6.021/Notes/2006-10-16

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  • V_m^o = \sum_n \frac{G_n}{G_m}V_n
  • 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
    • J_n^a+J_n^p=0 for all n where J_n^a is the active current (pump) and J_n^p is the passive current (electro-diffusion).
    • Define quasi-equilibrium: no net flux but requires energy
    • J_m = 0 = \sum_n G_n(V_m^o-V_n) + \sum_n J_n^a
    • V_m^o = \sum_n \frac{G_n}{G_m}V_n - \frac{1}{G_m}\sum_n J_n^a
      • 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
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