The Compound Action Potential of the Frog Sciatic Nerve

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science Department of Mechanical Engineering Harvard-MIT Divis...
Author: Laureen Roberts
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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science Department of Mechanical Engineering Harvard-MIT Division of Health Sciences and Technology

Quantitative Physiology: Cells and Tissues 2.791J/2.794J/6.021J/6.521J/BEH370J/HST541J

Fall, 1999

The Compound Action Potential of the Frog Sciatic Nerve

1 Introduction 1.1

Overview

This laboratory project is intended to provide an opportunity to learn about (1) designing an experiment, (2) acquiring, processing, and interpreting experimental data, and (3) communicating the results to others. You and your laboratory partner will dissect a sciatic nerve from a frog and mount it in an experimental chamber, so that you can stimulate the nerve and measure its electrical responses. Your work is divided into two parts. First you will make some “Basic Observations” that are outlined in this laboratory manual. Then, you and your partner will carry out a project that you design. With careful experimental design and some thought, you will be able to measure important properties of electrical responses of neurons. You may feel uneasy: how are you supposed to do (much less design) a nerve experiment before you’ve learned anything about nerves? Relax: this laboratory was designed to be completed before we learn about theories for what should happen. The point of the laboratory exercise is to determine what does happen. Thus, it will be more important to gather convincing evidence that your results are reliable (i.e., would you get the same results if you repeated your experiment?) than to argue that your results are consistent with some theory. This order, in which experimental observations precede the development of theoretical ideas, is typical in the development of scientific knowledge. Doing well in the laboratory will only require relatively simple ideas about all-or-none action potentials, thresholds, propagation velocities, and refractory properties. Adequate background material is contained in pages 1 to 20 of Volume 2 of the course text.

1.2

Structure of the Sciatic Nerve

The sciatic nerve (a macroscopic structure) is the main nerve trunk from the spinal cord to the leg. It consists of a bundle of nerve fibers (microscopic structures), each of which is the axon of a neuron, whose cell body is in (or near) the spinal cord. We will use the terms “fiber” and “axon” interchangeably. Axons are long, cylindrical processes that project from the cell body of a neuron and that act as a conduit for neural messages called action potentials. Some axons conduct action potentials toward the brain: they are called afferent fibers. Others, called efferent fibers, conduct action potentials away from the brain. The sciatic nerve contains both efferent and afferent fibers. Axons within the sciatic nerve differ in important structural and functional ways (Figure 1). Myelinated axons are surrounded by myelin, which looks in cross-section like tightly-packed, concentric rings around the perimeter of the axon. Other axons lack myelin. Axons that innervate  

m) than those that innervate internal organs and glands tend to be smaller in diameter ( 

skeletal muscles ( m). Smaller diameter axons tend to conduct action potentials more slowly than larger diameter axons (Figure 2). The thresholds, refractory periods, and the durations of action potentials differ across types of axons. Interpretation of the properties of compound action potential involves thinking of the sciatic nerve as a heterogenous population of nerve fibers.

2

Figure 1: Cross section of the sciatic nerve of a rabbit (Young, 1951). Each of these outlines is the darkly-stained layer of myelin that surrounds a single myelinated nerve fiber. Fiber diameters vary. Unmyelinated fibers, which are much smaller than myelinated fibers, are not visible with the histological method used to prepare the tissue for this picture.

Conduction velocity (m/s)



1.3

40 bullfrog

 

30

Figure 2: Conduction velocity versus fiber diameter for individual myelinated nerve fibers in the bullfrog sciatic nerve (Tasaki, 1953, adapted from Figure 65). The slope of the line indicates that the best fitting constant of proportionality is 2 m/s per  m. The fiber diameter was measured near the insertion of the nerve into the gastrocnemius muscle. Temperature was  C.

20 10



0



0



5 10 15 Diameter (µm)

20

Compound Action Potentials

As action potentials propagate along an axon, they produce electric potentials that can be recorded from the surface of the nerve. When a nerve bundle is stimulated, many axons produce action potentials synchronously. The resulting electric responses recorded from the surface of the nerve are called compound action potentials to distinguish them from the action potentials generated by individual axons. Compound action potentials can be measured as shown in Figure 3. Stimulus electrodes are applied to one end of the nerve; recording electrodes are located along the nerve. If the nerve is stimulated with a current pulse of sufficient amplitude, the action potentials produced in the fibers propagate toward the recording electrodes. The aggregate effect of the many action potentials is an extracellular wave of negative potential, moving along the surface of the nerve. If the recording electrodes are widely spaced (Figure 3, left panel), the wave of negative potential produces a negative pulse in recorded voltage  as it passes the recording electrode. At a later time, the  negative wave of extracellular potential passes the recording electrode, where it contributes a positive pulse to the recorded voltage  . If the electrodes are more closely spaced (center panel), the negative and positive parts of the recorded voltage  merge, and the resulting waveform is called a diphasic compound action potential. The propagation can be blocked by a number of methods including mechanical methods (pressure applied to the nerve or crushing the nerve with forceps), electrical methods (passing a blocking level of current through the nerve), or chemical methods (applying potassium chloride, local anesthetics, cocaine, or tetrodotoxin to the nerve). If 3

Widely spaced recording electrodes

Closely spaced recording electrodes

Nerve

" "

Nerve

$+

!v(t)



i(t)

" "

i(t)

Nerve

$+ !v(t)



i(t)

wave of negative potential reaches "−" electrode

" "

i(t)

#t !v(t)

Closely spaced with neural block



i(t)

i(t)

#t !v(t)

$+ !v(t)

#t !v(t)

#t

#t

wave of negative potential reaches "+" electrode

diphasic waveform

#t monophasic waveform

Figure 3: Three schemes for measuring compound action potentials. In each scheme, a current %&('*) is applied to two stimulus electrodes, and a voltage response +&('*) is measured across two recording electrodes (upper panels). The response to a pulse of current consists of two, temporally separated components, if the recording electrodes are widely spaced (left panels). A diphasic waveform results for more closely spaced recording electrodes (center panels). A monophasic waveform results if a portion of the nerve between the recording electrodes (shown as a dark band) is altered to block transmission of action potentials (right panels).

the compound action potential is blocked between the two recording electrodes (right panel) so that  it does not reach the recording electrode, a monophasic compound action potential is recorded. The monophasic compound action potential consists of one or more peaks of (negative) potential that last on the order of a millisecond.1 The maximum amplitude varies with the recording conditions but rarely exceeds a few millivolts. Multiple peaks might represent repeated action potentials produced by the same fibers or alternatively, sub-populations of fibers that differ in their propagation velocities and thus produce components with different delays. The shape of the compound action potential depends on the population of excited fibers within the nerve. If all of the fibers in the nerve have similar diameters, then the propagation velocities for action potentials will be similar. The resulting monophasic compound action potential will be brief. If the nerve contains a heterogeneous mix of fibers with different diameters (as in the bullfrog sciatic nerve), then the monophasic compound action potential will become broader as it propagates. If the distance between the stimulating and recording electrodes is sufficiently large, the monophasic compound action potential may consist of several peaks — each corresponding to a different subpopulation of fibers that conducts action potentials at a different velocity. Studying the electrical properties of the different peaks has led to insights about the thresholds, refractory periods, and velocities of propagation of action potentials in different subpopulations of fibers (Patton, 1960; Ochs, 1965; Ruch et al., 1965). 1

The convention of plotting negative monophasic action potentials as upward deflections (which is not used in this laboratory manual) is commonly used in physiological publications.

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1.4

Protocol is Important

The written record of your experiment is the original record of your work and the basis for everything that you conclude. Such records are often called protocol, and are usually kept in a special notebook with sewn binding (not a loose-leaf notebook), whose pages were numbered when the notebook was printed. Records are written in this protocol book in ink. The protocol book is the permanent record of your experiment. Protocol should be sufficiently detailed so that (1) the experiment could be repeated at some later time, (2) results from different experiments can be compared, and (3) so that your procedures can be reconstructed at a later time without relying on your memory. The first page for each experiment should give the date and time, as well as a brief description of the purpose of the experiment. All relevant procedures and observations should be entered in the protocol book and the time should be indicated regularly. Nothing should ever be erased. If an error is detected in some procedure or some reading, that should be noted in the book. The original observation should under no circumstances be obliterated so that it cannot be read. Perhaps you will subsequently find that the original observation was correct and that the correction was in error. The general rule is to write down everything that is done that may later become relevant. Scientists are rarely sorry that they wrote too much in the protocol book — only that they wrote too little. You do not have to purchase a special protocol book for this laboratory session. However, we do ask that you take protocol during your experiment, as a step toward learning about effective practices in experimental work. You will be asked to attach your protocol to your laboratory report, and we will assess the protocol as part of the grading procedure.

1.5

Use of Animals in Research

In this laboratory you will dissect a sciatic nerve from a bullfrog. As with all experiments with animals, the appropriateness of this experiment and the procedures that are used were reviewed and approved by the MIT Committee on Animal Care. In general, the methods meet the guiding principles of the American Physiological Society: Animal experiments are to be undertaken only with the purpose of advancing knowledge. Consideration should be given to the appropriateness of experimental procedures, species of animals used, and number of animals required. Only animals that are lawfully acquired shall be used in this laboratory, and their retention and use shall be in every case in compliance with federal, state, and local laws and regulations, and in accordance with the NIH guide. Animals in the laboratory must receive every consideration for their comfort; they must be properly housed, fed, and their surroundings kept in sanitary condition. Appropriate anesthetics must be used to eliminate sensibility to pain during all surgical procedures.

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2 Methods This section describes the experimental methods. Additional information, including photographs of the surgical procedures, is available at http://umech.mit.edu/6.021J/index.html. A video-taped demonstration of the surgery will be shown during the first 20 minutes of your laboratory session. Arrive on time so you can start the procedures immediately after viewing the the tape. This is a physiology experiment and experimental animals can carry disease. You may not eat or drink in the laboratory, and you must wear rubber gloves when you handle the animals.

2.1

Anesthesia

A bullfrog (Rana catesbeiana) is anesthetized by immersing it for about 20 minutes in tap water that contains MS222 (Ethyl 3-aminobenzoate, methanesulfonic acid), an anesthetic commonly used for aquatic animals. The concentration of anesthetic is 0.1 % by weight. The frog should become limp.

2.2

Solutions

Throughout the dissection and the course of the experiment, the frog sciatic nerve should be kept moist in Ringer’s solution (Table 1). Ringer’s solution approximates the ionic composition of the extracellular fluids of the frog, and a sciatic nerve bathed in Ringer’s solution can remain electrically responsive for hours. KRinger’s and Sucrose solutions are also available for students interested in investigating the effects of changes in ion concentration on electrical responses. Concentration Ringer’s KRinger’s (mmol/L) NaCl 85 1.8 KCl 1.8 85 Na, HPO2.75 2.75 1.7 1.7 CaCl, NaHCO. 25 25 Dextrose 4 4 Sucrose 0 0

2.3

Sucrose 0 0 0 0 0 0 241

Table 1: Compositions of bathing solutions. The predominate ions in Ringer’s are Na / and Cl 0 , which is typical for normal extracellular fluids. The predominate ions in KRinger’s are K / and Cl 0 , which is typical for intracellular fluids. The sucrose solution contains neither NaCl nor KCl, but sucrose is added so that this solution has the same osmolarity as the others. The pH of each solution has been adjusted to 7.4.

Dissection of the Sciatic Nerve

General precautions.

1 Use the bluntest instrument that will accomplish the job. Finer instruments may cause damage, e.g., rupture of blood vessels.

1 Cut parallel to the nerve. It is elastic but is easily cut if approached perpendicularly. 6

1 Never close the jaws of the scissors without visual confirmation that the nerve will not be cut.

1 Keep the nerve wet with Ringer’s solution (not with blood) at all times during the dissection. 1 Avoid picking up the nerve with forceps: handling should always be done by gently lifting

the nerve on a blunt instrument or by an attached thread. Stretching can destroy the action potential generating mechanism in the nerve fibers. Detailed description. The sciatic nerve runs down the leg between the large thigh muscles (Figure 4), i.e., between the semimembranosus and both the vastus externus and internus muscles. It branches several times and the peroneal branch is found deep between the two large calf muscles, i.e., the peroneus and gastrocnemius muscles.

Vastus externus muscle Vastus internus muscle

3

Semimembranosus muscle

2

Gastocnemius muscle

Peroneus muscle

Figure 4: Dorsal (back) view of frog musculature (Carolina Biological Supply Company, 1965, adapted from Review Sheet 55).

1. The frog is the source of your experimental material. Weigh the frog and measure its length from snout to vent. Record these as part of your record of assembling an experimental system. 7

2. Decapitate the frog with scissors. With a pithing needle, destroy (i.e., mosh up) the brain and the spinal cord. The frog’s muscles will twitch during these manipulations. Pithing greatly reduces subsequent muscle contractions, thus simplifying the dissection. 3. Place the frog on its back in the dissecting tray. Grasp the thin wall of skin and muscle that overlie the viscera of the lower abdomen with forceps and pull it up and away from the viscera. Using dissecting scissors, make a horizontal incision in the thin wall, and cut through the wall — first to the left and up the left side of the abdomen, then to the right and up the right side of the abdomen. Lift the thin wall of skin and muscle up and cut it off to expose the viscera. 4. Slide the viscera up to uncover the spinal column and emerging sciatic nerve. The nerve is white and cylindrical and should be distinguished from tendons and the surface connective tissue (fascia) of muscles, both of which are white but are usually flatter and shinier than nerves. Cut off the portion of the frog above the spinal cord entrance of the sciatic nerve, including the viscera. 5. Grab the spinal column with a pair of forceps and with another pair of forceps grab a fold of skin on the frog and pull down to remove the skin from the legs. If this proves difficult, grab the muscles on each side of the spinal column with a pair of forceps and with a third pair of forceps grab a fold of skin on the frog and pull down to remove the skin. 6. Free the sciatic nerve from surrounding tissue by cutting the surrounding tissue parallel to the nerve being careful not to cut the nerve. After the portion of the sciatic nerve in the abdomen has been freed of other tissue, slide small curved forceps underneath the sciatic nerve near its insertion into the spinal cord, attach surgical thread to forceps and pull through. Tie off one of the sciatic nerves at the backbone where it leaves the spinal cord, leaving about 2 inches of thread attached for manipulating the nerve. Cut the nerve between the knot of thread and the spinal cord. 7. Free the portion of the nerve in the abdomen from all surrounding tissue from the part attached to the thread down to the hip joint. Try to minimize bleeding when you dissect the nerve. Often the smaller blood vessels can be crushed with a hemostat and then safely cut without causing much bleeding. If you inadvertently cut a large vessel, clamp it shut with a hemostat and wash away the blood with frog Ringer’s solution. Be sure to keep the nerve wet at all times. 8. When the nerve is free, poke a hole through the frog’s back by spreading the musculature apart and pull the thread gently through from the ventral (abdominal) to the dorsal (back) side. Do not tug on the nerve. 9. Dissecting the nerve at the hip is tricky. Switch to the dorsal side (flip the frog over) and expose the nerve in the thigh where it lies deep between the large thigh muscles. To do this, pull apart the two large groups of thigh muscles and pin them down so that their inner sides are exposed. Cut through the overlying membranes and uncover the nerve and the nearby blood vessel. Dissect the nerve free near the hip joint. Once the nerve is visualized on both sides of the hip joint dissect through the hip joint. Take your time here and cut parallel to the nerve and detach the tissue from the nerve. Always make certain that the nerve is not between the blades of the scissors when you cut. You will notice that the sciatic nerve has many branches throughout its course. These may be cut at any time, although for best results 8

cut them when the entire nerve is free of surrounding tissues. Cutting a branch of the nerve may cause muscle contractions. 10. Midway down the thigh the sciatic nerve branches in two. You want the branch that goes above the knee and down to the foot (the peroneal nerve). Separate and pin the muscles of the calf apart. Follow the nerve from the thigh to the knee. The dissection of the nerve through the knee is similar to its dissection through the hip. Before freeing the nerve at the knee, dissect the nerve in the calf. When you are sure you can visualize the nerve, cut the tendon which covers the nerve at the knee. Hemostat and cut any small blood vessels that cross over the nerve. 11. Free the nerve down the length of the calf to the ankle. Tie off the nerve at the ankle, leaving about 2 inches of thread for mounting. Cut the nerve just beyond where it is tied, and cut away any remaining branches. 12. Measure the length of the nerve without stretching it.

2.4

Mounting the Nerve in the Chamber

Stimulating electrodes

S3

S1

Make sure the stimulus is off by disconnecting the stimulus and recording electrodes. Keeping the nerve moist, lay it over the silver electrodes in the nerve chamber with the large end of the nerve over the closely spaced stimulating electrodes (Figure 5). Insert the threads through the

R11

R12

Recording electrodes

R10

R9

R8

R7

R6

R5

R4

R3

R2

R1

S2

Plexiglass cover

Figure 5: The nerve chamber. There are 12 recording electrodes spaced 1 cm apart. There are 3 stimulating electrodes spaced 0.5 cm apart.

holes in the ends of the chamber and extend (do not stretch) the nerve to its original length. Then secure it in place with tape attached to the thread and chamber. A small drop of Ringer’s solution should be laid at each electrode-nerve crossing to ensure electrical connection. Cover the bottom of the chamber with Ringer’s solution. Be careful not to short-circuit the electrodes; do not allow the Ringer’s solution to reach the level of the electrodes in the chamber. Squirt a few drops of Ringer’s solution on the rim of the chamber and cover with a Plexiglass slab to provide an airtight seal. This keeps the atmosphere in the chamber saturated with water and prevents the nerve from 9

drying out. The nerve will be surrounded by moist air which acts as an electric insulator. The three closely-spaced electrodes are normally used for electrically stimulating the nerve, and the remaining electrodes are normally used for recording.

2.5

Stimulation and Recording

A block diagram of the experimental apparatus is shown in Figure 6. The signal generator produces two outputs: a trigger pulse that used to synchronize the oscilloscope and the computer, and stimulus pulses that pass through the stimulus isolator to produce pulses of current to stimulate the nerve. The voltage response from the surface of the sciatic nerve is amplified by the differential amplifier and fed to both the oscilloscope and the computer.

2

3

3

+ Signal Generator −

Stimulus Isolator

+ −

6Two channel Oscilloscope

Nerve

$+ −

Differential 4 Amplifier

5

Computer

Trigger

Figure 6: Block diagram experimental arrangement.

2.5.1

Stimulus Generation

The signal generator (Grass model S88) produces a periodic stimulus. Each period consists of a pair of pulses whose parameters are independently controlled (Figure 7). The output of the signal generator drives a stimulus isolation unit (Axon Instruments model Isolator-10) that converts an input voltage, which is referenced to ground, to an output current that is isolated from ground. For this laboratory the stimulus isolator is preset to the “1 mA” setting which gives a transconductance

of 100 A/V. The output of the stimulus isolator drives the stimulating electrodes of the nerve chamber (Figures 5 and 6). The center electrode is the cathode. The two outside electrodes should be connected together to serve as anodes. This stimulation configuration reduces the threshold current required to stimulate the nerve and reduces the spread of the stimulus current along the nerve. A technical problem with electric stimulation is that a portion of the stimulus current produces a voltage input to the recording amplifier which is called a stimulus artifact which can obscure the nerve response. The circuit topology shown in Figure 6 is intended to reduce the stimulus artifact. However, the size of the stimulus artifact is also affected by the geometrical arrangement of the stimulus and recording electrodes. The lengths of unshielded wires should generally be kept as small as possible. 10

3

S1 duration

3

Repeat

3

S2 duration

3 S2 7volts

S1

7volts 3

S1 delay

3

S2 delay

Train period Trigger

Trigger

Figure 7: The stimulus consists of a periodic train of pulses whose repetition rate is controlled by changing the Train Rate knob of the signal generator. Each period consists of two pulses (S1 and S2) whose delays (S1 delay and S2 delay) from the trigger pulse, amplitudes (S1 volts and S2 volts), and durations (S1 duration and S2 duration) can each be controlled.

2.5.2

Response Measurement

Responses of the sciatic nerve preparation are fragile (voltages are small, impedances are high) and are easily corrupted by electric interference (especially from the computer). Therefore, an amplifier is used to amplify and buffer the neural responses. The amplifier is a differential amplifier with two high-impedance inputs: a non-inverting input (red wire) and an inverting input (green wire). The amplifier has a nominal gain of 100 (the measured gains, which may vary by as much as 12% from the nominal value, are indicated on each amplifier), a frequency response that is flat in the 89 :;< kHz, and a wideband noise floor of 0.7 mV rms. The amplifier saturates frequency range at output voltages of =?> V. The oscilloscope has two input channels. One channel is used to monitor the stimulus and the other is used to monitor the response. The oscilloscope also has a trigger input, which is connected to the synchronization output of the signal generator. This triggering arrangement allows synchronization of the scope sweep with the stimulus pulses. As part of your setup procedure (i.e. before you attempt to stimulate the nerve), check out the operation of the Grass S88 signal generator. Connect the “Monitor Output” of the S88 to the oscilloscope. Set up a stimulus protocol consisting of a train of two pulses with a train period of

200 ms. Set the delay of the first pulse to be minimal and its duration to 100 s. Set the delay of

the second pulse to 2.5 ms and its duration to 200 s. Measure the amplitude and timing of the stimulus with the oscilloscope. Make sure that the scope’s horizontal sweep vernier is set in the calibrated position.

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2.6

Data Acquisition and Processing

The laboratory computer (an IBM compatible) is interfaced to an analog-to-digital conversion system that has two analog inputs: channel A and channel B. The analog-to-digital conversion system is programmed to monitor channel B for the arrival of a synchronization pulse from the stimulus generator. When a synchronization pulse is detected, periodic sampling of channel A, which is connected to the output of the preamplifier, begins immediately. The sampling interval is

< < 20 s and the samples have 16 bit resolution within the range to volts. Sampling continues for 15 ms to give a sequence of 750 samples. 2.6.1

Activating the Software

The main program for acquiring and processing data is called frog. This program stores results and temporary files in the current working directory. To avoid confusing your data with that of another group, each laboratory group should store results in a separate directory. Please use the following naming convention. If you are in laboratory group B2, then type the DOS commands C:> mkdir \frog\b2 C:> cd \frog\b2 to make a new directory named c:\frog\b2 and to make that directory the current working directory. Then type C:\FROG\B2> frog to activate the main program. The frog program provides facilities to acquire data, to save and plot results, and to obtain hardcopy. All of these facilities are directly accessible from a single main control screen illustrated in Figure 8. The control screen includes a graphic area (top half) where results can be plotted, a text area (bottom half) where notes about results can be recorded, and a collection of buttons to activate specific facilities described in the following sections. 2.6.2

Acquisition of Data

Three buttons provide data acquisition facilities. Pressing Get Wave causes the computer to (1) pause until it receives a synchronization pulse from the stimulus generator, (2) convert the next 15 ms of output from the preamplifier to a digital representation, and (3) display the resulting waveform in the graphic area. Pressing Continuous causes the computer to perform Get Wave operations repeatedly. This mode of operation simulates the operation of an oscilloscope and the resulting display should look quite similar to the oscilloscope display. When Continuous has been pressed, other data acquisition buttons are erased, and only one function can be activated – Stop Continuous. Pressing the Avg 10 button causes the computer to collect 10 consecutive responses and to display the average. Newly acquired data are plotted as a white trace in the graphic portion of the screen.

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+β Continuous

Print Notes Get Wave

Avg 10

G = 100

Print Plot

++ + 5 –– – Electrode Voltage (mv)

__ A7

–3.1

__ A6

–4.3

__ __ __

++ + –5 –– –

– 0 + Stored Waveforms Prev Page A0: A1: A2: A3: A4: A5: A6: A7: A8: Next Page A9:

1

2

Time (msec)

3

4

– 5

t = 1.520 +

Notes 31-Aug-94 6:58 -- amplitude = 27 uA; duration = 0.1 ms 31-Aug-94 6:59 -- amplitude = 28 uA; duration = 0.1 ms 31-Aug-94 7:03 -- amplitude = 29 uA; duration = 0.1 ms

31-Aug-94 7:12 -- positive electrode = #3, negative electrode = #4 --- before crushing nerve 31-Aug-94 7:10 -- positive electrode = #3, negative electrode = #4 --- after crushing nerve

Figure 8: Appearance of monitor screen after the acquisition of data via the frog program. The waveforms shown are from a bullfrog sciatic nerve in response to stimulus pulses presented with a repetition rate of 10/s, an amplitude of 28  A, and a duration of 100  s. One waveform (dashed line) was recorded before — and the other (solid line) was recorded after — the nerve was crushed at a location between the two recording electrodes.

2.6.3

Saving Waveforms

Waveforms can be stored on the computer’s disk for later analysis. Storage identifiers consist of a single letter (A-Z) followed by a single digit (0-9). When data have been acquired and have not yet been stored, the Save Wave button appears on the screen. Pressing this button prompts for a save identifier as follows Save as: __

Type save ID or to abort.

Type a letter and a number or press the key to exit the prompt. Notice that this prompt and all others in the frog program are captive in the sense that they preclude all other operations while they are on the screen. You can dismiss this prompt with a valid response or to abort. 2.6.4

Storing Notes with Waveforms

One line of notes can be associated with waveforms to facilitate on-line waveform identification and manipulation. Notes are displayed in the lower part of the screen, 10 at a time. The 13

Next Page and Prev Page buttons select the set of ten waveforms whose notes are displayed. When a waveform is saved, the page of notes associated with that waveform is automatically selected and the date and time-of-day are automatically entered on the note line for that waveform. You may add text to the note or modify existing text by pressing the button to the left of the note. This button activates an editing mode prompt. Press text keys to add text, to delete text, or strike the Return key to exit the prompt. Notes can be modified at any time. Simply select the appropriate page (using the Next Page and Prev Page buttons) and click on the button to the left of the appropriate note. Relation between notes and protocol records. Notes are not substitutes for appropriate entries in your protocol book! Notes only provide information about one measurement. It is generally impossible to understand the context of one measurement in isolation. The context, working hypotheses, test setup, and tentative conclusions should all be recorded in your protocol records along with a record of waveform IDs. 2.6.5

Plotting Waveforms

Any newly acquired waveform that has not yet been saved to the disk plus as many as seven stored waveforms can be simultaneously plotted in the graphic area. Buttons provide facilities to choose waveforms, adjust scales, and obtain numerical plot values using a mouse-controlled cursor, as described in the following sections. Scales. Voltages displayed on the screen are scaled by a constant G. To make the displayed voltages correspond to those at the amplifier’s input, use the G= button to set G to the gain of the amplifier, which is nominally 100 (more exact values are indicated on each amplifier). The maximum and minimum values of the scales on both the abscissa and ordinate can be changed using the nearby +, ++, -, and -- buttons. Pressing + or ++ increases the number by a small or large amount respectively. Pressing - or -- decreases the number by a small or large amount respectively. Selecting waveforms. The color-keyed buttons to the right of the plot can be used to select stored waveforms for display. Pressing one of those buttons initiates a prompting sequence. Enter a letter and a digit to select a stored waveform or strike the spacebar to erase the entry or strike to abort the prompting sequence. Using the cursor. To obtain numerical values from the plotted waveforms, move the cursor to the graphical area of the display and press the mouse button. A vertical line will appear, and the position of that line can be changed by moving the mouse left or right. The time selected by the vertical line is indicated just under the last of the color-keyed buttons to the right of the plot (see Figure 8). Values of the plotted waveforms are also indicated as numbers typed to the right of the corresponding color-keyed button.

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2.6.6

Hardcopy

Hardcopies of the graphical portion of the display can be obtained by pressing the Print Plot button. This button produces an encapsulated PostScript file in the current directory and then initiates a sequence of messages on the campus computer network that will ultimately produce a sheet of paper on the laser printer located in the laboratory. Hardcopies of the notes can be obtained by pressing the Print Notes button. This button produces a text file named NOTES.TXT in the current directory and sends that file off to the laser printer. The encapsulated Postscript files and NOTES.TXT are not deleted when the printing is complete. These files provide opportunities to print additional copies of the plots or to electronically paste the plots into your laboratory report. The file for the first plot that you make is named PLOT001.EPS, the second is named PLOT002.EPS, and so forth. Typesetting and electronic cut-and-paste are NOT required: these facilities are made available only for those who wish to use them. 2.6.7

Simple Waveform Arithmetic

Waveforms can be scaled (i.e. multiplied by a constant) and added to other waveforms using the button. Pressing this button adds the waveform that is plotted with a red trace with a [email protected] scaled replica of the waveform plotted with a blue trace. The scale factor @ is solicited by a prompt that is invoked each time the button is pressed. The resulting waveform is displayed [email protected] using a white trace and can be saved to the disk by pressing the Save Wave button. 2.6.8

File Formats

This section provides information about how the frog program saves waveforms on the disk. This information is not necessary to use the frog program or to obtain hardcopies. However, this information could be used to convey data obtained from the frog program to other waveform processing or plotting programs. The use of other programs is not required: the information is provided only for the benefit of students who wish to make use of other programs. When waveforms are saved to the disk, two files are produced — a binary file and an ascii file. The file names are derived from the waveform identifier. The binary file associated with A0 is called A0.BIN and the ascii file is called A0.ASC. The binary file contains two fields. The first is 100 bytes in length and contains the notes associated with the waveform. The first byte of this field identifies the length of the notes text and subsequent bytes contain the ascii codes for the text. The second field in the binary file contains 750 sixteen-bit integers representing the waveform. A value B ?<  < of > CD> represents V and a value of > CD> represents V. The ascii file contains 751 lines of text. The first line contains notes associated with the waveform. Subsequent lines contain decimal numbers representing voltages in mV. The numbers in both the .BIN and .ASC files represent voltages measured at the input to the analog-to-digital converter of the computer. Neither of these representations account for the preamplifier gain factor G.

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2.6.9

Exiting the Program

The frog program can be terminated at any time by pressing the Exit key. Data sessions can be resumed simply by restarting the program. No data are lost by exiting and restarting. 2.6.10

Network Services

The laboratory computers are connected to the campus computer network. Use of the campus computer network is NOT required. This information is included only to help those interested in transferring their results to another computer (for further signal processing or for figure preparation). The laboratory computers support remote computer login using telnet. To activate telnet type C:\FROG\B2> telnet comp-name where comp-name represents the name of the computer (e.g. athena.dialup). The laboratory computers support file transfers to other computers using ftp. To activate ftp type C:\FROG\B2> ftp comp-name where comp-name represents the name of the computer (e.g. athena.dialup). 2.6.11

Floppy Disks

The laboratory computers support 1.4 Mbyte floppy disks, which can be used to save your files for future use (e.g., to make figures for your laboratory report) or to transfer your files to other machines. Use of the floppy disks is not required.

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3 Experiments 3.1

Basic Observations

The purpose of these observations is give you some experience with basic features of compound action potentials, before you begin your project. Try to complete these three observations in less than 1/2 hour. 1. Determine threshold current (about 10 minutes). Threshold is defined as “a point at which a physiological effect begins to be produced.”

Determine the threshold current for the compound action potential for pulses with 100 s duration, repeating at a rate of 10/s. Use the two most distal recording electrodes. Your method should be well defined, though it may have some arbitrary constraints. Start with a weak stimulus and gradually increase the level. You should observe a CAP about

2 ms after the stimulus with a current of a few tens of A. Notice that the vertical axis gain of your oscilloscope can influence your ability to detect a response. Is the compound action potential an “all-or-none” response? Cautions. Avoid large currents, which can damage the nerve. Make sure that the stimulus

isolator is set for “1 mA” and remember that this means that 100 A of current will be delivered to the nerve for every volt from the Grass S88. 2. Identify response components (10 minutes). Observe that the recorded waveform consists of an early component that occurs within a fraction of a millisecond after the stimulus and a later, diphasic component that occurs after a delay of a few milliseconds. Which of these is the compound action potential? Explain. What is the other component? 3. Create a monophasic response (10 minutes). Record a compound action potential from the most distal pair of recording electrodes. Next, crush a small portion of the nerve, mid-way between the recording electrodes using forceps or a hemostat. Record the new response and compare it to the pre-crush waveform. Describe the effect of crushing on the compound action potential. Notice. This response record can serve as a standard against which you can test responses later in the session to assess the stability of your preparation.

3.2

Your Project

Your project is the main educational experience of this laboratory. You and your partner should plan your project well in advance of going to the laboratory. You need not study material on compound action potentials (or cellular mechanisms) beyond reading pages 1-20 in Volume 2 of the course text. The goal is to design and conduct an experimental test of an hypothesis related to compound-action-potential (CAP) behavior. If your knowledge of theories for neuroelectric phenomena is weak, that’s fine; you only need to think through your test of your hypothesis. 17

The following example projects are concerned with stimulus-response relations, spatial variations in the response, or effects of external agents. You may choose one of these or you can construct an entirely new one. The descriptions given here are incomplete. Your plan should be well-defined. Keep it simple so that you can complete the work, including some preliminary plotting of results and thinking about interpretation within a one-hour lab session (dissecting the nerve and doing the basic observations will take at least 2 hours). Your experimental manipulations should avoid actions that may alter the nerve’s responsiveness over a long term. 3.2.1

Projects Exploring Stimulus-Response Relations

CAP responses are generally not linearly related to the stimulus. A project may focus on a feature of the CAP and its dependence on the stimulus. Four examples follow.

1 Iso-response contours Motivation: Non-linear systems are hard to characterize. One possibility is to look for a set of inputs that are “equivalent” in that they produce identical responses. Hypothesis: A set of rectangular-pulse stimuli (height E and duration F ) can be found for which the CAP response is identical. Methods: For each of 10 pulse durations, determine the pulse height required to produce a particular response. The function EGHFI that describes the stimulus parameters yielding a fixed response is a “iso-response contour” called a “strength-duration” curve.

1 Characterizing post-response excitability Motivation: After a nerve has responded to a stimulus, its response properties are temporarily changed. The most prominent change is that for a few milliseconds after a response the nerve is less responsive, or “refractory.” Hypothesis: The refractoriness of a frog sciatic nerve can be described by an iso-response curve (such as Figure 1.13 on page 13 of Volume 2 of the course text) for the second of two stimuli. Method: Stimulate with a pair of short pulses. Vary the interval J between the first and second. Determine how the height of the second pulse EK, must be chosen so that EK,LMJN describes an iso-response contour for the response to the second pulse.

1 Does refractoriness disappear for small CAP’s? Motivation: A simple stochastic description for a population of nerve fibers might be that all are identical but each has a threshold value that is described by a probability distribution. In response to a short stimulus pulse all neurons will respond whose thresholds are exceeded by the stimulus. With this model, if a stimulus is so small that only a small fraction (say 1%) of the fibers respond, then 99% will not be refractory for a second stimulus delivered shortly afterward. Hypothesis: If stimulus level is low enough, the response to a second pulse will be essentially identical to that of an identical first pulse independent of the interpulse pulse delay. 18

Method: Straightforward.

1 Response components. Motivation: Peripheral nerves are made up of nerve fibers of different diameters (Figures 1 and 2). Plots of numbers of fibers in particular diameter ranges have peaks indicating distinct size classes. These categories might have different response properties, e.g. different thresholds, propagation velocities, refractory periods. Hypothesis: Smaller nerve fibers have higher thresholds and lower propagation velocities than larger fibers. Method: Investigate the fine structure of the monophasic compound action potential. Is it unimodal, or are there multiple peaks? Two peaks may represent populations of fibers with different diameters. Determine whether each of the peaks has the same or a different threshold.

1 Where is the CAP initiated? Motivation: The electric stimulus is delivered to a region of the nerve defined by the stimulus electrode locations. Does a propagated action potential begin at one or the other stimulus electrode? Hypothesis: The anode is the site where the CAP is initiated. Methods: Measure the time of occurence of some feature of the response for different configurations of the stimulus electrodes. For example, interchange the anode and cathode. Alternatively, connect the output of the stimulus isolator to electrodes that are usually used for recording (i.e., R1-R12). 3.2.2

Projects Exploring Spatial Variations in Response

1 CAP amplitude and nerve diameter Motivation: If each nerve fiber generates a similar response, then a large nerve consisting of many nerve fibers should generate a larger CAP than a smaller nerve which contains fewer fibers. Hypothesis: CAP amplitude will decrease monotonically with decreasing nerve diameter. Methods: Try to demonstrate that the hypothesized relation holds for several stimulus configurations, e.g. stimulating at both the small and large ends of the nerve.

1 CAPs represent propagating waves. Motivation: Neural signals generated at one end of the nerve produce a CAP at the other end. A common view is that a stereotyped pulsatile waveform propagates along the nerve fibers from one end to the other. Hypothesis: All features of the CAP’s spatial dependence along the nerve can be interpreted as a sum of waveforms generated by a pool of similar neurons in which propagation velocity increases with fiber diameter. 19

Methods: Observe waveform of CAP at different recording locations and compare features of the response (e.g. time of peak, height of peak, width of peak) to predictions based on your hypothesis.

1 Superposition of responses from branches. Motivation: Careful dissection of the nerve below the frog’s knee can yield two branches of roughly equal size. These branches can then span over common recording electrodes and thereby extend the length of many fibers in the recording chamber. Hypothesis: The response recorded from the region where two branches are in contact with the recording electrodes is the sum of the responses recorded with each branch alone. Methods: Record with branch “a” alone, branch “b” alone, and both “a” and “b” on the electrodes. Try to maintain the quality of contact of electrodes to nerve branches. Controls (repeats after manipulation of branches) will be important. 3.2.3

Projects Exploring External Agents

Numerous possibilities exist for applying disturbances that may affect the neural response. Categories of agents include chemical, electric, mechanical, and thermal. Chemical possibilities include ions that are important in action potential generation (Na/ and K / ), and agents that affect neural responsiveness (e.g. novacaine, caffeine, alcohol). Electric disturbances include active application of (say) direct current to a section of the nerve, or passive alteration of the conductivity of the nerve’s environment. In every case the methods are similar. We present one example.

1 Conductivity around the nerve and propagation velocity. Motivation: If action potentials propagate through the flow of currents from one region of a nerve fiber to an adjacent region, then decreased resistance to current flow should speed up the propagation. Hypothesis: Increasing the conductance between two locations on the nerve on the outside of the nerve will increase the propagation velocity in that region. Methods: Stimulate at one end, record at the other. Place an external resistor between two electrodes near the center. Describe the change in response and inferred propagation velocity.

3.3

Practical Considerations in Choosing a Topic

Projects can involve any of the topics discussed in Section 3.2 or a topic of your own creation. If you create a novel project, you must obtain any supplies or equipment that is not part of the standard laboratory setup described in Methods. For example, studying the effects of caffeine on the compound action potential is a good project. However, we do not stock caffeine: you would have to obtain the caffeine. Also, studying the effects of the shape of the electric stimulus (e.g., rectangular versus triangular waveforms) could be interesting. However, our electrical stimulator (Grass S88) generates only rectangular pulses. You would have to obtain a suitable waveform generator. 20

When you choose your topic, remember that your experiment should take approximately one hour to complete. Think through how many measurements you will need to make and how long it will take to make each measurement. For example, it could take a long time — possibly hours — to reverse the effects of a drug. Reversal time often depends on the size of the dose. Therefore, it is generally prudent to investigate effects of small doses first. Formulate a specific and testable hypothesis, and center your project on that hypothesis. Avoid vague hypotheses, such as: “I would like to understand how temperature affects the compound action potential.” Instead choose a more narrrowly focused hypothesis, such as: “Decreasing the temperature of a nerve will decrease the conduction velocity of the compound action potential.” This more-focused hypothesis is testable: it can be true or false. If you form a clear hypothesis, you will be able to plan a logical set of measurements to test the hypothesis, and you will be able to come to a clear conclusion when you write your report. When you do your experiment, you may get unexpected results. For example, you may have planned to measure temperature-induced changes in velocity of the compound action potential, but you may also find large changes in amplitude. There may even be a temperature below which there is no compound action potential at all. You should explore unexpected results and try to understand their bases. Your aim should be not simply to reject or accept your hypothesis, but to develop insight into the phenomena. For example, perhaps compound action potentials fail to occur at low temperature because the threshold current is larger at low temperatures. If so, it might be better to determine the threshold current for each new temperature and then measure the conduction velocity when the stimulus current is equal to (for example) twice the threshold current. Keep in mind that this is an experimental project. Your goal is to characterize what happens, not why it is happening. Theoretical ideas about neural mechanisms will be the basis for your second project (the Hodgkin-Huxley project).

3.4

Control Observations

Control observations are important parts of the design of any experiment, particularly when investigating living systems, which are labile. The purpose of a control observation is to determine whether the variable that is directly manipulated by the experimenter is the one that controls the change in response. Suppose, for example, that you wish to determine the effect of crushing the nerve on the compound action potential. You could (1) measure the response between two electrodes, say R7 and R8, (2) crush the nerve at a point between those two electrodes, and (3) repeat the measurement. Now suppose that the responses are different. How do you know that the difference was caused by the crushing? Perhaps in the process of crushing, you also moved the nerve to a different part of the electrode that is corroded so that it makes a poor electric connection to the nerve! Perhaps you stretched the nerve so that it was damaged at a site that is remote from the crushing site! Perhaps you tilted the experimental chamber just enough so that saline in the bottom of the chamber now shorts out one of the electrodes! Control observations are intended to assess the extent to which factors that are not part of the experimental design are contributing to response patterns. A good control observation for the nerve crushing example would be to measure not only the response between R7 and R8 but also

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the response between R6 and R7. The intentional manipulation is the crushing between R7 and R8, which should have no effect on the response between R6 and R7. Therefore, if crushing the nerve also changes the response measured between R6 and R7, then the manipulation did more than just affect the nerve at the site of the crush. One variable that is not under the control of the experimenter is the passage of time. Each observation that you make will happen at a different time, and it is important to know the extent to which differences in responses simply reflect the passage of time. To assess this effect, one can design a control in which a particular measurement is periodically repeated throughout the

experiment. For example, one could measure the diphasic response between R4 and R5 to a 10 A

pulse of current with a duration of 100 s at the beginning of the experiment and at 10 minute intervals throughout the experiment. If the responses differ, then the passage of time is an important factor that must be considered when the data are interpreted.

4 Proposals, Reports, and Logistics 4.1

Scheduling a Laboratory Session

Students should schedule a time slot for their laboratory session by submitting an electronic schedule form, available on our home page (http://umech.mit.edu/6.021J/index.html). At that time, you may also request a partner. The laboratory accomodates 8 students in each session. We will work out the laboratory schedule on the afternoon of September 17. You have the best chance to get your most desired time slot by submitting your schedule form BEFORE SEPTEMBER 17 AT NOON. After initial laboratory assignments have been made, you will be permitted to change your laboratory session only if you request the change more than 24 hours before your assigned slot and only if there is an open slot in the schedule at your desired time. The laboratory schedule will be posted on the WWW.

4.2

Proposal

After your laboratory session has been scheduled, you should meet with your partner to plan your project and to write a proposal. The proposal should contain a brief statement of the hypothesis you propose to test and the method that you will use to test it. Include a list of the experiments you will perform and the measurements you plan to make in each experiment. Indicate how the measurements will be used to help you test your hypothesis. The proposal should fit on a single sheet of paper. A sample proposal is shown in Figure 9. The proposal should be submitted before 5 pm on Monday, September 20, 1999. Electronic submission via email2 to [email protected] is encouraged. The staff will review the proposals and make suggestions. Acceptable proposals will be APPROVED; flawed proposals will be REJECTED. Proposals that are not approved may be revised and resubmitted. All proposals must be approved before 5 pm on Friday, September 24, 1999.

2

Please submit simple ascii text; please do not submit vendor-specific formats.

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Proposal: Effects of Temperature on Compound Action Potentials of the Frog Sciatic Nerve Partner Names (E-mail): Partner One ([email protected]) and Partner Two ([email protected]) Hypothesis: Decreasing temperature will decrease the velocity of the compound action potential of the frog sciatic nerve. Background: The speed of many chemical reactions tends to increase as temperature increases. Therefore, it seems plausible that the speed of neural conduction might similarly depend on temperature. Procedure: We will obtain a 100 mL sample of Ringer’s solution on the day before our laboratory session, and place the solution in a refrigerator to chill it to approximately 4  C. After performing the basic observations described in the laboratory manual, we will rinse the nerve with chilled Ringer’s solution and place 10 mL of chilled Ringer’s solution in the bottom of the nerve chamber. We will place a small thermocouple in contact with the distal end of the nerve to monitor it’s temperature. We will then record diphasic compound action potentials at three pairs of electrodes: R1 and R2; R3 and R4; and R5 and R6. These measurements will be repeated once a minute for 10 minutes. We will record the temperature at the time that each measurement is made. The speed of the compound action potential will be measured by dividing the distance between the first and last pairs of electrodes (4 cm) by the difference between the times of the first negative peak of the compound action potential measured on the first and last electrode pairs. Measurements using the center pair of electrodes will be used to check consistency: if the speed measured from the first pair to middle pair differs significantly from that measured from the first pair to last pair, we will investigate the source of the difference. We obtained a thermocouple by special arrangements that we made with the TA. We have also tested the basic method by measuring the temperature of a piece of thread that was mounted in an experimental chamber as though it were a nerve. We found that the temperature increased from about 15  C to about 25  C over a time course of about 10 minutes. We therefore expect that we have time to repeat this experiment three times to check the repeatability of our results. Figure 9: Sample proposal.

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4.3

Project Report

The project report should be concise. Do not repeat material that is easily referenced. For example, there is no need to reproduce any figure from this laboratory manual or from the course text: simply refer to it. Technical writing is necessarily directed at some particular intended audience. Write the project report as though it were to be published in a journal that is read primarily by students who have taken this subject. Thus, you can assume some working knowledge about the subject. The project report should contain the following sections. Cover Page. On the cover page include the title of the laboratory session, the authors’ names, your laboratory subsection, the dates of the laboratory session(s), and the name of your partner (if not a co-author). Abstract. The abstract is a one paragraph ( O 100 words) summary of the report including the question investigated, the methods used, and the principal results and conclusions. Your intended audience should be able to understand the abstract without having to read any of the report. This section should be written last. Introduction. The introduction is a brief section (about 1 page) designed to motivate the reader. Include background information on the problem, hypotheses to be tested, significance of the work, etc. You may give citations to material in this laboratory manual or elsewhere. The introduction should be directly relevant to your report; broad discussions of neurophysiology or brain function are not needed. Methods. Briefly describe any special methods that you used that are not in this laboratory description. Give details of calculations used to obtain the results. Do not repeat material that is in this description; just refer to it. Results. Describe the measurements (whether or not they fit with expectations) in the results section. Generally, results can be communicated more efficiently and accurately with pictures and graphs than with words alone. Describe those aspects that are important to your interpretation, but omit interpretations from this section. A collection of printed graphs without a written description of their relevance is unacceptable as a results section. Students frequently err on the side of including a large number of graphs and little description of their relevance. You need only include results that are relevant to your conclusions. Most of us have trouble leaving things out. Ask yourself why a particular result is a necessary part of your story; omit those that aren’t necessary. Discussion. In the discussion section, assess the results for dependability and accuracy, and interpret results in the light of other knowledge. The discussion section can include relevant speculations and ideas for improving the experiment to test the hypotheses more rigorously. Appendix. The appendix should include a copy of the protocol taken during the laboratory session.

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4.4

Grade

The grade for the experimental project will be based on the proposal and on the project report using the following considerations: Proposal (10%). The proposal should reflect a carefully constructed plan. Thinking about what you plan to do before entering the laboratory is crucial to collecting meaningful data when you are there. Late proposals will receive no credit. First draft & Critique (10%). Your first draft and your critique of a colleague’s first draft will be graded primarily for completeness. Protocol (10%). The protocol should provide enough information so that a reader can follow the course of the experiment. Indeciphereable scribbles will receive no credit. Report structure (10%). The sections of the report should be coherent. Clarity/Conciseness (20%). A good report is easy to read. The content of each paragraph and each graph should be clear. Everything included in the report should be there for a reason. Points will be deducted for extraneous material. Reports should be less than 10 pages long, unless there are good reasons for additional pages. Conceptual correctness (20%). Are there clear errors? Are the results confused? Are the results (which follow directly from the measurements) confused with the interpretations (which rely on information other than what was observed)? Insightfulness (20%). Insightfulness can be demonstrated by (1) proposing an experimental method that can resolve some scientific issue, (2) carrying out experiments and/or analyses that lead to clear conclusions, (3) preparing a report that demonstrates a clear understanding of the strengths and weaknesses of your results and analyses. Simply performing one of the standard experiments and showing unmotivated measurements will receive 0 points. Clever design of an experiment or imaginative analysis of the results will receive 20 points. Demonstrating a clear understanding of your experiment, your analyses, and what can be concluded is sufficient for 10 points. DUE DATES ARE FIRM, AND THERE IS A SEVERE LATENESS PENALTY. The grade for a late report will be multiplied by a lateness factor

PRQ  S

0UTWV -

 S , > 0UTWVYX

where  is the number of hours late. The lateness factor is plotted in Figure 10. Notice that the maximum grade for a report that is more than ONE DAY LATE is less than 50%.

References Carolina Biological Supply Company (1965). Frog musculature. Ochs, S. (1965). Elements of Neurophysiology. John Wiley & Sons, Inc., New York, NY.

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Lateness factor L

1.0



0.5



0.0

[one day 1

Z

10 100 Time t past deadline (hours)

Figure 10: Lateness factor.

Patton, H. D. (1960). Special properties of nerve trunks and tracts. In Ruch, T. and Fulton, J. F., editors, Medical Physiology and Biophysics, pages 66–95. W. B. Saunders Company, Philadelphia, PA. Ruch, T. C., Patton, H. D., Woodbury, J. W., and Towe, A. L. (1965). Neurophysiology. W. B. Saunders Company, Philadelphia, PA. Tasaki, I. (1953). Nervous Transmission. C. C. Thomas, Springfield, IL. Young, J. Z. (1951). Doubt and Certainty in Science. Oxford University Press, London.

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