Flux coupling

The present analysis shows that when a thermodynamic gradient is first applied to a system, there is a transient regime in which dynamic order is induced and in which the dynamic order increases over time. The driving force for this is the dissipation of first entropy (i.e., reduction in the gradient), and what opposes it is the cost of the dynamic order. The second entropy provides a quantitative expression for these processes. In the nonlinear regime, the fluxes couple to the static structure, and structural order can be induced as well. The nature of this combined order is to dissipate first entropy, and in the transient regime the rate of dissipation increases with the evolution of the system over time. 

Zerangue, N. and Kavanaugh, M. P. (1996) Flux coupling in a neuronal glutamate transporter. Nature 383,634-637. 

Fig. 2. Schematic diagram of the stoichometry of ion flux coupling and the chloride channel activity of glutamate transporters. Glutamate is coupled to the co-transport of 3 Na+, 1K+, and the countertransport of 1 K+. In addition, glutamate and Na+ binding to the transporter activates an uncoupled chloride flux through the transporter.

Up to this point it has been tacitly assumed that A and B move independently across the reaction product. This can be true for intermetallic compounds, but not for ionic crystals in which there is always a flux coupling due to the condition of electroneutrality. Let us formulate this coupling condition in a general way in the form... 

These relations limit the extent of the flux coupling and reflect the tendency to reduce the entropy production. Thus, instead of dissipating the Gibbs energy com-... 

Having established the driving force for the dissolution of crystalline BO in crystalline AO, , we can now formulate jB and jA by using V/7, as the driving force for the individual ionic fluxes. The flux coupling... 

The cation fluxes can be expressed as usual using Eqn. (4.49). If we consider the simplest case by neglecting all flux couplings other than those through site conservation and electroneutrality, Eqn. (8.8) yields (see Eqn. (4.99))... 

Further demonstrations of this sort of counterflow phenomenon for many different substrates in virtually every type of cell have been used as functional hallmarks of carrier-mediated transport. Experimental demonstration of this effect precludes transport being mediated either by simple diffusion or by fixed pores in the membrane. In reviewing 20 years of experimental work related to the carrier hypothesis, LeFevre (1975) lists a number of key functional properties of carrier mediated transport, all of which have stood the test of the subsequent 20 years. These include saturation of transport with increased substrate concentration and associated phenomena such as competition between similar substrates, high rates of unidirectional transport, and countertransport. Also covered are flux coupling (including trans effects and cotransport), chemical specificity, inhibition by protein-specific reagents, hormonal regulation, and a steep dependence of the rate of transport on temperature (included only to bemoan its common inclusion in textbooks ). 

Historically important as an example of flux coupling, and one that was investigated in detail becoming a paradigm for coupled transport, was the sodium coupled glucose transport system of the small intestine and kidney (see below). This was a symport (or co-transport) rather than an antiport, normally carrying glucose into the cell coupled to a flow of sodium ions in the same direction. 

Figure 6. Cross section of the sample with three pick-up coils (a, b, c) aligned along [001]. Schematic presentation of magnetic flux coupling to the ddifferently shaped parts of the sample (1, 2, 3), together with the turns of the coil [1,2].

If we consider Oj" and h as carriers, we refer, e.g. to chemical diffusion of oxygen in La2CuC>4. Writing down the one-dimensional transport equations (Eq. 103) for ionic and electronic carriers and considering flux coupling and electroneutrality, we immediately obtain for this case (see, e.g., Ref.173)... 

Modern opinion views the Nernst-Plank theory as a special case of applying the thermodynamics of irreversible processes to ion exchange. It may also be argued theoretically and experimentally that the observed characteristics of ion exchange rate behaviour can only be fully explained by including chemical reaction as a flux-coupling mechanism as well as the diffusion potential. From a research standpoint it is most probable that future theoretical advances in ion exchange kinetics will result from the further application of non-equilibrium thermodynamics. 

Electroneutrality is maintained by having the counterdiffusing cation fluxes coupled. Note that for this to happen, the system must be predominantly an ionic conductor, that is, t < // — if not, decoupling of the fluxes will occur (see below). 

C. (2013) Increased lysine production by flux coupling of the tricarboxylic acid cycle and the lysine biosynthetic pathway - metabolic engineering of the availability of succinyl-CoA in Corynebacterium glutamicum. Metab. 

Another assumption concerns the rate controlling species. In the LSW theory, the species that controls the grain growth is the solute in the matrix. For compounds, however, the controlling species may vary. Maintenance of the correct chemical composition of the grains also requires a flux coupling of the species in the matrix. This composition constraint can be met by an effective diffusion coefficient as in the case of the diffusion in an ionic compound (see Section 13.1). 

Multicomponent diffusion, multiple driving forces, flux coupling... 

Consider transport into and through a flat surface. Excess fluxes along the surface are two-dimensional vectors. Though very interesting, they will not be considered here. The fluxes in the homogeneous phases (described above) are normal to the surface, and these normal components are scalars. This has an important consequence the normal components of heat and mass fluxes couple to the driving force for the chemical reaction at a surface. 

In the present treatment the effect of the delayed neutrons and the effect of temperature-flux coupling on the reactor kinetics are handled separately along the general lines previously developed for the stationary-fuel systems. Although in general these two factors must be considered jointly, there are many practical situations wherein the two effects can be separated. The intent here is primarily to simplify the analysis so as to focus attention on one feature at a time. 

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