Topologically Defined Neuronal Networks Controlled by Silicon Chips

CHAPTER 2. NETWORKS OF DEFINED TOPOGRAPHY
grooves or right in the middle between both cells.
Figure 2.23: Synaptic conductances obtained from the
detailed model G cable
syn , plotted against the values from the
isopotential model Gsyn. The black line is a guide to the
eye with a slope of 1, the blue line is a linear fit to the
values up to Gsyn =1.3 and the red line results from fitting
all values. Intercept with the y-axis is 0 for all.
In fig. 2.23 the exact conductance G cable
syn is plotted versus the values obtained from the isopotential
model. The latter are slightly too small, since all data points lie above the black line with slope 1.
Fitting only values below Gsyn=1.3 yields the blue line of slope 1.13, denoting an average deviation of
13%, which is identical to the results in [79]. If the entire data set is fitted a slope of 1.20 is obtained,
shown by the red line. The error of the simplified model increases as Gsyn increases, as illustrated by
almost all data points with Gsyn >1.3 located above the blue line.
This behavior is obvious from eq. 2.30. The bigger Gsyn in the denominator, the larger the influence
of the correcting terms λr tanh L. With increasing synaptic conductivity, the voltage drop in the neuritic
cables rises with respect to the voltage drop across the synapse. Neglecting it, as in the isopotential
model, results in a larger deviation. The other source of error is governed by the current leaving through
the neurite membrane, which depends on the membrane conductance g.
In conclusion, the results obtained from the isopotential model are acceptable with most of the networks
studied here. Only in strongly coupled pairs with conductances Gsyn=3nS do errors rise to 32%.
Comparing the synaptic conductance of defined networks grown in SU-8 structures with those on UVpatterned
substrates raises an important question. Why is the coupling generally stronger in the topographic
structures? Except for the irradiated regions on the UV-patterned surfaces, cell culture conditions
are quite similar. Both substrates are homogeneously coated with poly-L-lysine and covered by
a layer of conditioning factors. Effects of different chemical environments on synapse formation can
therefore be largely ruled out.
To assess the influence of the patterns themselves, a control network was grown on a plain, unirradiated
substrate. Fig. 2.24 shows this 3 neuron network, yielding a synaptic conductance between neurons 1
and 2 Gsyn=0.39 and between neurons 2 and 3 Gsyn=1.67. The respective values clearly correlate with
the maximum number of possible signaling paths connecting both cells. 2 synapses for the cell pair
1 and 2 and 6 synapses for pair 2 and 3 as revealed by the number of neurites intersecting the dashed
lines in fig. 2.24. Even though the relation between overall conductance and number of connections is
not linear, due to variations among individual synapses, it can be concluded that a large Gsyn usually
implies several synapses connected in parallel. In that case, the resulting conductance is given by the
sum of the single ones; for a discussion refer to subsection 2.4.2.
This finding is further supported by attempts to localize synapses by sequential staining with Lucifer
Yellow. The weakly coupled cell pair depicted in fig. 2.19 with Gsyn=0.25 is only in physical contact
at a single spot where the neurite of cell 2 touches the soma of cell 1. In contrast, the exact position of
the synaptic connection is not known in the network shown in the bottom row of fig. 2.21, which has
a very large conductance of Gsyn=2.33. The neurites from both cells do not just meet at one point but
grow along side each other in the horizontal groove. Due to the large contact area it is very likely that
not only one but several synapses exist, explaining the strong coupling.
Fasciculated outgrowth has not been observed on UV-patterned substrates [79]. (This might also result
from the special culture protocol, where pairs were measured immediately after they had formed a vis-
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