3.2 Manual Iterative Searches for best fit
In the more complex situation of modeling a nerve cell, involving morphology
as well as channel types and densities, it is very difficult to apply
conventional algorithms and one must try to find the best assignment of parameters
such as morphological
values, and channel characteristics (types and densities) by trial and error.
The presence of multiple
minima in parameter space requires a very extensive search for the best overall or
"global
minumum" to give confidence in the assignments.
In such cases, a very useful and helpful approach is to employ multiple data sets or
types, all of
which must be reasonably fit simultaneously (by a single parameter set). For example,
when
I was trying to find the best assignment of Hodgkin-Huxley channels in a presynaptic terminal, I attempted to
find a simultaneous match to five records of presynaptic current observed at five
different locations
along the length of a neuromuscular junction with a "loose patch" electrode.
Presynaptic
sodium current flowed inward at the heminode (just beyond the end of the myelin) and
the
return circuit was via potassium current flowing out of the distal part of the terminal.
Thus any
change of assignment of local channel density altered all of the current patterns.
Therefore when I was able to find a set of patterns all of which were similar to the
corresponding record, I had far greater confidence that I was close to the density
parameters in the terminal than I could have had from a fit to a single record only.
The figure
above, reproduced from Lindgren & Moore (1989)
illustrate the quality of fit to five records with a
single parameter set.