Understanding the cell as an electrical circuit

Basic voltage clamp experiment

To understand how the RC filter properties of the membrane determine a cell’s voltage response, consider how a voltage step applied to the inside of a cell alters the current injected through an electrode (see Figure 1B). Initially, a square shaped voltage step leads to an instantaneous jump in current (the initial peak). This current then decreases exponentially (falling flank) to reach a steady state. Contrary, when the voltage step is reversed, we observe a large instantaneous current of the opposite direction that decreases exponentially until it reaches steady state again. Controlling the membrane voltage and measuring the resulting current in this way constitutes a basic voltage clamp experiment.

How do the properties of the electrode and cell membrane influence the shape of the current curve (see Figure 1B)? Initially, the entire current charges the membrane capacitance with no current flowing across the membrane resistance. Thus, the amplitude of the initial fast current is entirely determined by the size of the voltage step and the electrode resistance (which is defined as the sum of the resistance of the electrode and the resistance of the electrode’s connection to the cell). As the membrane capacitance becomes more and more charged, an increasing fraction of the injected current flows across the membrane resistance. Once the capacitance is fully charged the system reaches steady state and the entire current flows across the membrane resistance. In the steady state, the amount of current required to maintain the membrane voltage is only determined by the membrane resistance and Ohm’s law applies (steady state current = voltage step / membrane resistance, or Is = Vs / RM).

The values of membrane capacitance and membrane resistance determine how quickly this steady state is reached: the larger the capacitance or the resistance, the longer the charging will take. The time constant describing this charging is known as the membrane time constant t and is equal to the product of membrane resistance and membrane capacitance (t = CM * RM, assuming Rs<<<RM).