6.021/Notes/2006-10-13

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  • injury potential V (when cell is broken open )is less than 0
    • V depends on extracellular concentration of potassium c^o_K
    • higher c^o_K means higher V
    • V does not depend on c^o_{Na}
  • Bernstein model(1902)
    • new concept: rest: Jm = 0
    • time to reach rest much smaller than steady state
    • Jm = 0 = JK = GK(VmVK)
    • Thus Vm = VK
    • membrane is selectively permeable to K and has the potential needed to counteract diffusion
  • Baker, Hodgkin, Shaw (1962), squid giant axon data
    • c^i_K\uparrow\rightarrow V^o_m \downarrow, c^o_K\uparrow\rightarrow V^o_m \uparrow, c^o_K=c^i_K\rightarrow V^o_m\approx 0
    • measurements supported Bernstein model
  • Data doesn't fit exactly with Bernstein model for all cells
  • Multiple ionic species
    • J_m = J_1 + J_2 \ldots J_n
    • Define V_m^o as the membrane voltage at rest Jm = 0
    • J_m = \sum_n G_n(V_m^o-V_n) = 0
    • \sum_n G_nV_m^o=\sum_n G_nV_n
Gm = Gn
n

    • V_m^o = \sum_n \frac{G_n}{G_m}V_n
      • The membrane potential is the weighted sum of Nernst potentials
    • Assume K, Na, and all other ions
    • Nernst potentials: K = -72mV, Na = +55mV, other (leakage) = -49mV
    • V_m^o = -60mV
  • But change in concentration not only changes Vn, also changes Gn
  • Hodgkin-Huxley model (to be discussed in more detail later)
    • \sum_n G_n(V_m^o)\cdot (V_m^o-V_n) = 0
  • Rest is not equilibrium
    • rest is that there's no change in charge but they doesn't imply no flux
    • The flow of sodium can compensate for the flow of K at rest
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