On 11/10/2004 Ted Carnevale <firstname.lastname@example.org
If I understand correctly, the classical definition of
length constant isn't very meaningful except in idealized
situations, so I need to look at something else.
Yep. "Length constant" is not just inadequate but actually
misleading as an indicator of electrical signal spread in neurons.
NEURON's impedance tools offer several different ways to quantify
the spread of electrical signals in a cell: if synaptic
inputs behave as current sources (small change in dendritic
Vm), we want to look at Ztransfer, but if our synaptic inputs
behave as voltage sources (big change in dendritic Vm), we
need to use Vmeasure/Vinject, right?
The best measure to use depends jointly on the properties of the cell
and of the synaptic inputs.
First, ask whether the cell is acting as an "integrator," or is it
more of a "coincidence detector"? It's acting as an integrator
if it's firing more or less tonically at a rate governed by dV/dt
during the interspike intervals. Individual psps are small, and
most spikes are preceded by a smoothly rising depolarization
(e.g. like the spikes in invertebrate bursting neurons--imagine
a plot of tan(theta) vs. theta). It's more of a coincidence detector
if there's a lot of baseline fluctuation (as might be caused by
individual large psps or erratic synchrony of smaller inputs), so
that spikes occur sporadically on top of some of these bumps.
If it's acting more like an integrator, then somatopetal current
transfer (Ai_in, the fraction of synaptic current that actually
reaches the soma) is the right parameter, because dV/dt at the
soma depends on the net current that reaches the soma. This
is the same as somatofugal voltage transfer (Av_out, the fraction
of somatic voltage fluctuations that reaches the synapse), so plot
log(Aattenuation) for the Vout direction. Integration is inherently
slow, so try a frequency of 0 (DC) first.
If it's acting more like a coincidence detector, then ask whether the
synaptic inputs are more like current sources or voltage sources.
Here's how to decide if they're more like current or voltage sources:
Current flow during synaptic activation is gs(t)*(Vm - E), where Vm
is membrane potential at the location of the synapse and E is the
equilibrium potential for the synaptic conductance gs. If Vm stays
closer to Vrest (resting potential at the synapse) than to E for at least
half of the synaptic charge that enters the cell, the synapse is more
like a current source. About the only time a synapse might act like a
voltage source is during tonic high frequency presynaptic activation,
and even then you'll probably need to have simultaneous activation
of other synapses onto the same dendritic branch.
For current sources, Ztransfer is the right measure, and that's
symmetric so Vin vs. Vout is a non-issue--use the log(A) vs. X
tool but Plot / Ztransfer. If they're voltage sources, you'll want
log(Attenuation) for the Vin direction. In either case, you'll want a
nonzero frequency because coincidence detection is inherently a
time-dependent phenomenon. What frequency? For the cells that
David Jaffe and I examined, we chose 25 Hz because it produced
results that were similar to what we saw when we actually marched
a model synapse (based on experimental measurements in the same
cells) around a couple of model cells and plotted peak somatic EPSP
as a function of synaptic distance. If you're dealing with garden
variety EPSPs with similar characteristics, you'll probably be ok with
25 Hz, but you might want to run a test or two in your own