Facilitated flux across a membrane

As a first approach the flux of solutes across membranes can be described by the simple linear equation  

The magnitude of the proportionality constant L is an indicator of the permeability of the membrane for the solute in question. Experimentally, we can manipulate this parameter, for instance by the addition of specific ionophores. Thus, uncouplers of oxidative phosphorylation increase the permeability of a membrane for ions, while valinomycin increases the permeability for ions. Addition of these ionophores will increase the flux of the respective ions (at equal electrochemical potential gradient) and, therefore, increase the dissipation of their gradient. 

It may be instructive to note that the system will come to equilibrium with respect to the solute when the flux equals zero. From the above equation it is evident that this happens when the electrochemical gradient of the solute is zero or, in other words, when its electrochemical potential is equal on the two sides of the membrane. 

The fluxes of solutes across membranes may be coupled. A clear example is the case of nigericin-induced exchange. This ionophore is a weak acid of which 

In this case the flux-force relation for the elemental reaction may be written as (the reader should note that for simplicity we take here an example where the extra constant of Eqn. 28 is negligible)  

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