6.021/Notes/2006-10-25

Hodgkin-Huxley

 * squid giant axon
 * action potentials don't depend on pumps (can knock them out and still have AP)
 * for action potential, either $$G_{Na}$$ increases or $$G_{K}$$ decreases to increase membrane potential towards $$V_{Na}$$
 * experimental data indicates $$G_{Na}$$ goes up
 * but which is cause and which is effect? does action potential cause change in sodium conductance or does change in sodium conductance cause action potential?
 * Space clamp (Curtis)
 * converts 2D to 1D $$V_m(z,t) \rightarrow V_m(t)$$
 * Voltage clamp (Hodgkin)
 * Takes space clamp but also fix membrane voltage
 * Can't have action potential if voltage is fixed, but can study membrane response
 * Responses are all graded
 * General strategy of Hodgkin-Huxley
 * apply voltage step
 * measure response
 * make circuit model $$V_m(t) \rightarrow J_m(t)$$
 * run circuit backwards $$J_m(t) \rightarrow V_m(t)$$
 * see if get action potential (and win Nobel prize)
 * A voltage step leads to an impulse of current
 * looks like a a capacitor's response
 * membrane is like capacitor ~1$$\mu$$F/cm$${}^2$$
 * capacitive response is linear so can subtract it by adding response to depolarizing step with an equal hyperpolarizing step
 * this gives the non-capacitive response
 * As increase $$V_m^f$$ (final value of the voltage step)
 * persistent outward current increases
 * transient inward current becomes transient outward current
 * flips about +57mV, close to $$V_{Na}$$
 * transient part likely due to Na
 * Set $$V_m^f=V_{Na}$$ so that the sodium current must be 0. The response then is $$J_K$$.
 * To get $$J_{Na}$$, keep the membrane potential the same but change $$c^o_{Na}$$ which changes $$V_{Na}$$