Stochastic Modelling of Single Ion Channels - Computational Neuroscience: A Comprehensive Approach - page 130

under certain conditions, allowing electrically charged ions to pass through the pore
under the influence of a small electrical potential difference between the intracellular
and extracellular sides of the membrane. Typically, different kinds of channels allow
the passage of different ions, such as Na + , K + , Ca 2 + or Cl − .

The flow of these

charged ions constitutes a flow of electrical current.
The opening and closing of ion channels is called gating. The major types of gat-
ing mechanism are voltage gated (where channels respond to changes in the mem-
brane potential) and ligand activated (where channels are activated by binding with
molecules of certain chemicals): other types of channel may respond to changes in
temperature or stretching by a mechanical force.
All electrical activity in the nervous system appears to be regulated by ion channel
gating, see for example [2]. Channels play a role in many diverse activities including
thought processes; transmission of nerve signals and their conversion into muscular
contraction; controlling the release of insulin, so regulating the blood glucose level.
Understanding their behaviour increases our understanding of normal physiology
and the effect of drugs and toxins on an organism, especially the human body. It
is therefore an important step towards developing treatments for a wide variety of
medical conditions such as epilepsy, cystic fibrosis, and diabetes, to name but a few.
Measurements of electrical currents that are the superposition of currents through
very large numbers of channels are called macroscopic measurements . For example,
in the decay of a miniature endplate current at the neuromuscular junction several
thousand channels are involved, a large enough number to produce a smooth curve
in which the contribution of individual channels is impossible to see. Early exam-
ples include [1, 64, 71]. In this case the time course of the current is often a sim-
ple exponential. Forms of macroscopic measurements include (a) relaxation of the
current following a sudden change in membrane potential ( voltage jump ), and (b)
relaxation of the current following a sudden change in ligand concentration ( concen-
tration jump ). In these cases too, it is common to observe that the time course of
the current following the jump can be fitted by an exponential curve, or by the sum
of several exponential curves with different time constants. An example is shown in
Figure 5.1 .
If, on the other hand, we record from a fairly small number of ion channels, the
fluctuations about the average behaviour become large enough to measure. Sup-
pose, for example, that there are 400 channels open on average: then the number
of channels open will vary by random fluctuations between about 340 and 460. In
[52, 53, 72] they showed how these fluctuations (or 'noise') could be interpreted in
terms of the ion channel mechanism. An elementary discussion is given in [27].
Since the pioneering patch-clamp experiments of Neher and Sakmann [65], the
techniques being further refined by [45], it has become routinely possible to observe
electric currents of a few picoamperes flowing through a single ion channel in a
biological membrane. A great deal of information about how this remarkable feat is
achieved is given in [70]. Apart from noise and some inertia in the recording system,
it soon becomes clear that we are essentially observing the opening and closing of
a pore in the macromolecule that forms the channel. When the channel is open
there is a current of approximately constant amplitude; when the channel closes the