Chapter 6 – Forces  247

is in the range −50 to −200 mV, with the negative sign due to energized net pumping out of

sodium ions compared against a smaller influx of potassium ions.

In many cells, the size of the equilibrium transmembrane voltage potential is finely con­

trolled, for example, in bacteria, Vmem is very closely regulated to –​150 mV. In some cells, for

example, during nerve impulse conduction, Vmem can vary due to a wave of depolarization

of voltage. In the resting state sodium ions are actively pumped out in exchange for potas­

sium ions that are pumped into the cell, energized by the hydrolysis of ATP. These sodium–​

potassium ion-​exchange pumps are essentially selective ion channels that exchange with the

ratio of three sodium to every two potassium ions, hence resulting in a net negative Vmem,

with the so-​called resting potential of ca. –​70 mV. During nerve impulse conduction the ion

pumps transiently open to both sodium and potassium causing depolarization of Vmem, rising

over a period of ~1 ms to between +​40 and +​100 mV depending on nerve cell type, with the

resting potential reestablished a few milliseconds later. The recovery time required before

another action potential can be reached is typically ~10 ms, so the maximum nerve firing

rate is ~100 Hz.

An open ion channel current is open in around one to a few tens of picoamperes. This is

roughly a millionth-​millionth the level of electric current that a TV or a kettle uses and is

equivalent to ~10⁶–​10⁸ ions per second, which even when sampled with fast GHz detector

bandwidth struggles to be single ion detection. Rather, the ion flux is the detection signature

for the presence of a single ion channel and of its state of opening or closure, or indeed some­

where in between as appears to be the case for some channels.

The area of membrane encapsulated by the patch clamp may contain more than one ion

channel, which impairs the ability to measure single ion channel properties, for example,

investigating whether there are heterogeneous short-​lived states between a channel being

fully open or closed. The measured current for a membrane patch enclosing multiple ion

channels will be the sum of the currents through each channel, and since each may be open

or closed in a stochastic (i.e., asynchronous) manner, this leads to difficulties in interpretation

of the experimental ion-​flux data.

Genetically modifying the cell to generate a lower surface density of ion channels

reduces this risk, as does inhibiting ion channel protein levels of expression from their gen­

etic source. Similarly, growing larger cells reduces the effective ion channel surface density.

FIGURE 6.10  Electric current flow through nanopores. (a) Patch clamping to capture one or a

few single-​ion channels in a patch of membrane at the end of an electrical “gigaseal” nanopipette

tip, which can generate (b) time-​resolved current measurements at the ion channel opens and

closes. (c) Synthetic nanopores can also be manufactured about solid substrate, for example,

graphene is then but mechanically very stiff and stable and so offers potential for high-​resolution

characterization of biopolymers, for example, sequencing of DNA as each nucleotide base pair

on translating through the nanopore results in different characteristic drop in electric current.

(Courtesy of Cees Dekker, TU Delft, the Netherlands.)