presynaptic terminal (determined on the same printout to be 85 mm
or 0.085 m) is, therefore, 8.5·10−2 m ÷ 80,000 = 1.06·10−6 m or
1.06 μm or ≈1 μm. Applying the same procedure, the width of the
synaptic cleft is estimated to be 475 nm (≈0.5 μm).
Similarly, application of the above procedure to the Morphometric Synapse Model yields ≈1 μm for the length of the presynaptic terminal and ≈20 nm for the width of the synaptic cleft.
Evaluation of the Results
Educational models of chemical synapses, like the one shown in
Figure 2, generally provide a good indication of the relative proportions of the presynaptic terminal and the axon from which
this terminal emerges. For example, in the adult visual cortex,
terminal lengths between 0.5 μm and 2.2 μm, with a mean of
1.2 μm, have been measured (Stettler et al., 2006). Axon diameters in the central nervous system typically range between 0.1 μm
and 10 μm, but thinner axons are the most abundant (Perge et
al., 2012). Thus, a ratio of roughly 2:1 of the length of the presynaptic terminal to the diameter of the axon shaft, as depicted
in Figure 2, is well within the range of the proportions of axons
and terminals found in the central nervous system.
On the other hand, a width of 0.5 μm of the synaptic cleft, as
indicated by the Schematic Synapse Model, is far off – roughly by
a factor of 25. Electron microscopy studies have shown that the distance between the apposed synaptic membranes typically ranges
between 15 nm and 25 nm (Peters et al., 1991; Zuber et al.,
2005). As will be demonstrated in Part 2, this severe distortion of
the actual dimension of the synaptic cleft in many educational
models of chemical synapses, without mentioning that the dimensions of the synaptic components are not drawn to scale, has serious consequences for the predicted impact on neurotransmitter
diffusion time and concentration of transmitter molecules in the
synaptic cleft, and thus for the functioning of the synapse.
By contrast, the Morphometric Synapse Model presented in
Figure 1A depicts realistically the relative dimensions of axon
diameter versus presynaptic terminal length and synaptic cleft
width. If the diameter of the axon is 0.5 μm, then the presynaptic
terminal will be ~1 μm long and the synaptic cleft will be ~20 nm
wide. Furthermore, the synaptic vesicle shown in Figure 1B will
then have a diameter of ~40 nm, a value that falls well within
the size range of synaptic vesicles containing classical transmitters
such as glutamate (Zhang et al., 1998).
Part 2: Calculation of the Time Required
for Diffusion of Neurotransmitter across
the Synaptic Cleft
(1) In this part, the students will estimate (a) the time it takes
glutamate to diffuse from its release sites on the presynaptic
membrane across the synaptic cleft to the postsynaptic membrane and (b) the rate of diffusion. For these estimations, follow steps 2–4 below.
(2) In case of the Morphometric Synapse Model, the distance
between the apposed membranes is assumed to be 20 nm.
The diffusion coefficient of glutamate in the synaptic cleft
has been determined to be 330 μm2/s (Nielsen et al., 2004).
For the calculation, use Einstein’s approximation equation.
This equation approximates the average time t it takes a mol-
ecule with the diffusion coefficient D to diffuse in solution
over the distance x in one dimension:
(3) Repeat the calculation performed in step 1, now for the
Schematic Synapse Model, by assuming the distance
between the apposed membranes to be 500 nm.
(4) For both the Morphometric Synapse and the Schematic
Synapse models, determine the rate of diffusion by dividing
the distance (in meters) over which glutamate diffuses by the
diffusion time (in seconds).
(5) To express the rate by a more familiar measure of speed,
kilometers per hour (km/h) or miles per hour (mi/h), multiply the rate determined in step 3 by a factor of 3.6 or
Einstein’s approximation equation predicts that a 25-fold increase
in cleft width, from 20 nm to 500 nm, results in a 625-fold
increase in diffusion time, from ~0.606 μs to ~378.788 μs. These
diffusion times translate into mean rates of diffusion of 0.033 m/s
or 0.12 km/h or 0.074 mi/h (at an assumed cleft width of 20 nm)
and 0.0013 m/s or 0.0048 km/h or 0.0030 mi/h (at an assumed
cleft width of 500 nm). For comparison, continuous tracking of
nocturnal activity of garden snails has indicated that these animals
travel at average speeds of up to 1 m/h ( http://www.exeter.ac.uk/
news/featurednews/ title_315519_en.html); they are, thus, 30 or
300 times faster than glutamate diffusing across a synaptic cleft
of 20 nm or 500 nm width, respectively.
Evaluation of the Results
The above calculations provide some important perspectives. As
expected from diffusion as a passive process, the rate at which glutamate diffuses across the synaptic gap is low, particularly when
expressed by measures used in everyday life. However, the seemingly paradoxical situation that the glutamate molecules, nevertheless, diffuse from the presynaptic membrane to the postsynaptic
membrane within an extremely short period of time can be readily
resolved by taking the width of the synaptic cleft into account,
which is just a few nanometers.
The calculations also help overcome a frequent misunderstanding: that the total delay time of 200 μs between the opening of the
fusion pore on the presynaptic membrane and the opening of the
channels associated with the glutamate receptors is due to the time
it takes the transmitter molecules to diffuse across the synaptic
cleft. In fact, the latter is just ~1 μs and, thus, contributes rather
insignificantly to the total delay time.
However, it is important for students to appreciate the fact
that diffusion time increases with the square of diffusion distance.
Synapses with disproportionately wide clefts, as they are depicted
in the Schematic Synapse Model and in many other models used