1. The Hodgkin and Huxley Model of the Action Potential
By Jaclyn Eisdorfer

2. The Resting Membrane Potential (RMP)
Negative resting potential with a value of about -70mV
Produced by active transporters
ATPase Pumps: primary active transport
Ion Exchangers/Cotransporters: secondary active transport

3. Electrochemical Equilibrium (Ex)
X = ion species
When one type of ion is permeable, there is an exact balance between two opposing forces:
1) Chemical Energy: the concentration gradient = NRT*ln[Xout/Xin]
2) Electrical Energy: the opposing electrical concentration = NzFE
Nernst Equation:

4. Action Potential (AP) Makes the mem potential positive
Propagated along the length of axons
How information is transferred
Elicit an AP: ionic current passes across the membrane of a neuron to depolarize the RMP
Meaning ions flux across the membrane down their concentration gradient and take electrical charges with them
Flux due to asymmetric distribution of ions in intracellular and extracellular spaces

5. AP Nomenclature Rising phase: membrane rapidly depolarizes
Overshoot: positive membrane potential during AP
Falling phase: membrane rapidly repolarizes
Undershoot: hyperpolarization

6. Materials – Giant Squid Axon
Obtained from the hindmost stellar nerve of Loligo forbesi
Large axon diameter = faster conduction of APs because low internal cytosolic resistance
Allows squid to propel forward
AP is the same in squid and vertebrate axons but waveform of AP is different

7. Materials – Intracellular Microelectrodes
Two long silver wires
Wires thrust down the axis of the giant squid axon
Wires were insulated except for terminal portions that were exposed
Current was applied between the current wire and the earth
Potential difference across the membrane could be recorded from the voltage wire and an external electrode

8. Materials – Feedback Amplifier
Negative feedback was employed meaning that any spontaneous change in membrane potential caused an output current to flow in a direction which restored the membrane potential to its command voltage (desired potential)

9. Method – Voltage Clamp Method (VCM)
Type of intracellular recording that simultaneously controls (“clamps”) membrane potential (generates a voltage across a membrane) and measures underlying permeability changes (measures ionic currents) as a function of membrane potential and time
Allows researcher to determine:
Which types of ion channels are opened or closed
When they open
How they respond to voltage

10. Iinto axon = Iacross mem
VCM Steps
1. Measures membrane potential, Vm, across the membrane with an intracellular microelectrode placed inside the cell
2. Measures the difference between Vm and the desired potential (called the command voltage)
3. Feedback amplifier utilizes negative feedback to pass current through microelectrode, Ie, into the axon that is proportional to this difference making Vm=Vcommand
4. Measures the ionic current across the membrane
Iinto axon = Iacross mem

11. VCM

12. Experiments & Results Five Papers: Aim:
HH published a series of 5 papers that were concerned with the flow of electric current through the surface membrane of a giant nerve fiber
Experiments will be broken down by paper to avoid confusion
Determine the laws which govern movement of ions during electrical activity (i.e. during an AP)

13. Paper #1
Goals: Examine the function of the neuronal membrane under normal conditions
Outline the experimental method in each experiment in all 5 papers
VCM: V0= 0 (RMP) depolarized to V1 (command voltage)
Exp 1: : Axons gave all-or-nothing AP of ~ 100 mV when stimulated with a brief shock
Threshold of AP seen at ~ 15 mV
Depolarizations < mV gave graded responses

14. Paper #1 (continued)
Exp 2: Feedback amplifier made the membrane potential undergo a sudden displacement to a new level, V1, where it was held constant for ms
Membrane had brief Cm and an ionic current
Depolarizations > 15mV gave outward currents that decreased with time
Depolarizations of mV gave an initial inward current, followed by a large and prolonged outward current
Inward current disappeared at ~ 110 mV and was replaced by an outward current

15. Paper #2
Goals: : Identify which ions carry the different phases of the membrane current
VCM: V0= 0 (RMP) depolarized to V1 (command voltage)
Exp 3: Initial phase of inward current was reversed in sign by replacing the extracellular Na ions with choline ions

16. Paper #2 (continued)
Exp 4: Finding the critical value when Na inward current changed to outward
Critical value = peak: normally ~ 110 mV wit normal extracellular [Na]
Lower/higher value of peak with decreased/increased extracellular [Na]
Ex: lowering extracellular [Na] decreases rate and amplitude of AP
Therefore HH realized depolarization leads to a rapid increase in permeability which allows Na ions to move in either direction through the membrane
Initial phase of ionic current
Delayed outward current was little affected by replacing Na ions with choline
Simple assumptions led HH to resolve ITOT to INa and IK
gNa rises rapidly to max and then decreases in an exponential curve
gK rising more slowly along an S-shaped curve and maintained at high levels for long periods of time

17. Paper #3
Goals: Examine the effects of sudden potential changes on the AP/ionic conductance
VCM: membrane potential is restored from V1  V0 and also changed V1  V2
Exp 5: Repolarization of axon during period of depolarization (high Na permeability) is associated with a large outward current which decreases rapidly along an exponential curve

18. Paper #3 (continued)
Exp 6: “Tail” of inward current disappears if extracellular [Na] is removed
Time course of gNa during VCM can be calculated from the variation of the “tail” of inward current with the duration of depolarization
Exp 7: Repolarization of membrane during high K permeability is associated with a “tail” of outward current at RMP and inward current above a critical potential of ~ mV above RMP
Suggests gK is a function of time which rises when the nerve is depolarized and falls when it’s repolarized

19. Paper #4
Goals: Outline how inactivation process decreases Na permeability after the AP has undergone the initial rise associated with depolarization
Exp 8: Steady depolarization of 8 mV decreases the INa associated with a sudden depolarization of 45 mV by ~ 60%
Depolarization gradually inactivates the sys which enables Na ions to cross the membrane
Exp 9: In steady state, inactivation appears to be almost complete if the membrane potential is decreased by 30 mV and is almost absent if its increased by 30mV

20. Paper #5
Goal: Combine previous experimental data and turn it into mathematical models
Next few slides will break down the following equations:

21. Capacitive Current (Cm)
Instantaneous and short
Due to hyperpolarization which occurs during the undershoot after an AP fires because K permeability becomes even greater than it is at rest
It’s a redistribution of charge across the axonal membrane
Other than this, no other current flows due to hyperpolarization

22. Determining Conductance (gx) for Na and K
Can’t use 1st order equations to define both conductances
Then HH thought of conductance as particle movement: voltage sensitive increase in conductance is due to change in position of a charged particle in the membrane
In this way, an electric field change would elicit a probability change that would follow a 1st order time course
1st order kinematics also accounts for exponential decay of conductance
But 1st order doesn’t account for the lag in onset of conductance
HH then raised the 1st order conductance equation to a power which:
Provides delayed onset (lag) of conductance
Provides exponential decay of conductance upon repolarization
Incorporates gK and gNa respective voltage sensitivities
Provides the non-linear relation between the steady amplitude and level of depolarization

23. Kinetics of gK
1st eq:
n = probability of particle being in the correct position to open the K channels
n4 = 4 particles have to be on the proper side of the membrane to open the K gate
gK eq = fraction of K channels that are open at any given time
2nd eq: the rate constants, α and β, change n from being a function of membrane potential to a function of voltage
gKbar = constant
αn and βn = rate constants that vary with voltage but not time
n varies between 0 and 1 because it’s a probability
n = the portion of particles inside the membrane
1-n = portion outside membrane
αn determines rate of transfer from outside to inside
Βn determines rate of opposite direction

24. Kinetics of gNa
1st eq:
m = probability of particle being in the correct position to open the Na channels
m3 = 3 particles have to be on the proper side of the membrane to open the Na gate
gNa eq = fraction of Na channels that are open at any given time
h = probability the “ball” on the chain of the Na channel is hanging free
2nd and 3rd eqs: the rate constants, α and β, change m and h from being functions of membrane potential to functions of voltage
gNabar = constant
All α’s and β’s = rate constants that vary with voltage but not time
All are transfer rate constants
m and h vary between 0 and 1 because they are probabilities
m = the portion of activating particles inside the membrane
1-m = portion outside membrane
h = the portion of inactivating particles on the inside
1-h = portion on the outside

25. Kinetics of Leaky Current
Small current essential in achieving a net current of zero at RMP
Leaky current is a small constant value and it’s not voltage sensitive
Inward rectifying K channels are an example of a leaky channel during rest

26. HH Model is Still Applicable Today!
The End 

27. References
Huxley AL and Hodgkin AF. Measurement of Current-Voltage Relations in the Membrane of the Giant Axon of Loligo. Journal of Physiology 1: , 1952.
Huxley AL and Hodgkin AF. Currents Carried by Sodium and Potassium Ions Through the Membrane of the Giant Axon of Loligo. Journal of Physiology 1: , 1952.
Huxley AL and Hodgkin AF. The Components of Membrane Conductance in the Giant Axon of Loligo. Journal of Physiology 1: , 1952.
Huxley AL and Hodgkin AF. The Dual Effect of Membrane Potential on Sodium Conductance in the Giant Axon of Loligo. Journal of Physiology 1: ,1952.
Huxley AF and Hodgkin AL. A Quantitative Description of Membrane Currentand Its Application to Conduction and Excitiation in Nerve. Journal of Physiology 1: , 1952.
Purves, Dale. Neuroscience. 5th ed., Oxford University Press, 2018.
Vandenberg, Carol. “Neurobiology.” Oct. 2016, Santa Barbara, California.