Realistic models for the future

We thank Roman for his comment and his insightful contributions
to nonlinear cable theory, and encourage him to continue down
that path.

In Schachter et al (2010) we sought to use detailed compartmental
models that were calibrated to physiological data in order to
answer outstanding questions regarding function of the
direction-selective ganglion cell, and also to raise new avenues
of exploration. In doing so we made decisions on how to set the
multitude of free parameters guided by data from our own labs and
the work of others.

To answer Roman's comment directly: we claim our model indicates
that the spread of depolarization in dendrites due to synaptic
input is "isolated" to the extent that it substantially declines
within a short distance from the point of input -- and that this
property is responsible for independent spike generation at
different dendritic loci. The preliminary work in Poznanski
(2004) does not deal with morphologies as complex as the DSGC.
If we understand correctly, his analysis dealt with a single
unbranched cable with a diameter of 4um.

Contrary to Roman's claim, our study did not require any
"on-path" rule, but instead disproved a widely-held hypothesis
that realistic on-path inhibition could be responsible for
blocking spike propagation from dendrites to soma.

Nor did our study require electrotonically isolated dendritic
patches -- instead, this was one of the results that emerged from
our biophysically realistic simulations. Neither our simulations
nor conclusions depended on the initial measurements of the space
constant without active channels. The reason is that most of the
simulations included calibrated densities of voltage-gated
channels to test the cell's properties of spike initiation and
propagation. These simulations showed that PSPs that came from
distal dendritic loci were attenuated when recording from the
soma spike, but that spike propagation was not dependent on the
attenuation properties of the dendrites nor on inhibition of
realistic strength.

Our simulations once calibrated showed the same independent spike
initiation at different dendritic loci that had been shown by a
previous study (Oesch et al., 2005). Thus our active models
verified our preliminary result that the dendritic regions are isolated.

Without diminishing the importance of Poznanski (2004), the
analytical techniques described in that paper are not sufficient
for the level of analysis we achieved using compartmental models,
for several reasons:

1) Poznanski (2004) used strong leak conductances in place of
delayed rectifier potassium channels. Intuition would seem to
indicate that this replacement is insufficient for matching spike
shapes from phase plots to the extent we have done in Schachter
et al (2010), making the analytical solution in Poznanski (2004)
difficult to verify. Also, Ih channels play a significant role
in matching the DSGC's response to hyperpolarizing current
injection. Active Ca-channels and Ca-activated potassium channels
play a significant role in matching spike adaptation to
depolarizing current injection. Proper calibration of the DSGC
model to physiological data requires these channels, and their
roles are not addressed in Poznanski (2004).

2) Poznanski (2004) studied specifically the back-propagation of
action potentials in the dendrites, whereas the main focus of our
paper was on forward propagating dendritic action potentials. We
look forward to future advances in the area of ionic nonlinear
cable theory that can elucidate the behavior of dendritic spikes
in branched morphologies with non-uniform diameters.

3) The analytical formulations in Poznanski (2004) provide no way
to simulate hundreds of active synapses in the way we did in
Schachter et al (2010), leaving the investigator without a
way to study direction-selective effects.

4) Poznanski (2004) reports computation times of days in order to
come up with solutions. Although computer speeds have improved
somewhat in the interim, we feel it's safe to say our
multicompartment models take far less time to run than models in
Poznanski (2004), while still providing sufficient accuracy. The
current morphological limitations of analytical models
notwithstanding, we could not have produced the results we did
given the computation time reported in Poznanski (2004).

However, overall we agree that utilizing simulations of sparse
distributions of Na-channels is an interesting and important
avenue for further exploration.

Mike Schachter
Nick Oesch
Robert Smith
Rowland Taylor