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Virtual Lab Student Experiment User`s Manual

1. 7 5 8 0 3 4 5 6 7 8 Threshold Intensity u amp cm Thresholds at Different Time Periods Following Excitation The existence of a refractory period is a special feature of an excitable membrane A nerve membrane must recover from the previous impulse before it can fire again Overview Task Overview Task 25 D Temperature Dependence All biological processes are sensitive to temperature and the nerve action po tential is no exception Raising the temperature increases the velocity of mol ecules and most often this speeds things up In this experiment we will vary the temperature from 0 to 40 C and observe the effect on action potential param eters such as peak height and duration Since the action potential is a complex process you should be prepared for some surprises Load Propagated AP 1E Elementary and set up the display The easiest way to study temperature dependence of the action potential is to use the multiple run option Click the Multiple button and choose Temperature as the parameter to be varied To avoid cluttered graphs run one series from 0 to 20 C and a second series from 20 to 40 C Use the Arithmetic Series Type and choose the proper number of runs to give curves gt apart Print the two graphs and label each curve with its corresponding temperature At what temperature did the squid axon stop functioning Are you surprised What is the approximate temperature range of a squid
2. Capacitance refers to the ability of the membrane to store charge without build ing up a large voltage If the capacitance is large one must move more charge across the membrane to get the same membrane voltage change Use this con cept to try to explain your results Resting Membrane Potential Vary the external potassium concentration K o from 0 1 to 5 X normal to do this choose Environment from the Set Parameters pop up menu and measure the resting membrane potential for each value use the Zoom and Cursor fea tures to get accurate values Record the data in the table Membrane Potential External K Resting Membrane Potential mV K o x normal Resting Membrane Potential mV 2 3 4 5 o x normal How many millivolts does the membrane potential change for a 1 0x change in K o o Although the membrane potential is sensitive to K the magni tude of the change is somewhat smaller than the 58 mV per decade predicted for a membrane permeable only to K ions this is the value given by the Nernst equation for 1 8 5 C The reason for the smaller change is that this membrane is fairly permeable to Na and to other ions lumped together as a leak These ions also contribute to the potential lowering the magnitude of the change Experiment 2 Reconstructing the Axon The Passive Axon Now repeat the same experiment using external Na instead of internal and compare the resul
3. The number of open channels Now turn on gK gK plots the potassium conductance which is proportional to the number of channels that are open at any time Verify this by running the graph cursor across the plot and notice the correspondence channels open as gK rises and they close as gK falls Turn on E Both E and gK are plotted on the same axis so that the scale changes gK appears smaller in order to accom modate the larger magnitude of E You can restore the size of gK by holding down the shift key and clicking on the gK button Try it gK is now scaled on the right hand axis and is restored to its original size Again hold down the shift key and click on gK Scaling returns to the right hand axis This will work for any variable to change its scaling from one axis to the other simply hold down the shift key and click on the variable s button Turn off gK and E and turn on gNa gNa plots the sodium conductance which is proportional to the number of Na channels that are open at any time Run the graph cursor across the plot and verify the correspondence between open Na channels and gna Now turn on both E and gK This plot is a useful summary relating the opening and closing of the ion channels to the action potential at each moment of time Print your results Probability of finding an open gate Details of the Na channel states can be also be plotted Turn off gk and turn pNaf pNaf plots the fraction probability of fast g
4. s natural environment E Conduction Velocity To determine the conduction velocity of a nerve it is necessary to measure the times at which an action potential arrives at 2 electrodes at different locations on the nerve Mammalian nerves have conduction velocities in the range of 1 to 100 meters sec Compare these numbers with those you obtain from this large invertebrate nerve Load the Propagated AP 2E Elementary and set up the display This simulation will allow you to view the action potential from 2 electrodes one 0 8 cm and the other 2 cm from the point of stimulus Notice that distance along the axon is now plotted on the Y axis The axon is represented by a vertical orange stripe located just to the left of the graph A small icon marked S is placed at the beginning of the axon where distance 0 to represent the point where the stimulus is applied One icon marked R for recording electrode is placed at a distance of 0 8 cm from S another is placed at 2 cm Experiment 1 Experiment 11 26 Properties of Excitation and Conduction Properties of Excitation and Conduction Recorder a a E Da C 1m 3d Print Save Done Fig 1 3 Recorder display To measure the conduction velocity in meters per sec you need the time at which the peak reaches the 0 8 cm electrode and the time at which it reaches the 2 0 cm electrode This distance 2 0 0 8 1 2 cm 012 meters The rele
5. conduct faster In this experiment you will test this conjecture yl Experiment 1 Properties of Excitation and Conduction Ui Task Load the Propagated AP 2E Advanced and set up the display Measure the conduction velocity at different axon radii by filling in the table below and plot the graph You can change the radii by using the Set Parameters menu and selecting membrane from the popup menu Axon radius will be the last entry in the dialog box that follows Alternatively you can choose Multiple runs but to avoid screen clutter do not try more than two runs at a time Temperature Time at 0 8 cm msec Time at 2 0 cm msec Velocity meters sec Velocity meters sec 20 15 Velocity m sec Radius micra A high conduction velocity is important for quick response it has a high sur 28 Experiment 1 Properties of Excitation and Conduction vival value How does the squid nerve compare with mammalian nerves 29 YL Experiment 1 Properties of Excitation and Conduction UT Overview Task 30 G Multi Electrode Recordings Wavelike properties of nerve impulse action potential conduction can be seen when we record from several sites In these experiments we begin by stimulat ing at one end and observing the action potential as it passes different positions along the length of the axon Next we stimulate in the middle of the axon to check for one or two way conduction Finally we a
6. i e the recovery period Experiment 4 Reconstructing the Axon Voltage Gated Sodium Channels Dual Clamps Clamp 2 gNa Peak onset msec x normal z E 6 c xX e o a s Z D o 5 10 15 20 Clamp 2 onset msec Channel Response to Depolarization Depends on the Starting Point You may have noticed in the Gate Animation that at rest when E 66 mV many of the slow gates are closed We have already seen that when we depolarize the membrane more of the slow gates close This raises the question of whether we can force more gates to open by going in the opposite direction i e hyperpolarize by making E more negative than 66 mV To test this set up the following pattern of clamps for a control Clamp1 onset msec 0 5 intensity mV 66 0 duration msec 10 0 Clamp2 onset msec 11 0 intensity mV 20 0 duration msec 10 0 63 Experiment 4 Reconstructing the Axon Voltage Gated Sodium Channels Clamp 1 holds the potential to near its resting value and then Clamp2 tests it with a standard depolarizing clamp Run the simulation with gna on and there should be no surprises it looks like our first record Now we test what happens if the holding potential i e intensity1 is made more negative To prepare for the comparison activate the O button overlay on the Display so that the screen will not be erased when we initiate the second run Set up the clamps for the ex
7. while potentials below this value generate negative currents sending into the axon This is called the reversal potential Since comp IK it is also the equilibrium potential for K Effects of Membrane Polarization Voltage Clamp Maximum Response Half mv IcomppA cm Time msec gK x normal The equilibrium potential for K can also be calculated from the internal and external K concen trations by use of the Nernst Equation i e EK RT F In Ko Ki 58 log Ko Ki IN Yu Experiment 3 Reconstructing the Axon Voltage Gated Potassium Channels Steady State IK Membrane Polarization Maximum IcomppA cm2 90 45 0 45 90 Voltage Clamp mV Response Time Membrane Polarization Response Half Time msec 90 45 0 45 90 Voltage Clamp mV 44 it Vu Experiment 3 Reconstructing the Axon Voltage Gated Potassium Channels K Conductance Membrane Polarization gg x normal 90 45 0 45 90 Voltage Clamp mV 54 SVL Experiment 4 Reconstructing the Axon Voltage Gated Sodium Channels A Membrane Action Potentials Blocking the Overview K Channels In this experiment we look at the Na channels in a membrane in the absence of channels This can be accomplished by inhibiting the channels with tetraethyl ammonium ion or by expressing the Na channel gene in a cell such as the Xenopus egg The Na channel differs from the channe
8. 3 Taken together these curves yield a comprehensive characterization of the ion channels Refractory Properties Further insight into the refractory period can be obtained from experiments which use two clamps To prepare for dual clamps click on the time button on the Current Source and increase the Recording Time to 24 msec and set up the following pattern of clamps by clicking on Eset Clamp1 onset msec 0 5 intensity mV 20 0 duration msec 10 0 Clamp2 onset msec 11 0 intensity mV 20 0 duration msec 10 0 This provides a depolarization to 20 mV with sufficient time for the channels to respond fully to the new membrane potential A rest period of 0 5 msec follows and then depolarization is repeated Run the simulation Turn gna and turn any other variables off the Display It is apparent that the rest period was not sufficient The response to the second stimulus much smaller than the response to the first This is because most of the slow gates have closed in response to the depolarization and 0 5 msec is not long enough for them to reopen The channels are deactivated and are not able to open in response another stimulus Run the Gate Animation to see this How long will it take for the channels to recover Using the Slider to vary Clamp 2 onset run 10 runs ranging from 11 to 20 This shows the gradual recovery of the channels as the slow gates reopen Plot the peak of gna versus Clamp 2 onset
9. Corporation Helvetica Times and Palatino are registered trademarks of Linotype Hell The Bio QUEST Library and Bio QUEST Curriculum Consortium are trademarks of Beloit College Each Bio QUEST module is a trademark of its respective institutions authors All other company and product names are trademarks or registered trademarks of their respective owners Portions of some modules software were created using Extender GrafPak by Invention Software Corporation Some modules software use the Bio QUEST Toolkit licensed from Project Bio QUEST Virtual Laboratory Student Experiment Manual A Collection Candidate Module by Robert Macey Tim Zahnley Table of Contents Introduction Quick Start Guide Experiment 1 Properties of Excitation and Conduction Experiment 2 Reconstructing the Axon The Passsive Axon Experiment 3 Reconstructing the Axon Voltage Gated Potassium Channels Experiment 4 Reconstructing the Axon Voltage Gated Sodium Channels Experiment 5 Explaining the Action Potential Experiment 6 Simulated Feedback Diagnostic Problems Elementary Diagnostic Problems Advanced 12 29 35 46 56 67 70 71 JL Introduction This simulation program is based on the Nobel Prize winning Hodgkin Huxley model for excitation of the squid axon which set a new paradigm in neurophysi ology The program simulates an excised axon from a squid and allows you to perform experiments by applying stim
10. Reminder of Gate animation for K channels Run the Explain gate animation if you have not done it Click on Interpret on the bottom menu and select Explain from the popup list The following is a quick summary Figure 3 1 shows the gate animation with only the channels drawn 44 IIN VL Experiment 3 Reconstructing the Axon Voltage Gated Potassium Channels closed K channels open K channels outside x ocd electrical force inside n l _ Kions inside cell diffusion force concentration gradient Figure 3 1 Gate animation for K channels The thick orange red line represents the axon plasma membrane The high t concentration is shown on the inside of the cell poised to exit There are two arrows associated with the ion the red arrow represents the electrical force acting on each ion tending to move it across the membrane The brown arrow representing the diffusion force or the tendency of the ion to diffuse across the membrane out of the cell down its concentration gradient An arrow pointing upwards denotes a force on the ion pushing it out of the cell A downward arrow pushes into the cell The net force on the ion is the algebraic sum of the two forces red concentration arrow minus brown electric arrow There are two requirements for the net flow of an ion through a membrane 1 There has to be a net force in the direction of flow 2 There has to be an open pathway or channel
11. by poisoning certain types of channels Measurements of ion flow through the membrane can then be used to make inferences about gates opening or closing under your prescribed force membrane voltage The interpretation is much simpler in this model where the membrane does not contain any functional Na channels A Experiment 3 Interpret 47 Reconstructing the Axon Voltage Gated Potassium Channels How the Voltage Clamp Works To familiarize yourself with the voltage clamp go to the Interpret pop up menu and choose Voltage Clamp Run through the series of diagrams which illustrate the voltage clamp applied to a channel It is summarized below At rest the concentration gradient red arrow figure 3 2 causing to diffuse out of the cell is through channels outlined by red vertical bars is nearly balanced by the electrical force membrane voltage brown arrow acting in the opposite direction As a result very little leaks out Forces acting on Kt outside cell Membrane voltage m o inside cell Concentration i g gradient e y 9 Figure 3 2 The membrane at rest Arrows show the forces acting on K ions When the voltage clamp is turned on a small pulse of negative charge is deliv ered to the external membrane surface an equivalent positive charge is also delivered to the internal surface This new charge is just sufficient to jump the membrane potential from 65 mV to say 20 mV See Figure
12. charge mov ement of D A 9 Te E saa J 0 s Figure 3 5 Electrode compensates for K flux by delivering negative charge to outside Thus the compensating current delivered by the external electrode is a precise measure of the leaving the cell The value of the voltage clamp is due to the fact that even with modern technology it is not possible to chemically measure the small amounts of that enter or leave the cell within a fraction of a millisec ond but the charge delivered by the voltage clamp can be measured routinely Running the Voltage Clamp Open Voltage Clamp Only K Gates Notice that the interface is modified In previous experiments you began on the left with a current source that we called the Stimulator You set the parameters intensity and duration for the stimulus current and recorded the resulting action potential with the Voltage Recorder on the right hand side of the screen You measured what happens to the mem brane voltage when you imposed a given pattern in our case a Square wave of current In the voltage clamp we reverse the process We insist on a pre scribed voltage and measure what we have to do to insure that the membrane responds accordingly Instead of tossing in some charge and watching what the membrane does we attempt to control the membrane s behavior I Yu Experiment 3 Reconstructing the Axon Voltage Gated Potassium Channels Display Time Run Multipl
13. option to 25 e print Experiment 1 Properties of Excitation and Conduction 18 C_ Propagated Action Potential Experiment Recorder Run Stim Display Multiple Time Print Save Done TB stim 1 intensity 200 Quit interpret Glossary Set Parameters New Experiment Fig 1 1 Virtual Lab Screen showing the recorder slider and control buttons Make notes of what you see on the printout Notice the initial negative resting potential Observe that the action potential spike shoots past 0 and becomes positive As the nerve recovers notice the negative afterpotential It is more negative than the resting potential Notice that the entire action potential is bounded by 2 lines labeled EK and ena These symbols stand for the equilib rium potentials for and Na ions respectively It was known even before the mechanism of the action potential was understood that these 2 ions were essential for nerve activity We will come back to this point in later experiments Take readings of the voltages at the resting potential peak of the action poten tial and lowest point of the afterpotential There is an easy way to do this e bring the mouse cursor onto the screen it will turn into a cross e bring the cross slightly above the point of interest say the action potential peak e click and hold the mouse switch down then drag a box around the point e when you release the mouse switch the recorder will zoom in to th
14. same as the time required for 50 of the K channels to open The only way for Icomp to change is by changing the number of open channels because the concentrations do not change within the short time of the clamp 51 VL Experiment 3 52 Reconstructing the Axon Voltage Gated Potassium Channels Study the effect of depolarization on channel opening in detail by using the Slider to do 10 runs in the Eset Intensity range from 90 to 90 mV This Slider setup allows the voltage to be clamped at 2 different times during a single run Use only a single clamp for this experiment set the Intensity for the second clamp to 0 Plot Icomp it is equal to IK and gK Use the Cursor and Zoom features to determine the peak Icomp gK and the speed of response the time required to reach 50 of the maximum Icomp Record your data in the table below and then plot it against depolarization voltage clamp voltage Taken together these three curves yield a good characterization of the chan nels They are useful in the understanding of the basis of excitation The first two items where is it IK going and how long does it take it to get there are fundamental questions you would want to ask about any dynamic variable Interpolate the plot of maximum icomp vs depolarization to find the membrane potential where maximum icomp 0 Membrane potentials above this value will generate positive currents sending out of the axon
15. size of plotted variables may change The next version will include an option for user defined scales i Vu Quick Start Guide 3 Zoom Click and drag the mouse to draw a rectangle over any portion of the graph you wish to view in detail When you release the mouse auto scaling is turned off and the axis limits are adjusted so that the portion that was in the rectangle now fills the window 4 Unzoom Click the un zoom Z button on recorder This button simply turns on auto scaling for all axes ENLARGE THE DISPLAY 1 Click the up Arrow button on the recorder The display is enlarged and the arrow button now points downward 2 Undo the display enlargement Click the down Arrow button on the recorder The display is returned to its original size Arrow button now points downward TOGGLE BUTTONS ON RECORDER 1 Click on Glossary on the bottom menu and select Buttons from popup list This glossary defines all the buttons that are used Click Done 2 Try some of the toggle buttons on the recorder In particular L toggles legend P toggles parameter list O toggles overlay G toggles Grid Up Arrow Down Arrow toggles recorder size AUTO COMPARE RUNS WITH DIFFERENT PARAMETERS 1 Click on Multiple on the stimulator A Multiple Runs dialog box appears Set it up as follows 2 Select Intensity1 this corresponds to Stim 1 intensity from the Param eter popup menu 3 Specify 10 runs to be performed i A Quick S
16. through the membrane In Figure 1 open channels are represented by the openings outlined with red vertical bars that extend across the membrane The number of open channels is proportional to the conductance gK which can be plotted Each channel contains a single gate which blocks the channel when it is closed Some of these gates are open and some are closed at any particular membrane potential voltage but as the voltage becomes more positive more gates are found in the open position YL Experiment 3 Reconstructing the Axon Voltage Gated Potassium Channels UT Task Overview 46 Non Linear K Channels are Responsible for the Undershoot Look at the trials you have run for this exercise Note that during a long stimulus E first rises and then falls to a lower level even though the stimulus is maintained This is due to the sluggish voltage activated channels finally opening in response to a depolarization stimulus causing E to rise and become less negative This allows to leave the cell more rapidly leaving uncompen sated negative charge behind Correlate this response with the opening of K channels shown in the animation You may have to use large stimuli for the channels to show up in the animation Once activated the channels are also slow to turn off when the stimulus is removed This is apparent in the graph where E drops slightly below its resting value negative afterpotential
17. will stay in this state as long as the depolarization is maintained The experimenter actually measures the net current icomp Just as in 3A lcomp shows the charge flow required to keep the voltage at the desired value e g 20 mV But now this charge is required to balance the flow of both Na and K Ignoring the very small contribution of other ions teak we write Icomp INa IK In this simulation we follow the usual convention a positive icomp corresponds to positive charge moving out of the cell a negative icomp corresponds to posi tive charge moving into the cell The dip in the curve is negative and it corresponds to Na entering the cell while the later rise is due to leaving You can verify this by poisoning the Na channels First click the O Overlay button on the Display so that you will have a normal control to compare with the poisoned channels Next look for nNa the number of Nat channels by selecting Membrane from the Set Parameters menu and set nNa 0 Run the simulation The dip disap pears Finally to verify the contribution reset nNa to 1 and set nK 0 so i A Experiment 5 Explaining the Action Potential UT Overview Task 74 that all of the channels are poisoned Run the simulation now the late positive current plateau disappears Print the results and label your print You should have a family of 3 curves which clearly identify the contributions of Na and Similar
18. 3 3 below IL VL Experiment 3 Reconstructing the Axon Voltage Gated Potassium Channels External electrode Brief pulse of negative charge reduces membrane potential depolarizes Membrane Figure 3 3 Voltage clamp is turned on This new membrane potential tending to force positive charge into the cell is too small to balance the tendency of to diffuse out of the cell In addition the membrane depolarization opens more channels Figure 3 4 48 I Yu Experiment 3 Reconstructing the Axon Voltage Gated Potassium Channels K channels op n in eean Ne b Cae centrat 3 i e Figure 3 4 K channels open and K flows from cell K diffusing out of the cell would add positive charge to the outside and change the membrane potential However the voltage clamp monitors E and prevents any change by adding one negative charge for each that crosses the membrane to leave the cell see Figure 3 5 1 The negative charge added to_the solution is an ion not a bare electron The identity of the ion depends on the type of electrode and need not concern us We have not shown the intracellular electrode which acts in a similar way by absorbing the excess negative charges lions left behind by K when it moves to the outside 49 m Experiment 3 Reconstructing the Axon Voltage Gated Potassium Channels Task 50 electrode delivers charge negates
19. Axon Voltage Gated Sodium Channels Ui Reminder 56 After the excitation has subsided the axon remains depolarized most fast gates are open but the slow gates are closed Use the Gate Animation described below and drag the graph cursor vertical dashed line back and forth and to help interpret your results Na channels differ from channels when the membrane is stimulated the Na channels open very quickly and remain open only for a very short time You can also see this by plotting gNa the Na conductance which is proportional to the number of open Na channels This is interpreted in terms of two voltage activated gates controlling the Na chan nel Note Many axons have both Na and K channels but in some the Na channels are the only ones that are voltage activated i e have gates that respond to depolarizing the membrane In these cases opening of the fast Nat gates is again responsible for the rise of the action potential closing of the slow Nat gates is sufficient to begin the repolarizing phase and the abundance of continuously open K channels is sufficient to return the potential to an operative resting level Gate Animation for Na Channels Run the Explain gate animation if you have not done it Click on Interpret on the bottom menu and select Explain from the popup list The following is a quick summary closed Na channels closed Na channels fast gates closed fast gates clased slow gates open slow g
20. Ek ROQUES SS t py c 4 i Library VII Virtual Lab Student Experiment User s Manual Robert Macey University of California Berkeley Tim Zahnley University of California Berkeley A BioQUEST Library VII Online module published by the BioOQUEST Curriculum Consortium The BioQUEST Curriculum Consortium 1986 actively supports educators interested in the reform of undergraduate biology and engages in the collaborative development of curricula We encourage the use of simulations databases and tools to construct learning environments where students are able to engage in activities like those of practicing scientists Email bioquest beloit edu Website http bioquest org Editorial Staff Editor John R Jungck Managing Editor Ethel D Stanley Associate Editors Sam Donovan Stephen Everse Marion Fass Margaret Waterman Ethel D Stanley Online Editor Amanda Everse Editorial Assistant Sue Risseeuw Beloit College Beloit College BioQUEST Curriculum Consortium University of Pittsburgh University of Vermont Beloit College Southeast Missouri State University Beloit College BioQUEST Curriculum Consortium Beloit College BioQUEST Curriculum Consortium Beloit College BioQUEST Curriculum Consortium Editorial Board Ken Brown University of Technology Sydney AU Joyce Cadwallader St Mary of the Woods College Eloise Carter Oxford College Angelo Collins Knowles Science Teaching Foundation Terry L Dertin
21. and only slowly returns as the channels resume their resting configuration Cor relate this with the closing of channels in the gate animation This slow return of the channels to their resting state is related to the refractory period seen in the normal axon Use dual stimuli to illustrate this When the two long stimuli are applied close together the peak response of the second stimulus will be lower than the response to the first B Measuring the flow with a voltage clamp The voltage clamp experiment is not set up to stimulate the axon and observe the resulting membrane voltage action potential Instead you will 1 Jump the membrane voltage to a preset level 2 Hold it fixed at that level 3 Record the charge delivered to the membrane surface that is required to keep the membrane voltage from changing This experimental arrangement called a voltage clamp is one of the most valuable techniques in neurophysiology It allows you to change the voltage and hold it at a chosen value not letting it run away as it normally does when you stimulate it This is exactly what is needed to study what happens on depolarization stimulation Depolarization is the force which opens or closes gates You can choose the size of the depolarization and it will stay where you put it while you monitor the flow of ions current through the membrane Infor mation about specific ions can be obtained by removing some of them from solution or
22. ates closed te y 4 ON i 5 open Na channels closed Na channels ast gates open fast gates open slow gates open slow gates closed Figure 7 Membrane gate animation with only Na channels The continuous paths through the membrane represent open channels The more paths the more channels The number of continuous paths is proportional to the conductance gNa which can be plotted For there is either a full path or no path corresponding to one gate open or closed see Exercise 3 For Na it is more complicated there are two gates The slow gates are on the inner bottom side of the membrane When they are open they contribute only half a path The fast gates are represented on the outer top side of the mem brane they also contribute one half path For Na to pass you need a full path both gates must be open VAL Experiment 4 Reconstructing the Axon Voltage Gated Sodium Channels UT Overview Task 57 The Na gates are illustrated further in the following diagrams where it can be seen that any given channel has 4 possible states State Fast Gate Slow Gate State 2 is the only open channel which permits passage of Na all others States 1 3 and 4 are impermeable Follow the gate animation as you drag the graph cursor B Measuring Na flow with a voltage clamp The voltage clamp concept is explained in Experiment 3B and in the Interpret Explain Voltage Clamp This exper
23. ates that are open at any time u A Experiment 5 Explaining the Action Potential UT Recall Interpret 69 Again run the graph cursor across the plot and notice the correspondence fast gates open as pNaf rises and they close as pNaf falls Turn pNaf off and turn on pNas This will plot the fraction probability of slow gates that are open at any time As you run the graph cursor across the plot notice how the slow gates close and open as pNas falls and rises Now turn off E and turn on gna This plot shows how the opening of Na channels gna is determined by the actions of the two gates Actually gna is the proportional to the product pNaf X pNas Print the plot The same exercise can be repeated for px the fraction of gates that are open But since channels only have one gate there is a one to one correspon dence between open channels and open gates pk gives no more infor mation than gk 1 Threshold If a nerve is stimulated with weak electrical shocks nothing seems to happen When the stimulus is repeated many times with each stimulus a little stronger than the last eventually a point will be reached where the nerve responds by transmitting an action potential The strength of stimulus just barely able to excite is called the threshold Stimuli below threshold do not work stimuli above threshold produce action potentials 2 All or None A stimulus above threshold excites but the size of the response i
24. ced and run ning the simulation with close attention to the gate animation Propagated AP 15E This simulation provides a 3d graphic visualization of the all or none wave like nature of impulse propagation by recording from 15 sites along the axon It also shows how subthreshold stimuli decay with distance from site of stimula tion Best seen in 2d but can also be done in 3d with zoom This type of experiment is useful in understanding propagation it gives a measure of how far downstream a local disturbance can reach and is important for understand ing impulse conduction The space constant and its dependence on other pa rameters can be evaluated from this data Propagated AP 1 5E Smid Again recording from 15 sites the axon is stimulated in the middle rather than at one end The simulation provides a nice visual demonstration in 3d that the action potential travels in both directions from the site of stimulation Propagated Action Potential 15E S2ends Now the axon is stimulated at both ends so that the two impulses run into each other They annihilate each other because they run into each other s refractory period This shows the importance of the refractory period in excitable structures particularly the heart where it prevents chaotic impulses from taking control Pharmacology Na Channel Blocker This simulation provides a demonstration of a local anesthetic acting on a seg ment of the axon The simulation shows acti
25. charges across the cell membrane and if you move the charges slowly weak stimulus intensity it should take a longer time to reach threshold long stimulus duration Try the simulation and see what happens Load the Propagated AP 1E Elementary experiment as you did in the first ex periment Set up the Display and move the slider out of the way Set the stimulus duration to different values and determine the threshold intensity for each The strength and duration values may be varied with the slider To get values not accessible from the slider click the Stim button When the dialogue box appears type in the values that you want Record your values in the table below and plot the threshold strength vs the pulse stimulus duration in the graph to obtain a threshold intensity strength vs duration curve This is often simply called a strength duration curve yl Experiment 1 Properties of Excitation and Conduction Ui Overview 22 Strength Duration 200 hreshold Intensity 150 T 3 2 2 J a 50 0 1 2 3 4 5 Threshold Intensity u amp cm Notice that no matter how long you stimulate a minimum value of stimulus intensity is required The minimum strength below which a nerve cannot be stimulated is called the rheobase Mark it on your graph Also mark the dura tion required if the nerve is stimulated at twice the rheobase value This dura tion is called the chronaxie If you did the experim
26. current source electrodes to stop E from drifting and to minimize the error The actual instruction is simply a electrical signal proportional to the difference between E the membrane potential and eset This difference E Eset is defined as the error and the proportionality constant is called the Gain The compensating current sent to the membrane by the current source is then comp Gain E Eset Gain error The Gain is really the sensitivity of the control system with a large Gain a small error will induce a large feedback response The negative sign in front of the gain shows that whenever the error is positive i e E is more positive than Ese the current source compensates by sending negative charge to the mem brane z A Experiment 6 Simulated Feedback atl Task 77 Returning to the result of the first run click on the icomp button to remove it from the plot E and eset should be plotted on the display if they are not click on their buttons The steady state error revealed by deviation of E from Eset 20 mv This is a common property of feedback systems It occurs in natural physiological regulators like the endocrine system as well as in hardware that we have simulated You might expect that the error could be reduced by in creasing the sensitivity of the system Can you reduce this by increasing the Gain Can the error be reduced to zero by making the gain larger and larger Increase the Gain
27. d Models These are exactly the same simulations they differ only in their presentation Elementary models are limited in the number of variables that can be plotted and in the number of parameters that can be changed Elementary models can plot 4 variables a Stimulus b Membrane Potential c Na and K Equilibrium Potentials They can change a The stimulus parameters for two stimuli b The concentrations of Na and K on either side of the membrane c Temperature T Vu Introduction These variables and parameters are intuitive and easily grasped by a beginner Nevertheless elementary models still provide a large array of experimentation In contrast advanced models allow plotting of 13 different variables and changes in at least 22 parameters The number of possible combinations is staggering Propagated AP 1E This simulates the simplest experimental scenario An axon is stimulated at one discrete site initiating a nerve impulse The impulse travels from the site of stimulation and passes another site downstream where it is recorded by an intracellular electrode This is the opening default model Using the elementary version a beginner can study a Threshold stimulus intensity b All or None Response Strength Duration Curves d Refractory Periods e Temperature dependence of the size and shape of the action potential f Dependence of any of the above on Na and K Cj In particular he she can study h
28. downstream from the stimulus All 3 should be full scale action potentials at this point In future runs you will block channels at the 2 0 cm electrode and see if the impulse can still get through to the third electrode Block increasing percentages of the channels at 2 0 cm and find the point where the electrical disturbance is insufficient to pass the action potential on to the 3 2 cm electrode Record your observations in the table below Na Channels Blocked fl Peak Height at 2nd Acti 35 on Potential at Electrode mV 3rd Electrode es or No Experiment 1 Properties of Excitation and Conduction Experiment 1 Properties of Excitation and Conduction 36 Think about your results in terms of the nerve s safety factor the nerve can lose a lot of channels in a small patch and the impulse can still get through Al though the electrical response at the second electrode is diminished it still may be sufficient to excite areas around it which have not been anesthetized How much can you diminish the height of the action potential before it will fail to excite the adjacent region This is sometimes referred to as a safety factor for conduction Now look at your results from another perspective Suppose that the nerve under consideration is a pain fiber and that you are trying to relieve a patient s pain by inhibiting it When you have succeeded in blocking 50 of the chan nels you might assume that
29. e Figure 3 6 Voltage clamp interface t Control usually implies feedback and the voltage clamp is no exception We begin on the right hand side where the Voltage Recorder Amplifier monitors the membrane behavior voltage and sends signals through the wire on top pf the diagram back to the current source These signals instruct the current source on how much electrical charge to feed back to the membrane to insure that the potential does not stray from the desired level which we have prescribed with the Eset button on the amplifier Run the simulation with the default settings The default Eset will begin the clamp at 0 5 msec by jumping the membrane potential from 65 mV to 20 mV and will keep it at this value for 10 msec Drag the Cursor to different positions and use the Gate Animation to see how the gates open in response to a sudden depolarization As you will see they respond slowly taking about ____ msec for 50 opening Note that the channels do not close as long as the voltage clamp is maintained Compare this behavior with that of the Na channels in the next experiment The graph has a plot of Icomp the current the electrode must supply to compensate for ion movements across the membrane Because there are no Na channels in this membrane Icomp is essentially equal to the current across the membrane IK It should not be surprising that the time required for Icomp to reach 50 of its maximum value is the
30. e 7 Multiple Runs Parameter on Y Values Number of runs Initial value Ee Final value Series type Arithmetic O Geometric Keep Runs Separate O Compute Mean Compute Mean SD Fig 1 2 Multiple Run dialog box Select on2 an abbreviation for Stim 2 onset from the Parameter popup menu This specifies that we will set a sequence of times when the second stimulus is to be applied Set the initial run at 3 msec and the final at 9 msec Choose the Arithmetic Series Type This will give 7 runs with the second stimulus delivered at 3 4 5 6 7 8 and 9 msec after the run starts This is indicated in the Values list in the dialog on the right The runs will be superimposed upon a single graph Click on OK and watch the curves as they are plotted For the first few the second stimulus will not elicit an action potential As the period between stimuli increases a second action potential will appear Since this is a threshold stimulus when a second action potential occurs you know the stimulus was beyond the refractory period Print out your graph and on it mark a rough estimate of the refractory period To get it closer you will have to stimulate at shorter intervals Raise the stimulus strength to the highest value available 200 and repeat the experiment Did action potentials occur at intervals where they did not in the first set of runs If a large stimulus elicits an action pote
31. e axon Load Propagated AP 15E Advanced and set up the display Click the Stim button and reduce the stimulus intensity to the subthreshold value of 40 Click the Run button and observe the resulting 3D plot What you see are 15 curves each 0 4 cm from its neighbor This plot does not show much because the scaling is poor To get better scaling click the 3D Toggle This puts the display into a 2D mode superimposing the 15 curves Next click the EK and ena Toggles to turn them off You should see a nice display of the local response at different points as you move away from the stimulating electrode Print a copy of the recording The highest peak occurs in the electrode 0 4 cm from the stimulus the next highest 0 8 cm from the stimulus and so on Although you have 15 curves you will probably find only 6 or 7 of them of sufficient height to take measurements Measure the peak heights of the useful curves use the Zoom and Graph Cursor features enter the data in the table below and plot the graph Peak Height mV Distance from Stimulus cm a ai Peak Height mV 2 4 70 o 0 5 1 0 1 5 2 0 2 5 Distance from Stimulus cm Notice that the subthreshold response curves do not decay directly back to their starting points but undershoot that level This shows that the nerve is responding in an active fashion even in the subthreshold region AVS Experiment 1 Properties of Excitation and Conduction UT Ove
32. e dialogs are accessible in the advanced models i fu Quick Start Guide 16 MULTI ELECTRODE MODELS 1 Click on New Experiment and select Propagated A P 15E Advanced Run it and click on Display This shows the propagated action potential as recorded at 15 equidistant sites along the axon by 15 independent electrodes 2 Click on 3D button on recorder The graph is now redrawn in 3d pre renaissance perspective The Y axis now shows distance cm However there is a voltage calibration on the right of the graph At the left there is a miniature axon running vertically Recording elec trodes icons R are placed in register with the plot that shows the recording at that position The S icon shows the site of stimulation By dividing the time between peaks into the distance between their respective electrodes you can calculate the velocity of the nerve impulse Its easier to do more resolution with Propagated A P 2E try it GET HELP 1 Button and Model Glossaries are described above 2 Click on Interpret from bottom menu and select Explain from the popup Follow the explanation of the Gate Animation The same interactions for any experiment can be accomplished in the following step 3 RUN any model with any parameters that yield a full action potential 4 Click on Interpret from bottom menu and select Gate Animation from the popup Drag the graph cursor dotted vertical line on the left in the graph and note
33. e properties of the normal one Once you 80 LL A Diagnostic Problems Advanced have decided which property has been altered study the effects of changing the magnitude of the alteration until you arrive at a good estimate of how much the property has been perturbed in the experimental axon Summarize the evidence you have gathered which supports your conclusions 3 Give a qualitative account of why your diagnosis makes sense This should take account of how the action of the channel gates leads to the observations you have cited 4 Examine whether your interpretations are unique Are there any other alterations that could have produced the same observations that you have cited 81
34. e region within the box IIN Yu Experiment 1 Properties of Excitation and Conduction 19 e click the I switch this will put a moveable graph cursor a vertical dashed line on the screen e move the mouse with the button held down to center the graph cursor on the point of interest The time in msec and the voltage in mV will appear at the top of the screen e to get out of the zoom mode click the Z toggle switch Record the values for your action potential resting potential mV action potential peak mV occurring at m S e c afterpotential minimum mV occurring at Note that the stimulus starts at 0 25 msec in these experiments Since you produced an action potential the initial stimulus intensity of 200 was obviously above threshold Now lower the magnitude of the stimulus to about 100 by dragging the slider to the left and release the mouse button Each time you release the mouse after moving the slider the stimulator will automatically activate as though you had clicked the Run button In this case a new action potential results 100 is still above threshold Now again move the slider to the left and lower the stimulus to a very low value say 10 No action potential will occur because the stimulus is subthreshold Test different values of stimulus strength by moving the slider until you find the lowest value that will elicit an action potential Now click on the check box labeled Fine in the slider window T
35. ecause it isolates the excitation process from propagation making it easier to interpret There are no up or down stream currents It can be used to study all of the properties discussed in the first model but from a different perspective Further the experimental setup is one step closer to a voltage clamp and makes the passage to voltage clamping seem more natural Passive Axon No Voltage Activated Gates This model simulates the Membrane Action Potential experimental setup ap plied to a primitive inexcitable axon The axon leaks Na K and possibly other ions through inert channels but these channels have no voltage activated gates the channels do not open or close in response to membrane voltage The axon has a normal ion distribution high K on the inside and high Na on the outside It has a nearly normal resting potential because K ions leak out faster than Na ions leak in This simulation shows a The axon is inexcitable b Its response is symmetrical If you change the sign of the stimulus the response also changes sign but has the same size and shape c Its response is linear If you sum stimuli you sum the response d Its response time depends on the membrane capacitance Passive Axon Only K Gates This model simulates an axon that has intact voltage activated potassium K channels but no voltage activated sodium Na channels This is one step toward the construction of a fully functioning axon The axon is still inexc
36. ems Elementary Overview Open Problem 1 and run the experiment You will see two action potential recordings In these simulations there are two axons under your electrodes a normal control and an experimental which has had one of its properties altered Action potentials from the normal axon colored brown are denoted by E and those from the experimental colored purple are denoted by Ep When you run the stimulator you excite both axons with the same stimulus pattern Further if you change the external ion concentrations or the tem perature the same conditions will hold for both axons Each time you run the experiment both action potentials are recorded You will be able to change any of the properties of the control but you will not be able to change prop erties of the experimental Task Your problem is to give a descriptive workup of the difference between these two axons This should include a simple description of the action potentials that you see as well as how they both respond to any of the measurements that you have learned to make Your decision on what to include and how to describe it is part of the problem 79 Vu Diagnostic Problems Advanced Overview Open Problem 1 and run the experiment You will see two action potential recordings In these simulations there are two axons under your electrodes a normal control and an experimental which has had one of its properties altered By properties we mean any of t
37. ent correctly you saw that the weaker stimuli required longer durations to reach threshold So the qualitative answer to the question raised in the introduction is yes if the stimulus is weak you can compensate by using a longer duration However this is only true within a certain range Below the rheobase increasing the stimulus duration has no effect C Refractory Period After a nerve has been fired there is a short period of time during which it is inexcitable This is called the absolute refractory period Following this there is a period of time during which the nerve can be fired but only with a stronger stimulus This period is designated the relative refractory period Refractory periods are determined by giving a second stimulus just after the appearance of the action potential In this simulation we will determine the refractory period of the nerve we studied in the previous 2 simulations A L Experiment 1 Properties of Excitation and Conduction at Task 23 Again load Propagated AP 1E Elementary Set up the display as before We will use 2 different procedures to check the refractory period The first will use the multiple run capability of the program Click on the Stim button and when the dialogue box opens set the durations of both stimuli to 0 25 msec Set both intensities to the threshold value for this duration about 70 Next click on the Multiple button The following dialog will appear At Number of runs typ
38. ential Period 2e gt HOU e H e es e u A Experiment 5 Explaining the Action Potential UT Overview Task 73 Run the corresponding simulations to verify your predictions Print the results and provide the reasoning that forms the basis for your predictions B Voltage Clamp Na and Channels Open Voltage Clamp Ideal This simulates a normal axon under voltage clamp conditions Familiarity with Experiment 3B is assumed Recall that in a voltage clamp experiment you 1 Jump the membrane voltage to a predetermined level 2 Hold it fixed at that level 3 Record the ion flow through the membrane that is required to keep the membrane voltage from moving Run the simulation While the response of the axon in Exercise 3B was governed exclusively by channels the axon in this simulation has operative Nat channels as well as channels Look at the gates in the cartoon as you scroll through the simulation drag the graph cursor At the start t 0 with no clamp turned on there are plenty of slow Na gates open but no fast ones Now move forward in time as the clamp is turned on the membrane depolarizes fast gates open and for some time the slow gates are also still open Na can get through But soon even though the depolarization is maintained the slow gates close and Na can no longer pass At the same time open channels begin to appear The mem brane
39. ents of Na and K The concentration gradient of limits the resting potential K equilibrium potential while the concentration gradient of Na limits the height of the action potential Nat equilibrium potential Just as a stick of dynamite contains its own explosive energy the axon membrane is loaded with explosive energy in the form of ion gradients although this description captures the essence of the excitation process the precise position where excitation occurs is a bit more complicated because we have ignored contributions of the leak current One further qualification is that the process must take place before the late response K channels open Na channels close has time to develop n A Experiment 5 Explaining the Action Potential UT Task 72 For a brief msec or two following excitation the axon is no longer excitable This recovery phase called the refractory period can be divided into two phases The earliest phase is the absolute refractory period where the threshold appears to be infinite and no stimulus will suffice In the later phase the relative refractory period the threshold returns to normal The basis for the refractory period is found in the late effects After the first msec of excitation the slow Nat gates close and remain closed for a brief time despite the fact that E is near rest These gates were slow to respond to the initial depolarization and they are equally slow in respond
40. eriment it can be approached in the laboratory as well If the Na channels of a nerve are poisoned with tetrodotoxin the resulting membrane will be very similar to the one studied here Alternately it is possible to express the channel gene in a cell such as the Xenopus egg and then study the channels with electrodes Testing the Membrane with Voltage Gated Potassium Channels Load the experiment Passive Axon Only K Gates This axon is identical to the membrane studied in experiment 2 except that it has voltage sensitive chan nels Set the Recording Time to 20 msec Run a simulation at stimulus values of 50 4 A cm2 and 10 msec Print the curve and compare it with the ones that you obtained in experiment 2 leaky axon without any voltage activated channels The shapes of the curves are very different because you have activated t channels in this experiment How would you explain your results For help go to the Interpret pop up menu and choose Gate Animation Drag the graph cursor vertical dashed line back and forth and use the screen gate animation described below to help interpret your results This will give you a picture of the plasma membrane penetrated by channels figure 2 As you move the cursor along the graph channels will open and close As you can see the channels do not open instantaneously when the nerve is stimulated How many milliseconds after the stimulus do you see the maximum channel opening
41. erties of Excitation and Conduction UT Overview Task 34 J Na Channel Blockers Many local anesthetics act by binding reversibly to the membrane protein that forms the Na channel and blocking Na from entering the axon The axon becomes inexcitable and cannot propagate an action potential Procaine and lidocaine are examples Other Na channel blockers secreted by marine or ganisms are classified as paralytic poisons but their basic action is similar to local anesthetics Tetrodotoxin derived from the puffer fish and saxitoxin from microscopic dinoflagellates are prime examples of these neurotoxins The source of saxitoxin is particularly interesting because these microorganisms prolifer ate in certain seasons to such an extent that they impart their reddish color to the water giving rise to the red tide At that time shell fish feeding on them become contaminated with the poison and are not edible In this experiment we will apply a Na channel toxin at a single location in the middle of an axon and find out how much inhibition is required to block pas sage of the impulse Load experiment Pharmacology Na Channel Blocker and set up the display Find the slider which allows you to set the percentage of Na channels that are blocked Set to percentage to 0 This will run the experiment and you will see 3 curves Toggle the 3D button and you will see the nature of the experiment The 3 curves are taken 0 8 2 0 and 3 2 cm
42. g Murray State University Roscoe Giles Boston University Louis Gross University of Tennessee Knoxville Yaffa Grossman Beloit College Raquel Holmes Boston University Stacey Kiser Lane Community College Copyright 1993 2006 by Robert Macey Peter Lockhart Massey University NZ Ed Louis The University of Nottingham UK Claudia Neuhauser University of Minnesota Patti Soderberg Conserve School Rama Viswanathan Beloit College Linda Weinland Edison College Anton Weisstein Truman University Richard Wilson Emeritus Rockhurst College William Wimsatt University of Chicago Copyright Trademark and License Acknowledgments Portions of the Bio QUEST Library are copyrighted by Annenberg CPB Apple Computer Inc Beloit College Claris Corporation Microsoft Corporation and the authors of individually titled modules All rights reserved System 6 System 7 System 8 Mac OS 8 Finder and Simple Text are trademarks of Apple Computer Incorporated HyperCard and HyperTalk MultiFinder QuickTime Apple Mac Macintosh Power Macintosh LaserWriter Image Writer and the Apple logo are registered trademarks of Apple Computer Incorporated Claris and HyperCard Player 2 1 are registered trademarks of Claris Corporation Extend is a trademark of Imagine That Incorporated Adobe Acrobat and PageMaker are trademarks of Adobe Systems Incorporated Microsoft Windows MS DOS and Windows NT are either registered trademarks or trademarks of Microsoft
43. g the Action Potential Experiment 5 Explaining the Action Potential 70 i e the concentration gradient of i opposite direction is almost balanced by E pushing in the At rest the membrane is polarized Many slow gates are open but most rapid gates are closed so that most channels are closed When the membrane is stimulated its response to the depolarization can be divided into 3 time phases 1 An early response when the rapid gates open quickly Na channels open Now both gates are open so that channels become freely permeable to Na and Na rushes into the axon causing E to rise in the positive direction 2 A late response A moment later the slow Na gate closes The mem brane is no longer highly permeable to Na the rapid inflow of Na ceases In addition the slowly responding gates in the t channel open and t flows out of the axon causing E to fall in the negative direction 3 A recovery phase Still later all gates return to their original resting position With a weak sub threshold stimulus not enough Na flows in to overcome the outflow of and the axon repolarizes With a stronger supra threshold stimulus more Na channels open so that Nat inflow exceeds outflow the net flow of charge is now positive inward and the axon is depolarized even further But this opens even more Nat channels which causes more depolarization A vicious cycle ensues the membrane potential takes off in the
44. he following e internal Na concentration e internal K concentration e membrane capacitance e number of voltage activated Na channels e number of voltage activated K channels e number of leak channels e rate constant for opening fast Na channels e rate constant for closing fast Na channels e rate constant for opening slow Na channels e rate constant for closing slow Na channels e rate constant for opening K channels e rate constant for closing K channels e axon radius Action potentials from the normal axon colored brown are denoted by E and those from the expeimental colored purple are denoted by Ep When you run the stimulator you excite both axons with the same stimulus pattern Further if you change the external ion concentrations or the temperature the same conditions will hold for both axons Each time you run the experiment both action potentials are recorded You will be able to change any of the properties of the control but you will not be able to change properties of the experimental Task Your problem is 1 Give a descriptive workup of the difference between these two axons This could include a simple description of the action potentials that you see as well as how they both respond to any of the measurements that you have learned to make Your decision on what to include is part of the problem 2 Try to diagnose which property has been changed You may attempt to mimic the experimental axon by altering th
45. he upward direction i e mMINa mINa This makes it easier compare it with IK To optimize the scaling Keep E on the left axis and move IK and mina onto the right axis if they are not already there You can shift the axis of any variable by holding the shift key down and click on its button Find the approximate threshold and then click on the fine check box to gain greater control Now find an accurate threshold You can do this by clicking on the right hand or left hand arrow on the slider to add or subtract very small increments to the intensity Notice that below threshold INa remains lower than IK However when threshold is reached ina overtakes IK Print a plot of the currents when the stimulus is just barely below threshold and compare it to a print of the plot where the stimulus is just above threshold These results follow provided the late response has not had time to develop In some cases with stimuli that are just under threshold the na may momentarily exceed jx only to fall back as the late response K channels open Na chan nels close sets in To see an example of this repeat the above experiment with the temperature set at 1 8 The all or none response arises naturally out of this positive feedback once the response is triggered the positive feedback drives the membrane potential to its maximum value near the Nat equilibrium potential The size of the action potential is determined by the concentration gradi
46. his will make the slider more sensitive and enable you to find a more accurate lower bound for an adequate stimulus To the Record the value that you find This is the threshold strength for a duration of 0 25 msec Do not change the stimulus duration in this experiment We will come back to duration later Why do you think there is a threshold in nerve stimulation Are there any other phenomena in nature like this You might consider a chemical reaction or the lighting of a fuse Compare the spike height of an action potential elicited with a threshold stimu lus with those of action potentials elicited by greater stimuli Are the heights the same Do the action potentials differ in shape A good way to compare the action potentials is to click on the O Overlay button at the bottom of the recorder screen This will superimpose records from different experiments It is easier to compare the records if you reduce the display time to 5 msec To do this click the Time button on the recorder This opens a dialogue box that allows 20 you to reset the display time When you have a graph that answers the ques tions print it and make notes on it as before A Experiment 1 Properties of Excitation and Conduction UT Overview Task 21 Since this is the first experiment it is a good time to experiment with the various controls to see what they do You have used many of them already Consult the Virtual Lab Quick Start for guidance on the o
47. how both the driving force arrows and the channel states change These forces and states correspond to the position of the cursor and are used to interpret each detail of the graph This animation is quantitative it will interpret the details and unique properties of any simulation 5 Click on Interpret from bottom menu and select Equilibrium Potential from the popup 6 Click on Interpret from bottom menu and select Explain Voltage Clamp from the popup Af Experiment 1 Properties of Excitation and Conduction Overview Task 17 A Threshold and All or None Response If a nerve is stimulated with weak electrical shocks there is a local disturbance but a propagated action potential does not occur As the stimulus intensity is raised the local disturbance gets larger and finally at a critical intensity or threshold an action potential occurs and is transmitted along the length of the nerve In contrast to local disturbances it is much larger and its height does not diminish as it travels along the length of the axon Further increasing the stimulus strength does not increase the size of the propagated action potential This is behavior is called all or none In this experiment you will find the threshold of a nerve and see what the action potential looks like Then you will raise the stimulus strength to values above threshold and observe the effect upon the magnitude and shape of the action potential Open the Virtual Lab by double c
48. icomp will be negative Na flowing into the cell while others will be positive Na flowing out of the cell Assuming INa Icomp find the membrane potential clamped voltage intensity1 where maximum na 0 use interpolation to zero in on the correct value This is the equilibrium potential for Na It can be calculated from the internal and external Na concentrations by use of the Nernst equation Membrane potentials above this value will generate positive currents sending Na out of the axon while potentials below this value generate negative currents sending Na into the axon Na conductance gNa reflects number of open Na channels The Na conductance ais a more useful indicator of the channel behavior because it is proportional to the number of open Na channels and unlike lcomp INa it is always positive Although ais not directly measurable it is easily calculated from Icomp The computer carries out this computation for us and you can toggle it on and off the display by clicking on the gna button Using the display buttons turn Icomp off and gna ON 1By definition 9 na Ina E Fwa In our case na comp and E Fse so that Na comp set ENa Experiment 4 Reconstructing the Axon Voltage Gated Sodium Channels 59 Using the Slider run 1 0 different experiments with different values of the clamped voltage intensity1 within the range of say 90 mV to 90 mV Use this data u
49. iment follows a similar routine to Experiment 3B but now we continue with an axon that has its channels blocked and we monitor the response of Na channels to sustained depolarizations The results illustrate the experimental evidence that upon depolarization the Na channels are first activated i e they open and then they close even though the depolarization is maintained Run the Explain Voltage Clamp in the Interpret popup menu if you have not done it Interpret I comp Open Voltage Clamp Only Na Gates The default eset is set to begin the clamp at 0 5 msec by jumping the membrane potential E from 65 mV to 20 mV and keeping it at this value for 10 msec Run the simulation and remember that 1 There are no activated channels Therefore for most depolariza tions ion flow through the membrane is practically all due to Na ions In this Case icomp is equal to Ina 2 The membrane potential is clamped at a given value and does not change Since the Na concentrations also do not change within the short time 1 0 msec of the clamp it follows that none of the driving forces for ion flow change The only way for lcomp to change is by a change in the number of open Na channels Notice that in response to a sustained depolarization the icomp which is now equal to the Na current first rises and then falls even though the depolariza tion is maintained Print the result AVS Experiment 4 Reconstructing the Axon Vol
50. ing to the repolarized membrane In addition the voltage activated gates are still open and this drives E below the resting potential creating the negative afterpotential With the slow Na gates closed and the gates open it is difficult if not impossible for Na inflow to exceed outflow i e to reach threshold You can illustrate this by plotting the mINa and IK that result from a second stimulus delivered in the refractory period However To make this plot intelligible you may have to use the zoom to se some of the results How do the activities of the Na K pump influence the action potential They don t at least not directly Any contributions by the pump to is swamped out by the more massive movements of the ions through the channels The pump does not cycle often enough to make a difference during activity However action potentials are very brief and the axon is at rest most of the time During rest there is ample time for the slow cycling of the pump to restore the small amounts of Na and that have leaked through channels activated during the action potential From your knowledge of the excitation process complete the following table by predicting i e Increase decrease or no change the effects of changing or Na ion concentrations on the items listed in the titles to the last four columns Pnredidtionsasi g Naik Threshold Action Negative Relative Na o e K i neis After Refractory Potential pot
51. itable but its response is now nonlinear and non symmetric The slow accommodative effects of K channels are evident as the response rises to a maximum and falls away despite the continued presence of a prolonged stimulating current The seeds of a refractory period are also evident from the undershoot that occurs when the stimulus is removed This is an ideal time to introduce voltage clamping because interpretations involve only one significant ion with a simple channel with only one gate Passive Axon Only Na Gates This model another step toward a fully functioning axon is the complement of the last one Passive Axon Only K Gates Now all the K channels are blocked and only Na channels remain These channels are more complex because they contain 2 different gates a fast one and a slow one The absence of K gates makes interpretation of Na Channel behavior much simpler This axon is excit able but only if it has been artificially hyperpolarized just prior to the stimulus T A Introduction Further once it is stimulated it will remain depolarized with no prospect of re excitation unless it is artificially hyperpolarized Voltage clamping is again the ideal way to study the opening and closing of the two channel gates After studying the last three models the user is prepared to tackle a more de tailed description and interpretation of intact axon behavior This can be accomplished by reopening Membrane Action Potential Advan
52. l in that it has 2 gates The gates are referred to as the fast gate and the slow gate which describes their rates of opening and closing Maintaining the Resting Potential Loss of channels presents a problem because a high permeability is required to maintain the resting potential If the axon is depolarized at rest many slow Na gates will be closed There is no possibility of reopening them by further depolarization and excitation will not occur To circumvent this in this experiment the potential is forced to remain at its normal rest value of about 65 mV until ready for stimulation Experimentally this can be accomplished with a voltage clamp Testing the Membrane With Voltage Gated Sodium Channels Stimulate this axon and compare it with the results in Experiment 3 axon with K channels but without any voltage activated Na channels Record your data in the table below and print a representative response curve Response of Na Channels to Brief Stimulation Stimulus Intensity Response Peak Afterpotential A cm mV Minimum mV As you can see excitation occurs but the membrane potential does not return to the normal resting potential Is the response all or nothing Can the membrane be excited at its new more positive membrane potential Test by giving a second stimulus a few milliseconds after the peak Is the second response all or nothing 55 YL Experiment 4 Reconstructing the
53. le action potential the actual amounts of Nat and that move in or out of the axon are very small they have significant effects on E but the concentra tions of Nat and hardly change This is illustrated in the program the concentration arrows do not change during the action potential drag the graph cursor back and forth even though the E arrow does Recall that a stimulus causes a brief increase in the number of open Na chan nels f the stimulus is weak only a few channels open and the membrane is hardly perturbed However if the stimulus is sufficiently strong i e if it is stron ger than a critical level called the threshold then the number of open Na channels becomes very substantial Na ions poised at high concentration outside the axon leave their negatively charged partners behind on the outside and rush in fast enough to overwhelm the moving out The inside of the cell is inundated with positive charge so that the polarity is reversed now the inside is positive and the outside negative A moment later the Na channels close and extra t channels open The membrane becomes very permeable to K t moves out making the membrane potential even more negative than it was at rest driving it very close to the equilibrium potential Finally after several msec the extra channels close and the membrane returns to its resting condition lon Currents To see the inflow and outflow of ions add the sodium c
54. licking on its icon Click on Propagated Action Potential when it appears on the screen When the experiment is loaded you will see a screen with an axon recording instruments and a slider for changing parameters see fig 1 As you can see from the slider the initial stimulus parameters are 200 A cm2 for the intensity and 0 25 msec for duration These are the values for the first stimulus Ignore the second stimulus its strength has been set to 0 so that it will not occur in this experiment The stimulus pattern is displayed on the small stimulator screen on the left To stimulate the axon click the Run button on the stimulator In a few moments after you have stimulated the axon on the left and after the impulse passes along the axon to the recording electrodes on the right you should see an action potential plotted on the small recorder on the right Click the Display button on the recorder This will enlarge it and make it easier to view the action potential trace To further enlarge the view click on the upward pointing arrow at the bottom of the screen Clicking on a downward pointing arrow will reduce the view Drag the slider to the bottom of the screen where it will not obscure the view You are now ready to do the experiment Before going on print a copy of the screen and take a look at your action potential To do this e if you want a grid click the G toggle button e click the Print button e set the Reduce or Enlarge
55. livered to the middle of the axon Distance 3 2 Is the propagation confined to one direction or does it travel in either direction with equal ease Colliding Action Potentials Load Propagated AP 15E S2ends Advanced and set up the display This pro gram stimulates a nerve from both ends at the same time The excitation ad vances towards the middle of the axon from each end and eventually the 2 action potentials will collide If the action potential waves cross they will form an X pattern on the screen This is what happens with ocean waves they pass right through each other Press the Run button and see what happens with ac tion potentials Were the waves able to cross or were they blocked Can you use the refractory period to explain this blockage Why might the blockage of colliding action potentials be a useful feature for the heart yl Experiment 1 Properties of Excitation and Conduction Ui Overview Task 31 H Subthreshold Local Response The nerve does respond to subthreshold stimulation but the response is weak and diminishes from the point of stimulation Subthreshold responses are im portant in physiology because they can summate with others sometimes reaching the threshold magnitude On the molecular level they produce disturbances in membrane channels that can affect the activity of the nerve In this experiment we will look at a subthreshold response at 15 different electrodes as it spreads along a nerv
56. lmost entirely by the precise timing of Na and t gates as they open and or close in response to changes in mem Rate of change of E mV msec brane potential E The gate animation gives a visual picture of the position of these gates at any particular time The following table Figure 5 1 is a simple qualitative reminder about how these gates respond to changes in E membrane Recall potential 67 AL Experiment 5 Explaining the Action Potential Task As E decreases becomes more negative Closes Opens Closes Closes Opens Figure 5 1 Move the graph cursor around and try to interpret the results remembering that 1 Changes in E reflect changes in net charge on the inner surface of the membrane 2 Increases in net charge are promoted primarily by positively charged Na ions moving into the cell and opposed by positively charged ions moving out 3 Movements of Na or are determined by the net force on the ion as well as the number of channels that are open to that ion 4 Both fast and slow Na gates must be open in the same channel in order for the channel to be open Clean up the display More precise information about channels and gates can be obtained directly from the plot To prepare for this clean up the display by turning off all the plotted variables e g E Stim ENa EK as well as any of the currents ina IK IL Isum The display should be empty and all of the variable buttons will be gray
57. ly from the graph window A run will be initiated after each slider drag when the mouse is released Each time a new run is completed the plot in the display window is erased and replaced by results of the new run 2 Fine control Click on the Fine check box next to Stim 1 I ntensity in the Slider window This will place the last position of the Slider in the middle of the bar and increase the sensitivity of the slider by a factor of 10 Move the Slider back and forth and forth Toggle off the Fine control by clicking again on the Fine check box 3 Compare runs toggle click on the O button on recorder for overlay 4 O0nce more move Slider for Stim 1 intensity back and forth Now the display window is no longer erased after each run Instead each new run is superimposed on the results of previous runs As long as overlay is toggled on screen erasure will not occur This holds independently of how you initiate the run e g with sliders or with the run button 5 Get rid of Slider by clicking close box in upper left hand corner 6 Retrieve Slider window by selecting it from Set Parameters on bottom menu i Vu Quick Start Gu ide 13 SELECT PLOTTING VARI ABLES 1 Click on the Stim button in the graph window The stimulus rectangular wave disappears 2 Click on the Stim button again The stimulus rectangular wave reappears Clicking any of these variable but tons on the graph toggles that variable on or
58. n labeled with a cross the second button on the left on the recorder display A graph cursor in the form of a vertical dashed line will appear on the display and numerical values corresponding to the position of the cursor appear on the upper part of the display 2 Drag the cursor back and forth Numerical values of any plotted variable can be obtained directly from the display at any position of the cursor i A Quick Start Guide CHANGE THE EXPERI MENT 1 Click on New Experiment in the lower menu and select Membrane Action Potential Elementary from the popup menu list 2 Click Run button Now in contrast to the last simulation the entire axon is stimulated simulta neously There is no propagation because there is no place for the impulse to go This is shown very nicely in the screen animation where large electrodes elicit an excitation uniformly over the entire stretch of axon Note that the ani mated impulse is first green color coded to Na and then red color coded to K reflecting the initial increase in Na permeability followed by an increase in K permeability This experimental setup is very useful because it isolates the excitation process from propagation making it easier to interpret There are no up or down stream currents USI NG SLIDERS AND OVERLAY 1 Change parameters Move Slider for Stim 1 intensity back and forth Sliders provide a quick way to change a parameter and run the model direct
59. nels we now employ a simpler experimental set up Instead of stimulating the axon at one discrete location and recording the response at another site we now stimulate the entire axon simultaneously Run the simulation and watch the screen animation where large electrodes elicit an excitation uniformly over the entire stretch of axon This experimental setup is very useful because it isolates the excitation process from propagation making it easier to interpret There is no propagation because there is no place for the impulse to go This axon has an ionic distribution similar to a typical axon high inside high Na outside It has a negative membrane potential because the inert channels transport ions in preference to Nat and other ions Record the membrane potential E Start by varying the strength of the stimulus to see if you can produce an action potential The initial values have been set at 50 mA cm2 and 2 5 msec Try stimuli from about 20 to 200 mA cm2 For each stimulus record the maximum voltage in the table below Reverse the signs of the stimuli and observe the results Were you able to elicit an action potential Now subtr membrane potential from each of the peak values in the table Is the magnitude of the response symmetrical when you reverse the sign of the stimulus Are the shapes amp magnitudes of the response curves symmetrical when you change the sign Print graphs which support your answer 37 Experime
60. nt 2 38 Reconstructing the Axon The Passive Axon When you are done load Membrane Action Potential Elementary Is the re sponse symmetrical when you change the sign of the stimulus Symmetry Intensity Peak Voltage mV Peak Voltage E mV Testing for Linearity of Response Reload Passive Axon No Voltage Activated Gates Now change the duration of the stimulus to a longer value so that the response curves flatten out and reach a steady state Duration used _________ Keep this new duration constant and vary the stimulus strength from 20 to 200 mA cm Record the values in the table below and then plot the membrane voltage vs stimulus strength to see if the response is linear i e do the points fall on a straight line Experiment 2 39 Reconstructing the Axon The Passive Axon Linearity Intensity Peak Voltage mV u amp cm E 0 D B e c p f E S 0 50 100 150 200 Stimulus Intensity u amp cm2 How does this response differ from the all or none response of a real axon Does the passive membrane have a threshold Testing for a Refractory Period Use 2 identical stimuli to test for a refractory period in the passive axon Use the slider to vary the Stim 2 Onset Does the magnitude of the response change if you change the time interval between 2 pulses __________ __ Is there a refractory period Response to Second Stimulu
61. ntial at a time where a Experiment 1 Properties of Excitation and Conduction Properties of Excitation and Conduction threshold stimulus does not is the axon in the absolute or relative refractory period Print your graph and mark the range which is in the relative refractory period In the second procedure we will measure the thresholds at different time periods after the first action potential To do this leave both stimulus durations at 0 25 and set the first stimulus intensity at the threshold value about 70 The second stimulus intensity will be varied using the slider Set the Stimulation 2 Onset at 3 msec to start Vary the stimulus strength with the slider to determine the threshold Write your findings in the table below If you cannot elicit a second action potential with the highest intensity write ref in the table Increase the onset time by 0 5 msec and determine the threshold at this time point Repeat until you have threshold values from 3 to 8 msec Note In the experiment the first action potential peak occurs at about 1 6 msec so a second stimulus at 3 msec is given 1 4 msec after the peak Plot the threshold intensity vs time At what time is the refractory period over for this nerve How does the refractory period of a nerve set the maximum rate at which a nerve can fire 200 Duration Threshold Intensity 3 0 3 5 4 0 4 5 5 0 100 5 5 Duration msec 6 0 6 5 50 7 0
62. off 3 Click on Glossary on the bottom menu bar and select Models from popup list This glossary defines all the variables and parameters that are used Click Done ADJ UST PLOTTING AXES AND SI MULATION TI ME 1 Change the Y axis Click on the Stim button while holding the shift key The stimulus rectangular wave is now plotted on the left Y axis Do it again it shifts to the right axis Holding the shift key while clicking a button moves the variable from one Y axis to the other 2 Change the time x axis Click the Time button on the recorder A dialog appears which allows you to change the simulated time of the next run A corresponding change in the time axis will appear in the next graph The same dialog can be reached via the Set Parameters select Control menu in the bottom menu bar SCALI NG 1 Auto Scale toggle enaand EK off the graph The scaling on the left axis is adjusted so that the other plotted variables are shown in greatest detail commensurate with their size In this mode each time a change is made the plotted variables will continue to occupy the full graph but the numbers on the left axis may change 2 Fixed Scale toggle enaand Ek on the graph ENa and EK are both plotted as defaults They are upper and lower limits to the action potential they fix the scaling making it easier to assess changes visually In this mode each time a change is made the numbers on the left axis remain fixed while the
63. on potential records before after and at the site of the block Movement of the slider shows different degrees of block Conduction fails when the height of the record at the site of the block falls to about 1 6 of the control This corresponds to the textbook figure of a safety factor of 6 for conduction of an impulse i e each normal action potential gen erates 6 times the current required to excite the next region Toxicology Scorpion Toxin This simulation provides a demonstration of the effects of alpha scorpion toxin LE A Introduction 10 Voltage Clamp I deal This model presents a standard voltage clamp simulation where voltage control is obtained by setting the membrane voltage equal to the target voltage This is the companion to Membrane Action Potential Voltage Clamp Simulated In this voltage clamp simulation the voltage control is simulated This includes a user controlled gain together with an unavoidable delay The system can show steady state error oscillations and instability It is a useful exercise for demon strating common properties of feed back control Voltage Clamp Only K Gates This is the companion to Passive Axon Only K Gates Voltage Clamp Only Na Gates This is the companion to Passive Axon Only Na Gates Voltage Clamp Scorpion Toxin This is the companion to Toxicology Scorpion Toxin Problem 1 These models present the user with two axons One is a normal control axon the othe
64. or to the point where Isum just crosses the zero line and changes from negative positive charge flowing in to positive positive charge flowing out At this moment E has reached its maximum value moments before it was increasing moments later it will decrease In fact the rate of change of E is proportional to jum You can verify this by picking off the slope rate of change of the action potential at convenient points and plotting the slope versus isum TO compute an approxi mate slope you need two points on the curve that fairly close together say no more than 5 mV apart Denote these two points by E1 and E2 and their corresponding times as t1 and tz The slope at the point midway between E1 and E2 will be approximately Slope E2 E1 t2 t1 Try it for at least 3 points When you plot the slope versus isum you should get a Straight line Slope of action potential sum Crossing zero going u Crossing zero coming down This is only true for the membrane action potential When the action potential is propagated Currents originating from up and downstream portions of the axon act like an external elec trode and also contribute to the rate of change of E F A Experiment 5 Explaining the Action Potential atl Rate of Change of E I sum E mV Rate of change of E mV msec l Isum Aem sum wave Opening and closing of gates depends on E The behavior of the axon is governed a
65. ow the resting potential depends on K but not Na while the peak of the action potential depends on Na but not K This was one of the major clues prompting the formulation of the modern theory of exci tation Using the advanced model allows a more detailed analysis of the above as well as the opportunity to do many more experiments For example an advanced user could also invoke changes in a Membrane capacitance b Numbers of Na K or Leak channels c Rate constants for either opening or closing of any or all of the 3 gates residing in the Na or K channels Propagated AP 2E This model is similar to the above Propagated A P 1E But now there are two recording electrodes at different positions along the axon By dividing the time between peaks into the distance between the electrodes the user can calculate the velocity of propagation of the impulse independently of any uncertainties about the latency of excitation The dependence of velocity of conduction on axon radius temperature Na and K membrane capacitance etc can be studied Membrane Action Potential Here in contrast to the Propagated A P simulations the entire axon is stimulated simultaneously There is no propagation because there is no place for the T Vu Introduction impulse to go This is shown in the screen animation where large electrodes elicit an excitation uniformly over the entire stretch of axon This experimental setup is very useful b
66. perimental run as Clamp1 onset msec 0 5 intensity mV 90 0 duration msec 10 0 Clamp2 onset msec 11 0 intensity mV 20 0 duration msec 10 0 Run the simulation and compare the gNa lcomp etc in the two cases Print the graphs Check out the Gate Animation to help interpret your result This result is generally true Most ion gates are only partially activated or deactivated at resting potential It allows the system to move in both directions and has physi ological implications 2 A Experiment 5 Explaining the Action Potential E Overview Task Recall Task 65 A Membrane Action Potentials Finally we reconsider the normal axon with a full complement of voltage activated Na and channels The temperature is lowered to 6 C to slow things down and make them easier to track Our objective will be to interpret the qualitative properties of the axon e g threshold refractory period all or none response in terms of the action of the channel gates Open Membrane Action Potential Advanced Open the Environment dialog from the Set Parameters popup menu and change the Temperature to 6 Run the simulation Analyze your results using the gate animation with the Graph cursor as well as plots obtainable from the variable buttons on the graph n interpreting these data remember that the amount of charge movement neces sary to make substantial changes in E is very small During the short time of a sing
67. positive direction with an explosive velocity as the interior of the axon becomes more and more positive But this rapid upward movement of the membrane potential does not persist Soon E becomes positive and large enough to oppose Na entry despite the open channels i e E approaches the Na equi librium potential where the concentration gradient moving Na inward is just balanced by E pushing Na out At the same time the delayed effects begin to appear Nat channels close and voltage activated channels open outflow exceeds Na inflow and the net flow of charge is now positive outward E plum mets toward its resting value overshoots momentarily and comes very close to the K equilibrium potential because the voltage activated channels are still open making the membrane even more permeable than it was at rest Finally the repolarized membrane closes the voltage activated channels and E returns to its resting value u A Experiment 5 Explaining the Action Potential UT Task Interpret 71 From this description we see that the threshold is determined by the stimulus strength that is able to cause an inward Na flow to exceed the outward flow From that point onward the stimulus plays no further role because the seeds of the positive feedback vicious cycle reside in the axon itself Verify this by plotting IK and mina aS well as E on the same graph mina is the Same aS ina except that it is plotted in t
68. r has been perturbed by changing one of its parameters The user is asked to give an empirical description of the perturbation and then to perform tests to try to determine the nature and the extent of the perturbation A Quick Start Guide OPEN PROPAGATED A P 1E ELEMENTARY RUN THE SI MULATI ON 1 Click Run button on stimulator This button will always initiate a new run independently of whatever running mode multiple runs sliders etc has preceded it or whether the Slider palette is active The screen animation shows an action potential initiated in a discrete position under the stimulating electrodes and traveling to the recording elec trodes where it is picked up and displayed in miniature on the small recorder 2 Click Display button on recorder for a larger view A Slider palette window will be floating on top of the graph 3 Drag the Sliders window out of the way e g place in lower right hand corner CONTROL THE STI MULUS 1 Click Stim button on stimulator A dialog appears allowing you to control the intensity duration and time of onset of two independent stimuli The second stimulus is used to explore refrac tory periods etc 2 Enter 3 100 and 0 6 for time of onset intensity and duration respectively for stimulus 2 Then click Done Note that the new stimulus pattern is plotted in the stimulator display 3 Click Run button on stimulator RETRI EVE NUMERI CAL VALUES 1 Click on the butto
69. results can be obtained by running simulations where first external Na o is reduced to a minimal value the lowest the computer will allow then Nato is reset to normal and internal K i is reduced to a minimal value Results obtained in these and similar experiments over a range of values for Eset provided the basis of our current understanding of excitation and the voltage clamp technique remains one of the most powerful analytical tools in membrane biology It allows you to study in detail how the membrane potential governs ion channels C Strange Action potentials Scorpion Toxin The sodium channel agents discussed in the Experiment 1 blocked the Na conductance of the channel and reduced the action potential height In this experiment we will look at the action an alpha scorpion toxin that produces bizarre looking action potentials First you will observe how the normal action potential changes as more and more scorpion toxin is applied Then you will perform tests to elucidate where and how the toxin is acting Load experiment Toxicology Scorpion Toxin and set up the display This experi ment will be run in approximately the same way as the channel blocker experi ment In this case however the toxin is applied to the whole nerve not to just a patch of the axon Using the slider set the percentage inhibition to different values of your choice in the range from 0 to 100 Click on the O overlay button and select several values e
70. ropagated AP 2E Elementary set Nao to 0 4 and find out Is the electrical disturbance of the 0 4 curve an action potential K Effects We now do a similar experiment in which Ko is varied measuring effects on the same parameters as before Start by resetting Nao to 1 0 Vary Ko from 0 2 to 2 0 The design of the experiment is left up to you Use single or multiple runs as you wish The choice of the Ko values other than the 2 extremes is also left up to you Choose values that will show significant effects When you get your curves measure the same parameters as you did in the Na experiments Put the data for 5 or 6 good curves in the table below Max Rise Rate Max Decline Rate Afterpotential Ko x normal Peak Height mV x eight mV mV msec mV msec Minimum mV 2 0 0 2 Which parameters were most affected by Ko On one of your curves mark the Na and K sensitive parts of the action potential Predict what will happen if you change internal K Run a few curves to test your prediction Summarize all the evidence you have concerning the role of Na in the action potential Similarly summarize the role of K in the action potential Data similar to that in your tables seems to point to the existence of special channels for Na and K that open and close during different phases of the action potential We will examine the properties of these channels in future experiments yl Experiment 1 Prop
71. rview Task 32 l Sodium and Potassium Effects Excitation is based on the sequential movements of sodium and potassium ions across the membrane But how could you show this How would you even show that they are important One simple way is to replace them in the solution that bathes the nerve and see what happens to the action potential A more subtle approach would be to replace them gradually i e change their concen trations in steps In this way the process action potential does not simply disappear Instead it may become gradually distorted If you can key the changes in concentration to corresponding changes in action potential you may begin to acquire clues about what each ion does In this exercise you will simulate experiments originally done by Hodgkin Katz amp Huxley where they varied the external Na and K concentrations and observed the effect on the action potential Load the Propagated AP 1E Elementary experiment and set up the display Na Effects We will study the Na effects by varying external Na which is the way the experiment was first done Later people learned how to change the internal Na by perfusion but this is technically more difficult and can be done only with the largest nerves Click the Multiple button set the number of runs at 6 and choose Nao as the parameter to be varied You will find that the default value for all 4 of the ion parameters Nao Nai Ko Ki is 1 0 This simply means that
72. s Stim 2 Onset 40 Peak Voltage mV Experiment 2 Reconstructing the Axon The Passive Axon Testing the Effect of Membrane Capacitance on Response Time Pick a stimulus strength and duration that will give a substantial change in mem brane potential The duration must be long enough for the response to reach a steady state Run the simulation and record the resting potential and the value of the membrane potential response Subtract the resting potential Em from the membrane voltage response to get the magnitude of the voltage change Next divide the voltage change by 2 to get the 50 response Find the 50 response voltage on your graph and use the zoom feature to get the time of the 50 response Subtract 0 5 msec from this time value because the stimulus onset was at 0 5 msec to get the half time of the response Record this value in the table Now vary the membrane capacitance to see how it affects the half time of the response To change the capacitance go to the Set Parameters Menu and choose the Membrane option You may change the capacitance from 0 1 to 5 X the normal value Plot the half time of response vs the membrane capacitance Response Time Capacitance raat Membrane Voltage Change 50 Response Half Time x normal Voltage mV mV mV msec Half Time msec 41 Experiment 2 Reconstructing the Axon The Passive Axon 42
73. s independent of the strength of stimulus All action potentials are the same no matter how large the stimulus the response is all or none This behavior is similar to a fuse once lit the size of the spark that travels along is independent of the size of the match that initiated it 3 Refractory Period The recovery period following excitation when the axon appears to be inexcitable is called the refractory period 4 Negative Afterpotential During an action potential E quickly rises to a positive maximum then falls below its negative resting potential and then slowly rises back to its resting potential as it fully recovers This final portion of the action potential where E is below the resting potential is called the negative afterpotential To interpret these properties recall that the inside of the axon has high K the outside high Na Further the membrane potential is a measure of the electri cal force on a positive charge Finally remember that the amount of charge movement necessary to make substantial changes in E is very small During the short time of a single action potential the actual amounts of Na and that move in or out of the axon are very small they have significant effects on E but the concentrations of Na and hardly change At rest the axon is permeable mostly to K but not much t leaks out because the opposing membrane potential E is close to the equilibrium potential Experiment 5 Explainin
74. se the graph cursor to pick off the data points from each run to plot at each level of depolarization 1 The maximum gNa 2 The steady state pNaf 3 The speed of activation of the Na channels as indicated by the time taken from the beginning of the clamp to the time where pNaf reaches half of its steady state value 4 The steady state pNas 5 The speed of deactivation indicated by the time taken from the beginning of the clamp to the time where pNas reaches half of its steady state value Effects of Membrane Polarization on Na Channel Gates Voltage Clamp Maximum Na pNaf Steady pNaf Response pNas Steady pNas Response mV x normal State Half Time msec State Half Time msec m Experiment 4 Reconstructing the Axon Voltage Gated Sodium Channels Slow Gate Open Steady State E 2 p w mej n o Zz a 90 45 o 45 90 Voltage Clamp mV Fast Gate Response Time E oO E fi xe x g i 3 8 o 5 Z Qa 90 45 0 45 90 Voltage Clamp mV 51 61 pNas Response Half Time msec INa x normal 90 90 Slow Gate Response Time E 45 o 45 Voltage Clamp mV Peak Na Conductance E 45 0 45 Voltage Clamp mV VU somera Reconstructing the Axon Voltage Gated Sodium Channels 62 Note that when pNaf increases pNas decreases and vice versa Compare the response time curves with the gate response time observed in exercise
75. sk what happens when two impulses arrive at a head on collision Action Potentials Propagate As Waves Load Propagated AP 15E Advanced set up the display and run the simula tion Click on Display and then click on the up arrow to obtain the largest display Looking at the vertical orange axon in the Display you will again see the stimulus icon S located at the beginning of the axon where Distance 0 but now there are 15 recording sites spaced 0 4 cm apart The recording corresponding to each site is shown on the plot just adjacent to the site The wavelike character of the propagated action potential is apparent on the plot and it is easy to watch how it changes when any parameter is changed Changes in temperature provide a good example To prepare first click on the Time button on the small Display or alternatively select Control from the Parameter popup menu Change the time setting in the dialog from 5 to 10 msec Run the simulation and then click on the O overlay button on the Display Now change the temperature from 18 5 to 0 select Environment from the Parameter popup menu to arrive at the dialog that allows temperature to be changed Run the simulation again to obtain a graphic display of how temperature changes the shape of the action potential as well as its velocity of propagation One or Two Way Conduction Load Propagated AP 15E Advanced set up the display and run the simula tion Here the Stimulus is de
76. specially in the higher ranges gt 75 to show the dramatic changes in the action potential as more and more toxin is applied Print your results IN A Experiment 5 Explaining the Action Potential 75 To identify the site of action of the toxin load experiment Voltage Clamp Scorpion Toxin and set up the display To check out the channels poison the Na channels by selecting Membrane from the Set Parameters menu and set nNa 0 Run the simulation and overlay the responses for several levels of toxin include 0 and 90 Print your results Now to check Na channels reset nNa to 1 and set nK 0 so that all of the channels are poisoned Again run the simulation and overlay the responses to several levels of toxin including 0 and 90 Finally print these results From the voltage clamp curves you should be able to distinguish the site of action of the toxin Do you think the toxin exerts its affect on a the gates b the fast Na gates c the slow Na gates Why Do you think it makes these gates respond faster or slower Can you use your conclusions to interpret the shape of the action potential a A Experiment 6 Simulated Feedback Overview Task I nterpret 76 The voltage clamp experiments that you have run in exercises are simulations of an ideal feed back exerting perfect control over the membrane voltage In this experiment we simulate a more realistic case where control is less
77. tage Gated Sodium Channels Ul Interpretation Task 58 Na channels first open and then close because of the operation of a fast and a slow gate within each channel At rest most fast gates are closed but slow gates are open Upon depolarization first the fast gates open creating a number of open channels both gates open Then the slow gates close shutting down these channels To follow this click on the Display button and open the Interpret Gate Animation Drag the graph cursor vertical dashed line to different positions and use the cartoon to see how the Na gates open and close in response to a sudden depolarization You can also see the dynamic properties of the channel plotted directly on the display Click on the na button to plot the Na conductance which is propor tional to the number of open Na channels Now make room for other plots by turning the a Off simply click the na button once more Click the pNaf and pNas buttons This will plot the fraction of open fast gates probability of finding an open fast gate and the fraction of open slow gates respectively These fractions probabilities range from 0 all closed to 1 all open Com pare the response times for the opening of the fast gates and the closing of the slow gates With a single clamp use the Slider to run a few different experiments with different values of the clamped voltage intensity1 within the range of say 90 mV to 90 mV Note that some
78. tart Guide 15 4 Enter 0 in the Initial value and 100 in the Final value fields respectively 5 Select the arithmetic series radio button 6 Click OK to start the runs The program will automatically run the program 10 times and changing the intensity with each run as indicated in the parameter list This same routine can be used to compare variations of any parameter in the popup menu list Note that the resulting run s will be added to the graph if Overlay is on If you want any previous runs to be discarded be sure to turn off Overlay before starting the runs SET PARAMETER VALUES 1 Click on the Na or K near the axon An Environment dialog appears which allows you to change the concentra tions of Na or K inside or outside the axon as well as the temperature 2 Click on the Set Parameters menu and select whatever from the popup list All parameters that are user accessible can be changed in the dialogs from the popup list ADVANCED MODELS 1 Click on New Experiment and select Membrane Action Potential Advanced run it and click on Display on the recorder More plotting variables are accessible in the advanced models than in the elementary ones 2 Click on Glossary on the bottom menu and select Models from popup list This glossary defines all the variables and parameters that are used Click Done 3 Click on the Set Parameters menu and select whatever from the popup list More parameters and mor
79. than perfect because there are unavoidable delays caused by the time it takes the system hardware voltage recorder amplifier current source electrodes to re spond to any deviation in the membrane potential from its targeted value Eset AS a result the instructions sent back to the current source as well as the compensating current sent to the membrane always lag behind they are always a little outdated As you will see this causes errors the actual membrane potential continuously deviates from the targeted eset Attempts to force it closer to the target may cause the system to become unstable Open and run the experiment Compare the traces of E and Eset In the previous experiments with the ideal voltage clamp they were identical but now E never seems to really match the targeted value ese Why In the ideal experiment the identity between E and eset was forced by a mathematical artifice they were defined to be equal To understand the more realistic simulated clamp we need to follow the chain of command in more detail Gain and Error When the Run button is clicked the recorder amplifier sends the appropriate amount of charge to the membrane to make the membrane potential equal to the desired eset and the membrane will respond it has been stimulated To maintain E close to eset the recorder amplifier monitors E at all times and continuously instructs the current source to add positive or negative charge via the
80. the relevant concentration is 100 of normal If you change it to 0 5 you will have 50 of normal while a change to 2 designates 200 of normal Set the initial value of Nao at 1 2 and the final value at 0 2 This will give 6 runs at Naos of 1 2 1 0 0 8 0 6 0 4 and 0 2 Look at the 6 curves on your screen There are 4 definite action potentials a definite failure and one the curve for Nao 0 4 that could be either How can you decide whether or not this curve is an action potential Look at it for a minute or two to see if there are any distinguishing features We will come back to this curve after we have analyzed the others Print the graph and then use the Zoom and Graph Cursor features to measure the following parameters for each curve peak height maximum rate of rise maximum rate of decline and negative afterpotential minimum Put your data in the table Peak Height mV Max Rise Rate Max Decline Rate Afterpotential NAD Gc normal mV msec mV msec Minimum mV 1 2 1 0 0 8 0 6 0 4 0 2 Experiment 1 Properties of Excitation and Conduction Which parameters are affected by Na the most How much does the peak height change if you reduce external Na by half Now let s return to the 0 4 curve It is impossible to tell whether this is an action potential or a local response from shape or size alone A definitive test is to see if it is propagated in an all or none fashion Load P
81. thers and try all of the controls Note that the first set of buttons below the screen Stim E ENa EK are toggles that allow you to change what is plotted The lower set L O Z G allow you to add legends control the graph cursor overlay unzoom add a grid or change display size Other buttons in this row allow you to Print or Save graphs If you click Done the graph will be reduced to its original small size At the bottom of the screen are pop up menus that allow you to Quit Set Param eters or go to a New Experiment If you click the Interpret or Glossary buttons you will get information about the definition of symbols and the interpretation of the results you see on your screen Selecting the Multiple button on the stimu lator will open a dialogue box that will let you program the computer to do several sequential runs in which one of the parameters is systematically varied in this experiment we did this with the slider and the overlay feature The Stim button allows you to change stimulation intensity and duration we used the Sliders in this experiment instead B Strength Duration Curve In the previous simulation we found that a threshold stimulus intensity was re quired to fire a nerve In this simulation we did not vary the stimulus duration and this raises the question can you compensate for a weak stimulus by applying it for a longer time It is tempting to answer yes Depolarization of a nerve requires movement of
82. ts Membrane Resting Membrane Potential mV Nato x normal Resting Membrane Potential mV o 1 2 3 4 5 Potential External Nat Na o x normal For an explanation of the electrical potential across a membrane permeable to only one ion equilibrium or Nernstian potential go to the Interpret pop up menu and choose Equilibrium Potential As you work through the examples you will see that at equilibrium the electrical forces acting on the ions are exactly balanced by diffusional forces If an ion cannot penetrate the membrane it cannot come to equilibrium and in general the electrical and diffusional forces acting on it will not be balanced If an ion is not at equilibrium across a membrane the concentration gradient represents stored electrical energy and might be thought of as a tiny battery for that ion If a conductance path is opened across the membrane the stored electrical energy can be tapped for doing work i e for making action poten tials A Experiment 3 Reconstructing the Axon Voltage Gated Potassium Channels Overview Task Recall A Membrane Action Potentials In this experiment we add voltage sensitive t channels The potassium channel of the squid axon has a single voltage regulated gate to the bare passive axon Adding this feature will change the properties of the membrane in significant ways but it will not result in a functioning axon Although this is a thought exp
83. uli or clamps after setting the environment of the axon changing its properties and or adding drugs or toxins Using the program tools you can create experiments which explore a variety of nerve properties ranging from classical phenomena such as threshold summation refractory period impulse propagation to more modern concepts of channels gates and eventually even molecular events This simulation provides insight about the hypothesized mechanisms of excitation in a way that is not practical with animal preparations These ideas can be explored at both elementary and advanced levels You can dive into a full blown propagating action potential with 15 recording electrodes or you can begin with an inexcitable axon and gradually patch in the component parts In every case there are animations linked to the computations which will help you interpret any experiment that you specify The experiments described in this manual are merely suggestions You are encouraged to move beyond these limitations by proposing your own prob lems and experiments The program is feasible because computations are performed with an ultra high speed software engine specialized for very rapid computation of solutions to both ordinary and partial nonlinear differential equations Linking this engine to a flexible multimedia object oriented development program has provided a programming environment that is both powerful and unique SUMMARY OF MODELS Elementary and Advance
84. until you find the transition point where the feedback becomes unstable This instability shows up as wild oscillations in E or become too large for the computer to handle In the experimental hardware analog the amplifier output voltage either oscillates or saturates or as the Run 8 simulations with different values of Gain and plot the error y axis versus the Gain x axis below Mark the maximum usable gain minimum error on your graph Gain Steady State Error Versus Gain Steady State Error mV gt e lw 2 B N gt me N 0 100 200 300 400 LE VL Experiment 6 78 Simulated Feedback Stability As the gain gets larger the sytem becomes unstable because the outdated in structions are too large causing icomp to overcompensate When this over compensation is large E will overshoot its target by a wide margin The control system then tries to correct this overshoot by sending a large signal in the opposite direction As this hunting for the target continues the system may show sustained wild oscillations or the currents and voltages may grow larger and larger until the system breaks down amplifier saturates Positive Feedback A functioning voltage clamp is based on negative feedback In our example lcomp Gain error Try changing it to a positive feed back Using even a small gain 1 so that Icomp error leads to an explosive instability A Diagnostic Probl
85. urrent va and the potassium current K to your plot access these by using variable buttons on the graph By convention outward flow of positive ions K in our case is positive and inward flow Na ions is negative Make sure that all currents are scaled on the right hand axis otherwise it will dwarf E You can switch Y axes by holding the shift key while clicking on the variable button You can also plot the net current sum to see the net flow of positive charge This will consist almost entirely of K and wa The only other flow of charge is called the leakage current 1 Try plotting it to show that it is negligible Experiment 5 Explaining the Action Potential during excitation Note how small the stimulating current is compared to the sodium or potassium currents or even the net current It gives some indication that the axon is loaded with its own energy source ion gradients that have been set up by the Na K pump and ready to be triggered by a small distur bance In making this comparison be sure to scale the Stim and other currents on the same Y axis It is now apparent that a relatively small current stimulus evokes an enormous response of membrane currents emphasizing the explosive nature of the excitatory process Rate of change of E is proportional to sum When isum is negative positive charge flows into the cell E will increase when it is positive E will decrease Verify this by moving the graph curs
86. vant times in msec are easy to read off of the graphs using the zoom and graph cursor features To convert to seconds multiply the msec by 0 001 Measure the times for temperatures from 0 to 30 C at gt intervals To change temperature in this simulation use the Set Parameters button Choose Environ mental and this will provide a menu to change the temperature Calculate the conduction velocities from the equation Conduction Velocity meters sec distance meters time sec 0 012 meters ET sec0 8 Overview Record the data in the table below and plot the graph 27 Temperature Time at 0 8 cm msec Time at 2 0 cm msec Velocity meters sec o 5 10 15 20 25 Velocity m sec o 10 15 20 25 30 Temperature C Load Propagated AP 15E Advanced and run action potentials at 25 and 30 o C Print the graphs What signs did you see of nerve failure at high tempera ture F Conduction Velocity Depends On Radius Action potentials are conducted along axons because each excited segment electrically excites the next adjacent region which in turn excites the following region The speed of conduction depends on how far downstream the electrical effects of an excited region can reach Given these facts you might anticipate that axons with larger diameters will offer less resistance to the downstream propagation of these electrical effects so that larger diameter axons would
87. you had reduced the pain 50 Would this be correct A Experiment 2 Reconstructing the Axon The Passive Axon Overview In the first set of experiments we investigated the electrical properties of nerves the threshold refractory period temperature sensitivity conduction velocity and so on We found that these properties were very dependent on the concentrations of Nat and ions on the alternate sides of the cell membrane To explain these ionic dependencies it was suggested that ions carried charges across the membrane through special channels that could be opened and closed In the next set of experiments we will reconstruct the properties of a nerve We begin by stimulating a primitive inexcitable axon It leaks Na K and possibly other ions through inert channels but these channels have no voltage activated gates the channels do not open or close in response to membrane voltages The axon has a normal ion distribution The simulation shows the basic properties of a leaky membrane In experiments that follow voltage dependent channels will be added for t and for Na We will see how properties of the membrane change as these channels are added Task Testing the Inexcitable Axon Load the experiment Passive Axon No Voltage Activated Gates Notice that the interface has been modified the stimulating electrodes run the length of the axon In addition to simplifying the axon by removing the voltage activation of the chan

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