Biomedical Engineering Reference
In-Depth Information
central region with no edge effects.
10.4.2
Number of connections
There are two principal problems regarding the number of connections in a detailed
network model. The first is finding experimental data on the statistics of connections
between the different cell types in a model. There is a paucity of such data for
many brain regions. The second is that almost all models must have fewer cells and
connections than the biological system because of insufficient computer resources.
10.4.2.1
Estimation of number of connections
The number of synapses per olfactory bulb mitral cell,
n
syn
, has not been experimen-
tally determined. However, it can be estimated from other measurements. The num-
ber of synapses in the EPL of adult mice has been estimated by electron microscopy
as
10
9
[28]. It is unclear whether this estimate is of reciprocal synapses
or of individual synapses (a reciprocal synapse consists of an excitatory-inhibitory
pair). In the latter case, the number of reciprocal synapses will be half the above
estimate. An indirect estimate gives a very similar result: the number of spines on
the peripheral dendrites of a single granule cell has been measured as 144-297 in
mice [42] and 158-420 in rabbits [25]. Assuming 200 spines per cell and one
reciprocal synapse per spine, taking the number of mitral cells per mouse OB as
38400
(
1
.
1
±
0
.
3
)
×
[32] and the ratio of granule:mitral cells as 150
[36], then the number of
10
9
. The number will be
slightly higher for rabbit, as there are about 60000 mitral cells [32].
Assuming a constant density of synapses on mitral/tufted cell dendrites, it would
be expected that mitral cells, which are larger, would have more synapses than tufted
cells. The total secondary dendrite lengths for rabbit mitral and middle tufted cells
have been measured as 15016 mm and 4050 mm respectively [25]. Therefore, taking
the ratio of tufted:mitral cells as 2.5 [36],
synapses in the mouse EPL
=
200
×
38400
×
150
=
1
.
15
×
10
9
1
.
1
×
14 mm
−
1
=
)
.
Synaptic density
1
(10.1)
38400
(
15016
+
2
.
5
×
4050
so the number of synapses per mitral cell is approximately 1
.
14
×
15016
=
17000
and the number per tufted cell is 4600.
These calculations assume that all synapses involve a mitral/tufted cell, and so they
ignore centrifugal inputs onto interneurons in the EPL. Therefore these are probably
slight overestimates.
In practice, it was not possible to simulate a network with several thousand synapses
per mitral cell, and a value of 500 synapses per cell was used. The reduced number
of synapses was compensated for by a granule cell model that was more excitable
than found experimentally.
In the cerebellar granule cell layer model of Maex and De Schutter there were
an average number of 602 synapses from granule cells onto each Golgi cell, corre-
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