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Membrane Properties: Resistance, Capacitance, and Electrophysiology

Introduction

This lab illustrates passive electrical properties of cell membranes while introducing basic principles of electrophysiological recording, data acquisition, and analysis. Intracellular and extracellular recordings of electrical activity in the nervous system are the basic tools of neurophysiology. From them have descended today’s most powerful methods of studying nerve cell activity, voltage clamping and patch clamping. Passive electrical properties of excitable tissue are critical factors that determine electrical conduction in nerve cells (Siegelbaum and Koester, 2013). For example, space and time constants determine the conduction velocity of action potentials and the temporal/spatial integration of synaptic potentials in the brain (Byrne and Shepherd, 2009; Koester and Siegelbaum, 2013).

Model Membrane

You will first use a battery and a model membrane to simulate the electrical activity of a neuron. The model membrane is a ladder-like chain of resistors that approximates the steady-state electrical characteristics of a real cell membrane. Figure 1.1 represents the model membrane schematically. In this model, Rm (membrane resistance) represents the resistance of all the ion channels in the cell membrane, Ri (internal resistance) represents the resistance of the cytoplasm, and Ro (outside resistance) represents the resistance of the extracellular fluid. A battery will simulate an electrical potential traveling through the membrane. Instead of the electrodes, amplifiers, and oscilloscope that are required for real neural recordings, you will use a voltmeter to examine the response of the model membrane. Figure 1.2 shows how the recording techniques you will use with the model membrane correspond to those used in real cells.

Intracellular Recording

Figure 1.3 shows the setup for intracellular recording. Connect the voltmeter at the middle of the model membrane. Be sure that the positive electrode is placed on the designated inside of the resistor ladder and that the negative electrode is directly across from it on the outside. Start with the battery at the left end of the model with the positive terminal connected to the inside and the negative terminal connected to the outside. Record the voltage at the voltmeter. Now move the battery to the right, moving both the positive and negative terminals over by one position and recording the voltage for that battery position. Continue this procedure until the battery has reached the right end of the model membrane. At each battery position, record the voltage level and the position of the battery (node 1, 2, 3, etc.).

Extracellular Recording

Figure 1.4 shows the setup for extracellular recording. This time, place both terminals of the voltmeter on the outside of the model membrane. Connect the voltmeter near the middle of the model, leaving two resistors between the terminals, as shown. As before, move the battery from one end of the model membrane to the other, recording the position and voltage at each node.

Model Membrane Questions

  1. Plot voltage vs. position for both intracellular and extracellular recordings.
  2. Is the maximum voltage the same for both types of recording? Why or why not? For help answering this and the next two questions, refer to Video 1.1, Current Flow, and note that the voltmeter measures the difference in potential between the positive and negative electrodes.
  3. The extracellular recording changed polarity when the battery passed the electrodes. Why? Why did this not happen with the intracellular recording?
  4. What happened to the extracellular recording when the battery was between the voltmeter electrodes? Why?
  5. Describe the decay of the voltage from its peak in the intracellular recording. Calculate a space constant from the measured voltages (solve for λ in Equation 4, Passive Spread, Vx = V0e−x/λ, where V0 is the voltage measured when the battery was at the recording site and Vx is the voltage measured when the battery was x nodes away from the recording site). Compare this value with one calculated from the resistances using Equation 3, Space Constant (λ = (Rm/(Ri + Ro))½; Rm is 10 kΩ, Ri is 1 kΩ, and Ro is 100 Ω in the model membrane). In the model and in real biological membranes, Ro is so small compared to the other resistances that it can usually be ignored.
  6. How would an increase or decrease in Rm or Ri affect the spread of voltage in a neuron? (Explain using Equation 3, Space Constant (λ = (Rm/(Ri + Ro))½.) Why is this even important to consider? (Hint: Think about how action potential conduction velocity depends on the spread of electrical current along an axon.)
  7. With the values of Ro, Ri, and Rm, calculate the input resistance of the model membrane with Equation 5, Input Resistance (Rinput = ½(Rm(Ri + Ro))½). Input resistance is a measure of the cell’s total resistance, which includes membrane, axoplasmic, and extracellular resistance. How could you measure this value in the model membrane? Why is this an informative experimental parameter? Design an experiment to measure Rinput in a real cell. (Hint: You could calculate Rinput by Equation 1, Ohm’s law, E = IR.)

Time Constant

A complete model of the axon would include the capacitance of the cell membrane. A capacitor is an electronic device that consists of two conducting plates separated by a thin insulator. Since the lipid bilayer is an electrical insulator between two conducting areas (extra- and intracellular fluids), it acts as a capacitor, while ion channels act as resistors. A voltage change on one side of a capacitor causes redistribution of charge on the other side. For example, if one side of a membrane becomes more positive, positive ions are repelled from and negative ions are attracted to the other side. This redistribution of charges takes time, after which the membrane reaches a steady state and no current flows. When the voltage across the membrane returns to its initial value, charges separated by the membrane flow again, discharging the membrane capacitance. In effect, current flows across the membrane capacitance only when voltage across the membrane changes.

You will work with a simple RC (resistor-capacitor) circuit to model membrane responses to voltage changes. Membrane capacitance is parallel to membrane resistance as shown in Figure 1.5, which shows a model of the membrane complete with capacitance and with batteries representing changes in Vm. The RC circuit you will use represents an intracellular recording from one patch of membrane when the voltage is changed.

Connect the RC circuit to the stimulator and oscilloscope as in Figure 1.6 (depending on the stimulator, your instructor may suggest reversing the + and − connections). Set the stimulator to produce a single pulse of 1 to 2 V amplitude and about 200 ms duration. On your oscilloscope or computer screen, observe the difference between the square pulse produced by the stimulator and the more slowly rising and falling pulse coming out of the RC circuit. Make sure that the duration of the pulse is long enough that the RC response is clearly flat at the top before the pulse ends.

Measure the time constant of the RC circuit, that is, the time it takes for the output to reach 63% of the peak value. Now decrease the duration of the stimulator pulse and see how this affects the peak amplitude of the RC-filtered response. Next, set the stimulator to produce a pair of brief pulses, each about 5 ms duration, with a 50 ms delay between their onsets. (Figure C.4 summarizes stimulator settings.) Gradually decrease the delay between pulses and see how the RC responses are affected.

Time Constant Questions

  1. Show a plot of the RC response. How well does your measured time constant match the time constant calculated from the values of R and C in Equation 2, Time Constant (τ = RC), given that R = 10 kΩ and C = 1 μF? How could you measure the time constant of a real neuron?
  2. What happened to the amplitude of the output of the RC circuit as you shortened the input pulse?
  3. What happened to the output of the RC circuit as you decreased the delay between two brief pulses?
  4. For simplicity, capacitors representing the capacitance of the membrane were omitted from the model membrane. What difference would it have made to your intracellular and extracellular recordings if membrane capacitance (Cm) had been included in parallel with membrane resistance (Rm) in the model membrane?
  5. Point out the biological membrane analogs of the RC circuit components. Briefly discuss the importance of the membrane time constant for the behavior of a neuron. For example, compare the effects of long and short time constants on (a) the temporal spread of voltage changes such as those initiating an action potential and (b) the summation of synaptic potentials. Refer to the results from Questions 2 and 3 in your answer.

Periodic Waveforms

For the last exercise in this series, you will record a real biological signal and send it to your oscilloscope and computer to analyze its waveform. If available, you will measure the electric organ discharges (EODs) of an electric fish. If electric fish are not available, you may use a finger-pulse transducer, the output of a microphone, or some other periodic waveform using equipment your instructor provides. The following instructions and questions apply in principle to these other waveforms.

You will use the EOD as an introduction to your recording and analysis equipment and to think of creative ways to analyze the temporal patterns of a rhythmic signal. For the fascinating details of the generation and use of the EOD, see the review by Moller (1995). This exercise focuses on the tools we have to characterize bioelectrical signals.

Your electric fish will be in a small plastic box with a piece of pipe for a shelter. Figure 1.7 shows how to connect the electrodes and recording apparatus. To get the largest EOD signal, place the positive and negative electrodes as far apart as possible. Adjust the time base of your oscilloscope or data acquisition software to capture and expand a spontaneous single EOD. Measure its duration and the peak-to-peak amplitudes of its different waveform components. For example, in the waveform of Figure 1.7, measure the amplitudes of the different positive and negative peaks. Because EODs are rapid events often having complex waveforms lasting less than 1 ms, set your computer to sample at 100 kHz (100,000 samples/s). Look at several EODs from the same fish to estimate the variability of these waveform characteristics. Decrease the sampling rate and note the effect on the recorded EOD waveform.

Now set the time base of the recording equipment to record 30 s of EODs. Examine the temporal parameters of this series of EODs. Think about how you could quantitatively describe this train of pulses. (Hint: Pulse interval is a good parameter to work with.) Compare EOD patterns when the fish is leisurely swimming around, hiding in its shelter, or disturbed from a tap to the box or other stimulation.

Periodic Waveform Questions

  1. Show a plot of an EOD with your measurements of its waveform properties.
  2. Describe what happened to the recorded EOD waveform as you decreased the sampling rate.
  3. Present an example of your analysis of the temporal characteristics of EOD patterns under different conditions of the fish’s behavior.

References