246 6.6  Electrical Force Tools

this technique may be used both for purification and for characterization, for example, to

estimate the molecular weight of a sample by interpolation of the positions on a gel against a

reference calibration sample. Isolation of a protein using 2D-​E is often a precursor to analysis

using mass spectrometry.

6.6.2  ELECTROPHYSIOLOGY

The lipid bilayer architecture of cell membranes is disrupted by natural nanopores of ion

channels. These are protein structures that enable controllable ion flow into and out of cells.

They generally involve high specificity in terms of the ions allowed to translocate through

the pore and often use sensitive voltage gating and other molecular mechanisms to achieve

this. The presence of these nanopore molecular complexes can be investigated using patch

clamping.

The resistance of an open ion channel in a cell membrane is a few GΩ; therefore, any

probe measuring electric current through the channel must have a resistance seal with the

membrane of at least a GΩ, hence the term gigaseal. For a nanopore of cross-​sectional area

A through which ions in a solution of electrical resistivity ρ translocate a total axial distance

length l, then the nominal resistance is given by ρl/​A as expected from Ohm’s law, plus an

additional access resistance (see Hall, 1975) due to either ion entry or ion exit to/​from a cir­

cular aperture radius a of ρ/​4a. Thus, the total electrical resistance Rchannel of an ion channel

is approximated by

(6.33)

R

a

l

a

channel ⁼

+



^



^

ρ

π

1

4

Usually a glass micropipette tipped with a silver electrode is pressed into suction contact

to make a seal with very high electrical resistance greater than the GΩ level (Figure 6.10a).

Time-​resolved ion-​flux measurements are performed with the micropipette in contact

either with the whole intact cell or with the attached patch of membrane excised from the

cell either by keeping the current clamped using feedback circuitry and measuring changes

in voltage across the membrane patch or, more commonly, by clamping the voltage to a set

value and measuring changes in current. Current measurements are often made in conjunc­

tion with physical or chemical interventions that are likely to affect whether the ion channel

is opened or closed and to probe a channel’s mode of operation, for example, by adding

a ligand or drug inhibitor or by changing the fixed voltage level, typically set at ~100 mV

(Figure 6.10b).

The physical basis of the equilibrium level of voltage across a selectively permeable bar­

rier, such as the cell membrane with pores through which ions can selectively diffuse, is

established when the osmotic force due to differences in ion concentration either side of

the membrane is balanced by the net electrostatic force due to the electrochemical potential

on the charged ion in the presence of the membrane voltage potential. As discussed previ­

ously in this chapter, the osmotic force is entropic in origin; however, the electrostatic force

is enthalpic. The combination of both forces gives rise to another depiction of the Nernst

equation (see Chapter 2):

(6.34)

V

RT

nF

A

A

mem

out

in

=

[ ]

[ ]

ln

where Vmem is the equilibrium voltage across the cell membrane with charged ion A with n its

ionic charge in equivalent number of electrons per ion, having concentrations (A) inside and

outside the cell (R is the molar gas constant, T the absolute temperature, and F the Faraday

constant). With several ions, the equilibrium potential can be calculated from the fractional

contribution of each using the more general Goldman equation. For many cell types, Vmem