Tutorial: RC Circuits 2

Background reading for this tutorial is the section on RC circuits. Additional information on the function of electrical filters can be found in the Signal Processing section.

A parallel RC circuit acts as a low-pass filter of injected currents. A low pass filter blocks high frequency components of the signal but allows lower frequency components to pass. For a square pulse current signal, the high frequency components are the portion of the signal where current flow changes very rapidly (the start and end of the current pulse).

The electrical filtering function of cell membranes has a significant impact on the signal processing properties of neurons by shaping the voltage response of the cell to current flow. In vivo these currents will be mediated by the opening of ligand-gated ion channels located at synapses or by the opening of voltage-gated ion channels.

Experiment 1: Time Constant

We can examine this filtering effect by injecting a square current into an RC circuit (Figure 1). The high frequency components of the original current signal are removed by the RC filter leaving a slower response. The extent to which this happens depends on the time constant of the cell. In this experiment examine the effects of changing the time constant of the cell on the peak and shape of the voltage response to an injected current.

Figure 1 An RC model of the passive electrical properties of an electrically compact cell with a variable time constant.

1. Increase the stimulus current to 100 pA. Then, gradually reduce the length of the current pulse. Notice how short current pulses (1 or 2 ms) are almost completely attenuated in a cell with a typical membrane time constant (\(\tau_{m}\)= 10 ms).

2. With a short current pulse (1 or 2 ms) examine the effect of changing the cell’s time constant. Notice that the cell becomes a ‘better’ electrical component when the time constant is shorter because the voltage response more closely reflects the time course of the current input.

Question:

1. Why aren’t cells ‘better’ electrical components, with much shorter time constants?

Experiment 2: Membrane Resistance

In this experiment examine the effect of varying the membrane resistance with a fixed membrane capacitance.

Figure 2 RC model of an electrically compact cell with a variable membrane resistance.

1. Inject 100 pA current for 10 ms.

2. Gradually reduce the membrane resistance. Notice how the time constant decreases, which is theoretically desirable, but the voltage response also decreases greatly, so a larger input current is required to get the same change in membrane potential.

Question:

1. Why don’t cells have lower membrane resistance to improve the frequency response of the cell i.e., reduce the membrane time constant?