**Botany online** 1996-2004. No further update, only

Ions, too, can cross membranes. Their diffusion properties generate
an electric gradient. This gradient cannot be kept upright without
energy consumption. Cations and anions (M^{+} and A^{-})
pass the membrane according to their selectivity. This means that
the flow of cations is not solely dependent on the cation concentration
[M^{+}] but also on the anion concentration [A^{-}].
The influx of [M^{+}] into the cell - or any other compartment
- is consequently described by FICK's diffusion law:

influx M = P_{M}[M^{+}]_{e}[A ]_{e}

where P_{M} is the permeability coefficient and [M^{+}]_{e}
and [A^{-}]_{e,} respectively, are the extracellular
ion concentrations. The efflux of the cell is:

efflux_{M}= P_{M}[M^{+}]_{i}[A ]_{i}

[M^{+}]_{i} and [A^{-}]_{i} are
the ion concentrations within the cell. At an equilibrium (same
ion distribution at the in- and the outside and therefore no overall
electric charge) are

[M^{+}]_{i}[A^{-}]_{i}= [M^{+}]_{e}[A^{-}]_{e }or

g = [M

^{+}]_{e}/ [M^{+}]_{i}= [A^{-}]_{i}/ [A^{-}]_{e}

where g is the so-called **DONNAN equilibrium**. It is 1, if
only freely permeating ions are present. But in a cell can usually
a high proportion of bound ions be found, for example in most
negatively charged proteins (P_{r}). To achieve electric
neutrality have

[M^{+}]_{e}= [A^{-}]_{e}

to meet the requirement

[M^{+}]_{i}= [A^{-}]_{i}+ [P_{r-}]_{i}

This means that

[M^{+}]_{i}> [A^{-}]_{i}

and that the DONNAN - equilibrium has a value clearly smaller
than 1. Consequently is the concentration of freely diffusing
ions always higher at the inside than at the outside. The ion
distribution of both sides of the membrane is uneven: a membrane
potential (E_{D}) exists. It is described by the **NERNST
equation**:

E_{D}= (RT / FZ) ln ([M^{+}]_{e}/ [M^{+}]_{i}) = RT / FZ ln ([A^{-}]_{i}/ [A^{-}]_{e})

where R is the gas constant, T is the absolute temperature, F is the FARADAY constant and Z is the charge of the ion in question. By transformation of the equation and after putting in the corresponding numbers is the following equation obtained

E_{D}[mV] = 62 log [M^{+}]_{e}/ [M^{+}]_{i}

The net flow through a membrane is the difference between influx
and efflux. In any given membrane potential is the ion diffusion
influenced by the concentration and the electric gradient. The
influx is decisively affected by the extracellular concentration.
The potential which goes with it is the potential difference between
the extracellular space and the membrane: the driving force is
the electrochemical potential B_{e}:

B_{e}= C_{e}e (ZFE_{e}/ RT)

where C_{e} is the extracellular ion concentration. The
ratio of efflux and influx is

efflux / influx = B_{i}/ B_{e}= (C_{i}/ C_{e}) e (ZFE_{D}/ RT)

where E_{D} is the difference between E_{i} and
E_{e}. This relation is called the **USING flux relation**.
It can be applied to find out whether a measured potential difference
tallies with a calculated one. If the efflux to influx ratio is
larger than B_{i}/ B_{e} (efflux / influx >
B_{i}/ B_{e}) then has it to be assumed that additional
energy has been invested in order to attain the measured potential
difference. That is, the formula offers a test to distinguish
between active and passive transport.

© Peter v. Sengbusch - Impressum