BIONB/BME/ECE 4910 Neuronal Simulation Assignments 1, Spring 2013
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1 BIONB/BME/ECE 4910 Neuronal Simulation Assignments 1, Spring 2013 Tutorial Assignment Page Due Date Week 1/Assignment 1: Introduction to NIA 1 January 28 The Membrane Tutorial 9 Week 2/Assignment 2: Passive Axon February 4 (through changes in Cm) Week 3/Assignment 3: Unmyelinated Axon 79 February 11 Myelinated Axon 85 Week 4/ Assignment 4: Equilibrium Potentials 17 February 18 Week 5/Assignment 5: Neuromuscular Junction 57 February 25 Week 6/Assignment 6: Postsynaptic Inhibition 63 March 6 Week 7/No assignment Week 8/Assignment 7: Interactions of Synaptic 67 March 27 Potentials Week 9/No Assignment Spring Break Week 10/Assignment 8: Ca Action Potential 51 April 1 Week 11/Assignment 9: Voltage Clamping a Patch 35 April 8 Week 12/No Assignment Week 13/Assignment 10: AP Threshold 29 April 24 Week 14/ No Assignment Week 15/No Assignment 1 Moore, J.W. and A.E. Stuart (2007) Neurons in Action, Vers. 2. Sinauer Associates, Inc. Sunderland, MA
2 Assignment 1 Simulation: Introduction to Neurons in Action (NIA) and The Membrane Tutorial Due: 28-Jan-2013 These simulations are designed to make you familiar with the functions of NIA so you can use the program for future exercises. You are encouraged to explore the options of each simulation. Go beyond what is mentioned in the accompanying book and worksheet and try asking some questions of your own. This program is well designed, easy to use, and will greatly enhance your understanding of neurophysiology. This question sheet should be used as a framework to complete the simulations. Do not limit your exploration and curiosity to these questions. Each simulation section is bold and underlined. The bold headings in each simulation are the subsections where you can find those questions. Use the page number to get the context of each question. Please read each section thoroughly before starting the simulations and answering the questions. Capture and reproduce screen shots to illustrate particular simulations that address the questions you are answering. Introduction to NIA Questions (pp 1-7) Familiarity with NIA. To become familiar with the overall layout of the NIA panels and graphing windows Stimulating and recording. To understand how to stimulate your preparation and record the results Experimenting. To become adept at performing an experiment in NIA by changing parameters Observing the action potential. To reproduce the first key observations of the action potential: its dependence on Na and K ions Do experiments: Change the extracellular Na concentration, [Na]o, and then the intracellular Na concentration, [Na]i. 1. In the Hodgkin and Katz paper, how did the amplitude (their Figures 4 and 8) and rate of rise (their Figure 10) of the action potential depend on the Na concentration? (p. 6) 2. By how much can you reduce the [Na]o and still get an action potential? (p. 6) 3. How should the plots change if the [Na]i is doubled? (p. 7) 4. What happens if you set the [Na]i to the same value as the [Na]o? Do you get the same result as when you set the [Na]o to the same value as the [Na]i? (p. 7)
3 5. Describe what happens to the action potential when you increase the [K]o in several steps. (p. 7) Experiment with the concentration of [K]o. 6. What happens if you increase [K]o to 2000 mm? (p. 7) 7. From both of these experiments, what part of the action potential do you conclude depends on the [K]? (p. 7) The Membrane Tutorial Questions (pp 9-15) To understand, through experimentation, how a current pulse changes the voltage across a membrane: o when it is only a plain lipid bilayer o when it has only a Na/K pump that establishes a resting potential o when it has, in addition to the pump, a voltage-insensitive, non-selective "leakage" conductance o when it has, in addition to the pump and leakage channels, the voltagesensitive Na and K channels described by Hodgkin and Huxley To understand capacitance and capacitive currents and why they are important for understanding neuronal signaling Experiment with charging a lipid bilayer with a current pulse. 1. Calculate the expected rate of change of membrane voltage from the equation for capacitive current. (p. 11) 2. Is the slope of the voltage change directly proportional to the current amplitude? Should it be? (p. 11) 3. How is the slope of the voltage change related to the capacitance? (p. 12) 4. In your own words, describe capacitive currents. (p. 12) Establish a resting potential by adding the Na/K pump. 5. Does the value of the resting potential affect the slope of the voltage ramp in response to a current pulse? (p. 12) Add "leak" channels. 6. Measure the amplitude and time constant of the voltage change. (p. 13) Add Hodgkin-Huxley (HH) voltage-sensitive channels.
4 7. Why is the capacitive current so large? (p. 14) 8. Do you know at what point in the action potential the capacitive current is at its peak? (p. 14) 9. At what point in the action potential does the capacitive current cross zero? (p. 14) 10. During the falling phase of the action potential, why is the capacitive current more prolonged but smaller than during the rising phase? (p. 14) 11. Will spikes continue to be generated at this rate indefinitely? (p. 14)
5 Assignment 2 Simulation: The Passive Axon Due: 4-Feb-2013 The Passive Axon Questions (pp 73-77) To observe the passive spread of a voltage change along an axon in response to injected current To measure the "length constant" of the axon To experiment with how membrane resistance and axon diameter affect the passive spread of a voltage To investigate whether a change in membrane capacitance affects passive spread To observe passive spread when the electrode is located at different positions along this "closed-ends" axon Measure the length constant (L) of the axon. 1. In your own words, what is the length constant and how is it important to neurons? (p. 75) 2. What is the length constant you measured for this axon? (p. 76) How does the length constant change with membrane resistance? 3. How quickly does the current decline when you multiply the leakage conductance by 4? (p. 76) 4. How does the value of length constant compare to your original measurement? (p. 76) How does the length constant change with axon diameter? 5. What are the new values of the initial voltage, the voltage at 1/e of the initial voltage, and the length constant? (p. 77) 6. How does this value of length constant compare with your original measurement? (p. 77) How does the length constant change with membrane capacitance? 7. Change the membrane capacitance and determine if and how much the length constant changes. (p. 77)
6 Assignment 3 Simulation: The Unmyelinated Axon and the Myelinated Axon Due: 11-Feb-2013 The Unmyelinated Axon (pp 79-83) To understand the mechanisms that underlie propagation of the action potential along the axon To relate the shape of the action potential as a function of time to its shape as a function of space To observe the effects of changing diameter and temperature on the shape and velocity of the propagating action potential Record the action potential as a function of time at various locations along the axon. 1. The axon is stimulated at its left end and the action potential is recorded at the center of the axon. Would you see a similar recording if you stimulated the axon at its right end? (p. 80) Observe the effect of changing the axon diameter on impulse propagation. 2. By how much must you reduce the diameter of the axon so that you can see more of its waveform in the movie? (p. 82) 3. When you reduce the diameter, why can you see more of its waveform? (p. 82) 4. As the axon diameter is decreased, less current is necessary to stimulate it. Why is this? (p What happens to the delay of the action potential with respect to the stimulus? (p. 82) 6. Is the shape of the action potential affected when the axon's diameter is changed over two log units? (p. 82) Observe the effect of changes in temperature on the propagation of the impulse. 7. How is the action potential affected when you warm the axon by 5 degrees? (p. 82) 8. As you increase the temperature, do you find a point where the action potential fails? Exactly how does it fail, and why? (p. 82) Measure the velocity of propagation of the impulse.
7 9. Using the difference in the time of zero-crossing for the impulse at each of these recording sites, and the 8000 µm length between them, calculate the impulse conduction velocity (velocity = length/time). (p. 83) 10. Keep your plot of velocity versus diameter for comparison with a similar plot you will make in the next tutorial for the myelinated nerve. There is a critical diameter below which myelination confers no advantage. The Myelinated Axon Questions (pp 85-88) To observe that the impulse does not "jump" from node to node but spreads out, covering many nodes at once To measure the velocity of impulse propagation in myelinated nerve and compare it to unmyelinated nerve To change the degree of myelination and the temperature two clinically important factors and observe the effect on conduction velocity Observe the shape of the impulse in a myelinated axon. 1. Is there any marked difference in shape, timing, or amplitude between the currents flowing into the node and the currents you observed underlying the action potential in the Unmyelinated Axon tutorial? (p. 86) Observe impulse propagation in a myelinated axon. 2. The impulse will propagate along the axon from the stimulating electrode, at the left end, to the right. Are you surprised by its peculiar ratchet-like appearance? Are they real or an artifact of doing experiments with a simulator? (p. 86) Measure conduction velocity and determine how the degree of myelination affects velocity. 3. As you did in the Unmyelinated Axon tutorial, use the crosshairs to measure the time at which each action potential reaches some reference point; it is best to choose the time at which the rising phase crosses zero. The recording electrodes are 8000 µm apart. Using this information, calculate the velocity. (p. 87) 4. What is the relation between number of myelin wraps and the axon's capacitance and conductance? (p. 87) 5. Measure and plot (manually) the velocity versus the number of wraps. Does increasing the number of wraps above 150 offer a proportional increase in the velocity of propagation? (p. 87)
8 What is the effect of temperature on the propagation velocity? 6. Do the small, myelinated axons of frogs conduct at roughly the same velocity as the unmyelinated huge axons of squids? (p. 87) 7. By how much is the impulse in myelinated axon slowed when it is cooled from the default temperature of 22 C to 6.3 C? (p. 88) 8. Plot the velocity as a function of temperature by cooling and warming the myelinated axon by increments or decrements of 5 or 10 C. (p. 88)
9 Assignment 4 Simulation: Equilibrium Potentials Due: 18-Feb-2013 Equilibrium Potentials (pp 17-21) To understand equilibrium potentials by calculating them using the Nernst equation and experimenting with ion concentrations To understand how the resting potential depends on the relative permeabilities (conductances) of Na and K To understand how signals can be generated by changing the ratio of the conductances to Na (gna) and K (gk). Experiment with a glial cell, which is solely permeable to K ions. 1. The K channel density (gk) is set to one. Should this matter to our calculation of EK? (p. 19) 2. Plot E K versus [K] o. (p. 19) 3. What value of [K] o will cause E K to be exactly zero and why? (p. 19) 4. If the [K] values were reversed such that [K] o = 124 and [K] i = 5 mm, what would be the value of E K? (p. 19) 5. For the same values of [K] o and [K] i, will E K be different in a mammal than in these simulations? (p. 19) What would happen to Vm if the membrane were to become permeable only to Na ions? 6. Make a plot of E Na versus log [Na] o. (p. 19) What determines the "resting potential" and how does it depend on ion concentrations? 7. A typical neuron is permeable to both K and Na ions, although far less so to Na than to K. What then determines the value of V m at which the neuron "rests," V rest? (p. 20) 8. Measure V m using the crosshairs option from the submenu. Why is V m resting at this value? (p. 20)
10 9. If you could measure the Na and K currents flowing across the membrane at a gk:gna ratio of 50:1, what would you observe? (p. 20) 10. Divide the default value of [Na] o (140 mm) by two, then four or more, and rerun the simulation. Why is the resting potential so insensitive to the Na concentration? (p. 20)
11 Assignment 5 Simulation: The Neuromuscular Junction Due: 25-Feb-2013 The Neuromuscular Junction (pp ) To observe the relationships between the ACh-gated conductance, the resulting current (the EPC), and the voltage change in the muscle fiber (the EPP) To experiment with the reversal potential of the ACh-gated EPC and EPP To discover the effect on the EPP of adding voltage-gated channels to the muscle fiber Observe the relation between synaptic strength (conductance) and EPP amplitude. 1. Why does the time course of the synaptic currents have considerably shorter durations and different shapes than those of the conductance changes? (p. 59) 2. What shapes the time course of the EPP? (p. 59) 3. As the conductance increases, the EPP approaches an asymptotic value. What is the significance of this value? (p. 59) Determine the reversal potential of the ACh-gated EPP. 4. What is the value of the reversal potential? (p. 60) 5. What determines the amplitude of each current? (p. 60) How do voltage-sensitive channels affect the shape of an EPP or an EPSP? 6. Can you explain the shape of your subthreshold EPP in this active membrane?
12 Assignment 6 Simulation: Postsynaptic Inhibition Due 6-March-2013 Postsynaptic Inhibition (pp 63-66) To understand how an IPSP "clamps" the membrane voltage To understand disinhibition To probe what happens to membrane excitability following an IPSP Although there are few questions in this simulation, please elaborate as much as you can about each question. Change some of the parameters on your own and report these results. Excite a cell by disinhibiting it. 1. Do you agree with the authors' observations and explanations in this experiment? Why or why not? (p 65) 2. What is different about the action potential (threshold, amplitude) in these two cases and why? (p 66) Are there changes in excitability following an IPSP? 3. Can you explain these rather complex results?
13 Assignment 7 Simulation: Interactions of Synaptic Potentials Due: 27-March-2013 Interactions of Synaptic Potentials (pp 67-71) To observe how EPSPs sum in a passive membrane To experiment with summation of EPSPs in an active soma membrane (membrane containing voltage-gated Na and K channels) To discover how both EPSPs and IPSPs can affect subsequent membrane excitability To realize that EPSPs can be inhibitory and IPSPs can be excitatory, contrary to accepted nomenclature Although there are few questions in this simulation, please elaborate as much as you can about each question. Change some of the parameters on your own and report your Summation of EPSPs in a passive postsynaptic membrane 1. How do two EPSPs, caused by two sequential action potentials in the presynaptic neuron, interact when the postsynaptic membrane is passive? (p. 68) 2. Is summation linear? Describe why or why not. (p. 68) 3. In your own words, will summation always be linear for any conductance change? (p. 69) Summation of EPSPs in a postsynaptic membrane with voltage-gated Na and K channels: Time is of the essence! 4. Why does this EPSP not generate an action potential? (p. 69) 5. Over what period of time does the first EPSP affect the ability of the second EPSP to generate an impulse? (p. 69) Combining two subthreshold EPSPs 6. Explain the changes in the amplitude of the action potential and the conductances that you observe. (p. 70) 7. What do you predict will happen when you increase the time of onset of the second EPSP further, until at least 17 ms? Explain your results. (p. 70) What are the effects of an IPSP on membrane excitability?
14 8. Can you explain your observation when you deliver your IPSP and EPSP? (p. 70) 9. If the reversal potential is at the resting potential of 65 mv, for example, what is the consequence for the EPSP? (p. 70)
15 Assignment 8 Simulation: Ca Action Potential Due 1-April-2013 Ca Action Potentials (pp 51-55) To generate a Ca-dependent action potential and observe its special characteristics, particularly how it differs from a Na-dependent action potential To generate a hybrid action potential and observe the contributions of the voltagegated Na and Ca channels to its various phases To mimic the basic features of the cardiac action potential Compare Na-dependent and Ca-dependent action potentials and their underlying currents. 1. If you keep the same stimulus parameters as those that elicited the Na action potential, you will observe that the voltage response is subthreshold. What is a possible explanation for this failure? (p. 53) 2. Increase the current amplitude in steps of 0.1 na until you see changes in the falling phase of the Ca action potential. What is happening? (p. 53) 3. What are the main differences between the Na and Ca action potentials and their currents? (p. 53) 4. Compare the Ca action potential generated by increasing the duration of the stimulus with that generated by increasing its amplitude. (p. 53) Experiment with hybrid action potentials in which both Na and Ca carry the inward current. 5. Why does the Na current (INa) (red trace) have two phases? (p. 54) 6. The dip in the INa occurs at t = 1.4 ms. What is the action potential doing at this moment? (p. 54) 7. Why is the Ca current (ICa) (brown trace) so delayed? (p. 54) 8. Why does the ICa turn off faster than the INa even though Ca channels do not inactivate and Na channels do? (p. 54) 9. Are you changing the percentage of channels that are open in the population, the density of open channels, or both? (p. 54)
16 10. As you increase gca, what happens to the plateau of the action potential and why? (p. 54) 11. Are you affecting the rising phase of the action potential? Why or why not? (p. 54) 12. What is the most obvious change in the action potential as you increase gna? (p. 54) 13. Does increasing gna affect the repolarization of the action potential, and, if not, why? (p. 54) 14. The membrane now depolarizes very quickly into the range in which the Ca channels open ( 30 mv and above). Does this mean that the ICa now contributes to depolarizing the patch? (p. 55) 15. The time course of repolarization of the membrane now seems to vary with gna. Why is this? (p. 55)
17 Assignment 9 Simulation: Voltage Clamping a Patch Due: 8-April-2013 Voltage Clamping a Patch (pp 35-41) To plot currents in response to individual depolarizing voltage steps and to plot families of voltage steps. To plot the conductance increases (due to the opening, closing, and inactivation of the channels) in response to these voltage steps To experiment with "tail currents" (which give information on the time course of the closing of the channels when the voltage is returned to rest) To use the voltage clamp to demonstrate that a portion of the Na channels are inactivated at rest. To experiment with the effect of temperature on the kinetics of the conductance changes Observe the Na and K currents in response to a step depolarization. 1. How big is the Na current here? (p. 36) 2. What accounts for the difference in the magnitude of the Na current in these two situations? (p. 37) 3. Plot the peak INa (y-axis) as a function of Vm (x-axis). Compare your plot with the classic figure from the work of Cole and Moore (1960). (p. 37) Observe families of currents. 4. Where is threshold? (p. 38) 5. Why do the maximum currents continue to grow with level of depolarization? (p. 38) 6. Why do the inward currents grow larger with depolarization, then smaller? (p. 38) 7. What is special about the voltage at which the Na current is zero? (p. 38) 8. Why are the currents outward at large depolarizations? (p. 38) Observe "tail" currents. (Tail currents carry a lot of useful information. Please make sure you understand this concept!)
18 9. What causes the Na tail current to jump to a value that is larger than the value just before the end of the pulse? (p. 39) 10. Can the amplitudes of the jumps in Na tail currents be used to measure the time course of gna during the step? (p. 39) Demonstrate inactivation of the Na conductance. 11. Should the current patterns during the pulse mirror the conductance patterns for each ion? (p. 40) Observe the effect of temperature on the Na and K conductance kinetics. 12. Observe how the change in temperature affects the kinetics of the conductances and therefore the currents. What is the rate of change of the kinetics? (p. 40)
19 Week 10 Simulation: Threshold: To Fire or Not to Fire Due 24-April-2013 Threshold: To Fire or Not to Fire (pp 29-34) To investigate whether threshold is a fixed voltage in neurons To understand how threshold depends on the duration of the stimulus and the importance of this relation for synaptic transmission To explore the determinants of firing frequency in a train of action potentials generated by a sensory receptor potential Is there a critical current or voltage threshold? 1. Is there a critical stimulus current separating "all" from "none"? (p. 31) 2. Is there a critical voltage threshold? (p. 31) Does threshold change with temperature? 3. Plot threshold voltage as a function of T o and describe the changes in threshold at different temperatures. (p. 31) Treating myasthenia gravis 4. Why does the subthreshold voltage stay depolarized for such a long time before it finally returns to rest? (p. 32) 5. Will a few neurotransmitter quanta more or less make a difference in whether a synaptic potential near threshold causes a neuron to fire? (p. 33) 6. By how much must you now decrease the amplitude of the current pulse to bring a pulse of this duration to a subthreshold value? (p. 33) Longer synaptic potentials 7. What relationship between duration and stimulus amplitude do you find in this time range? Is it different from that for brief pulses? (p. 33) 8. Why is the shape of the subthreshold stimulus the same for the 10 ms and the 20 ms pulse? (p. 33) Mechanosensory receptor potentials
20 9. Why do you observe damped oscillations and then a train of impulses as the amplitude is increased? (p. 34) 10. Does the rate of firing encode the amplitude of the stimulus? (p. 34) How is the peak amplitude of the action potential affected by nearness to threshold? 11. What happens to the peak of the action potential? (p. 34)
The action potential travels down both branches because each branch is a typical axon with voltage dependent Na + and K+ channels.
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