UCB Nervous system manipulation patent

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the patent should be close to our project we are building an RC circuit that illustrate the nervous system

THE PATENT MUST BE NON-EXPIRED

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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. 4/18 2 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. 4/18 3 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 4/18 4 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 4/18 5 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. 4/18 6 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: 4/18 7 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: 4/18 8 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: 4/18 9 4/18 10 1. WHAT FACTORS affect the distance (passive spread) of signal travel down an axon? 𝟏 v ~ 𝐑𝐚𝐱𝐨𝐧 ∗𝐂𝐦𝐞𝐦 ~ v~ ~√ 𝟏  𝑹 𝒎𝒆𝒎 𝑹 𝒂𝒙𝒐𝒏 V~~√ 4/18 11 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 4/18 12 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 (τ ) 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 μm 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. 4/18 13 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: 4/18 14 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? 4/18 15 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 τ as it models charging and discharging across the membrane: 10. Compare τ 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, : 4/18 16 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 4/18 17 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. 4/18 18 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 4/18 19 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. 4/18 20 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. 4/18 21 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 μm and ρaxoplasm ~ 1 Ω*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 might we consider the extra-cellular fluid has a zero resistance in the wire model? See Fig. 4. 3. Calculate the membrane resistance, Rmem, through the membrane, assuming the same 1 mm segment: $r_{axon}$~5 μm, membrane thickness = tmem ~ 10 nm, ρmembrane ~ 108 Ω*m. Use the same equation as 1, but with an area equal to the surface area of the cylinder, $A_{mem} = 2 \pi r_{axon} l$, and a resistor length of Lmem = tmem.See Fig. 5 Fig. 4 Fig. 5 4/18 22 For passive conduction, we expect the signal voltage through the axoplasm to drop off with distance from the stimulating source due to the leakage of current through the membrane such that, $$V(x) =V_{0}e^{\frac{-x}{\lambda}}$$(2) where λ is the signal distance over which signal maintains reasonable strength. A plot of V(x) vs. x will appear as a decaying exponential. Over a distance of λ, the voltage will drop to $\frac{1}{e}$ of its initial value. $\frac{1}{e} \approx\frac{1}{3}$ Alternatively, one may plot ln(V(x)) vs. x which yields a straight line. The slope of the straight line is found by taking the natural logarithm of both sides of Eq. (2) to obtain, $ln(V(x)) =\frac{x}{\lambda}+const.$(3) We see that the slope of the straight line is related to λ such that $m =\frac{-1}{\lambda}$ . The signal distance, λ, is large if there is little leakage through the membrane and short if there is more leakage. λ is found to depend on the ratio of the membrane to axon resistance, $$\lambda =1mm*\sqrt{\frac{R_{mem}}{R_{axon}}},$$(4) where the resistances are obtained as above from a 1 mm segment of axon length. Large membrane and small axon resistances will lead to the longest signal lengths. Concept Checkpoint 1: 1. Use the resistances you calculated above for 1 mm of axon length to compute the ratio, $R_{mem}/R_{axon}$, and the signal distance over which voltage signals may propagate assuming passive conduction alone. 2. Compare this signal distance with the distance from your toes to your spine. Do you see the need to boost the signal with active transport or wrap the axon in myelin? 4/18 23 3. Discuss the effect on the characteristic drop-off distance if the radius of the axon were to increase. 4. Discuss the effect on the characteristic drop-off distance if the membrane thickness were to increase. 5. Call over a TA or instructor and explain your conclusion to them. 6. Have your ID card ready to scan to receive credit for your explanation. 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 determined by the RC time constant, $$\tau=R_{mem}*C_{mem}$$ (5) A plot of membrane voltage vs. t for a capacitor charging through a resistor rises asymptotically toward the ultimate voltage as shown. The time constant, τ, is the time for the capacitor to charge to 1-1/eth ~ 0.63 of its final value. Compute the capacitance through the 1 mm segment of membrane using $$C=\kappa\epsilon_0\frac{A}{d}$$ (6) 4/18 24 assuming a dielectric constant for the membrane,$\kappa_{membrane}$ ~ 5, and $\epsilon_0$=8.85×10^(-12) m^2/N*C^2. (Hint: When deciding on A for your capacitance calculation, consider what is acting as the capacitor. Where are charges building up? When looking for d, consider how far the built up charges will be from the “ground”.) Calculate the time constant, $\tau=R_{mem}*C_{mem}$ for 1 mm of axon. The speed at which passive signals will travel down the axon will be determined by the signal distance divided by the time constant, $$v=\frac{\lambda}{\tau}$$ (7) Concept Checkpoint 2: 1. Calculate the approximate speed of nerve impulses using this axon model, assuming passive conduction without myelination. 2. Qualitatively describe a person’s reflex time given the speeds predicted by the passive conduction model with unmyelinated axons. 3. What is the effect on speed if axon resistance in reduced? 4. What is the effect on speed if the membrane capacitance in increased? 5. Call over a TA or instructor and explain your conclusion to them. 6. Have your ID card ready to scan to receive credit for your explanation. 4/18 25 Experiment: Unmyelinated Passive Conduction Examine the nearly completed, pre-assembled electronic circuit analogous to the unmyelinated axon relying on passive conduction. Identify the spine of series resistors representing the internal axon resistances and decode the color bands to determine the values, Raxon. Identify the resistors and capacitors representing the membrane, use the color band to determine the resistances, Rmem, and record the capacitance printed on the side of capacitors, Cmem. Compare the ratio of circuit resistor values, Rmem/Raxon, to the ratio of those computed for a real axon. Identify the strip of blue-colored holes all connected within the bread board as a connecting “bus” representing the extracellular fluid. Your circuit should have 3 repeated units representing sections of axon. Add an additional unit for a total of 4 units representing length segments along the axon, making certain that the polarity of the capacitor has the negative (shorter) lead in the extracellular fluid bus consistent with the capacitors already in place. Ideally, this sequence of segments would continue for a long distance. 1. Measure the end-to-end length of a single resistor segment. Use the resistor values and length of a resistor to predict the signal distance for passive conduction through your electronic circuit,$$\lambda=segmentlength\sqrt{\frac{R_{mem}}{R_{axon}}} $$(cm or m). 2. Use the membrane resistance and capacitance values to predict the characteristic RC time constant for your electronic circuit,$$\tau=R_{mem}*C_{mem}$$ (s). 3. Predict the speed of an impulse down your circuit using, $$v=\frac{\lambda}{\tau} $$(cm/s or m/s). 4. Connect the OUTPUT voltage generator leads to the front edge of your axon network with the positive, red (stimulus) lead connected to the first axon resistor and the ground, black lead connected to the extracellular fluid bus. Connect three voltage sensor probes (A → C) across the progression of membrane resistors with positive, red probes at points corresponding to axoplasm and negative, black probes attached to the extracellular bus.| 4/18 26 | 5. In Data Studio, indicate that voltage sensors are attached to inputs A, B, and C. Set the Sampling rate to 1,000 Hz. Click on the Signal Generator icon and set the generator to produce a 1.0 Volt, 0.5 Hz Ramp-Down wave to start manually when the user clicks On. Set it for the Off position until ready. 6. Drag-and-drop a graph icon onto the Signal Generator. Drop the Graph1 icon repeatedly onto Inputs A, B and C for a total of 4 plots appearing with the same time axis. 7. Click Start to begin collecting data and then shortly thereafter, click the Signal Generator On for at least one complete cycle (one cycle takes 2 seconds at 0.5 Hz), then Off and Stop recording data. 8. A suitably-scaled examination of the graphs should reveal a progression of ramp-down waves that begins tall and sharp for the signal generator voltage while becoming progressively weaker, broader (less distinct) and delayed in time for voltages further down the chain. 9. Use the x-y tool to measure the voltage and time-delay, t – t0, of each peak relative to the stimulus. The distance, x, down the “axon” is determined by the length of a single resistor times the number of axon resistors preceding the point of measurement. Fill in the appropriate table in your e-journal. 10. Use Graphical Analysis to plot ln(V(x)) vs. x and perform a linear fit to determine the signal distance, λ, for your circuit as in Eq. (3). 11. Compare the measured λ with the prediction you made using $$\lambda=segment length\sqrt{\frac{R_{mem}}{R_{axon}}} $$(cm or m). 12. Plot x vs. t-t0 and perform a linear fit to determine the speed of the signal. Compare the measured speed with the prediction, $$v=\frac{\lambda}{\tau} $$(cm/s or m/s). Myelinated Passive Conduction Remove all but the last of the membrane resistors and remove all capacitors from the circuit. You will need to move the ground wire from the PASCO interface to clip onto the final resistor and then stack all black, negative voltage sensor negative sides the back of that clip. Notice that the voltage sensor lead ends have a port on the back side to accept the next lead. Your final circuit should have one back alligator clip attached to the end of the final resistor, three red positive clips from the voltage sensors in the same places on the resistors and the input lead still connected to the first resistor. 4/18 27 How does this model a myelinated segment of axon, terminated by the bare membrane of a node of Ranvier? (Hint:This is a perfect, infinite resistance, myelin simulation. This may seem counter intuitive (our unmyelinated simulation had resistors and capacitors, but the myelinated has no membrane resistors), but by having no connection at all we are creating infinite resistance. This is a “best case scenario” myelin.) Repeat the measurements made for the simulated unmyelinated axon, but note the absence of any time delay. What do you conclude about the speed of a signal down this circuit? This time, plot V(x) vs. x for the myelinated model circuit and perform a linear fit. On the same graph axes, (use the Data menus to add a New Manual Column enter Voltage Data from unmyelinated circuit, click on vertical axis label choosing More to make two plots on same axes) plot V(x) for the unmyelinated model and perform a curve fit to the decaying exponential function, $A e^{(-B*x)}+C$. How does the strength of the signal at the end-of-the-line voltage (V(x) at junction C) for the myelinated model signal compare with the strength of the unmyelinated signal at the same location? To build a circuit modeling the propagation of an action potential down the axon, we would need to have a signal generator repeating the signal at each junction along the axon and triggered by the voltage in the neighboring junction. Concept Checkpoint 3: 1. Discuss with your partner why passive conduction alone is inadequate for long axons in terms of speed, distance and clarity of signal. 2. Explain how myelination aids in the conduction of nerve impulses. 3. Call over a TA or instructor and explain your conclusion to them. 4. Have your ID card ready to scan to receive credit for your explanation. eJOURNAL REPORT 6 Instructions ▪ ▪ ▪ ▪ Download the attached WORD file. Complete the report in WORD being sure to remove prompt text. You may wish to modify borders in the tables. Submit your report by uploading the WORD in our class Learninghub site. If the Learninghub site is down, email the completed report file directly to a lab TA or to physics@andrews.edu. Score: /30 Layout: /2 ▪ ▪ ▪ ▪ Title: Names: (Indicate who the scribe was. Alternate duties for each lab.) Date Time In & Out: 4/18 28 Preliminaries: /4 ▪ ▪ Personalized Statement of Objectives: Methods Used: (Insert a labeled webcam image of apparatus. Describe what and how measurements are made.) ▪ Predictions: 1. Assume following axon values: raxon ~ 5 μm, membrane thickness ~ 10 nm, ρaxoplasm ~ 1 Ωm, ρmembrane ~ 108 Ωm a. Calculate the axoplasm resistance, Raxon, for a 1 mm segment. Raxon = ….Ω b. Calculate the membrane resistance, Rmem for a 1 mm segment. Rmem = ….Ω c. Why is the extra-cellular fluid assumed to have no resistance? 2. a. Calculate the resistance ratio, Rmem/Raxon: b. Calculate the characteristic signal distance: c. How does this compare with distance from toe to spine? Why is the action potential needed? d. How would signal distance change if axon resistance were increased? e. How would signal distance change if membrane thickness were increased? 3. Assuming a dielectric constant for the membrane, κmembrane ~ 5 a. Calculate the time constant for 1 mm of axon. b. Calculate the speed of a signal along the axon. c. How would these speeds affect reflex time? d. How would the speed vary if axon resistance were increased? e. How would the speed vary if membrane capacitance were increased? Checkpoint 2 Data: /8 and Results: /6 Part 1. Unmyelinated Passive Conduction Model Circuit 1. Describe your data collection techniques for measuring signal speed with circuit. 2. Identify the resistors representing axoplasm and determine their resistance. 3. Identify the resistors and capacitors representing membrane resistance and capacitance and determine the amount of resistance and capacitance. 4. Compare the ratio of circuit resistances, Rcircuit mem/Rcircuit axon, with your previously calculated values for an axon. 5. Measure the length of an axoplasm circuit resistor. 6. Compute the signal distance for your circuit from circuit components.$\lambda = resistor length \times \sqrt{R_{circuit mem}/R_{cirucit axon}}$ 7. Compute the RC time constant for your circuit from circuit components, τpred circuit. 8. Predict the speed of impulses through your circuit, vpred circuit. 9. Fill in the Table below, and provide a title: Table 1 Location x (cm) V(x) [Volts] Stimulus 0 1.0 ln(V(x)) t-t0 (s) 0 Junction A 4/18 29 Junction B Junction C Analysis 1. 2. 3. 4. 5. Insert your Graphical Analysis ln(V(x)) vs. with linear fit below: Comment on linearity of graph: What is the significance of your graph? What is the significance of the slope? Compare λmeasured = -1/slope with the predicted signal distance, $$\lambda_{pred circuit} = resistor length \times \sqrt{R_{circuit mem}/R_{circuit axon}}$$ using the percent error.$\%Err = \frac{ | \lambda_{pred} - \lambda_{measured}|}{\lambda_{pred}}\times 100 \%$ 6. Insert your Graphical Analysis x vs. t-t0 below: 7. Comment on linearity of graph: a. What is the significance of your graph? b. What is the significance of the slope? 8. Compare vmeasured = slope with the predicted speed, $v_{pred} = \frac{\lambda_{pred circuit}}{\tau_{pred circuit}}$ using the percent error.$\%Err = \frac{ | \lambda_{pred} \lambda_{measured}|}{\lambda_{pred}}\times 100 \%$ Part 2. Myelinated Conduction Circuit Model 1. Describe your Myelinated Model circuit measurements: 2. Record Voltage and distance in Table 2 below, provide a title for the table: Table 2 Location x (cm) V(x) [Volts] Stimulus 0 1.0 Junction A Junction B Junction C Analysis 1. Insert your Graphical Analysis Voltage vs. distance Graph with linear fit to the myelinated model and include a plot of the unmyelinated measured Voltage vs. distance with a curve fit to a decaying exponential function, A*exp(-B*x)+C. a. (To make two plots on the same axes, in the Data Studio Menu choose Data then New Manual Column, title appropriately, enter values of unmyelinated voltage measurements, double-click on vertical axis title, choose More and check both plots). 2. Comment on closeness of the fits: -What is the significance of your two plots? a. Compare the strength of the linearly decreasing myelinated signal at Junction C with the strength for the exponential decay unmyelinated signal at Junction C. b. Why is Passive Conduction inadequate for long axons? c. How does myelination aid in the conduction of nerve impulses? 4/18 30 d. Why is signal regeneration at the Nodes of Ranvier important? Checkpoint 3 Conclusion: /4 Good points to address are: ▪ ▪ ▪ What is the relation between voltage and distance in passive conduction, unmyelinated axons? What physical properties of the axon affect the speed of a nerve impulse in an axon? What is the relation between voltage and distance in myelinated axons? Abstract: /4 This is a formal statement of what this laboratory experiment was all about. Included in this paragraph should be something about: ▪ ▪ ▪ The Objectives Your Results Your Conclusions Certification: /2 ▪ ▪ Document your completion of this lab with your partner by inserting a webcam photo of yourself, your partner, your apparatus, and your TA. Include a statement that the work done in this lab and submitted in this report is yours and your partners. 142l06sum15.txt · Last modified: 2015/06/09 12:30 by garnett Page Tools ▪ Show pagesource ▪ Old revisions ▪ Backlinks ▪ Back to top Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 3.0 Unported etermined by the RC time constant, $$\tau=R_{mem}*C_{mem}$$ (5) 4/18 31 A plot of membrane voltage vs. t for a capacitor charging through a resistor rises asymptotically toward the ultimate voltage as shown. 4/18 32 http://pierce.wesleyancollege.edu/faculty/brhoades/courses/Bio325manual/lab8.h2.gif The conduction speed of a nerve signal depends on the rate of charging or discharging an R-C circuit. The time t needed to charge or discharge a simple series electrical circuit containing resistance and capacitance has an exponential functional form of exp (-t/RC). The time constant t is the value of t when it equals RC, t = RC. A decrease in either Raxon or C will decrease the time constant and the capacitor will charge or discharge faster. NOTES: Mechanisms for spread of the nerve impulse. A: continuous conduction in an unmyelinated axon. Amplitude scale is in millivolts.B: discontinuous (saltatory) conduction from node to node in a myelinated axon. In the diagrams, the impulses are shown in their spatial extent along the fiber at an instant of time. The extent of the current is governed by the cable properties of the fiber. [From Shepherd (559).] giant axon of squid (1mm dia.) = 13 mm - mammalian nerve fiber (1 micron dia.) = 0.2 mm passive spread of the depolarizing current is the rate limiting step on an action potential if ri is high - current spread is not as far, speed of the action potential is slower - if rm is high - internal current spread is farther, speed is faster - the velocity of the action potential depends on the rate at which the membrane capacitance ahead of the action potential can be charged 4/18 33 - this depends on cm and ri - if cm is high - the longer and more charge it takes to charge the capacitor and the slower the action potential passive spread of the depolarizing current between the nodes is the rate limiting step on an action potential - depends on how much current is lost due the three cable properities 1) if the internal membrane resistance (ri) is high - current spread is not as far, speed of the action potential is slower 2) if the membrane resistance (rm) is low- current is lost and so current spread is slower and the action potential slows down myelin increases rm so that little current is lost, passive spread of the current is further 3) if the membrane capcitance (cm) is high - the longer and more charge it takes to charge the capacitor and the slower the action potential myelin decreases cm so that less current is lost in charging the capacitor and more is available to spread down the axon 4/18 1 Topic 11: Nerve Conduction 11.1 INTRODUCTION The human nervous system contains roughly 100 billion neurons, connected in elaborate networks that transmit information from one location in the body to another. Consisting of the brain and spinal cord, the central nervous system interprets sensory input, initiates muscle contraction, and carries out all other cognitive tasks. The nerves that communicate messages between the central nervous system and the rest of the body compose the peripheral nervous system. Despite the enormous complexity of the nervous system, there are aspects of neuron function that can be understood from simple physical principles. One of those aspects is the propagation of electrical impulses along neurons. Since neurons send information to one another via electrical signals, we can treat them like classical electrical circuits. In this topic we will review basic concepts in neurobiology and then describe the circuit model. 11.2 NEUROBIOLOGY REVIEW Neurons can be divided into three main parts: the soma, or cell body, which contains the nucleus and other organelles, and two types of fiber-like extensions called dendrites and axons. Dendrites receive inputs from other cells and conduct signals towards the cell body. Axons conduct signals away from the cell body towards their tips, where they are then passed on to other neurons or to muscle cells. A neuron may have many dendrites but usually has only one axon, which can be as long as 1 m. The junction between the axon of one neuron and the dendrite or cell body of another is called the synapse. Dendrites and axons increase the distance over which cells can communicate and allow for complex neural networks that enable intelligence. Figure 1. Structure of the neuron. Information travels through a neuron in the form of an electrical impulse, called an action potential. Action potentials are unidirectional, self-propagating changes in ion concentration over the plasma membrane, as shown below in Fig. 2. Copyright © 2004 by Kathryn Thompson, Meredith Stewart, and Juan Rodriguez 2 Fig. 2. A charge disturbance propagates down an axon, causing the electrical potential to change as it passes through a particular site. If an electrode is placed at this site, the potential there changes in time in a manner similar shown in the trace. In order for one neuron to pass the signal on to the next, the action potential must cross the synapse. This can occur in one of two ways. Electrical synapses let the signal pass unchanged—ion currents flow directly between neurons via gap junctions, allowing the action potential to pass from presynaptic to postsynaptic membranes without delay or loss of signal strength. Chemical synapses work much differently, by a process called neurotransmission. When the action potential reaches the synapse, the electrical signal is converted to a chemical signal, which can then be interpreted differently by the various post-synaptic cells, depending on their chemical receptors. Chemical synapses are highly advantageous because they can be more tightly regulated than electrical synapses. An explanation of how neurotransmission works is too complicated for our purposes, but it is worth noting that chemical synapses are either excitatory, meaning that they add to the possibility of an action potential being generated, or inhibitory, meaning that they make the event less probable. The average neuron receives inputs from about 10,000 synapses, which must be integrated with respect to space and time. If the spatial and temporal sum of all the potentials reaches some threshold potential (~65 mV), the neuron fires, sending an electrical signal down its axon. Copyright © 2004 by Kathryn Thompson, Meredith Stewart, and Juan Rodriguez 3 Figure 3. An action potential is generated if the spatial and temporal sum of all excitatory and inhibitory connections reaches the threshold value. All action potentials have roughly the same strength. Thus, the intensity of the stimulus is encoded in the frequency of action potentials rather than in their magnitude. For example, if you burn your mouth on a hot cup of coffee, more action potentials (not stronger ones) are generated so that your brain recognizes the danger. Signal frequency ranges from 1 to 100 action potentials per second. While most neurons share the same basic structure, they vary greatly in length and speed of signal propagation. In the brain where axons are as short as 0.01 mm, signals travel 0.5-2.0 m/s. In the limbs, however, axons can be up to 1.0 m in length and carry signals at 100 m/s. By examining the electrical properties of neurons, we can see what factors determine the speed of propagation. 11.3 ELECTRICAL PROPERTIES OF NEURONS Enclosed in the membrane of any cell is a jellylike substance that contains both inorganic and organic matter. In the cell body, this substance is called cytoplasm, but in the axon it is called axoplasm. For an inactive neuron, the axoplasm has an overall negative charge. This is because proteins, amino acids, phosphates, and other negatively-charged entities inside the cell cannot cross the selectively-permeable cell membrane. Two types of positively-charged ions, potassium (K+) and sodium (Na+), can cross the cell membrane through selective ion channels. Normally there are more potassium ions inside the cell than outside, whereas there are more sodium ions outside the cell than inside. To combat the dissipation of the concentration and electrical gradients of these ions, a chemically driven pump works to move sodium out of the cell and potassium into the cell. Its mechanism is described in Figure 4. Copyright © 2004 by Kathryn Thompson, Meredith Stewart, and Juan Rodriguez 4 Figure 4. Cyclic mechanism of the sodium-potassium pump. Due to these ionic effects, the resting potential of the axoplasm is about –90 mV relative to the extracellular fluid. When a neuron is stimulated, voltage-gated sodium channels open to allow sodium ions to enter the cell. Because the positive charges make the cell less negative, this event is called depolarization. If the potential is depolarized to –65 mV, an action potential is generated that propagates to the end of the axon. Below this so-called threshold potential, the stimulus will propagate only a short distance down the axon before fading away. Most neurons in vertebrate nervous systems have an insulating layer around their axons, called the myelin sheath. The sheath is formed by supporting cells, called Schwann cells, that wrap around the axon, as shown in Figure 4. Figure 4. Structure of a neuron with myelinated axon. Between Schwann cells are small regions of exposed axon called nodes of Ranvier. These nodes contain the voltage-gated ion channels that allow action potentials to propagate down the axon, so that the signal jumps from node to node. This method, called saltatory conduction, allows signals to propagate much faster in myelinated neurons than in those without a myelin sheath. The neuronal membrane and myelin sheath form an insulating layer between the conducting axoplasm and extracellular fluid, as illustrated in Figure 5. Copyright © 2004 by Kathryn Thompson, Meredith Stewart, and Juan Rodriguez 5 Figure 5. Axon as an insulated wire. When the action potential appears in a part of the axon, the voltage change that occurs there causes nearby charges to move toward it or away from it, as depicted in Fig. 6. Fig. 6. Movement of charges inside the axon in response to a stimulus. It is this movement of these charges, i.e. their electrical current, that dictates how fast the action potential travels along the length of the axon. As we shall see in this topic, these currents are limited not only by the electrical resistance they encounter but also by the way they interact with charges across the membrane ( the membrane capacitance). Resistance In the neuron, there are two substances that exhibit electrical resistance: the axoplasm itself and the cell membrane plus myelin sheath, if present. The electrical resistance R along the length of the axon follows the same principles as a wire: R= ρl , π r2 Copyright © 2004 by Kathryn Thompson, Meredith Stewart, and Juan Rodriguez (1) 6 where the resistivity ρ is a constant that depends on the medium and l and r are the length and radius of the wire, respectively. Figure 7. A wire of length l and radius r has resistance R, given by Eq. (1). Intuitively this equation makes sense, because charges encounter less resistance when they travel shorter distances (smaller l) or when there are more pathways through which they can travel (larger cross section πr2). For both myelinated and unmyelinated neurons, the resistivity ρ of the axoplasm is 2.0 Ω·m. If the average neuron has an axon 1 mm long and a 5 µm radius, we can use Eq. (1) to find that the resistance of the axoplasm Raxoplasm = 2.5·107 Ω. This huge value indicates that axons are actually poor electrical conductors. The cell membrane is also permeable to charge; its resistance is not infinite, even when myelinated. Rather than depending on cross-sectional area, the resistance through the membrane depends on the surface area of the axonal membrane: R= ρ 2π rl (2) For an unmyelinated axon (UA), ρUA = 0.20 Ω·m2. So, again for an average axon 1 mm long with radius 5 µm, RUA = 6.4·106 Ω. Myelinated axons (MA) have a much higher resistivity, ρMA = 40.0 Ω·m2, so RMA = 1.3·107 Ω. Capacitance Recall that a capacitor is an electrical device that stores charge. It consists of two conductors side by side, separated by some insulating substance called the dielectric. The ability to store charge comes from the attraction that charges in one plate experience toward the charges in the other. A simple capacitor, like the one below, requires a voltage to be applied across the conducting metal plates first, in order to move the charges from one plate to the other. If both sides were electrically neutral to begin with, then moving positive charges from one plate automatically implies that a net negative charge of identical magnitude is left behind. Copyright © 2004 by Kathryn Thompson, Meredith Stewart, and Juan Rodriguez 7 Figure 8. A plate capacitor. The amount of charge Q that can be drawn from one to the other depends not only on the voltage V apllied across the plates, but also on the separation d between the two plates, and the total surface area A between them: Q = εAV / d The amount of charge stored for every volt applied across it, that is Q/V, is referred to as capacitance. The capacitance of a parallel plate capacitor is therefore C= εA d . (3) In Eq. (3), ε is a constant varies depending on the dielectric material present between the conducting plates. This constant is known as the permittivity. Again, the equation makes sense intuitively because the larger the surface area between the plates the more charge can be stored. Furthermore, the smaller their separation, the greater the attraction between the charges, which also increases the capacity for charge storage. For a lipid bilayer, ε = 5·10-11 F/m (F is the symbol for Farad, the SI unit of capacitance) and d = 50 Ǻ = 5·10-9 m. Thus, the capacitance per unit area for an unmyelinated axon is C ε 5 ⋅10−11 F = = = 10−2 2 . (unmyelinated axon) −9 A d 5 ⋅10 m For myelinated axons, the myelin sheath contains a membrane that wraps around the axon a couple of hundred times. This multilayer arrangement effectively increases the thickness of the lipid bilayer by a factor of 200 (1 µm total thickness), so capacitance per unit area for a myelinated axon is: C ε 5 ⋅ 10 −11 F = 5 ⋅ 10 −5 2 (myelinated axon) = = −6 A d 1 ⋅ 10 m Summary of Electrical Properties The electrical properties of neurons are summarized by the diagram and tables below. Copyright © 2004 by Kathryn Thompson, Meredith Stewart, and Juan Rodriguez 8 Figure 8. The physical model shows wires, two resistors, and a capacitor that approximate the physical flow of charge through real axons. Unmyelinated Axon (UA) Myelinated Axon (MA) axoplasm resistivity ρaxoplasm = 2.0 Ω·m ρaxoplasm = 2.0 Ω·m wall resistivity ρUA = 0.20 Ω·m2 ρMA = 40.0 Ω·m2 wall capacitance/area C/A = 10-2 F/m2 C/A = 5·10-5 F/m2 Table 1. Useful constants. 11.4 INTERPRETATION OF IMPULSE PROPAGATION As explained in the Introduction, neurons are connected so that action potentials travel between them in only one direction. The electrical properties of nerve cells discussed in the last section suggest that impulse propagation can be modeled as an array of resistors and capacitors, as shown below in Fig.9. Figure 9. Physical model of neural connections. The analysis of this electric circuit is complex, requiring the use of differential equations, but we can gain insight by considering how each repeating unit modifies the electrical signal. Copyright © 2004 by Kathryn Thompson, Meredith Stewart, and Juan Rodriguez 9 Propagation Speed For simplicity, we will at first ignore the wall resistance. For one circuit unit (i.e. one neuron), the voltage changes over time according to the equation V (t ) = V0 (1 − e − t / RaxoplasmC ), (4) where Vo is the resting potential. Eq. (4) is graphed below. Figure 10. Voltage V1 of a single neuron as a function of time. By convention, the time required for the exponential term e-t/RC to reach e-1 is defined as the charging time. Thus, for this simple circuit, the charging time is τ = RaxoplasmC. When we add another unit, the problem gets a bit more complicated. According to the model, the first unit charges up before the second unit begins to charge. With every additional unit, there is an additional delay of τ = RaxoplasmC. Figure 11. The circuit with two neurons charges twice as slow as the circuit with one. Since a unit must charge completely before it can discharge to the next unit (like the allor-none action potential), there is a time delay equal to τ in the propagation of the electrical signal between two units. If the length of each unit is x, then the speed of propagation is given by. ν= x x = t RaxonC Copyright © 2004 by Kathryn Thompson, Meredith Stewart, and Juan Rodriguez 10 Substituting the expressions for the resistance of the axoplasm Raxoplasm (=ρax/πr2) and the capacitance/area of the membrane C(=2πrx) into the expression for the velocity we obtain: v= = x ⎛ ρ axon x ⎞ ⎜ ⎟(c 2πrx ) ⎝ πr 2 ⎠ r (5) 2 ρ axon cx The r dependence in the numerator of equation (5) accounts for a fundamental rule of neurobiology: the wider the axon, the faster the axonal speed of propagation. For myelinated neurons, the myelin sheath covers the axon in 1 mm-long sections. Thus, within each myelinated section, one would predict that v = 5 ×10−6 m /(2 × 2.0Ω.m × 5 ×10−5 F / m2 ×1×10−3 m) ≈ 20m / s . For unmyelinated neurons, for which c ~ 10-2 F/m2, the speed of propagation is 200 times slower or 0.1 m/s. Clearly the latter would not be suited for nerve communication over long distances Recall that our calculations do not take into account the resistance of the cell membrane and myelin sheath. Including it leads to leakage of the electrical signal through the wall, called signal attenuation. For a single unit, the effect is profound, as shown below. Figure 12. The voltage is much lower if we consider the wall resistance. Note that the two resistors in Fig. 12 are in series. Such a sequence of resistors acts as a voltage divider, that is, the voltage across Rwall is a fraction of V0 given by Rwall/(Raxon+Rwall). You can infer from this that the signal decreases by this factor every time it propagates through one of these segments. Therefore, as the signal propagates through several such segments, the voltage decreases geometrically with the number of units traveled, i.e. −x v = vo e λ , Copyright © 2004 by Kathryn Thompson, Meredith Stewart, and Juan Rodriguez (6) 11 where x is the distance traveled down the circuit. The value of λ is 0.05 cm for unmyelinated neurons and 0.7 cm for myelinated neurons. When we graph Eq. (6), we see that myelinated nerve fibers carry nerve impulses farther. 1 Unmyelinated axon Myelinated axon Strength of signal 0.8 0.6 0.4 0.2 0 0 -0.2 0.2 0.4 0.6 0.8 Distance traveled (cm) 1 Figure 13. Signals travel farther through myelinated axons. According to our estimates, nerve impulses cannot travel much more than about 1 cm. But we know that some axons in the body can be up to 1 m long! In order to allow their signals to travel greater distances, neurons amplify their signals chemically. The mechanism, shown in Fig. 14, employs membrane-bound protein channels that act as ion gates. One type of gate allows some of the abundant Na+ ions in the extracellular fluid to briefly diffuse into the cell. This infusion of positive ions amplifies the action potential. Shortly after the Na+ channel closes, another type of membrane channel open. This channel allows some of the abundant K+ ions to diffuse out of the cell, to the point they nullify completely and rapidly the action potential. In this way, the neuron is promptly readied for additional stimuli. Once positive charges diffuse into one area of the membrane, it creates an increased potential that affects neighboring ion gates, as shown in Fig. 14. This triggers a chain reaction, whereby neighboring gates open and allow charge to diffuse in, which activate gates still further down the membrane, and so on. Although the potential returns to normal after the K+ channels open, Fig. 14 clearly indicates that the concentrations of Na+ outside and K+ inside the cell decrease after a neuron is activated one. Although the remaining concentrations are sufficient to amplify additional action potentials, eventually these concentrations must be returned to their original levels. This is why the sodium-potassium pump described in Figure 3 is so critical to maintaining those ionic concentrations for proper neuronal function. Copyright © 2004 by Kathryn Thompson, Meredith Stewart, and Juan Rodriguez 12 Fig. 14. Propagation and amplification of the action potential in an unmyelinated axon. Copyright © 2004 by Kathryn Thompson, Meredith Stewart, and Juan Rodriguez 13 Saltatory conduction As indicated above, action potentials travel rapidly through myelinated portions of axons because the membrane capacitance is much smaller in those regions. This is particularly advantageous when signals must transmit information over long distances. The range of travel is, however, limited to a few millimeters before the signal decays. For unmyelinated axons equipped with membrane ion channels, the signals can propagate indefinitely without loosing strength, but at a remarkably slow speed. To overcome the problem of long-distance communication without loss of signal, nature has developed a clever scheme that combines the advantages of myelinated and unmyelinated axons. The scheme is shown below in Fig. 15. Signals are allowed to propagate freely the length of myelinated portions, measuring roughly 1 mm each, until they reach the gaps (or nodes). There, the exposed part of the axon contains ion channels that boost the strength of the action potential back to its maximal value. Although the speed of propagation is slower there, the relative shortness of these segments (about 2 µm) imposes only a negligeable decay. Thus, as the action potential travels through these long axons, the action potential within appears to jump from node to node as it speeds through myelinated portions and slows at the nodes. This form of conduction is known as saltatory, a word derived from the latin to jump. Fig. 15. Propagation of action potentials through myelinated and unmyelinated regions of a myelinated axon. Copyright © 2004 by Kathryn Thompson, Meredith Stewart, and Juan Rodriguez Do a search on any current (non-expired) patent that pertains to some aspect of your group design project. Provide a copy of the patent along with a 1 page report (12 point font, single-spaced, 1 inch margins) explaining the invention and how it pertains to your design project. In addition, using realistic examples, explain the importance of patents and patent research in Mechanical Engineering fields (cite your sources). Each group member is required to submit their own report on a unique patent.
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Hi, here is the patent research :)..

Copy of Patent
Patent Application Publication

Pub. No.: US 2002/0188164A1

L00S

Pub. Date: Dec. 12, 2002

NERVOUS SYSTEM MANIPULATION BY
ELECTROMAGNETIC FELDS FROM
MONITORS
Inventor: Hendricus G. Loos, Laguna Beach, CA (US)
Correspondence Address: Hendricus G. Loos 3019 Cresta Way
Laguna Beach, CA 92651 (US)
Appl. No.: 09/872,528
Filed: Jun. 1, 2001
Publication Classification:
Int. Cl. .................................................. A61N 2700
U.S. Cl. .................................................................. 600/9

Patent Source:
https://patentimages.storage.googleapis.com/32/6c/4f/d5e625a5551cbc/US2...


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