# 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 $\displaystyle{ G_{Na} }$ increases or $\displaystyle{ G_{K} }$ decreases to increase membrane potential towards $\displaystyle{ V_{Na} }$
• experimental data indicates $\displaystyle{ G_{Na} }$ 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 $\displaystyle{ V_m(z,t) \rightarrow V_m(t) }$
• 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
• General strategy of Hodgkin-Huxley
1. apply voltage step
2. measure response
3. make circuit model $\displaystyle{ V_m(t) \rightarrow J_m(t) }$
4. run circuit backwards $\displaystyle{ J_m(t) \rightarrow V_m(t) }$
• 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$\displaystyle{ \mu }$F/cm$\displaystyle{ {}^2 }$
• 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 $\displaystyle{ V_m^f }$ (final value of the voltage step)
• persistent outward current increases
• transient inward current becomes transient outward current
• flips about +57mV, close to $\displaystyle{ V_{Na} }$
• transient part likely due to Na
• Set $\displaystyle{ V_m^f=V_{Na} }$ so that the sodium current must be 0. The response then is $\displaystyle{ J_K }$.
• To get $\displaystyle{ J_{Na} }$, keep the membrane potential the same but change $\displaystyle{ c^o_{Na} }$ which changes $\displaystyle{ V_{Na} }$