The more I think about this
sabsan wrote:simulate the population on a cluster and periodically (e.g., once every 40 time steps) perform the following actions:
- computing the extracellular potential globally evoked by the whole population in a given geometrical point;
using the value of the evoked potential to update the amplitude of the extracellular current (feedback control);
updating the extracellular potential at the cellular membranes as a consequence of the new extracellular current amplitude.
the more I think it is likely to give seriously misleading results unless the extracellular field is updated at a rate that accurately captures the time course of the current that the axon dumps into the extracellular medium.
"How fast should that be?"
Consider this simple model:
Code: Select all
create axon
axon {
L = 2000
diam = 1
Ra = 35.4 // standard HH cytoplasmic resistivity, cm, and channel densities
cm = 1
insert hh
nseg = 43 // segments < 0.1*d_lambda at 100 Hz
}
celsius = 6.3
A 0.1 ms x 2 nA current pulse applied to the 0 end (intensity approximately twice spike threshold) elicits a spike that propagates with conduction velocity ~ 558 um/ms near the middle of the length of the axon. The spike generates a dipole (current sink and source) that propagates at the same velocity, and the distance between the sink and source is only 140 um. So only 140/558 ~ 0.25 ms separates the sink (extracellular negativity) and the source (extracellular positivity).
Now, if we were sampling a sine wave with frequency f, we'd discover that the sampled waveform looks pretty ratty unless the sampling rate is at least 10*f. That's 5 samples per half cycle (interval between a positive peak and an adjacent negative peak). And it's barely adequate to give passable estimates of waveform peak amplitude and time course.
What this means, is that for good, old, cold, slow squid axon, the extracellular field really must be recomputed at intervals no longer than 0.25/5 = 0.05 ms. That's the _lower_ limit for an axon with a _slow_ spike mechanism. An axon with a fast spike mechanism demands more frequent recalculation of the extracellular field.
That suggests it may be impractical to do such simulations on a cluster--execution on a real parallel supercomputer may be required.