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• We can calculate the equilibrium potential using the Nernst Equation
  • $E_x = \dfrac{RT}{zF}\ln \dfrac{[X]_o}{[X]_i}$
  • Assume room temperature (25° Celsius)

Concentration Gradients and Resting Potential

• Neurons are permeable to Na+, Cl- and K+ ions
• Introduce an ion channel sodium Na+. Na+ starts flowing in
• $V_m$ is increasing since the potential difference is decreasing due to Na+ flowing in
• We now have a new steady state that’s higher than the original.
• However, then K+ and Na+ will eventually displace each other
• Need an Na+ and K+ pump (uses ATP), takes 3 Na+ pump out for 2 K+ back in
• Note that this is a steady state, not an equilibrium

Action Potentials

• If the membrane is depolarized past the threshold, voltage-gated Na+ open rapidly
• Na+ influx exceeds K+ efflux, makes more depolarization, more voltage gated open…positive feedback
• This new potential is $E_{Na+}$

Goldman Equation: $V_R$ with multiple species

• Conductance is how readily an ion crosses the membrane
• Permeability similar to diffusion constant
• $V_m = \dfrac{RT}{F}\ln \dfrac{P_\mathrm{K} [\mathrm{K}^+]o + P\mathrm{Na} [\mathrm{Na}^+]o + P\mathrm{Cl} [\mathrm{Cl}^-]i}{P\mathrm{K} [\mathrm{K}^+]i + P\mathrm{Na} [\mathrm{Na}^+]i + P\mathrm{Cl} [\mathrm{Cl}^-]_o}$

Passive Electrical Properties