Part 1 - Measuring Propagation Parameters

• Describe how membrane potential varies along an axon.

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

   

   • stimulus electrode was placed at $x=0.252475\mu m$$x = 0.252475\ \mu m$

   • we then have 4 different recording electrodes positioned at :

     • Red @ $x=0.01\mu m$$x = 0.01\ \mu m$

     • Blue @ $x=0.25\mu m$$x = 0.25\ \mu m$

       • this is the closest recording electrode to the stimulus electrode

     • Green @ $x=0.50\mu m$$x = 0.50\ \mu m$

     • Black @ $x=0.75\mu m$$x = 0.75\ \mu m$

   

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

   $$\tau =R_m\ast C_m$$
   $$\tau =\frac{C_m}{G_m}$$

   • so using the blue trace , as it should be the most accurate

   $$\mathrm{\Delta }V=\left(179.08\right)-\left(0\right)=-179.08mV$$
   $$-179.08mV\ast (1-\frac{1}{e})=-113.2001496750181055450265622$$

   

   $$\tau =\left(6.5ms\right)-(5ms(delay))=1.5ms$$

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   $$178.958\ast \left(\frac{1}{e}\right)=65.83496903315897848935189012$$

   

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

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

   $$\lambda =4050.0-2524.75=1525.25\mu m$$
   $$\lambda =\sqrt{\frac{R_m}{R_i}}$$
   $$\lambda =\sqrt{\frac{\text{diameter}\ast R_m}{4\ast R_i}}$$
   $${\lambda }^2=\frac{\text{diameter}\ast R_m}{4\ast R_i}$$
   $${\lambda }^2=\frac{\text{diameter}\ast G_i}{4\ast G_m}$$

   • where :

     • $i$$i$ = intracellular

     • $m$$m$ = membrane

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

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

3. 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

   $$\tau \approx 0.3ms$$
   $$\lambda \approx 1545.0\mu m$$

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

12. Return Cm to default value

13. Set stimulus amplitude to 18.56 nA

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

   • $V_m$$V_m$ decreased , because we have so many leak channels

   • lasts much longer in duration

   • spreads over larger distance

   $$\tau \approx 6.5ms$$

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

   $$\lambda \approx 2871.25\mu m$$

    

   

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

15. Keep stimulus amplitude at 18.56 nA

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

   • back to original timing

   • but spreads over much larger distance

   $$\tau \approx 2.18ms$$
   $$\lambda \approx 3663.25\mu m$$

   

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16. Decrease axon membrane diameter 5 fold to 2 µm

17. Return both GL and Cm to default

18. Set stimulus amplitude to 4.64 nA

19. Turn off the Keep Lines option

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

• spacial distribution condensed around injection site

7. Tabulate your results $(\tau ,\lambda )$$\left(\ \tau\ ,\ \lambda \ \right)$ from simulations

Experiment	$\tau \left(ms\right)$$\tau \left(\ ms \ \right)$	$\lambda \left(\mu m\right)$$\lambda \left(\ \mu m \ \right)$
1	1.5	1525.25
2	0.3	1545.0
3	6.5 , 10	2871.25
4	2.18	3663.25
5	1.35	685.25

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

• decreasing $C_m$$C_m$ speeds up depolarization phase

• decreasing $g_{\text{leak}}$$g_{\text{leak}}$ :

• makes depolarization last longer

• increases distribution spread

• decreasing diameter :

• decreases distribution spread

Part 2 - Measuring Propagation in Unmyelinated Axon

• Describe how membrane potential varies along a squid giant 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\mu m$$3000\ \mu m$

     • green is at $6000\mu m$$6000\ \mu m$

     • black is at $9000\mu m$$9000\ \mu m$

   • demonstrates decay of membrane potential along axon

   

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

   • red peak = 1.0 , 38.0444

   • black peak = 1.375 , 41.8389

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7. Decrease axon membrane diameter 10 fold to 50 µm

8. Set stimulus amplitude to 700 nA

• note shock artifact

3. Measure the action potential conduction velocity

   • red peak = 0.925 , 38.1178

   • black peak = 3.0 , 40.64

   $$v=\frac{\mathrm{\Delta }x}{\mathrm{\Delta }t}=\frac{8.9mm}{2.075ms}=\frac{4.289m}{s}$$

4. Tabulate your results ( conduction velocity ) from simulations ( 2.1 and 2.2 ). Provide descriptive arrows for changes along with numerical estimates.

• conduction velocity decreased

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

   

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

   $$v=\frac{\mathrm{\Delta }x}{\mathrm{\Delta }t}=\frac{8.9mm}{2.075ms}=\frac{4.289m}{s}$$

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$$d$ , and increase $A$$A$ slightly ,

     • overall reducing $C_m$$C_m$

   $$C_m=\frac{ϵ\ast A}{d}$$

   • where :

     • $ϵ$$\epsilon$ = membrane permittivity

     • $A$$A$ = surface area of the membrane

     • $d$$d$ = thickness of the membrane

   $$\text{Total Capacitance in Series}=C_{\text{total}}=\frac{1}{\sum _{i=1}^n\left(\frac{1}{C_i}\right)}$$
   $$\text{Total Capacitance in Parallel}=C_{\text{total}}=\sum _{i=1}^n\left(C_i\right)$$
   $$\text{Total Resistance in Series}=R_T=\sum _{i=1}^n\left(R_i\right)$$
   $$\text{Total Resistance in Parallel}=R_T=\frac{1}{\sum _{i=1}^n\left(\frac{1}{R_i}\right)}$$

    

   

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

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

3. Measure conduction velocity

   • red peak = 0.6 , 42.8067

   • black peak = 1.15 , 43.2358

   $$v=\frac{\mathrm{\Delta }x}{\mathrm{\Delta }t}=\frac{8.9mm}{0.55ms}=\frac{16.\overline{18}m}{s}$$

    

   

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10. Return membrane capacitance to 1 μF/cm2

11. Set stimulus strength to 700 nA

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

4. Measure conduction velocity

   • red peak = 0.925 , 38.8769

   • black peak = 3.05 , 42.2186

   $$v=\frac{\mathrm{\Delta }x}{\mathrm{\Delta }t}=\frac{8.9mm}{2.125ms}=\frac{4.188m}{s}$$

    

   

5. Tabulate your results ( conduction velocity ) from simulations

   Experiment	Conduction Velocity $\left(m/s\right)$$\left(\ m/s \ \right)$
   1	4.289
   2	16.18
   3	4.188

Part 4 - Measuring Propagation in Myelinated Axon

• Describe how membrane potential varies along a frog 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.

• https://youtu.be/YE4voIZaAgw

• action potential propagates down an axon

• the red electrode is at $1000\mu m$$1000\ \mu m$

• the black electrode is at $9000\mu m$$9000\ \mu m$

2. Determine how many nodes are above $0.0mV$$0.0\ mV$ at any particular time

   • only 1 at a time

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

   • red peak = 0.348925 , 34.2352

     • black peak = 0.773925 , 35.5364

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

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

   • 50 :

     • Myelin Capacitance = $\frac{0.019608\mu F}{c{m}^2}$$\frac{0.019608\ \mu F}{cm^2}$

     • Na Channel Density = $\frac{0.0023529S}{c{m}^2}$$\frac{0.0023529\ S}{cm^2}$

     • K Channel Density = $\frac{0.0023529S}{c{m}^2}$$\frac{0.0023529\ S}{cm^2}$

     • Leakage Conductance = $\frac{5.8824\ast {10}^{-6}S}{c{m}^2}$$\frac{5.8824 * 10^{-6}\ S}{cm^2}$

     

   • 20 :

     • Myelin Capacitance = $\frac{0.047619\mu F}{c{m}^2}$$\frac{0.047619\ \mu F}{cm^2}$

     • Na Channel Density = $\frac{0.0057143S}{c{m}^2}$$\frac{0.0057143\ S}{cm^2}$

     • K Channel Density = $\frac{0.0057143S}{c{m}^2}$$\frac{0.0057143\ S}{cm^2}$

     • Leakage Conductance = $\frac{1.4286\ast {10}^{-5}S}{c{m}^2}$$\frac{1.4286 * 10^{-5}\ S}{cm^2}$

     

   • 10 :

     • Myelin Capacitance = $\frac{0.090909\mu F}{c{m}^2}$$\frac{0.090909\ \mu F}{cm^2}$

     • Na Channel Density = $\frac{0.010909S}{c{m}^2}$$\frac{0.010909\ S}{cm^2}$

     • K Channel Density = $\frac{0.010909S}{c{m}^2}$$\frac{0.010909\ S}{cm^2}$

     • Leakage Conductance = $\frac{2.72723\ast {10}^{-5}S}{c{m}^2}$$\frac{2.72723 * 10^{-5}\ S}{cm^2}$

   

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

   • 50 :

     • red peak = 0.38375 , 31.7135

     • black peak = 1.08125 , 33.7286

     $$v=\frac{\mathrm{\Delta }x}{\mathrm{\Delta }t}=\frac{8000\ast {10}^{-6}m}{0.69750\ast {10}^{-3}s}=\frac{11.46953m}{s}$$

   • 20 :

     • red peak = 0.569187 , 26.701

     • black peak = 1.73199 , 28.3823

     $$v=\frac{\mathrm{\Delta }x}{\mathrm{\Delta }t}=\frac{8000\ast {10}^{-6}m}{1.162803\ast {10}^{-3}s}=\frac{6.87992m}{s}$$

   • 10 :

     • red peak = 0.575 , -60.9735

     • black peak = 2.475 , -64.9624

     $$v=\frac{\mathrm{\Delta }x}{\mathrm{\Delta }t}=\frac{8000\ast {10}^{-6}m}{1.9\ast {10}^{-3}s}=\frac{4.2105m}{s}$$

      

6. Tabulate your results ( conduction velocity ) from simulations

   Experiment	Conduction Velocity $\left(m/s\right)$$\left(\ m/s \ \right)$
   1	18.823529
   2	11.46953
   3	6.87992
   4	4.2105

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9. Return all parameters to default settings.

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

7. Describe what happens

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