2. Concepts
The intracellular and extracellular fluids have unequal concentrations of specific ions.
Na+ K+ Cl- H+ HCO3-
The differences in concentrations are maintained
by the expenditure of energy (work).

3. Nernst Potential VEq = RT/ZF ln(Cout /Cin)
Naout /Nain = 12/1 VNa = mV
Kout /Kin = 1/40 VK =
Clout /Clin = 30/1 VCl =
Measured Membrane Potential Vm = - 90 mV

4. Goldman
Theory:
Movement of ions across (through) the membrane is due to a Driving Force.
Driving Force = Diffusion Gradient + Electric Field

5. Goldman
Assumptions:
Permeability - Velocity of ionic movement across the membrane is proportional to
ion solubility in the membrane
ion mobility in the electric field
reciprocal of the membrane thickness
Constant Electric Field - Potential varies linearly with the thickness of the membrane

6. Goldman Equation: VEq = RT/ZF ln PKKout + PNaNaout + PClClin
PKKin + PNaNain + PClClout
Pi = Permeability Coefficient

7. Goldman If permeability of Cl- is either very small (nerve cells) or
very large (skeletal muscle)
Cl- ions can be ignored.
Let a = PNa / PK
VEq = - RT/ZF ln Kin + aNain
Kout + aNaout

8. Permeability VEq = - RT/ZF ln Kin + aNain Kout + aNaout
Presume permeability is due to macromolecules
(channels / pores) through the membrane that
are selective to specific ions (Na+ K+ Cl- H+ HCO3-).
What happens if the permeability changes?
What happens if the pores open/close completely?

9. Ionic Currents Electric current is the movement of charge per time.
Ions are charged particles.
How many ions per second = 1 ampere ?
Ionic Charge = 1.60 x coulomb
Faraday’s Constant = 9.65 x 104 coulomb per mol
Avogadro’s Number = 6.02 x 1023 ions per mol

10. Ionic Current Net Driving Force = Vm - VEq Vm = Membrane Potential
VEq = Nernst Potential
I » (Vm - VEq)
Let Proportionality Factor = Conductance g
Note: The transmembrane conductance is probabilistic and represents a population characteristic, NOT the value of a single pore.
If Vm - VEq < 0 implies positive ion enters the cell.
If Vm - VEq > 0 implies positive ion leaves the cell.

11. Ionic Currents Na+ K+ Vm = - 60 mV
Inject Na or K into the cell, Vm increases (less negative).
Eject Na or K from the cell, Vm decreases (more negative).
Therefore the flow of ions results in changes to the membrane potential.

12. Ionic Currents Change in Conductance Ionic Current Flow
Change in Membrane Potential
When a single ionic species flows, the effect is to drive the membrane potential TOWARDS the equilibrium (Nernst) potential for that ion.

13. Changes in Membrane Potential
Channel Sodium Potassium
Permeability
Conductance
Ionic/Current Flow Vm
Inward
Outward