The Hodgkin and Huxley Model of the Action Potential - PowerPoint Presentation

Slide1

The Hodgkin and Huxley Model of the Action Potential

By Jaclyn Eisdorfer

Slide2

The Resting Membrane Potential (RMP)

Negative resting potential with a value of about -70mVProduced by active transporters ATPase Pumps: primary active transportIon Exchangers/Cotransporters: secondary active transport

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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 = NzFENernst Equation:

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Action Potential (AP)

Makes the mem potential positivePropagated along the length of axonsHow information is transferredElicit 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 themFlux due to asymmetric distribution of ions in intracellular and extracellular spaces

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AP Nomenclature

Rising phase: membrane rapidly depolarizesOvershoot: positive membrane potential during APFalling phase: membrane rapidly repolarizesUndershoot: hyperpolarization

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Materials – Giant Squid Axon

Obtained from the hindmost stellar nerve of Loligo forbesiLarge 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

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Materials – Intracellular Microelectrodes

Two long silver wires Wires thrust down the axis of the giant squid axonWires were insulated except for terminal portions that were exposed Current was applied between the current wire and the earthPotential difference across the membrane could be recorded from the voltage wire and an external electrode

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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)

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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 timeAllows researcher to determine: Which types of ion channels are opened or closedWhen they openHow they respond to voltage

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VCM Steps

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VCM

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Experiments & Results

Five Papers:

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

Aim:

Determine the laws which govern

movement of ions

during electrical activity (i.e. during an AP)

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Paper #1

Goals: Examine the function of the neuronal membrane under normal conditions Outline the experimental method in each experiment in all 5 papersVCM: V0= 0 (RMP) depolarized to V1 (command voltage)Exp 1: : Axons gave all-or-nothing AP of ~ 100 mV when stimulated with a brief shockThreshold of AP seen at ~ 15 mVDepolarizations < 10-15 mV gave graded responses

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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 10-50 msMembrane had brief Cm and an ionic current Depolarizations > 15mV gave outward currents that decreased with time Depolarizations of 15-110 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

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Paper #2

Goals: : Identify which ions carry the different phases of the membrane currentVCM: 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

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Paper #2 (continued)

Exp 4: Finding the critical value when Na inward current changed to outwardCritical 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 APTherefore 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 currentDelayed outward current was little affected by replacing Na ions with cholineSimple assumptions led HH to resolve ITOT to INa and IKgNa rises rapidly to max and then decreases in an exponential curvegK rising more slowly along an S-shaped curve and maintained at high levels for long periods of time

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Paper #3

Goals: Examine the effects of sudden potential changes on the AP/ionic conductanceVCM: membrane potential is restored from V1  V0 and also changed V1  V2Exp 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

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Paper #3 (continued)

Exp 6: “Tail” of inward current disappears if extracellular [Na] is removedTime course of gNa during VCM can be calculated from the variation of the “tail” of inward current with the duration of depolarizationExp 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 ~ 10-20 mV above RMPSuggests gK is a function of time which rises when the nerve is depolarized and falls when it’s repolarized

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Paper #4

Goals: Outline how inactivation process decreases Na permeability after the AP has undergone the initial rise associated with depolarizationExp 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

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Paper #5

Goal: Combine previous experimental data and turn it into mathematical modelsNext few slides will break down the following equations:

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Capacitive Current (Cm)

Instantaneous and shortDue to hyperpolarization which occurs during the undershoot after an AP fires because K permeability becomes even greater than it is at restIt’s a redistribution of charge across the axonal membraneOther than this, no other current flows due to hyperpolarization

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Determining Conductance (gx) for Na and K

Can’t use 1

st

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 1

st

order time course

1

st

order kinematics also accounts for exponential decay of conductance

But 1

st

order

doesn’t account for the lag

in onset of conductance

HH then raised the 1

st

order conductance equation to a

power

which:

Provides delayed onset (lag) of conductance

Provides exponential decay of conductance upon repolarization

Incorporates

g

K

and

g

Na

respective voltage sensitivities

Provides the non-linear relation between the steady amplitude and level of depolarization

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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 voltagegKbar = constant αn and βn = rate constants that vary with voltage but not timen varies between 0 and 1 because it’s a probability n = the portion of particles inside the membrane1-n = portion outside membraneαn determines rate of transfer from outside to inside Βn determines rate of opposite direction

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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 free2nd and 3rd eqs: the rate constants, α and β, change m and h from being functions of membrane potential to functions of voltagegNabar = constant All α’s and β’s = rate constants that vary with voltage but not timeAll are transfer rate constantsm and h vary between 0 and 1 because they are probabilities m = the portion of activating particles inside the membrane1-m = portion outside membraneh = the portion of inactivating particles on the inside1-h = portion on the outside

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Kinetics of Leaky Current

Small current essential in achieving a net current of zero at RMPLeaky current is a small constant value and it’s not voltage sensitiveInward rectifying K channels are an example of a leaky channel during rest

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HH Model is Still Applicable Today!

The End



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References

Huxley AL and Hodgkin AF. Measurement of Current-Voltage Relations in the Membrane of the Giant Axon of

Loligo

. 

Journal of Physiology

 1: 424-448, 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

 1:449-472, 1952.

Huxley AL and Hodgkin AF. The Components of Membrane Conductance in the Giant Axon of

Loligo

. 

Journal of Physiology

 1: 473-496, 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: 497-506,1952.

Huxley AF and Hodgkin AL. A Quantitative Description of Membrane

Currentand

Its Application to Conduction and

Excitiation

in Nerve. 

Journal of Physiology

 1: 500-544, 1952.

Purves, Dale. 

Neuroscience

. 5th ed., Oxford University Press, 2018.

Vandenberg, Carol. “Neurobiology.” Oct. 2016, Santa Barbara, California.