The name is absent

43

Synaptic scaling profile of forked neuron

Figure 2.9: Strengths gb_s of alpha-function synaptic input needed at each compartment to get
a 0.2 mV peak soma depolarization. Dots were computed using the BT system, while circles were
computed using the nonlinear system. Notice that the conductance on the root branch increases
slowly with increasing distance from the soma, but at the branch point this trend splits. The
large difference at the junction occurs because of the disjoint radii of the root branch and the child
branches. Only one distinct set of points can be seen from 200-400 μm because the child branches
are identical.

each compartment, shown in Figure 2.9, in a total of 4.7 minutes. By contrast, the
nonlinear system would require about 100 minutes to do the same.

For more realistic morphologies, and more complex channel models, the one-time
cost of computing the BT matrices grows as (9(n³), but the speed-up gained from
using the resulting reduced system is substantial. As an example, neuron AR-1-20-
04-A (see Figure 2.6B) was discretized into 1121 compartments, each with length ≈
2 μm. We included I⅛_a and Iк currents following Hodgkin-Huxley kinetics, and used
Connor-Stevens kinetics (see Table B.2) (Connor and Stevens, 1971) for the A-type
K⁺ current Ia whose spatial distribution followed that suggested by (Hoffman et al.,
1997). The resulting system had 5 gating variables per compartment, and hence the

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