# 6.021/Notes/2006-10-16

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