The Voltage Clamp Simulation

Introduction

As is often the case in scientists’ efforts to develop a coherent picture of nature in all its facets, progress often hinges on technological advances. This has certainly been true with respect to the development of our current picture of the membrane events involved in production of the electrical signal termed and action potential. The technological advance was development of the voltage clamp apparatus. The significance of the voltage clamp apparatus is that it provides us with a way to look at changes in membrane conductance that occur over time scales on the order of ms or less. This gave researchers the ability to test important hypotheses about electrical activity in plasma membranes of excitable cells, whereas previously they had been pretty much limited to phenomenological descriptions of the cells’ electrical behavior.

The main purpose of voltage clamp experiments (including patch clamp experiments) is to gather data that allow calculation of the membrane conductance (g_m) for different ions and to monitor changes in g_m with time. A schematic diagram of the voltage clamp apparatus as used in the giant squid axon experiments looks like this:

The voltage clamp apparatus consists of a Feedback Amplifier, a Voltage Amplifier, and an Ammeter ( A ). The Voltage Amplifier is connected to a Voltage Electrode (V. E.) implanted inside the axon, and to the Feedback Amplifier. The Feedback Amplifier is connected to a Current Electrode (C. E.). Finally, a Ground Electrode completes the feedback and voltage circuits through an ammeter to ground.

The Voltage Amplifier is responsible for monitoring the membrane potential, V_m, and transmitting its value to the Feedback Amplifier. The Feedback Amplifier is responsible for maintaining V_m at the value desired by the experimenter. The ammeter displays the magnitude and direction of current flow through the membrane (I_m).

As indicated by the single-headed arrows in the circuits, information about V_m flows in only one direction, from the voltage electrode to the Voltage Amplifier, then to the Feedback Amplifier. Similarly, the clamping voltage is fed into the Feedback Amplifier by the experimenter. In contrast, current can -- and will – be sent in both directions through the I_m circuit by the Feedback Amplifier.

The first step in conducting a voltage clamp experiment is to set the value at which V_m is to be maintained. This value is termed the clamping voltage, and is entered into the Feedback Amplifier by the experimenter. Usually, the clamping voltage is entered into the feedback amplifier as a change in the membrane’s potential (dV_m) relative to its resting value, rather than as a specific V_m value.

As soon as the experiment is started by applying the clamping voltage to the axon’s membrane, the Feedback Amplifier commences comparison of the actual V_m with the desired clamping voltage. If V_m deviates from the clamping voltage, the Feedback Amplifier uses Ohm’s Law to calculate the value of I_m required to return V_m to the desired value (recall that V = I×R = I/g), and adjusts I_m based on the results of those calculations. Note that both the magnitude and the direction of the current are subject to control by the feedback amplifier, the direction being determined by whether the deviation from clamping V_m is a depolarization or hyperpolarization.

The sensitivity and response time of the system are such that V_m can be maintained with a few mV (or even nanovolts) of the clamping voltage at all times. The ammeter then records the magnitude and direction of I_m, These data allow calculation of time-dependent changes in g_m, which is the purpose of the voltage clamp experiment.

Not surprisingly, the voltage clamp experiment is still being used extensively by researchers in their efforts to understand the function of excitable cells. In fact, the technology has advanced to the point that the patch clamp apparatus allows researchers to look at the behavior of individual ion channels (the subject of another simulation in this series).

In this simulation of the voltage clamp experiment, you will work with the squid giant axon. This simulation is therefore a good complement to the Action Potential simulation you worked with previously.

What Does The Voltage Clamp Simulation Allow You To Do?

This simulation allows you to conduct voltage clamp experiments on a squid giant axon and observe the effect on trans-membrane ion currents (I_m) of changes you make in the values of several relevant parameters. Controls are provided that allow you to specify the numerical values for the clamping voltage (dV_m), external [Na⁺], and external [K⁺]. The clamping V_m can be depolarizing (dV_m > 0) or hyperpolarizing (dV_m < 0) relative to the membrane’s resting V_m.

What Does The Voltage Clamp Simulation’s Display Look Like?

When you first start the simulation, you will see a display that looks similar to the following:

The display contains two set of axes. The upper set will display tracings of current vs. time (in ms) out to 6 ms ( = 5 ms post-stimulus). The lower axis will display a graphical representation of the clamping voltage, dV_m. This feature will make it easier to keep track of your experimental progress.

Three slider/text field combinations are provided. The upper two allow you to specify the value of [Na⁺] and [K⁺] in the external medium in which the squid axon is immersed. Because this simulation is based on the squid giant axon, the default values for the two sliders are the same as the default values in the Action Potential simulation that you worked with earlier.

The third slider lets you specify the clamping voltage (dV_m;) for the axonal membrane. In keeping with convention, the slider specifies the clamping voltage as a change (dV_m) from the membrane’s resting V_m (see above). To the right of this slider are two checkboxes that allow you to specify whether the dV_m is depolarizing (dV_m > 0) or hyperpolarizing (dV_m < 0).

There are four checkboxes arrayed along the bottom edge of the display. Three of these allow you to specify which combination of I_m, I_Na+, and/or I_K+, you wish to have displayed on the axes, while the fourth lets you toggle the display of the numerical values for e_Na+, e_K+, and e_Cl-. Turning off the display of numerical values when they’re not necessary for interpreting your experimental results will help keep the display from becoming cluttered so quickly when you’re doing multiple runs.

The default settings generate a graph of total I_m versus time, just as you would observe if you were performing an actual voltage clamp experiment. However, the simulation also makes it easy to generate separate displays of the Na⁺ current and the K⁺ current, something that requires special experimental techniques when actually working with the squid giant axon.

If you select the Numerical Values checkbox, the numerical value of the maximum amplitude for I_total, I_Na+, and I_K+ will be displayed after each run. Each number will be displayed next to the peak to which it corresponds, with I_Na+ displayed in the left side of the display and I_K+ at t = 6 ms displayed near the display’s right edge. I_total will be displayed in two locations: its minimum or maximum value during the early inward current is displayed near the left-hand edge of the display (just to the left of I_Na+), while I_total at t = 6 ms is displayed near the right-hand edge of the display. As you will see, repeated runs with the Numerical Display checkbox selected will produce three columns of values, so a column heading for each will be placed near the top of the display above where the numerical values will be displayed.

When you initiate a simulation run, the clamping voltage is not applied until approximately 1 ms after the simulation commences. Thus, when you click the "Go" button, you will first see the resting membrane current (set to 0 in this implementation) displayed until t = 1 ms, when the membrane is abruptly clamped at the desired value. The graph then illustrates the time-dependent change in I_m, I_Na+, and/or I_K+ (depending on which of the choices at the bottom of the display are checked).

Finally, the clamping V_m (depolarizing or hyperpolarizing) is displayed in a separate graph below the graph of I_m. (In keeping with convention, what's actually displayed is not V_m; instead, it's really dV_m = (V_m – resting V_m), the numerical difference between the clamped V_m and the resting membrane potential.).