UCB Nervous system manipulation patent the patent should be close to our project we are building an RC circuit that illustrate the nervous system THE PATEN

UCB Nervous system manipulation patent the patent should be close to our project we are building an RC circuit that illustrate the nervous system THE PATENT MUST BE NON-EXPIREDread file screenshot carefully to understand the assignmentthank you 1
PASSIVE CONDUCTION ALONG NERVE CELLS – Notes for UMKC Project
Name: __________________________________
Physiology review:
http://phet.colorado.edu/en/simulation/neuron
http://upload.wikimedia.org/wikipedia/commons/d/de/1220_Resting_Membrane_Potential.jpg
Nerve impulses travel in our bodies as electrical signals. Whether it’s seeing or hearing something,
controlling a muscle, or just thinking, the transmission process along a nerve cell, or neuron, is the same:
A sufficient stimulus received by the cell body initiates a change in potential difference, or action
potential, which travels along the axon, to be transferred through a synapse to other neurons or muscle
cells. A single neuron can be a meter or more long, like those connecting our toes to our spinal cord.
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Two Types of Signal Conduction:
Active or Saltatory Conduction
Passive Conduction
We will focus on two principles:
1. The action potential is necessary to boost nerve signals over distances of more than a few mm.
Passive Conduction is inadequate for longer axons.
2. Myelination of axons (wrapping in heavy insulation material) can increase the distance and
speed of nerve signals in many axons.
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Physiology Notes: An axon can be as long as a meter (e.g. toes to spinal cord), so signals must travel
quite some distance and fairly rapidly. As part of the nervous system, myelin lines nerve fibers to
protect and insulate neurons. Myelin aids in the quick and accurate transmission of electrical current
carrying data from one nerve cell to the next. When myelin becomes damaged, the process involves
numerous health conditions, including multiple sclerosis. Dysfunction in the myelin of nerve fibers
causes the interruption of smooth delivery of information. Either nerve impulses can be slowed, such
that we can’t pull our hand away in time to avoid being burned, or mixed up, so we aren’t able to
determine if a pan is hot in the first place. This is akin to a pet chewing on a wire, causing the device to
dysfunction. When problems arise in nerves of the Peripheral Nervous System (PNS), neuropathy might
result, and when injury affects the nerves of the Central Nervous System (CNS), multiple sclerosis is
often diagnosed.
Homework: Read Notes on Passive vs. Active Conduction – see Blackboard
Tying Physiology to Physics of Electricity in the Body: MODELING PASSIVE
CONDUCTION
Two questions to consider:
1. HOW do the electrical properties of a myelinated nerve cell create regions of passive and active
conduction?
2. WHAT FACTORS affect the speed of travel down an axon?
We will do this by modeling passive
conduction in a myelinated axon.
Part 1: Review Capacitors and Capacitance: First, we need to review the principles of capacitors:
Review from valid source and try on https://phet.colorado.edu/en/simulation/capacitor-lab (hook up
plate charges, Electric Field Lines, Capacitance, Stored Energy and Voltmeter and experiment!)
1) What is the main purpose of a capacitor? Store electric potential Energy by storing separate +
and – charges
2) What is the difference between a capacitor and capacitance? Capacitor is a device (i.e.
defibrillator); capacitance: the capacity of a system that enables it to store charge – depends on
physical factors and voltage applied
3) Find two ways to decrease the capacitance of a capacitor: decrease A; increase d
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4) What do you need to do to charge and discharge the capacitor? Remove voltage
Part 2: ACTIVITY – Investigating the Rate of charging and discharging a capacitor:
V
–
+
A
d
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This is the voltage probe.
It is connected in parallel
with the capacitor.
This is the current probe.
It is connected in series
with the circuit.
The resistors go in series
with the circuit as you return
to the power supply
1. Trial 1: High resistance (56 ohms)
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
Make sure all connections are tight.
Open LabPro. Don’t start recording yet.
Set recording time to 100s (Experiment ->Data Collection -> set time to 100s).
Turn on the Power source. Turn the coarse current knob ½ turn. Turn the coarse
voltage up to 5V.
Zero both sensors by pressing the zero button at the top of the screen.
Start recording and then wait 15 – 20 seconds.
Plug the red alligator clip into the power supply – this will start the charging of the
RC circuit.
Once the capacitor fully charges (V-time graph stabilizes at ~5 volts), let it run about
5 seconds. Then, discharge the RC circuit by removing both the red and black
alligator clips from the power supply and touching them together. Hold them
together until the current reading goes to zero.
Take note of the time interval over which the capacitor charged to 5 volts and then
the time interval over which the capacitor discharged to 0 volts – you’ll mark this on
your printed graph.
Stop recording. Save and store results. You’ll record the next run over Trial 1.
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2. Trial 2: Low resistance (22 ohms)
a. Make sure capacitor is discharged! Do this by using an extra wire (from front
table) and touching both leads to the capacitor. If you are unsure of this step ask
for directions so you don’t get shocked.
b. Change resistor to low resistance (22 ohms)
PREDICTION: What do you think will happen to the time needed to charge and discharge?
c. Repeat steps e – j from Trial 1. Be sure to pay attention to any differences from
Trial 1. Save and store results. You’ll record the next run over Trial 2.
3. Trial 3: Make sure capacitor is discharged! Do this by using an extra wire (from front
table) and touching both leads to the capacitor. If you are unsure of this step ask for
directions so you don’t get shocked.
a. Leave low resistor in circuit and change to a capacitor with a smaller capacitance you’ll need to be sure to hook the red lead to the + terminal of the capacitor and
then hook the voltmeter across the terminals of the capacitor. Check this step with
your instructor before you run the trial!
PREDICTION: What do you think will happen to the time needed to charge and discharge?
a. Repeat steps e – j from Trial 1. . Be sure to pay attention to any differences from
Trial 2. Save and store results. .Save and store results. .
b. Title graph “Variables of RC circuit.” Print Graph and label the charging and
discharging for all three trials.
c. Mark and clearly label the time for charging and discharging for all three trials.
d. Which RC Circuit took the largest amount of time? The smallest amount of time?
Instructor Notes:
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Data Analysis:
1. What factors of capacitance and resistance contributed to the smallest amount of time needed
to charge and discharge the capacitor?
2. We can summarize this time by defining the time constant,
resistance and capacitance
?=
RC.
?, equal to the product of the
? is the time required to charge the capacitor, through
the resistor, from an initial charge voltage of zero to ?63.2 percent of the value of an applied
voltage, or to discharge the capacitor through the same resistor to ?36.8 percent of its initial
charge voltage.
3. Name two ways you can decrease the time constant of a RC circuit:
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MODELING PASSIVE CONDUCTION: HOW do the electrical properties of a myelinated nerve cell create
regions of passive and active conduction?
We’ll look at three axon “cable” properties: Raxon, Cmembrane, and Rmembrane:
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1. WHAT FACTORS affect the distance (passive spread) of signal travel down an axon?
??
v ~ ?????????? ????????? ~
v~? ~?
??
?
?? ??????
?? ????????
V~?~?
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The ratio between Rmembrane and Raxon is called the Length Constant (?):
The length constant (?) defines the distance the nerve signal will travel before it passively dies down to
37% of its original value.
The larger the ?, the farther the signal travels before needing to be regenerated = rate limiting to AP
? Summarize Factors that affect speed of travel down an axon:
Instructor Notes: Sum up: PASSIVE SPREAD OF IMPULSE:
Passive spread of the depolarizing current between the nodes is the rate limiting step on an action
potential. The current spread (?) depends on how much current is lost due to the three cable
properties:
To increase velocity down axon: decrease Raxon, decrease Cmem, Increase Rmem, increase ?.
1. If the axon internal resistance (ri) is high – passive current spread is not as far, speed of the
signal travel down the axon decreases
2. If the membrane resistance (rm) is low- current leaks through membrane and so current spread
is slower and the nerve signal travel decreases
a. Myelin increases rm so that less current goes through membrane (more down axon), passive
spread of the current is further and faster
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3. If the membrane capacitance (cm) is high – the longer and more charge it takes to charge the
capacitor and the slower the nerve signal travels
a. Myelin decreases cm (increases d) so that less current is stored in charging the capacitor and
more is available to spread down the axon
Summary Notes: Speed of propagation of nerve signal
***Three axon properties affect the speed of propagation of the nerve signal, the electrical resistance
Raxon within the core of the axon, the capacitance Cmembrane (related to the charge stored) across the
membrane, and the resistance of the membrane Rmembrane. A decrease in either Raxon or Cmembrane will
decrease the time constant (? ) and the capacitor will charge or discharge faster. An increase in Rmembrane
will reduce leakage of charge across the membrane and increase the distance the signal travels down
the axon before attenuating.
Capacitance of the Membrane: The lower the capacitance (or stored charge) of a membrane, the less
time it takes to depolarize it, thus the faster the propagation speed. The myelin sleeve is a good
insulator and this part of the axon has very low capacitance due to increased distance between the
conducting “plates” of the neuron. Because of the low capacitance, the charge stored is very small
compared to an unmyelinated section of a nerve with the same diameter and length resulting in the
conduction speed in myelinated fibers to be much faster than in unmyelinated fibers. [The
unmyelinated squid axons (~1 mm in diameter) have propagation speeds of 20 to 50 m/s, whereas the
myelinated fibers in man (about 10 ?m in diameter or 0.01 mm) have propagation speeds of around 100
m/s. This large conduction speed results mainly from the very small capacitance of the myelinated
axons].
Resistance along the Axon: The smaller the internal resistance of an axon the faster the propagation
speed. Internal resistance in the axon decreases as its diameter increases. For two axons with similar
properties differing only in diameter, the larger diameter axon will have a faster conduction speed than
an axon with a smaller diameter.
Resistance of Membrane: The greater the resistance of the membrane the less charge leaks out of the
axon and the farther the signal travels down the membrane before attenuating. Myelin is a good
insulator and increases the resistance of the membrane.
Velocity of Nerve Signal Travel: In a myelinated axon, the nerve signal travels very fast in the myelinated
portion and much slower in the unmyelinated sections (nodes of Ranvier). Due to passive conduction,
the nerve signal reduces in amplitude in the myelinated segment, but restores to full size in the
unmyelinated section. The difference between passive and active conduction makes the signal “appear”
to jump from one node of Ranvier to the next in saltatory (leaping) conduction.
Physiological Advantage: Signals in large diameter neurons can travel at a high propagation speed due
to the lower internal axon resistance provided by their large diameter. However, signals in small
diameter (unmyelinated) neurons would travel very slowly. The advantage of myelinated nerves in man
is their high propagation velocities in axons of small diameter. A large number of nerve fibers can thus
be packed into a small bundle to provide many signal channels.
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Assessment Questions:
1. What is the typical resting potential of a nerve cell?
2. What is the difference between active and passive conduction?
3. What circuit element should we use to model the inside of the axon (the axoplasm?) Why? Draw
this circuit element in the path of the current and give it an appropriate symbol.
4. Compare the resistance on the inside and outside of the nerve cell. Using factors of electrical
resistance, explain why they are different.
5. What circuit element(s) should we use to model the membrane? Why? Draw this circuit element
in the path of the current and give it an appropriate symbol.
6. The diagrams below illustrate an action potential in either an unmyelinated axon or the signal
transfer at the Noes of Ranvier. Use a resource to mark the areas in the box on the action
potential diagram.
Unmyelinated axon:
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Mark the following areas on the Neuron Action
Potential Diagram below:
•
•
•
•
•
•
•
•
Resting Potential
Initial Stimulus – Na gates open
Na gates open
Depolarization (Positive Feedback)
Na gates close; K gates open
Repolarization (negative feedback)
Hyperpolarization
Na/K pumps back to resting potential
7. What is the main advantage of myelinated nerve cells over unmyelinated nerve cells?
8. Study the pictures below, and answer the following questions regarding what myelination does
to increase the velocity of nerve signal propagation down the axon:
a.
What effect does myelination have on the capacitance of the membrane? Remember c ~
A/d with d representing the distance between the plates? How would this increase the
velocity of nerve signal travel?
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b. What effect does myelination (essentially an insulation of the membrane) have on the
resistance of the membrane? How would this affect velocity of propagation down the
axon?
9. Define ? as it models charging and discharging across the membrane:
10. Compare ? for myelinated vs. unmyelinated axons. Explain your answer.
11. Define ? .
12. How does ? compare for myelinated vs. unmyelinated axons? Explain your answer.
13. Summarize how the cable properties of the axon and membrane predict what happens to
velocity of nerve signal travel down the axon: To increase the velocity of the nerve signal travel
in passive conduction you would: (Explain each answer)
a. Internal resistance in the axon (Raxon):
b. Capacitance of the axon membrane (Cmem):
c. Resistance of the membrane (Rmem):
d. Length constant, ?:
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14. List three human functions possible due to neuronal communication.
15. MS, multiple sclerosis, is a demyelinating disease, which means the axons of neurons are intact,
however the myelin sheaths are damaged. Why would loss or damage to the myelin sheath be a
problem even if the axon was intact? Explain your answer in terms of physics principles discussed
in this activity
Bonus: Research Alzheimer’s Disease site https://www.nia.nih.gov/health/alzheimers-disease-factsheet and video https://youtu.be/0GXv3mHs9AU. How might you design a circuit to model changes
that occur in the brain in Alzheimer’s Disease?
•
What circuit elements in our model of nerve signal travel would you change? Keep the same?
Draw the circuit below.
•
Explain your answer in terms of physics principles discussed in this activity
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Future:
1) Write an inquiry based lab to expand on PH 3210 Alzheimer’s Lab done in S14. Create circuit
that shows MD and Alzheimer’s with a lightbulb. Follow current flow – rate and distance. USE
SNAP CIRCUITS AND AC.
Idea: USE DC Square Wave:
1. Pulse (on/off)
2. Increase frequency of pulse to make it behave more like AC.
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2) Progress to Kirchoff’s Laws and Voltage Change along passive conduction – see Notes
Due to Kirchoff’s Laws ?V decreases with successive RC parallel circuits in nerve signal transfer.
Lab: Use Breadboards and BL Lab or Lili Lab or SNAP CIRCUITS
http://www.andrews.edu/phys/wiki/PhysLab/doku.php?id=142l06sum15
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http://www.andrews.edu/phys/wiki/PhysLab/doku.php?id=142l06sum15
Time Dependence of Signal
Axon membranes have capacitance as well as resistance. If a short-duration pulse of voltage
is applied at one end of the axon, the capacitance of the membrane retards the rapid
propagation of the signal along the axon. The modified axon model which includes this time
delay is similar to the cylindrical membrane described above, but with a membrane capacitor
in parallel with each membrane resistor. The characteristic time for charging or discharging a
membrane capacitor will be d
General Physics New Experiment
Conduction Along Unmyelinated vs. Myelinated Axons
Objectives:
?
?
Examine the viability of using Passive Conduction alone to send nerve signals.
Determine how myelin resistance influences the distance a nerve signal can travel.
Equipment:
?
?
?
?
?
?
?
?
?
circuit board
circuit board lead (1), Banana lead (1)
alligator clips (7)
100 ohm resistor (4)
330 ohm resistor (4)
470 µF capacitor (4)
Pasco Volt sensors (3)
ruler
Computer with Signal Interface, Data Studio and Graphical Analysis software
Physical Principles:
Passive Conduction Along Unmyelinated vs. Myelinated Axons
Nerve impulses travel in our bodies as electrical voltage signals. A stimulus received by the cell body
initiates a change in the potential difference across the membrane. The resulting action
potential travels along the axon to be transferred through a synapse to other neurons or muscle
cells.
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An axon can be as long as a meter (e.g. toes to spinal cord), so signals must travel quite some
distance and fairly rapidly. This lab models so-called Passive Conduction which occurs when a
voltage signal is either (a) below the action potential threshold level necessary to stimulate Action
Potential or (b) where some axons are wrapped in a myelin insulating sheath (between the
uninsulated nodes of Ranvier). This rapid conduction of the signal from one node to the next with a
refreshing of the signal at each node is referred to as saltatory conduction.
This lab is intended to emphasize two principles:
1. The action potential is necessary to boost nerve signals over distances of more than a few mm.
Passive Conduction is inadequate for longer axons.
2. Myelination of axons (wrapping in heavy insulation material) can increase the distance and
speed of nerve signals in many axons.
For a great introduction to the concepts used here explore the highly educational animations at:
http://7e.biopsychology.com/av03.04.html
Procedure:
Note: If you have seven alligator clips rather than eight, you should use the circuit board lead to
connect the positive output side to the first resistor by plugging it into the bread board on the same
row as the free resistor foot.
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Time Independent Model
Our model for the unmyelinated axon will be a relatively high resistivity cylindrical membrane tube
with conducting axoplasm fluid inside and conducting extra-cellular fluid outside. If a DC voltage
stimulus is applied at one end, a passively spreading current propagates down the length of the
axon while also leaking current through the membrane’s passive ion channels into the extracellular
fluid. Both the voltage and current of the passive signal are rapidly reduced along the axon.
The following calculations will give you a feeling for the resistance involved in the axon.
1. Calculate the resistance, Raxon for a 1 mm segment along the length of the axon using $$R=rho
frac{l}{A}$$ (1), Assume $r_{axon}$~5 ?m and ?axoplasm ~ 1 ?*m . Note that the axomplasmic tube
for a length, Laxon = 1 mm and a cross-sectional area given by Aaxon = $pi r_{axon}^2$.
2. The extra-cellular fluid has a similar conductivity as the interior axoplasm. However considering
A in the equation $R = rho frac{l}{A}$, why …
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