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term so that it is proportional to the number of reduced variables. These techniques
rely upon having “snapshots” of the dynamics that are rich enough to reproduce the
full range of neuronal behavior. We introduce simple methods for obtaining these
snapshots, and we develop algorithms to eliminate unimportant snapshots and to
maximize the information in the important ones. When these tools are applied to
realistic cells, they can generate reduced systems of dimensions nearly two orders of
magnitude smaller than the originals and which yield highly accurate simulations in
an order of magnitude less time.
Application of these model reduction techniques is likely to have the greatest
effect on neuronal models with realistic ionic currents. Our simulations currently use
standard, but limited, channel kinetics. Behaviors such as action potential initiation
near the soma (Colbert and Pan, 2002) (Kole et al., 2008) rely upon better models
for the spatial conductance densities, as well as the inclusion of different channels
(Mainen and Sejnowski, 1998). Additionally, in this paper we have only considered
excitatory inputs, but inhibition plays a key role in modulating neuronal output,
both at the single cell and network levels (Brunel and Wang, 2003). Inhibition can
be included with no change to the present methodology.
An improvement of the model reduction technique can be made when it is applied
to cells with weakly excitable dendrites. One consequence of using such channel
models is that some distal branches do not experience action potentials, but rather
have more attenuated responses, which can result in poor snapshot dynamics. A