Resistive circuits
First, a few definitions. Current (I) is the net movement of charge through a point per unit time. Current may be produced by the movement of electrons in a metallic conductor, or by the movement of ions in a solution. A flow of one coulomb of charge per second is equal to 1 ampere (A) of current. A somewhat useful analogy is that electrical current is like the flow of water through a pipe.
In order to move charges (i.e. to create a flow of electrical current through a circuit), a source of potential energy must be applied. Voltage (V) is the potential difference between two points, i.e. the amount of work that is available to move electrical charge between the two points. The greater the voltage, the greater the current that will flow through a circuit. The unit of voltage is naturally the volt (V). Returning to the hydraulic analogy, it may help to think of voltage as electrical "pressure".
Conductance (g) is the ability of a physical object to pass current. The higher the conductivity of a circuit, the greater the current that will flow when a given voltage is applied. A material in which charges move very easily (such as copper wire), has high conductivity, while a material such as carbon has lower conductivity. Ion channels in neuronal membranes usually have selective conductivity; they conduct some ions more readily than others. The unit of conductance is the siemen (S). In plumbing terms, conductance is akin to the diameter of a pipe; the same amount of pressure will cause more water to flow through a large pipe than a narrow one. Resistance (R) is equal to the reciprocal of conductance: R = 1 / g. Resistance is measured in ohms.
The relationship between voltage and current in a resistive circuit is given by Ohm's Law, V = I * R, or V = I / g. A voltage of 1 V applied to a resistance of 1 ohm will cause a current flow of 1 A. Or, a current of 1 A passed through a resistance of 1 ohm will produce a voltage (measured across the resistance) of 1 V. Volts, amps, and ohms are useful units for engineering, but for electrical signals on a neuronal scale, the most appropriate units are millivolts (mV, 10-3 V), nanoamperes (nA, 10-9 A), and megohms (Mohm, 106 ohm). Conveniently, when you apply Ohm's law, these units cancel: V(mV) = I(nA) * R(Mohm). For example, applying a current of 1 nA to a neuronal membrane with an input resistance of 30 Mohm will produce a voltage change of 30 mV.
In a circuit consisting of a current or voltage source (e.g. a battery) and a single resistance, Ohm's law provides a complete description of the circuit's behavior. Analysis of more complicated circuits will require the use of several additional rules:
(1) When two or more resistors are in series, the currents passing through each resistor are equal. The total voltage across the series circuit is the sum of the voltages across each resistor.
(2) When resistors are in parallel, the voltages across each resistor are equal. The total current through the parallel circuit is equal to the sum of the currents through each resistor. Or, to put it more succinctly, voltages in series are additive, and currents in parallel are additive.
(3) When two or more resistors are in series, the total resistance is equal to the sum of their resistances (Rtotal = R1 + R2 + ... + Rn).
(4) When resistors are in parallel, their total resistance is given by: 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn. Since g = 1 / R, this is the same as saying that the total conductance is equal to the sum of the conductances: gtotal = g1 + g2 + ... + gn. In other words, resistances in series are additive, and conductances in parallel are additive.
Using these rules, you will be able to analyze the circuit shown in Figure 1. For each resistor, determine the current passing through the resistor and the voltage across the resistor (hint: begin by treating the parallel circuit R2 ... R5 as a single resistance). As a check of your calculations, the sum of the currents through R2 ... R5 should be equal to the current through R1.
For additional entertainment, replace the current source in the diagram with a voltage source of 100 mV, and repeat the analysis.
Resistive / capacitive circuits
Capacitance is the ability to store electrical charge. The unit of capacitance is the Farad (F). Physically, a capacitor consists of two conductors separated by an insulator (hence its schematic symbol, two parallel lines). Direct current (DC) cannot pass through a capacitor; the conductance of a capacitor for DC current is zero. Therefore, capacitance will not affect the steady-state or DC properties of a circuit. However, when a voltage that changes over time (AC) is applied to a capacitor, a capacitive current (Ic), proportional to dV/dT, will flow.
To examine the effects of capacitance, consider a purely resistive circuit consisting of a variable current source in series with a 50 Mohm resistor (Figure 2A). Initially, the output of the current source is 0, and there is no voltage across the resistor. At time 0, the current source is switched on and delivers a current of 1 nA. Immediately, a voltage of 50 mV will be produced across the resistor. When the current is stopped, the voltage will instantly fall to 0. Thus, a square pulse of current applied to a resistive circuit produces a square pulse of voltage. Now, add a capacitor in parallel with the resistor (Figure 2B). When the current is switched on, most of the current will flow into the capacitor (Ic), because dV/dT is initially large. Only a small fraction of the total current will flow through the resistor (Ir), producing a small voltage drop across the resistor. As the capacitor accumulates charge, Ic becomes smaller and Ir increases. The voltage change (V * Ir) will follow an exponential course, as shown in the figure. Finally, the voltage reaches a steady state, and since dV/dT= 0, no current flows through the capacitor. An RC circuit is characterized by its time constant (tau), which is equal to R * C. The time constant is the amount of time in which a voltage change will reach 63% (1-1/e) of its ultimate value (Figure 2C).
This example is relevant because a neuron is equivalent to a capacitance (the membrane) in parallel with a resistor (the total membrane conductance). The time constant of the membrane is important in determining the neuron's response to its inputs. Time constant is also a good indicator of the health of a neuron; decreases in Rm, such as those produced by bumping the electrode and tearing a hole in the cell, will produce a corresponding decrease in tau.
Microelectrode resistance and compensation
The very small diameter (about 1 µm) of the microelectrode tip impedes the passage of ions, and therefore the microelectrode has high (10s of Mohm) electrical resistance. When the tip of the electrode is inside a cell, the electrode resistance (Relec) is placed in series with the cell's membrane resistance (Figure 3). This presents a special problem for the neurophysiologist. As long as no current is passing through the electrode, there will be no voltage across Relec, and the measured potential that is "seen" by the electrometer (Vmeas) is equal to the true membrane potential (Vm). However, when current is passed through the electrode, a potential (Velec) is developed across the electrode. Since the electrode is in series with the membrane, the potentials add, and Vmeas is equal to the sum of Vm and Velec. In this lab, the resistance of the electrodes we will use (about 50 Mohm) is close to the Rm of the neurons we will record from. Therefore, if you do not account for electrode resistance, your measurements of Vm could be substantially inaccurate.
Conveniently, the electrometer has an electrode compensation circuit that subtracts a voltage, proportional to the amount of current being passed, from Vmeas. If the circuit is correctly adjusted or "balanced", the subtracted voltage will be equal to Ve, the effects of electrode resistance will be eliminated, Vmeas = Vm, and all is well. Figure 4 demonstrates the process of balancing the electrode. It's easiest to do so when the electrode is in the bath, by applying a current pulse to the electrode. Since the only resistance in the circuit is Relec, the compensation circuit is adjusted to eliminate all of the resulting voltage change. If the electrode is overcompensated, the voltage pulse will appear to reverse polarity.
Unfortunately, Relec seldom remains constant during an experiment. The tip of the electrode may clog or open up slightly when entering a cell, making it necessary to balance in the cell. This is a process of eyeballing the voltage response of the electrode and cell and eliminating the fast change in voltage due to Velec, leaving only the smooth charge curve produced by the membrane (Figure 4, bottom).
Isolation table and Faraday cage
In order to provide some isolation from mechanical vibration, the recording setup is mounted on a rigid steel table, which is supported by four pneumatic cylinders. The table should "float" on the cylinders. Before beginning recording, check that all corners of the table move easily up and down. Be sure that nothing is touching the table or the cage (the flexible light pipes are the worst offenders). Even with the air table, isolation is not perfect, and external vibration should be avoided. Handle everything on the table delicately, don't bump the lab benches, and try not to jump up and down when you get your first cell. The cage surrounding the air table provides shielding against capacitively-coupled sources of electrical noise. The cage should be connected to an electrical ground (e.g. the equipment rack) by a jumper.
Binocular microscope
You will use the binocular microscope at low power to determine the orientation of the ganglion, and at high power to visualize individual cell bodies. The microscope is also useful as a rangefinder; with some practice, you can determine the vertical position of the electrode tip by focusing up and down between the tip and the surface of the ganglion. The binocular microscope has adjustments for focus and magnification (zoom). One eyepiece is adjustable to compensate for differences between your eyes. The mounting boom of the microscope should be grounded.
Recording chamber and stage
The bottom of the plastic recording chamber is lined with transparent rubber, to which the preparation is pinned. Keep the chamber full of leech ringer, and change solution with a pipette every 30 min, unless you are in the middle of a successful recording. Change the bath solution immediately if you break an electrode.
Micromanipulator
Intracellular recording requires very precise and stable positioning and movement of the electrode. Neurophysiologists, usually acting on a dare, have occasionally attempted intracellular recording using hand-held electrodes, but such attempts are misguided and basically a waste of time. You will use a mechanical micromanipulator to maneuver your electrodes. Spend some time familiarizing yourself with the operation of the micromanipulator. It has three axes of movement: vertical, horizontal, and plunge. The plunge axis is parallel to the axis of the microelectrode, and will be used to make the final advance of the electrode into a cell. Each axis has both coarse and fine adjustments. Note that the fine adjustments have a limited range, as indicated by the 0-10 scale marked on the manipulator. Do not go outside of this range!
Electrode holder and headstage
The electrode holder provides a stable mechanical and electrical connection to the intracellular electrode. The holder has a bore that precisely fits the outside diameter of the electrode and a rubber gasket that clamps down on the electrode when the holder is tightened. Inside the holder is a small silver chloride pellet that makes electrical contact with the solution inside the electrode. The holder plugs into the headstage, a pen-sized cylinder that mounts on the micromanipulator and houses some of the electrometer circuitry.
Intracellular microelectrodes
Please do not even think about touching the electrode puller until you have had individual instruction in its operation. We will use microelectrodes that are formed in an electrode pulling machine by heating a glass capillary and applying tension until the capillary stretches and separates into two pieces. The microelectrode tapers to a slim shank, with a tip opening of about 1 µm diameter. The electrical resistance of the electrode is related to the tip diameter. A good electrode for leech neurons will have a resistance of 20-40 Mohm when filled with 4 M KCl. Handle electrodes carefully. The tip of the electrode is very fragile; if the tip comes in contact with anything, you can assume that it is broken. It's also sharp; if the tip comes in contact with your skin, you can assume that it will cause pain. Dispose of electrodes in the cans provided, not in the trash.
Electrometer (AM Instruments Neuroprobe)
The electrometer (also called an intracellular, or current clamp, amplifier) allows the measurement of intracellular potentials and injection of current through the recording electrode. The X1 (Vm) output of the electrometer should be connected to the CH 1 input of the oscilloscope, and the CURRENT output should go to CH 2. The electrometer also has a digital meter, which is more convenient to read than counting divisions on the oscilloscope screen. The meter will display either the electrode potential, injected current, or electrode resistance, depending on the setting of the pushbuttons below the meter.
In order to simply record intracellular voltage, there is actually very little that has to be done to the electrometer. The DC OFFSET control should be zeroed so that the meter reads 0 mV when the microelectrode is immersed in the bath (i.e. before entering a cell), and the LOW PASS filter should be set to about 10 kHz to reduce noise. That's it.
Things get more complicated when you want to inject current. There are two ways to inject current: with the electrometer's internal current source or with the external stimulator. The internal current source is controlled by three controls: the CURRENT knob and the CONT/OFF/ MOMEN. and POLARITY switches. The CURRENT knobs controls the amount of current generated by the internal source, and the POLARITY switch determines whether the internal current source is positive (depolarizing) or negative (hyperpolarizing). To inject a continuous current, move the switch to CONT. To inject a short pulse of current, press the switch to the MOMEN. position; the current will stay on until you release the switch.
Current pulses generated by the stimulator (see below) can be applied to the external CURRENT input. For this purpose, the switch must be set to CONT. Current generated by the internal source will add with current from the external stimulator. If you want to inject a current pulse from the stimulator without any current from the internal source, turn the CURRENT knob to its zero position.
As discussed above in Section 1, the electrometer has a compensation circuit to subtract electrode resistance from the measured electrode potential in order to give a true reading of Vm. The amount of compensation is adjusted by the DC BALANCE knob; the higher the electrode resistance, the higher the setting of the knob will need to be.
Stimulator (Grass Instruments SD9)
The stimulator simply provides a square voltage pulse of adjustable amplitude (0.1 to 100 V) and duration (0.02 to 200 ms). A pulse is produced each time the MODE switch is pressed to the Single position. If the same switch is set to the Repeat position, the pulse will repeat at the rate set by the Frequency control (0.2 to 200 Hz). To read these parameters, multiply the knob setting by the value of the multiplier switch.
You will use the stimulator primarily to deliver current pulses through the intracellular microelectrode. For this purpose, the output of the stimulator is connected to the Current Input of the electrometer. We have installed a resistor at the output terminals of the stimulator to reduce the output voltage so that an amplitude setting of 1 V will produce a current of 1 nA through the electrode. This has the added benefit of preventing enthusiastic neurophysiologists from zapping themselves, each other, or the equipment with excessive quantities of voltage.
Oscilloscope (Gould Electronics)
The oscilloscope displays voltage on the vertical axis and time on the horizontal axis. You will use the two channels to display membrane potential (CH 1) and injected current (CH 2). For CH 2, 10 mV on the oscilloscope corresponds to 1 nA of current. The oscilloscope can display a very wide range of voltages. The range for each channel is controlled by the V (increase) and mV (decrease) buttons. The range is expressed in V or mV per "division"; a division is one box on the screen. For intracellular recordings, the 10 mV/division range is usually appropriate: neuronal resting potentials are about -50 mV and action potentials are 80-100 mV in amplitude. The useful range of injected current is about +/-5 nA, which is +/- 50 mV on the oscilloscope, so CH 2 should be set to about 10 mV/division.
The time base of the oscilloscope is the amount of time represented on the horizontal axis, i.e. the amount of time taken for the oscilloscope beam to move across the screen. The time base is controlled by the sec (increase) and msec (decrease) buttons. A time base of 5 or 10 msec/div is usually good, but you may want to use slower speeds to examine the firing behavior of neurons.
An important concept in the use of the oscilloscope is triggering. Often, you will want to synchronize the oscilloscope trace with an external event, such as an intracellular action potential. The trigger circuit causes the scope to wait until a selected input reaches a threshold level before running a trace across the screen. The Source switch selects the input that does the triggering: Ch. 1, Ch. 2, or the External Trigger input. Most of the time, the triggering event will be an injected current pulse generated by the stimulator, so you will want to use the External Trigger input, which is driven by the stimulator.
Once a trace is on the screen, it will stay there until another trigger event occurs. To make sure that a valuable trace is not erased from the screen, press the Trace Hold button. This will "lock" the trace on the screen and cause the scope to ignore subsequent triggers while you admire and save your data. While the trace is on the screen, you can perform measurements using the POST STORAGE controls, as described in Section 3.
For other purposes, (such as measuring resting potential), you just want to see a trace on the screen, and there is no event to trigger the scope. In this case, press the Auto Trigger switch, and the scope will continuously re-trigger as soon as the previous sweep is complete.
Data acquisition system
After a trace is stored on the oscilloscope screen, as described above, you will often want to save it for further analysis. Way back in the old days (i.e. when I started grad school), this was usually done by photographing the screen with a Polaroid camera. Most late 20th-century researchers now use computers to record and analyze their data. To do so, you will use a Macintosh program called IGOR. The basics of the program will be described here, and a more complete demonstration will be provided in lab.
To launch the program, double-click on the Readscope icon on the Desktop, which will run the program and load a macro for reading data from the oscilloscope. When you have a trace on the screen that you want to save, press the Trace Hold button on the scope to lock it. In IGOR, pull down the Macros menu and select Readscope. The oscilloscope trace should appear on the computer display.
Once a trace is in IGOR, you have a few options. Additional traces can be overlaid on the existing graph with the Appendscope macro. Using the Readscope macro again will acquire a trace into a new graph. In the File menu, the Save option will save the data you have collected to disk. Be generous about saving your data; if you have even the slightest suspicion that you might want to see a trace again, save it. Just be sure to document each trace adequately and keep your data files organized.
Audio amplifier
The audio amplifier is useful for listening to the firing pattern of a cell once you have obtained a stable recording. At all other times, the audio amplifier is likely to produce disturbing buzzes and shrieks. Please keep the volume all the way down at these times to avoid annoying your colleagues and angering the faculty.
Oscilloscope fun
Turn on the oscilloscope. Unplug the cable from the CH 1 input, plug in the test leads (the cable with red and black clips on one end), and connect the red clip to the Cal 1v terminal on the scope. Set Ch. 1 to DC and On, select Auto triggering and adjust the V/DIV and TIME/DIV controls to visualize the square wave on the screen. Now, select Norm and CH 1 on the triggering control panel, and adjust the trigger level to stabilize the square wave. Determine its amplitude and duration. Try out the vertical and horizontal position controls. Press the Select Trace button to turn on cursor measurement; as you move the cursor with the left/right buttons, the horizontal (time) and vertical (voltage) coordinates of the cursor will appear at the bottom of the screen. Cursor measurements are relative to the horizontal and vertical baselines, which can be adjusted by selecting Dat. on the POST STORAGE/ DATUM panel and using the up/down and left/right buttons.
Ask one of the instructors to connect a waveform generator to the oscilloscope. Without looking at the settings on the waveform generator, adjust the oscilloscope to visualize the wave, and determine it's shape, amplitude, and period. Next, randomly change the waveform generator settings and have another member of your group do the same.
Model cell
Replace the cable that goes from the Vm output of the electrometer to the CH 1 input of the oscilloscope. Set CH 1 and CH 2 to DC, 10 mV/DIV, and the TIME/DIV to 10 msec. Set triggering to Auto, and you should see two traces on the screen. Position the CH 1 trace near the top of the screen. Connect the model cell to the electrometer probe (the alligator clip attaches to the ground screw on the back of the probe) and put the switch in the Bath position; in this position, the model cell simulates a high-resistance electrode sitting in the recording bath.
On the electrometer, set the LOW PASS filter to 10 kHz, and turn the rest of the knobs fully to the left (but do not click the small TRANSIENT knob completely off). Switch CURRENT INJECTION to off (center). Press the METER PROBE MV button; all other buttons should be out, and you should see a reading of 000 on the digital meter.
Set up the stimulator to apply a -1 nA pulse to the model electrode, and use the triggering functions of the oscilloscope to visualize the resulting voltage pulse. While you are doing so, experiment with external triggering vs. triggering from CH 1 and CH 2. Measure the voltage drop across the electrode and determine Relec. Use the electrode test function of the electrometer to read Relec directly on the panel meter. If the two measurements don't agree, figure out why. Now set the stimulator to repeat at about 2/sec. Use the DC BALANCE control to cancel out the electrode resistance (Figure 4). Try overcompensating Rm, and then apply a current with the internal current source. Observe that the response will appear to be backwards: as you apply a negative current, the measured voltage will become more positive. Re-balance the electrode and all should be well.
Switch the model cell to the CELL position. Apply the same current pulse that you used to balance the electrode previously and observe the response of the model cell. Determine Rm and the time constant (tau) of the simulated "membrane", and calculate Cm. Now turn the DC balance control all the way off, deliver a pulse, and observe the ugly sight of uncompensated electrode resistance (compare with Figure 4). Practice balancing the electrode in the cell. Once again, observe the effect of excessive Relec compensation.
Now that you have a thorough and complete understanding of the equipment, turn the power off on all the instruments and remove all of the connecting cables (the thick black ones) between the instruments. Don't remove the probe cable - it's a pain to reinstall, and it's obvious where it goes. Without looking at the diagram, figure out how to re-wire the rig in a logical manner (as a general rule, remember that outputs connect to inputs). When you think you've got it, check your work against the diagram. Hook up the model cell again and see if everything still works the way it should.
Deliver a current pulse to the model cell, store the trace on the oscilloscope screen, and use IGOR to read the scope. Change the size of the current pulse, store another trace, and overlay it on the previous trace. Practice using IGOR to display, analyze, and save traces, as discussed in the demonstration.
Micromanipulator and microelectrodes
Familiarize yourselves with the operation of the micromanipulator, taking care to observe the limited range of motion of the fine controls. Draw a diagram of the manipulator, showing the three axes of movement and their corresponding fine and coarse controls, and commit them to memory. It will be very useful next week to be able to operate the manipulator without looking at it.
Fill a recording chamber with leech saline and fix it to the recording stage with a few pieces of clay. Secure the ground electrode in the bath. Using a 1 ml plastic syringe that has been drawn to a fine, wispy tip, fill an electrode. Pull some 4 M KCl in to the syringe, insert the tip into the back of the microelectrode, and inject a drop of this solution into the very top of the electrode. Place the electrode vertically in a holder, and prepare a few more electrodes this way. In a minute or two the drop will run down, filling the tip. When you are ready to use an electrode, insert the filling syringe tip all the way and fill the electrode all the way to the top, withdrawing the syringe tip as you go. Place a drop of KCl into the electrode holder, insert the electrode, and tighten the plastic collar. Wipe off any excess KCl on the holder with a tissue and plug the electrode holder into the socket on the end of the probe.
Loosen the screw that allows the probe to rotate on the manipulator and rotate the probe into position over the chamber, being careful not to whack the electrode on the edge of the recording chamber. Practice lowering the electrode into the bath. Observe the tip of the electrode while you manipulate it. Practice following the tip of the electrode with the microscope focus as you advance it deeper into the bath.
With the electrode and ground wire in the bath, turn on the electrometer and adjust the Offset control for a reading of 0 (you may need to flip the +/- switch). If you can't zero the reading, the electrode may not be completely filled or the ground wire may not be making an adequate connection. If you're still having trouble, ask for help. Once the offset is zeroed in the bath, don't touch it again. Press the Elec. Test switch, and the display will show the resistance of the electrode in Mohm. About 20-40 Mohm is good. If the resistance is less than 20 Mohm, the tip is probably broken. Balance the electrode in the bath using the method described above.
That's about as far as you can go without some live tissue to record from. Take some time to be sure you understand all the equipment, and to troubleshoot any problems you may have discovered, such as electrical noise, poor visibility, vibration, etc.
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