Stochastic Modelling of Single Ion Channels - Computational Neuroscience: A Comprehensive Approach - page 146

Figure 5.6
An example showing four bursts of openings containing brief shuttings and separated
by longer gaps between bursts.

In the 5-state model we need to remove at least two states to separate the open and
shut states: we could remove any of the pairs ( 1 , 2 ) , ( 3 , 4 ) , ( 1 , 3 ) or ( 2 , 4 ) .So V = 2

and correlations would die away with lag n as a single geometric term.
Correlations between intervals are useful in telling us something about the con-
nectivity between open and shut states.
The results on correlations were given by Fredkin et al. [38] and were extended
by Colquhoun and Hawkes [30], Ball and Sansom [16], Ball et al. [7], Ball and Rice
[13] among others.
Colquhoun and Hawkes [30] also studied the distribution of openings and shut-
tings after a jump in agonist concentration or voltage. The first latency (time to first
opening) has a different distribution to subsequent shut time durations. 1

there continue to be differences among the subsequent durations of both open and
shut times; if V

If V >

1, however, all open time durations have the same distribution
(no matter if it is the first, second etc. opening after the jump) while all shut times
apart from the first latency have the same distribution. This happens because of the
independence of the various intervals.
Results on the distribution of openings and shuttings as a result of a finite pulse,
rather than a single jump, were discussed in [33].

=

5.5.5 Bursting behaviour

It is usually the case that openings seem to occur in bursts of activity: a sequence of
openings will be interspersed with brief shuttings and then there will be a long shut
period before the activity starts again. This behaviour can often be largely explained
by dividing the shut states into two categories: short-lived shut states and long-lived
shut states. For example, in the simple channel blocker, if the rate constant k − B is
large then the duration of a stay in the blocked state will be very short and a burst
of openings will most likely consist of oscillations between the open and blocked
states. An example of bursting behaviour is shown in Figure 5.6.
Considering the 5-state model as another example, we see that the mean duration