12.3. The full Hodgkin–Huxley mechanism and its molecular underpinnings[[Student version, January 17, 2003]] 475
10.30.50.70.open time, msnumber of channelsFigure 12.19: (Experimental data; numerical simulation.) Distribution of the durations of channel open times
in a ligand-gated ion channel (frog synaptic channels exposed to acetylcholine). The histogram shows how many
individual ion channels stayed open for various times following brief exposure to the activating neurotransmitter. The
curve shows an exponential probability distribution with time constantτ=3. 2 ms;the curve has been normalized
appropriately for the total number of observations (480) and the bin width (0. 5 ms). The first bin of data is not
shown. Compare the kinetics of RNA unfolding in Figure 6.10 on page 201. [Data from Colquhoun & Hawkes, 1983.]
relaxation formula (Equation 6.30). The situation with ion channels is somewhat complicated;
most have more than two relevant states. Nevertheless, in many circumstances one relaxation time
dominates, and we do find nearly exponential relaxation behavior. Figure 12.19 shows the results of
such an experiment. The figure also illustrates the similarities between the voltage-gated channels
studied so far in this chapter andligand-gated ion channels,which open in response to achemical
signal.
The channels studied in Figure 12.19 are sensitive to the presence of the moleculeacetylcholine,
aneurotransmitter. At the start of each trial, a sudden release of acetylcholine opens a number
of channels simultaneously. The acetylcholine rapidly diffuses away, leaving the channels still open
but ready to close. That is, the experiment prepares an initial nonequilibrium population of ion
channel states. Each channel has a fixed probability per unit time of jumping to the closed state.
The experimenters followed the time course of the membrane current, flagging individual channel-
closing events. Repeating the experiment to build a large dataset yielded the histogram of open
times shown, which matches the exponential curve e−t/^3.^2 ms.Though each channel is either fully
open or fully shut, adding the conductances of many channels thus gives a total membrane current
that roughly approximates a continuous exponential relaxation, analogous to that found in Hodgkin
and Huxley’s experiments for the potassium conductance upon sudden depolarization.
The complex, open-then-shut dynamics of the sodium channel is not a simple exponential, but it
too arises from the all-or-nothing opening and closing of individual sodium channels. Figure 12.17
makes this point graphically. The nine traces in panel (b) show successive trials in which a single
sodium channel, initially in its resting state, was suddenly depolarized. The individual traces show
only digital behavior. To simulate the behavior of a large patch of membrane, containing many
channels, the experimenters averaged 300 such single-channel time courses, obtaining the trace
in panel (c). Remarkably, the result resembles closely the time course of the sodium current in
space-clamp experiments (Figure 12.12c on page 467).