Concepts

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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).

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Nernst Potential

• VEq RT/ZF ln(Cout /Cin)
• Naout /Nain 12/1 VNa 66 mV
• Kout /Kin 1/40 VK - 97
• Clout /Clin 30/1 VCl - 90
• Measured Membrane Potential Vm - 90 mV

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Goldman

• Theory
• Movement of ions across (through) the membrane is
  due to a Driving Force.
• Driving Force Diffusion Gradient Electric
  Field

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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

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Goldman

• Equation
• VEq RT/ZF ln PKKout PNaNaout PClClin
• PKKin PNaNain PClClout
• Pi Permeability Coefficient

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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

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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?

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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 10-19 coulomb
• Faradays Constant 9.65 x 104 coulomb per mol
• Avogadros Number 6.02 x 1023 ions per mol

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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 lt 0 implies positive ion enters the
  cell.
• If Vm - VEq gt 0 implies positive ion leaves the
  cell.

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Ionic Currents
Vm - 60 mV
Na
K
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.
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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.

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Changes in Membrane Potential

• Channel Sodium Potassium
• Permeability
• Conductance
• Ionic/Current Flow
• Vm

Outward
Inward