# 6.021/Notes/2006-10-13

• 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