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: $$J_m=0$$
 * time to reach rest much smaller than steady state
 * $$J_m = 0 = J_K = G_K(V_m-V_K)$$
 * Thus $$V_m=V_K$$
 * membrane is selectively permeable to K and has the potential needed to counteract diffusion
 * Baker, Hodgkin, Shaw (1962), squid giant axon data
 * $$c^i_K\uparrow\rightarrow V^o_m \downarrow$$, $$c^o_K\uparrow\rightarrow V^o_m \uparrow$$, $$c^o_K=c^i_K\rightarrow V^o_m\approx 0$$
 * 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 $$J_m = 0$$
 * $$J_m = \sum_n G_n(V_m^o-V_n) = 0$$
 * $$\sum_n G_nV_m^o=\sum_n G_nV_n$$
 * $$G_m=\sum_n G_n$$
 * $$V_m^o = \sum_n \frac{G_n}{G_m}V_n$$
 * 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 $$V_n$$, also changes $$G_n$$
 * 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