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Understanding Ion Movement and Membrane Potential: The Role of Nernst and Goldman Equations

This article delves into the dynamics of intracellular and extracellular ion concentrations, revealing how energy is used to maintain unequal concentrations of ions such as Na+, K+, Cl-, and others. It explores the Nernst potential and Goldman equation, demonstrating how ion permeability affects membrane potential. The document discusses the mechanisms of ionic currents, the driving forces behind ion movement, and their impact on membrane potential. By examining conductance and alterations in ion flow, we gain insights into the fundamental principles guiding cellular excitability and signaling.

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Understanding Ion Movement and Membrane Potential: The Role of Nernst and Goldman Equations

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  1. 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).

  2. 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

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

  4. 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

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

  6. 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

  7. 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?

  8. 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 • Faraday’s Constant = 9.65 x 104 coulomb per mol • Avogadro’s Number = 6.02 x 1023 ions per mol

  9. 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.

  10. 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.

  11. 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.

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

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