3.8.4 Driving force

As we discuss in section 2.5.6, HH introduced by their Eq. (1) (reproduced by us as Eq. (2.42)) the basic decription of the membrane current during a voltage clamp with that ”the justification for this equation is that it is the simplest which can be used and that it gives values for the membrane capacity which are independent of the magnitude or sign of $V$ and are little affected by the time course of $V$”. (It is again a reversed approach: the capacity, per definitionem, means the ability to store charge and is one of the attributes of the medium instead of the electric characteristic of the tested circuit. For the case of clamping, it is an approximation that the temporal course of the clamping voltage is kept constant, the current remains constant. As we discuss in section 3.7.4, in the case of a constant current where $I=\frac{dQ}{dt}$, the voltage increase $dV$ on the capacity $C$ of the membrane is $\frac{dQ}{C}=\frac{I\ast dt}{C}$, so we can derive the ”driving force” (compare it to Eq. (2.13)) as they interpreted it

The direct constant current input $\frac{d}{dt}{V}_{PATCH}$ to the neuron cell body is a simple constant current that causes a constant membrane’s voltage derivative contribution. That is, if one checks the dependence of the output voltage on $\frac{d}{dt}V$ and $I$, in the presence of a constant $C$, one observes the same dependence. However, the currents are not necessarily constant.