6.021/Notes/2006-10-16

• [math]\displaystyle{ V_m^o = \sum_n \frac{G_n}{G_m}V_n }[/math]
• Rest is not equal to equilibrium
  • eventually all ions would equilibrate inside and outside and there would be no membrane potential
  • For this to not happen, must have pumps (primary active transport)
  • Pumps allow us to go from rest to equilibrium
  • treat as current source
  • [math]\displaystyle{ J_n^a+J_n^p=0 }[/math] for all [math]\displaystyle{ n }[/math] where [math]\displaystyle{ J_n^a }[/math] is the active current (pump) and [math]\displaystyle{ J_n^p }[/math] is the passive current (electro-diffusion).
  • Define quasi-equilibrium: no net flux but requires energy
  • [math]\displaystyle{ J_m = 0 = \sum_n G_n(V_m^o-V_n) + \sum_n J_n^a }[/math]
  • [math]\displaystyle{ V_m^o = \sum_n \frac{G_n}{G_m}V_n - \frac{1}{G_m}\sum_n J_n^a }[/math]
    • The first term is the "indirect effect" whereas the second term is the "direct effect" of the pump
    • Both terms depend on the pump as without the pump, both would be 0
  • All pumps have indirect effect but only some pumps have direct effect
  • A non-electrogenic pump has no net charge change (e.g. trade one sodium ion for one potassium ion)
  • An electrogeneic pump such as 3 sodium for 2 potassium would have net active current
• Active transport gets energy from glucose metabolism (namely ATP)
• Experiment shows that sodium and potassium transport are linked
  • Sodium is needed for potassium transport and vice-versa
  • Sodium is pumped out, potassium pumped in
  • The direct effect on membrane potential is negative