# 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 $\displaystyle{ c^o_K }$
• higher $\displaystyle{ c^o_K }$ means higher V
• V does not depend on $\displaystyle{ c^o_{Na} }$
• Bernstein model(1902)
• new concept: rest: $\displaystyle{ J_m=0 }$
• time to reach rest much smaller than steady state
• $\displaystyle{ J_m = 0 = J_K = G_K(V_m-V_K) }$
• Thus $\displaystyle{ V_m=V_K }$
• membrane is selectively permeable to K and has the potential needed to counteract diffusion
• Baker, Hodgkin, Shaw (1962), squid giant axon data
• $\displaystyle{ c^i_K\uparrow\rightarrow V^o_m \downarrow }$, $\displaystyle{ c^o_K\uparrow\rightarrow V^o_m \uparrow }$, $\displaystyle{ c^o_K=c^i_K\rightarrow V^o_m\approx 0 }$
• measurements supported Bernstein model
• Data doesn't fit exactly with Bernstein model for all cells
• Multiple ionic species
• $\displaystyle{ J_m = J_1 + J_2 \ldots J_n }$
• Define $\displaystyle{ V_m^o }$ as the membrane voltage at rest $\displaystyle{ J_m = 0 }$
• $\displaystyle{ J_m = \sum_n G_n(V_m^o-V_n) = 0 }$
• $\displaystyle{ \sum_n G_nV_m^o=\sum_n G_nV_n }$
• $\displaystyle{ G_m=\sum_n G_n }$
• $\displaystyle{ V_m^o = \sum_n \frac{G_n}{G_m}V_n }$
• 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
• $\displaystyle{ V_m^o = -60mV }$
• But change in concentration not only changes $\displaystyle{ V_n }$, also changes $\displaystyle{ G_n }$
• Hodgkin-Huxley model (to be discussed in more detail later)
• $\displaystyle{ \sum_n G_n(V_m^o)\cdot (V_m^o-V_n) = 0 }$
• 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