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In the presence of several different ions, the equilibrium of the cell
depends on the relative permeability of the ions. For this, we use
the Goldman-Hodgkin-Katz equation:
| |
(2) |

Permeability of an ion is dependent on a number of factors such as the
size of the ion, its mobility, etc.
During rest in the squid giant axon, the permeabilities have the ratio
*P*_{K}:*P*_{Na}:*P*_{Cl} = 1:0.03:0.1 so that
Since *P*_{K} dominates, this is close to *E*_{K}.
During an action potential the ratio is *P*_{K}:*P*_{Na}:*P*_{Cl} =1:15:.1
so that
Later on we will approximate the GHK equations by a linearized
version:

where the conductances *g* are proportional to the permeabilities.

HOMEWORK

- 1.
- Suppose the external potassium in a mammalian cell is increased by a
factor of 10. What is the new value of
*E*_{K}?
- 2.
- At a cell contains 80 mM sodium inside and has only
100 mM sodium outside. What is the equilibrium potential for sodium?
- 3.
- Using the same permeabilities for the mammalian cell as were
used for the squid axon, compute
*V*_{rest},*V*_{m} using the table
below.

** Next:** Ion concentrations and equilibrium
** Up:** Ionic basis of the
** Previous:** Nernst Equation
*G. Bard Ermentrout*

*1/10/1998*