The name is absent

57

Rather than simple thresholding we note that a number of investigations of single
compartment models have achieved better spike capturing by incorporating more so-
phisticated firing mechanisms. For example, (Fourcaud-Trocmé et al., 2003) includes
a voltage-dependent exponential term, while (Jolivet et al., 2006) and (Brette and
Gerstner, 2005) consider adaptive thresholding. For the class of morphologies and
channel distributions of the previous sections, adaptive thresholding, in our hands,
did not produce a significant improvement in spike accuracy. Regarding the imple-
mentation of an exponential integrate-and-fire model, we note that there is not a
natural means by which to nonlinearize our reduced quasi-active system. More pre-
cisely, as we observed at the close of §3.1, the reduced state ξ in (2.36) is governed
by the small but dense pair A_li and Bi and hence reflects a complex combination of
thousands of gating and voltage variables. The physiological soma potential does not
surface until after multiplication by eɪ. As such there is not a distinguished voltage
term in the differential equation for ξ, so it is not clear yet how one might apply a
biophysically inspired firing mechanism here.

2.8 Discussion

We have applied two distinct methods to the reduction of dimension of large scale
single neuron models. We have demonstrated that in typical settings one may reduce
models with tens of thousands of variables to models with merely tens of variables
that still accurately track the somatic subthreshold response of spatially distributed

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