Met a Neuron Manual

8/9/2019 Met a Neuron Manual

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MetaNeuron Manual

Eric A. Newman

Department of Neuroscience

University of Minnesota


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MetaNeuron 2002 Regents of the University of Minnesota. Eric A. Newman,

Department of Neuroscience. All Rights Reserved. For educational purposes only. Do

not copy or reproduce without permission. Contact Eric A. Newman at [email protected].

MetaNeuron was created and written by Eric A. Newman and Mark H. Newman. It was

inspired by Jerome Y. Lettvins transistor model of the axon, the MetaMembron. Thecomputer code was written by Mark H. Newman.

Version 1.03


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TABLE OF CONTENTS

Copyright notice 2Overview of operating instructions 4

Introduction 6

Operation of MetaNeuron 7

Lesson 1, resting membrane potential 10

Student exercises 10

Lesson 2, membrane time constant 12


Lesson 3, axon action potential 15


Lesson 4, axon voltage clamp 20


Lesson 5, synaptic potential and current 24


ILLUSTRATIONS

Figure 1. Membrane time constant 13

Figure 2. Temporal summation 14

Figure 3. Action potential generation 16

Figure 4. Refractory period 19

Figure 5. Voltage clamp currents 21

Figure 6. Recovery from Na+ channel inactivation 23

Figure 7. Time course of recovery from inactivation 23

Figure 8. Reversal of an excitatory postsynaptic potential 25


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OVERVIEW OF OPERATING INSTRUCTIONS

These instructions can be viewed in the MetaNeuron program by clicking the About

button at the right of the screen.

MACINTOSH VERSION: Maximize the program window after opening.

CHOOSE A LESSON

Click on one of the five tabs at the top of the screen to select a lesson. Each lesson runs

independently; changing parameters in one lesson will not affect the operation of other

lessons.

CHANGE PARAMETER VALUES

Parameter values can be changed in several ways:

1) Click on the up or down arrow buttons to the right of a parameter box to increment

or decrement the value by 1. Pressing the "Shift" key while clicking a button increments

the value by 10. Pressing the "Ctrl" key while clicking a button increments values by 0.1.

2) Click on a parameter box. Keeping the mouse button pressed, drag the mouse.

Moving the mouse up or to the right increases the value by 1. Moving the mouse down

or to the left decreases the value. As in method 1, the Shift and Ctrl keys change the

increments to 10 and 0.1, respectively.

3) Click on the number in a parameter box, type in a new value, hit "Enter".

MACINTOSH VERSION: The Shift and Ctrl key options and dragging the mouse

(method 2) do not work on Macintosh computers.

CURSOR

The X and Y values of points on the graph can be determined by moving the mouse over

the graph and clicking the left mouse button. The values, in units appropriate for the

yellow trace, are given in the upper right corner of the program window. The currently

selected point on the graph is indicated by crosshairs when the Show Cursor box is


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checked. Displayed X and Y values are confined to points along the yellow trace when

the Trace box is checked.

FAMILY OF CURVES

A family of curves can be generated by checking the Keep Previous Graphs box.

Graphs are retained as long as the box remains checked. A simple way to generate a

family of curves is to check the Keep Previous Graphs box, hold down the Shift key (to

increment in steps of 10), left click on a parameter box (e.g. stimulus amplitude) and

move the mouse to the right while keeping the left mouse button pressed.

DEFAULT VALUES

All parameters in a lesson can be reset to default values by clicking the Reset to

Defaults button.

MetaNeuron represents 1 cm2 of neuronal membrane. The membrane has a capacitance

of 1 F.


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INTRODUCTION

MetaNeuron is a computer program that models the basic electrical properties of

neurons and axons. The program is intended for the beginning neuroscience student andrequires no prior experience with computer simulations.

Different aspects of neuronal behavior are highlighted in the five lessons

presented in MetaNeuron. The first two lessons, Membrane Potentialand Membrane

Time Constant, illustrate the passive properties of neuronal membranes. The third and

fourth lessons,AxonAction PotentialandAxonVoltage Clamp, demonstrate how

voltage- and time-dependent ionic conductances contribute to the generation of the action

potential in the axon. The fifth lesson, Synaptic Potential and Current, illustrates how

synaptic potentials are generated through the activation of ionotropic neurotransmitter

receptors.

The lessons in MetaNeuron do not attempt to model the full complexity of

neuronal behavior. The simulations simplify neuronal properties, highlighting the basic

principles of neuronal function.

Other, comprehensive simulations of the neuron are available to students who

wish to investigate neuronal behavior in more detail. One simulation in particular,

NEURON, is recommended. It is available free to students at the website:

http://neuron.duke.edu/. A version of NEURON which includes a laboratory handbook,

Neurons in Action:Computer Simulations with NeuroLab, by John W. Moore and Ann E.

Stuart, can be purchased from Sinauer Press.


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OPERATION OF METANEURON

MetaNeuron simulations run automatically when the program is opened. A lesson

is selected by clicking the appropriate tab at the top of the screen. The five lessons in

MetaNeuron run independent of each other. If the parameters in one lesson are changed,the changes will not affect the operation of the other lessons.

Changing parameter values

Experiments are run in MetaNeuron by changing the values of the parameters

displayed in the top portion of the screen. Parameter values can be changed in several

ways:

1) Click on the up or down arrow buttons to the right of a parameter box to increment

or decrement the value by 1. Pressing the "Shift" key while clicking a button increments

the value by 10. Pressing the "Ctrl" key while clicking a button increments values by 0.1.

When running MetaNeuron on an older computer, the traces may update slowly.

Continuous updates can be disabled by unchecking the Continual Update box.

2) Click on a parameter box. Keeping the mouse button pressed, drag the mouse.

Moving the mouse up or to the right increases the value by 1. Moving the mouse down

or to the left decreases the value. As in method 1, the Shift and Ctrl keys change the

increments to 10 and 0.1, respectively.

3) Click on the number in a parameter box, type in a new value, hit "Enter".

MACINTOSH VERSION: The Shift and Ctrl key options and dragging the mouse

(method 2) do not work on Macintosh computers.

Parameters in boxes that are grayed out cannot be changed. The values of these

parameters are determined by other parameters on the screen or are not currently

activated. In theAxon Action PotentialandAxon Voltage Clamp lessons, parameters for

Stimulus 2 are activated when the Stimulus 2 On box is checked.

All parameters in a lesson can be reset to their default values by clicking the Reset

to Defaultbutton.


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Graphs of parameter values

Some of the parameters in a lesson are plotted in the graph in the lower portion of

the screen. The plots are color coded and corresponding plot labels are shown in the

upper left corner of the graph. Traces in the graph are updated every time a parameter

value is changed. When a parameter value is changed by moving the mouse (PC version

only), the traces update continually. When running MetaNeuron on an older computer,

this continual update may cause annoying delays. If this is the case, continual updates

can be disabled by unchecking the Continual Update box. Traces will then be updated

when the left mouse button is released after changing a parameter value.

The sweep duration, the total time displayed on the X-axis of the plots, is

controlled by the Sweep Duration parameter.

Family of curves

A family of curves can be generated in a graph by retaining previous traces. This

is done by checking the Keep Previous Graphs box. New traces are added to the graph

every time a parameter value is updated. All traces are retained as long as the box

remains checked. An easy way to generate a family of curves is to check the Keep

Previous Graphs box, hold down the Shift key (to increment in steps of 10), left click on

a parameter box (e.g. stimulus amplitude) and move the mouse to the right while keeping

the left mouse button pressed. Examples are shown in figures 5, 7 and 8.

Measuring traces with the cursor

The X and Y values of any point on a graph can be determined by moving the

mouse over the graph and clicking the left mouse button. The X and Y values, in units

appropriate for the yellow trace, are given in the upper right corner of the program

window. The currently selected point on the graph is indicated by crosshairs when the

Show Cursor box is checked. The crosshairs display is not shown when the Keep

Previous Graphs feature is selected.

When measuring the value of a point on a trace, it is convenient to confine the

cursor to the trace. This is done by checking the Trace box. With the box checked, the

Y values of the cursor are confined to points along the yellow trace, which represents


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membrane potential in some lessons and membrane current in others. To measure the

peak voltage of an action potential in theAxon Action Potentiallesson, for instance, first

check the Show Cursor and Trace boxes. Then move the mouse to the X position

corresponding to the peak of the action potential while keeping the left mouse button

pressed.

MetaNeuron represents 1 cm2 of neuronal membrane. The membrane has a

capacitance of 1 F.


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LESSON 1, RESTING MEMBRANE POTENTIAL

Lesson 1 illustrates how K+ and Na+ channels contribute to the generation of the

resting membrane potential in neurons. The neuron in this lesson is modeled by passive

conductances to K+

and Na+

. These conductances are voltage-independent and theneuron does not generate action potentials.

The concentrations of K+ and Na+, both outside and inside the cell, can be varied.

The program calculates the electrochemical equilibrium potential for each ion, based on

the ion concentration gradient across the membrane, using the Nernst equation,

[ ][ ]

=

i

o

ion

ionntialbrium poteion equili log58(mV)

where [ion]o and [ion]i are the concentrations of the ion outside and inside the cell,

respectively. The effect of temperature on the equilibrium potential is not included in

this version of the equation.

The resting membrane potential of the neuron is determined by the concentrations

of K+ and Na+ outside and inside the cell and by the permeability of the membrane to K+

and Na+. The relative membrane permeabilities to K+ and Na+ can be varied. The

membrane potential is calculated using the Goldman-Hodgkin-Katz equation,

where PKand PNa are the relative membrane permeabilities to K+ and Na+, respectively.

The term representing membrane permeability to Cl- is omitted in the MetaNeuron

simulation. Active membrane conductances are not modeled in this lesson.

Student exercises

1) Vary the concentrations of K+ and Na+, both inside and outside the cell. What

effect does this have on the electrochemical equilibrium potential of the ion? What is the

+

+=

++

++

iNaiK

oNaoK

NaPKP

NaPKPmV

][][

][][log58)(potentialmembrane


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Na+ equilibrium potential whenNa+ outequals 100 mM andNa+in equals 10 mM?

What is the Na+ equilibrium potential whenNa+ outequals 100 mM andNa+ in equals

100 mM? What is the K+ equilibrium potential whenK+ outequals 10 mM andK+ in

equals 100 mM? Why is this?

2) Starting with the default parameter values, vary the relative membrane permeability

to K+ and Na+. What effect does this have on the resting membrane potential? SetNa+

outto 100 mM,Na+ in to 10 mM, K+ outto 10 mM andK+ in to 100 mM. What is the

membrane potential when theNa+ permeability equals 0 and theK+ permeability equals

10? What is the membrane potential when theNa+ permeability equals 10 and theK+

permeability equals 0? What is the membrane potential when theNa+ permeability

equals 1 and theK+ permeability equals 10? Why is this?

3) Starting with the default parameter values, plot the value of the membrane potential

as a function of [K+]o over a [K+]o range of 0.2 to 100 mM. Regraph the data with the

membrane potential plotted as a function of log([K+]o). Can you explain why this second

plot has the shape that it does?

4) Reduce PNa to 0 and replot the membrane potential as a function of log([K+]o). What

accounts for the difference in the shape of this relation, compared to the one in

exercise 3?


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LESSON 2, MEMBRANE TIME CONSTANT

Lesson 2 illustrates the effect of the membrane time constant, , on the time

course of electrical responses in neurons. The neuron in this lesson is modeled by a

passive membrane resistance, R, a membrane capacitance, C, and a current source. Themembrane capacitance equals 1 F/cm2, or simply 1 F, since MetaNeuron represents 1

cm2 of membrane. The value of the membrane resistance as well as the time course and

amplitude of the current source can be varied. The neuron does not generate action

potentials.

The membrane resistance and capacitance together determine the time constant of

the membrane, as described by the equation,

CR =

The default values of the stimulus current source specify a positive, 1 msec long

pulse. This is a good approximation of the current generated when a fast excitatory

synapse is activated. Using the default current source parameters, MetaNeuron can be

used to assess the effect of the membrane time constant on the time course of single and

multiple synaptic responses.

The "Threshold" potential shown in the graph indicates the approximate voltage

at which action potentials will be initiated in a neuron. Note, however, that the neuron

model used in this lesson does not include active membrane conductances and will not

generate action potentials when the membrane potential exceeds the threshold value.

Measuring time constants

When a constant current is injected into a neuron, the membrane potential

depolarizes with an exponential time course (assuming that there are no active membraneconductances). Similarly, when the stimulus is turned off, the membrane potential

returns to the resting membrane potential with an exponential time course.

The rate at which the membrane potential increases and decreases is described by

the time constant, , of the exponential. is defined as the time it takes for the membrane

to increase or to decrease to 1-1/e (approximately 63%) of its final value. Remember that


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sufficient time must be allowed for the membrane potential to reach its plateau level in

order to make this measurement.

Student exercises

1) Using the default parameter values, determine the time constant of the membrane by

measuring the time it takes for the amplitude of the membrane potential to fall 63% of the

way back to the baseline value, after the current source is turned off. Does this value of

equal the membrane time constant calculated from the equation,

CR =

where is the membrane time constant in units of sec,R is the membrane resistance in

units of Ohmscm2 and Cis the membrane capacitance in units of F/cm2?

Increase the amplitude of the stimulus to 150 A and repeat your measurement of

the membrane time constant. Has it changed?

2) Using a stimulus amplitude of 150 A, vary the membrane resistance. What effect

does this have on the rising and falling phases of the response? Set the membrane

resistance to 2 k Ohmscm2. What is the membrane time constant, measured from the

falling phase of the response?

Figure 1. Membrane time constant.

A 150 A, 1 msec current pulserapidly depolarizes a neuron. At

the end of the pulse, the membrane

potential decays back towards theresting membrane potential with an

exponential time course. The time

constant of decay is more rapid fora membrane resistance of 2 k Ohms

than for a resistance of 10 k Ohms.

stimulus

10 k Ohms

2 k Ohms


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3) Reset to the default parameter values and increase the number of stimuli from 1 to 3.

Note how the responses add together. This superposition of responses is termed temporal

summation. Now reduce the membrane resistance from 10 to 2 k Ohmscm2. What

effect does this have on temporal summation? Note that changes in temporal summation

determine whether the response reaches the threshold level for firing action potentials.

Figure 2. Temporal summation.The three current pulses (bottom

trace) simulate three synaptic

responses. With a long membranetime constant (10 k Ohm

membrane resistance), the synaptic

potentials summate and reach the

threshold potential for firing anaction potential. With a short time

constant (2 k Ohms), the synaptic

potentials do not summate and donot reach threshold.

stimulus

"threshold"

membrane potential


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LESSON 3, AXON ACTION POTENTIAL

Lesson 3 illustrates how voltage- and time-dependent Na+ and K+ conductances

generate the action potential. The MetaNeuron model in this lesson is based on equations

developed by Alan Hodgkin and Andrew Huxley to describe the voltage-dependent Na+

and K+ conductances of the squid giant axon. The Na+ conductance in the MetaNeuron

model represents fast, tetrodotoxin-sensitive Na+ channels. The K+ conductance

represents delayed rectifier K+ channels. The values of some of the parameters in the

equations have been adjusted to simulate action potential generation in a vertebrate axon.

Several parameters controlling Na+ and K+ currents can be adjusted in the model:

The Na+ and K+ equilibrium potentials. Modifying these values will change the

driving force for ion flux through the Na+ and K+ conductances.

gNa+ max and gK+ max, the maximum membrane conductances. These

parameters represent the number of Na+ and K+ channels in the membrane.

TTX (tetrodotoxin) and TEA (tetraethylammonium). Selecting TTX blocks the

Na+ conductance. Selecting TEA blocks the K+ conductance.

Temperature. Raising the temperature reduces the time constants controlling Na+

conductance activation and inactivation and K+ conductance activation, resulting

in a faster action potential. The temperature factor has a Q10 of 3.0.

Activation of the neuron is controlled by several stimuli:

Stimulus 1. The delay, width and amplitude of this current pulse can be varied.

Stimulus 2. A second current pulse is added when the Stimulus 2On box is

checked. The second stimulus is used when measuring the refractory period of

the axon.

Holding Current. This continuous current source can be used alone or togetherwith the current pulses.

The graph displays the membrane potential as well as the Na+ and K+ equilibrium

potentials and the stimulus. In addition, Na+ and K+ conductances or currents are


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displayed when the appropriate buttons are selected in the Conductances and Currents

box.

Student exercises

1) Increase the amplitude ofStimulus 1. What effect does this have on the cellresponse? What is the threshold stimulus amplitude (in A) and the threshold voltage (in

mV) for initiating an action potential? (The threshold voltage is best measured by

adjusting the stimulus amplitude, in 0.1 A increments, until it is just below threshold for

initiating an action potential. Now measure the voltage at the peak of the response.

Measure the voltage using the cursor, with the Show Cursorand Trace boxes checked.)

Figure 3. Action potentialgeneration. Injection of current

into an axon triggers the generation

of an action potential. The peak of

the action potential approaches the

Na+ equilibrium potential. Theafter hyperpolarization reaches the

K+ equilibrium potential.

2) Vary the stimulus amplitude from 50 to 200 A in 10 A increments. Measure the

amplitude of the action potential and the time to the peak of the action potential for each

stimulus amplitude. Plot both the amplitude and time to peak of the action potential as a

function of stimulus amplitude. Why does the time to peak vary? Why does the action

potential amplitude vary so little?

3) Action potentials are often initiated at the axon hillock, where the axon leaves the

cell body. The axon hillock has a high density of Na+ channels, which lowers the

threshold for initiating an action potential. MetaNeuron can be used to measure the effect

of Na+ channel density on the threshold for action potential initiation. VarygNa max

Na+ potential

K+ potentialstimulus

membrane potential

0 mV


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from 200 to 380 mS/cm2 in 20 mS/cm2 steps. (Na+ channel density is proportional to

gNa max.) For eachgNa max value, determine the threshold for initiating an action

potential. Measure both the threshold stimulus amplitude (in A) and the threshold

voltage. Plot the threshold current and voltage as a function of gNa max. Why does the

action potential threshold vary as Na+ channel density is changed?

4) The symptoms of multiple sclerosis are caused by conduction failure due to the

demyelination of axons. In some patients, the symptoms of multiple sclerosis are

alleviated by cooling a patient while symptoms are exacerbated by an exercise-induced

rise in body temperature. MetaNeuron can be used to measure the effect of temperature

on action potential threshold. Adjust the stimulus amplitude so that it is just below

threshold for initiating an action potential. Now vary the temperature. How much does

the temperature have to be lowered to evoke an action potential? Starting again from the

default parameter values, adjust the stimulus amplitude so that it is just above threshold

for initiating an action potential. How much does the temperature have to be raised to

block initiation of the action potential? Why does action potential threshold depend on

temperature?

5) Set Stimulus 1 Amplitude to 150 A. The stimulus will evoke an action potential.Vary theNa+ potential. What effect does this have on the action potential? Why?

6) Using a Stimulus 1 Amplitude of 150 A and aNa+ potentialof 50 mV, varygK

max. What effect does this have on the width of the action potential? Why?


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7) Starting with the default parameter values, set Stimulus 1 Amplitude to 0 and Sweep

Duration to 20 ms. Now raise theK+potential(in the Membrane Parameters box) to

more positive values. As theK+ potentialis raised, you will observe the following

sequence of events,

The membrane potential depolarizes.

Spontaneous action potentials are generated.

The frequency of the action potentials increases.

The amplitude of the action potentials diminishes.

The action potentials die out as the membrane potential continues to depolarize.

Can you explain this sequence of behavior?

8) Starting with the default parameter values, set Sweep Duration (the total time

displayed on the X-axis) to 10 msec. Now decrease the amplitude ofStimulus 1 until it

reaches 200 A. You will observe that an action potential is evoked by the

hyperpolarizingstimulus! This phenomenon is called anodal break excitation. Can you

explain why a hyperpolarizing stimulus evokes an action potential?

9) MetaNeuron can be used to measure the time course of the refractory period which

follows an action potential. Two stimulus pulses are used to measure the refractory

period. The amplitude of the first stimulus is set to well above threshold and reliably

evokes an action potential. The amplitude of this stimulus remains fixed. The second

stimulus, which is initially set to a delay of 12 msec after the first stimulus, is used to

determine the change in threshold of the axon. The amplitude of the second stimulus is

adjusted until it is just strong enough to evoke a second action potential. The stimulus

amplitude is a measure of the threshold of the axon. The higher the threshold of the

axon, the stronger is the stimulus needed to trigger the second action potential.

Starting with the default parameter values, set Sweep Duration to 16 msec and

Stimulus 1 Amplitude to 150 A. Turn Stimulus 2 ON and set Stimulus 2 delay to 12

msec.


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With Stimulus 2 Delay at 12 msec, adjust Stimulus 2 Amplitude until it is just

large enough to evoke an action potential. This is the threshold amplitude. (The threshold

amplitude can be easily determined on PC computers by clicking on the Stimulus 2

Amplitude box and dragging the mouse while keeping the left mouse button pressed.

Move the mouse until an action potential is evoked.)

Reduce Stimulus 2 delay to 11 msec and once again adjust Stimulus 2 Amplitude

to the threshold level. Repeat this measurement forStimulus 2 Delays of 10 to 1 msec.

As you approach a Stimulus 2 Delay of 1 msec, reduce the delay in smaller steps so that

the threshold amplitude vs. delay relation can be determined more accurately. Note that

at small delays, the second action potential becomes smaller and is not an all or none

event. Use your judgment in determining a criterion for when the action potential is

evoked.

Plot the Stimulus 2 threshold amplitude as a function of Stimulus 2 delay. The

plot shows the time course of the refractory period following an action potential. What is

the duration of the absolute refractory period and the relative refractory period, based on

this experiment?

Figure 4. The duration of the

refractory period following an

action potential can be measuredusing a two pulse protocol. The

first stimulus pulse is well abovethreshold and reliably evokes an

action potential. The second

stimulus pulse is adjusted so thatit just triggers an action potential.

The amplitude of the second

stimulus is a measure of the

membrane threshold.


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LESSON 4, AXON VOLTAGE CLAMP

Lesson 4 uses the voltage clamp technique to reveal the properties of the Na+

channels and delayed rectifier K+ channels that generate the action potential. Na+ and K+

channels are both voltage- and time-dependent and it is difficult to analyze their

properties while action potentials are being generated. Channel properties can be

characterized, however, by measuring the currents flowing through the channels at a

fixed membrane potential. The voltage clamp technique, developed by Hodgkin and

Huxley in the 1940s, permits these measurements to be made.

The voltage clamp technique uses a negative feedback electronic circuit to hold

the axon membrane potential to a value (the command voltage) specified by the

experimenter. The circuit then measures the time-dependent currents flowing through

Na+ and K+ channels at that voltage. Typically, the membrane potential is first held at a

negative voltage near the resting membrane potential, theHolding Potential, and is then

stepped to a more positive voltage, determined by the Stimulus 1 and Stimulus 2

Amplitudes in MetaNeuron.

It is important to remember that action potentials cannot be generated when an

axon is voltage clamped. The currents that are measured under voltage clamp contribute

to the generation of the action potential, but these currents are not, in themselves, action

potentials.

Lesson 4 uses the same Hodgkin-Huxley model of the axon that is used to

generate action potentials in Lesson 3. The parameters in Lesson 4 are similar to those in

Lesson 3 as well. The only changes in Lesson 4 are that the axon is now voltage-clamped

and the stimuli used are command voltages rather than currents. The Holding Potential

parameter determines the voltage of the axon at the beginning of the experiment. The

Stimulus 1 and Stimulus 2 Amplitudes determine the voltage to which the membrane is

stepped during the two pulses. Note that these stimulus amplitudes represent absolute

voltages, not relative voltages added onto the holdingpotential.


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Student exercises

1) Increase Stimulus 1 Amplitude and note the development of a transient inward

(negative) current and a sustained outward (positive) current. What is the origin of these

two components of the current?

Figure 5. Transient inward Na+

currents and sustained outward K+

currents are recorded when theaxon is voltage clamped. This

family of eight voltage clamp

recordings was generated bystepping the membrane potential

from -70 mV to +70 mV in 20 mV

increments.

2) Starting with the default parameters, set the Stimulus 1 Amplitude to 0 mV. What

happens when the TTX or TEA boxes are selected? Why is this?

3) The K+ current can be viewed in isolation by blocking the Na+ current with TTX.

With the TTX box checked, measure the amplitude of the K+ current as a function of the

voltage of the test pulse (Stimulus 1 Amplitude). The K+ current should be measured

from its pre-pulse baseline level (which you can assume equals 0) to its plateau level, at

the end of the voltage pulse. Measure the current over a stimulus amplitude range of 70

to +70 mV in increments of 10 mV. Plot the amplitude of the K+ current as a function of

the test pulse voltage.

The K+ current can be converted to a conductance using the chord conductance

equation,

mequilibrium VV

current

=econductanc

where Vm is the test pulse voltage and Vequilibrium is the equilibrium potential for the ion,

membrane current

command voltage


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which does not change between trials. Use this equation to calculate the K+ conductance

at each test pulse voltage and plot the conductance as a function of voltage. What does

the conductance-voltage relation tell you about the voltage dependence of K+ channels?

4) Repeat this procedure to determine the current-voltage and conductance-voltage

relations for Na+. Select the TEA box and de-select the TTX box in order to view the

Na+ current in isolation. Measure the amplitude of the Na+ current as a function of

voltage over a stimulus amplitude range of 70 to +80 mV. Measure the Na+ current

from the pre-pulse level to the transient peak of the current. Note that the peak current

will be negative at some voltages and positive at other voltages. Plot the current-voltage

relation. Convert the currents to conductances using the chord conductance equation and

plot the conductance-voltage relation. What does the conductance-voltage relation tell

you about the voltage dependence of Na+ channels? In the current-voltage relation, why

is Na+ current negative at some voltages and positive at other voltages?

5) Na+ channels first activate and then inactivate when the membrane potential is

stepped from the resting level to a depolarized level. The channels do not begin to

recover from inactivation until the membrane is repolarized to a negative level.

MetaNeuron can be used to measure the time course of recovery of the Na+

conductancefrom inactivation by voltage clamping the axon and using two voltage command pulses.

Starting with the default parameter values, check the TEA box to view the Na+

current in isolation, turn on Stimulus 2, set Sweep Duration to 16 msec, Stimulus 1 and

Stimulus 2 Amplitude to +5 mV, Stimulus 1 and Stimulus 2 Width to 2 msec and Stimulus

2 Delay to 10 msec.

With Stimulus 2 Delay set at 10 msec, measure the amplitude of the peak Na+

current evoked by the second pulse (the current will be negative). Decrease the Stimulus

2 Delay to 9 msec and repeat the measurement. Continue measuring the Na+ current

amplitude for delays down to 0.1 msec, decreasing the delay in 1 msec increments. As

you approach a delay of 0.1 msec use smaller decrements in order to accurately

determine the time course of recovery from inactivation.


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membranecurrent

command

voltage

Plot the amplitude of the second pulse Na+ current as a function of the delay.

How does the time course of recovery from Na+ channel inactivation compare to the time

course of the refractory period following an action potential? Why are these two

processes related?

Figure 6. Recovery from Na+ channel

inactivation can be measured with thevoltage clamp technique using a two pulse

protocol. Stepping the membrane potential

from -75 to +5 mV evokes an inward Na+

current. Following a delay of 1 msec, asecond depolarization evokes a smaller

current, demonstrating that many Na+channels have not yet recovered from

inactivation. TEA has been selected to

block K+ currents.

Figure 7. The time course of recovery of

Na+ channels from inactivation is revealedin this family of voltage clamp recordings.

The two pulse experiment illustrated in Fig.

6 was repeated for delays ranging from 0.1

to 7.5 msec. The peaks of the inward Na+current plots outline the time course of

recovery from inactivation.


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LESSON 5, SYNAPTIC POTENTIAL AND CURRENT

Lesson 5 illustrates the synaptic voltages and currents generated at fast ionotropic

synapses. The neuron in Lesson 5 is modeled by a leak conductance and by the opening

of an ionotropic receptor conductance, simulating a synaptic response. The relative

permeabilities of the receptor to Na+, K+ and Cl- can be adjusted. Based on these relative

permeabilities, the model calculates the reversal potential of the receptor. It is important

to bear in mind that ionotropic receptors are normally permeably to either cations (Na+,

K+) or anions (Cl-) but not to both. The neuron in lesson 5 does not generate action

potentials.

The reversal potential of the ionotropic receptor can be determined

experimentally by varying the membrane potential of the neuron and noting the potentialat which the synaptic response reverses polarity. When synaptic voltages are measured

(Mode: Voltage) the membrane potential is varied by injecting current into the cell. This

is done by adjusting theHolding Current. (This mode of recording is also referred to as

current clamp.) When synaptic currents are measured (Mode: Voltage Clamp), the

membrane potential is varied by adjusting theHolding Potential.

The equilibrium potentials for Na+, K+ and Cl- in this model are +50, -77 and -75

mV, respectively. The resting membrane potential is determined by a leak conductance

having a reversal potential of -65 mV. The synaptic conductance is modeled with rising

and falling time constants of 0.1 and 1.0 msec.

Student exercises

1) Start with the default parameter values, with relative receptor permeabilities of Na+,

1.2; K+, 1; Cl-, 0. These default permeabilities represent an excitatory receptor such as

the AMPA glutamate receptor. Depolarize the neuron incrementally by increasing the

Holding Currentfrom 0 to 240 A in 30 A increments. What happens to the synaptic

potential, which is shown in the yellow (Membrane Voltage) trace, as the membrane is

depolarized? Plot the amplitude of the synaptic potential as a function of membrane

voltage. Measure the amplitude from the baseline to the peak of the synaptic response.

Note that the amplitude will be negative at some membrane voltages. What is the shape


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of the relation?

The reversal potential of the synapse is defined as the potential at which the

synaptic response reverses polarity. At what voltage does the synaptic potential reverse?

Does this agree with the reversal potential calculated by the model and displayed in the

Receptor Reversal Potentialbox?

Figure 8. Reversal of an excitatory

postsynaptic potential generated by

the opening of a receptor permeable

to both Na+ and K+. This family of

voltage responses was made bydepolarizing the neuron by injection

of a holding current. The synaptic

response reverses polarity when the

neuron is depolarized past 0 mV.

2) Starting with the default parameters, switch to Voltage Clamp mode. Now

depolarize the membrane incrementally by raising theHolding Potentialfrom -65 to +65

mV in 10 mV increments. Plot the amplitude of the synaptic current as a function of

holding potential. Measure the current amplitude from the baseline to the peak of the

synaptic response. At what voltage does the synaptic current reverse polarity? Is this the

same voltage as was calculated in exercise 1? What is the shape of the synaptic current

vs. voltage relation? Why does the relation have this shape?

The synaptic current can be converted to conductance using the chord

conductance equation,

reversalm VV

current

=econductanc

where Vm is the membrane potential specified by theHolding Potentialand Vreversal is the

reversal potential of the synaptic response. Use this equation to calculate the synaptic

conductance at each voltage and plot the conductance as a function of voltage. What is

the shape of the conductance vs. voltage relation? Is the synaptic conductance voltage-

dependent?

0 mV

membrane potential

Na+ potential

K+ potential


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3) Change the relative permeabilities of the receptor to Na+, 0.3; K+, 1; Cl-, 0. In

Voltage Clamp mode, measure the reversal potential of the current. At what voltage does

the current reverse polarity? Why has the reversal potential of the receptor changed?

4) Change the relative permeabilities of the receptor to Na+, 0; K+, 0; Cl-, 1. This

represents an inhibitory receptor, such as the GABAA receptor. In Voltage Clamp mode,

measure the reversal potential of the current. At what voltage does the current reverse

polarity? Why is this synapse inhibitory?

5) Starting with the default parameters, note the time course of the synaptic potential

and measure the time to the peak of the response. With the Keep Previous Graphs box

selected, switch to Voltage Clamp mode. Note that the time course of the synaptic

response has changed. Why is this?

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