Part 1 - Measuring Propagation Parameters

  1. Choose tutorial "The Passive Axon"

  2. Click on Voltage vs. Time Plot, 4 locations

    • Keep Lines

  3. Click on Voltage vs. Time Plot , expanded

    • Keep Lines

  4. Click on Voltage vs. Space

  5. Click on Axon Parameters

  6. Place stimulus electrode at ~0.25 by clicking on line

  7. Set delay 5 msec , duration 20 msec , amplitude 50 nA

  8. Set Total # ( ms ) to 50 msec

  9. Click on Reset & Run

    • try slower

  1. Describe what happens quantitatively. Sketch representative voltages traces to illustrate

    image-20250222095240385

    • stimulus electrode was placed at x=0.252475 μm

    • we then have 4 different recording electrodes positioned at :

      • Red @ x=0.01 μm

      • Blue @ x=0.25 μm

        • this is the closest recording electrode to the stimulus electrode

      • Green @ x=0.50 μm

      • Black @ x=0.75 μm

    image-20250222095125630

  2. Measure time constant at site of current injection and length constant

    τ=RmCm
    τ=CmGm
    • so using the blue trace , as it should be the most accurate

    ΔV=( 179.08 )( 0 )=179.08 mV
    179.08 mV( 11e )=113.2001496750181055450265622

    image-20250222122048425

    τ=( 6.5 ms )( 5 ms ( delay ) )=1.5 ms

    178.958( 1e )=65.83496903315897848935189012

    image-20250222122931368

    • so its somewhere between 4009.9 and 4108.91 , lets say 4050

    • then we have to subtract off 2524.75 still , so its :

    λ=4050.02524.75=1525.25 μm
    λ=RmRi
    λ=diameterRm4Ri
    λ2=diameterRm4Ri
    λ2=diameterGi4Gm
    • where :

      • i = intracellular

      • m = membrane

    • try Reset ( mV ) and then Continue for ( ms )



  1. Decrease axon membrane capacitance ( Cm ) 5 fold to 0.2 µF/cm2

  1. Describe what happens quantitatively , comparing timing and distance traveled ( sketch representative voltages traces )

    • much shorter duration , only 28 milli seconds

    • slightly increased the length constant

    τ0.3 ms
    λ1545.0 μm

image-20250222123438552



  1. Decrease axon membrane conductance ( leak , GL ) 5 fold to 0.06 mS/cm 2 ( 0.00006 S/cm2 )

  2. Return Cm to default value

  3. Set stimulus amplitude to 18.56 nA

  1. Describe what happens quantitatively , comparing timing and distance traveled ( sketch representative voltages traces )

    • Vm decreased , because we have so many leak channels

    • lasts much longer in duration

    • spreads over larger distance

    τ6.5 ms
    • actually , its more like 10 ms if you extend it out to let it reach steady-state voltage

    λ2871.25 μm

     

    image-20250222124250724



  1. Decrease axon membrane conductance ( GL ) and capacitance ( Cm ) 5 fold of control

  2. Keep stimulus amplitude at 18.56 nA

  1. Describe what happens quantitatively, comparing timing and distance traveled. Sketch representative voltages traces.

    • back to original timing

    • but spreads over much larger distance

    τ2.18 ms
    λ3663.25 μm

    image-20250222124434036



  1. Decrease axon membrane diameter 5 fold to 2 µm

  2. Return both GL and Cm to default

  3. Set stimulus amplitude to 4.64 nA

  4. Turn off the Keep Lines option

  1. Describe what happens quantitatively, comparing timing and distance traveled. Sketch representative voltages traces

τ1.35 ms
λ685.25 μm

image-20250222124917795

  1. Tabulate your results ( τ , λ ) from simulations

Experimentτ( ms )λ( μm )
11.51525.25
20.31545.0
36.5 , 102871.25
42.183663.25
51.35685.25

  1. Convince your Team members how charge flows along the axon.

Part 2 - Measuring Propagation in Unmyelinated Axon

  1. Choose tutorial "The Unmyelinated Axon"

  2. Click on Voltage vs. Time Plot, Quad Traces

  3. Click on Voltage vs. space

  4. Click on Axon Parameters

  5. Place stimulus electrode at 0.0 by clicking on line

  6. Click on Reset & Run

    • try Slower

  1. Describe what happens quantitatively , comparing timing and distance traveled. Sketch representative voltages traces.

    • The red trace is the action potential near the site of stimulation ( 0.1 mm )

    • The black trace at a recording electrode ~9 mm along the axon.

    • It propagates with a measurable delay at each recording site

      • blue is at 3000 μm

      • green is at 6000 μm

      • black is at 9000 μm

    • demonstrates decay of membrane potential along axon

    image-20250222134444680

  2. Measure the action potential conduction velocity in meter/sec ( use crosshairs )

    • red peak = 1.0 , 38.0444

    • black peak = 1.375 , 41.8389

v=ΔxΔt=( 9 mm )( 0.1 mm )( 1.375 ms )( 1.0 ms )=8.9 mm0.375 ms=23.73 mmms11031103=23.73 ms


  1. Decrease axon membrane diameter 10 fold to 50 µm

  2. Set stimulus amplitude to 700 nA

  • note shock artifact

image-20250222140053798

  1. Measure the action potential conduction velocity

    • red peak = 0.925 , 38.1178

    • black peak = 3.0 , 40.64

    v=ΔxΔt=8.9 mm2.075 ms=4.289 ms
  2. Tabulate your results ( conduction velocity ) from simulations ( 2.1 and 2.2 ). Provide descriptive arrows for changes along with numerical estimates.

  1. Examine action potential waveform ( Voltage vs Space graph ) , at time ( ms ) ~2.5 ms

    image-20250222142007692

Part 3 - Myelin Influence on Membrane Circuit ( Passive ) Properties

  1. Choose tutorial "The Unmyelinated Axon"

  2. Click on Voltage vs. Time Plot, Quad Traces

  3. Click on Voltage vs. space

  4. Click on Axon Parameters

  5. Set axon diameter to 50 μm

  6. Set stimulus amplitude 700 nA

  7. Click on Reset & Run

    • try Slower

  1. Measure conduction velocity ( continued from simulation 2.2 )

    • red peak = 0.925 , 38.1178

    • black peak = 2.95 , 40.1149

    v=ΔxΔt=8.9 mm2.075 ms=4.289 ms
  2. Describe how 9 additional wraps of membrane would alter the axon membrane capacitance. The equation for adding capacitances in series is shown below.

    • the wraps would increase d , and increase A slightly ,

      • overall reducing Cm

    Cm=ϵAd
    • where :

      • ϵ = membrane permittivity

      • A = surface area of the membrane

      • d = thickness of the membrane

    Total Capacitance in Series=Ctotal=1i=1n(1Ci)
    Total Capacitance in Parallel=Ctotal=i=1n(Ci)
    Total Resistance in Series=RT=i=1n(Ri)
    Total Resistance in Parallel=RT=1i=1n(1Ri)

     

    image-20250221143920165



  1. Mimic this increase in myelin wrapping by decreasing capacitance to 0.1 μF/cm2

  2. Decrease stimulus amplitude to 220 nA ( note stimulus artifact )

  1. Measure conduction velocity

    • red peak = 0.6 , 42.8067

    • black peak = 1.15 , 43.2358

    v=ΔxΔt=8.9 mm0.55 ms=16.18 ms

     

    image-20250222142633049



  1. Return membrane capacitance to 1 μF/cm2

  2. Set stimulus strength to 700 nA

  3. Mimic the influence on membrane conductance alone , reducing GL 10-fold to 0.03 mS/cm 2 ( 0.00003 S/cm2 )

  1. Measure conduction velocity

    • red peak = 0.925 , 38.8769

    • black peak = 3.05 , 42.2186

    v=ΔxΔt=8.9 mm2.125 ms=4.188 ms

     

    image-20250222143110697

  2. Tabulate your results ( conduction velocity ) from simulations

    ExperimentConduction Velocity ( m/s )
    14.289
    216.18
    34.188

Part 4 - Measuring Propagation in Myelinated Axon

  1. Choose tutorial "The Myelinated Axon"

  2. Click on Voltage vs. Time Plot, Dual Traces

  3. Click on Voltage vs. space

  4. Click on Myelinated Region Parameters

  5. Click on Reset & Run

  • The response is for a frog axon ( diameter of 10 μm ) with ten myelinated regions of 150 myelin wraps.

  • Each myelinated region is 1 mm long with nodes of Ranvier 3.2 μm long.

  • The red trace is the action potential at the 1st node and the black trace at the 9th node.

  1. Describe what happens.

  1. Determine how many nodes are above 0.0 mV at any particular time

    • only 1 at a time

  1. Measure the action potential conduction velocity in meter/sec ( use crosshairs )

    • red peak = 0.348925 , 34.2352

      • black peak = 0.773925 , 35.5364

v=ΔxΔt=8000 106 m0.425000103 s=18.823529 ms


  1. Decrease the number of myelin wraps successively to 50 , 20 , and then 10

  1. Describe what happens. Note changes in capacitance and Myelinated Region Parameters

    • 50 :

      • Myelin Capacitance = 0.019608 μFcm2

      • Na Channel Density = 0.0023529 Scm2

      • K Channel Density = 0.0023529 Scm2

      • Leakage Conductance = 5.8824106 Scm2

      image-20250222154139953

    • 20 :

      • Myelin Capacitance = 0.047619 μFcm2

      • Na Channel Density = 0.0057143 Scm2

      • K Channel Density = 0.0057143 Scm2

      • Leakage Conductance = 1.4286105 Scm2

      image-20250222155600824

    • 10 :

      • Myelin Capacitance = 0.090909 μFcm2

      • Na Channel Density = 0.010909 Scm2

      • K Channel Density = 0.010909 Scm2

      • Leakage Conductance = 2.72723105 Scm2

    image-20250222160259347

  2. Measure the action potential conduction velocity for each condition.

    • 50 :

      • red peak = 0.38375 , 31.7135

      • black peak = 1.08125 , 33.7286

      v=ΔxΔt=8000 106 m0.69750103 s=11.46953 ms
    • 20 :

      • red peak = 0.569187 , 26.701

      • black peak = 1.73199 , 28.3823

      v=ΔxΔt=8000 106 m1.162803103 s=6.87992 ms
    • 10 :

      • red peak = 0.575 , -60.9735

      • black peak = 2.475 , -64.9624

      v=ΔxΔt=8000 106 m1.9103 s=4.2105 ms

       

  3. Tabulate your results ( conduction velocity ) from simulations

    ExperimentConduction Velocity ( m/s )
    118.823529
    211.46953
    36.87992
    44.2105


  1. Return all parameters to default settings.

  2. Place stimulus electrode in the 4th node ( 0.5 )

  1. Describe what happens

    • there is more than one node at any given time above 0.0 mV

      • multiple nodes were depolarized at different times

    • the red and black recording electrodes are in the same spots

    • its just now we are syncing in time the black electrode picking up on the IClamp pulse as well

    • https://www.youtube.com/watch?v=EzSh_VHi8cA