Appendix A.2. Membrane potential and permeability for ions
If a passive transport mechanism transfers a charge zF across a membrane and the potential difference across the membrane ΔV0 (inside minus outside) is the value for zero current via this mechanism then23 PeffluxPinflux=ezFΔV0RTbecause this is then an equilibrium. If in addition the fluxes are proportional to the concentrations, i.e. the Ps are independent of concentration, this relation must hold for all potentials and the flux can be written as24 Jnet=Jinflux-Jefflux=Pinfluxcoutside-Peffluxcinside=Pinfluxcoutside-ezFΔV0RTcinsidewhere, however, Pinflux can be a function of potential (see e.g. [529, 530]).
For the blood–brain barrier the potential difference is normally small enough (< 4 mV) that when interpreting experimental data for passive transport the potential dependence of Pinflux and Pefflux is usually ignored. (It should be noted that potential must be considered explicitly when considering transport into and out of the cells as the potential difference between the inside and outside is much larger than the potential difference between ISF and plasma). The potential difference across the blood–brain barrier changes with pH of plasma and can take on appreciable values (for a review and references see [4]). The consequences of these changes for transport of ions other than H+ appear not to have been considered.