Structure-Based Models of NO Diffusion in the Nervous System - Computational Neuroscience: A Comprehensive Approach - page 114

1.0

d = 0 m

d = 225

µ

µ m

0.5

0.0

0 4

Time (s)

center (0 µ m) 225 m

µ

1.0

0.5

0.0

0.0 0.5 1.0

Figure 4.2
Concentration of NO plotted against time after synthesis for a hollow spherical source of
inner radius 50µ m and outer radius 100µ m for a 100 ms burst of synthesis. Here the solid
line depicts the concentration at the centre of the cell (0µ m ), whilst the dotted line shows
the concentration at 225µ m from the centre. Because the absolute values attained at the two
positions differ from one another markedly, the concentration is given as a fraction of the peak
concentration attained. These peak values are 7 . 25µ M (centre) and 0 . 25µ M at 225µ m . The
cell and the points at which the concentration is measured are depicted to the left of the main
figure. Note the high central concentration, which persists for a long time (above 1µ M for
about 2 s . Also, there is a significant delay to a rise in concentration at distant points which
is more clearly illustrated in the expanded inset figure. The square-wave shown beneath the
inset figure represents the strength function.

in its outer structure, we could use two ideal models, one with the outer radius set
to the minimum radius and the other with outer radius set to the maximum. In this
way analytical solutions can be employed to see whether or not the irregularity has
a significant effect. In fact we have seen that due to the speed of diffusion of NO,
small-scale irregularities (

5% of source size) have a negligible effect [35]. Using
such an approach we can also investigate the sensitivity of the diffusional process
to other parameters such as boundary conditions whose complexity make the ana-
lytical solution intractable. Thus, if we have to make simplifications to a model to
render derivation of the analytical solution tractable, we can tell whether or not these
simplifications generate gross inaccuracies.
The solution for the hollow sphere was examined for a burst of synthesis of dura-
tion 100 ms , with results shown in Figures 4.2 and 4.3. There are two points of note,
namely the length of time for which the concentration in the centre of the sphere
remains high and the significant delay between the start of synthesis and the rise of
concentration for points distant from the source (Figure 4.2). The cause of these phe-
nomena can be seen on examination of Figure 4.3. During the synthesis phase, the
concentration outside the cell rises very slowly. In the nucleus, however, a 'reservoir'
of NO starts to build up (Figure 4.3A), albeit relatively slowly when compared to the

± 2 .