Section 3 that there was a very close analogy between the formal description of an enzymatically catalysed chemical reaction and the formal description of transport. We can approach Fig. 11 in the same spirit. Consider countertransport, the left-hand figure. Here, B, and B2 can. 

Such primary active transport systems are perfectly equivalent formally to the secondary active transport systems discussed in the previous section. Both systems require that true flows of substrate or progress of a chemical reaction must take place for coupUng to occur, for it is these processes that drive the carrier from one conformation, state or side of the membrane to the other. Both systems require absolutely that the reactions between carrier and substrate at one side of the membrane are shielded from those at the other, so that a true displacement of the carrier-binding sites from accessible at one side of the membrane to accessible at the other must take place. In the case of the primary active transports, it is the chemical reaction which brings about this vectorial movement of the carrier, since the two components of the chemical reaction, product and reactant, must combine with different forms of the carrier. In the case of secondary active transport, it is transport of the driving substrate which brings about reorientation of the carrier. 

Abstract. Crown ethers derived from tartaric acid present a number of interesting features as receptor frameworks and offer a possibility of enhanced metal cation binding due to favorable electrostatic interactions. The synthesis of polycarboxylate crown ethers from tartaric acid is achieved by simple Williamson ether synthesis using thallous ethoxide or sodium hydride as base. Stability constants for the complexation of alkali metal and alkaline earth cations were determined by potentiometric titration. Complexation is dominated by electrostatic interactions but cooperative coordination of the cation by both the crown ether and a carboxylate group is essential to complex stability. Complexes are stable to pH 3 and the ligands can be used as simultaneous proton and metal ion buffers. The low extractibility of the complexes was applied in a membrane transport system which is a formal model of primary active transport. 

The physical mechanism of membrane water balance and the formal structure of modeling approaches are straightforward. Under stationary operation, the inevitable electro-osmotic flux has to be compensated by a back flux of water from cathode to anode, driven by gradients in concentration, activity, or liquid pressure of water. The water distribution in PEMs that is generated in response to these driving forces decreases from cathode to anode. With increasing/o, the water distribution becomes more nonuniform. the water content near the anode falls below the percolation threshold of proton conduction, X < X. This leaves only a small conductivity due to surface transport of water. As a consequence, increases dramatically this can lead to failure of the complete cell. 

Macrokinetics is the description and analysis of the performance of the functional unit catalyst plus reagents plus reactor. It leads to formal activation barriers called apparent activation parameter representing the superposition of several elementary barriers with transport barriers. It further delivers formal reaction orders and rates as function of the process conditions. These data can be modeled with formal mechanisms of varying complexity. In any case, these data can well describe the system performance but cannot be used to deduce the reaction mechanism. 

Since equations (1), (2a), and (3) are formally the same, it is necessary to find criteria to distinguish the three cases. This is possible because 6 varies so much with stirring speed, and the diffusion coefficient D is affected by viscosity while the parameters in chemical rates usually are not. Different metals dissolve at the same rate in the same solution if the rate is controlled by convection-diffusion. The activation energy of diffusive transport, as measured from temperature coefficients, is normally much lower than the activation energy of chemical processes (3000-6000 cal/mole compared to 10,000-20,000 cal/mole, although some chemical reactions do have lower values). 

Thus two varieties of rate coefficient have been extensively used. One is the number of reactant molecules chemically changed (or alternatively the number of product molecules formed) per unit (electronic) charge transported, p, which is formally, but not physically, analogous to the electrochemical equivalent in electrolysis. This concept was refined by Kirkby into the "activity of a discharge, P = dp/dz, the... 

Generalized Formalism A generalized membrane transport model, in the form of the black box models discussed earlier, can be considered in order to compare alternative mechanisms of water backflow in gradients of chemical potential, activity or concentration of water. Each of these gradients can be expressed by a gradient in w. The equation of net water flow is, thus,... 

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