AMPA/NMDA and GABAa/GABAb conductance ratios

Matt Jones jonesmat at physiology.wisc.edu
Tue Sep 17 21:27:18 EST 2002


"Bryan Price" <jprice1661 at earthlink.net> wrote in message news:<Wttg9.4994$Os3.351275 at newsread1.prod.itd.earthlink.net>...
> I may be asking the wrong group with this - please redirect me if needed.


Bryan,

Since you posted it on a neuroscience group, god help us if this is
the wrong group! But looking at the recent posts around here, god help
us anyway.



> I've been looking at some network models that focus on the delayed activity
> of NMDA currents in addition to the quick AMPA currents in biological
> neurons. The ranges of the conductances I have for these are
> 
> Excitatory
> AMPA: g(peak) ~ 0.1 - 0.3 ns, t(peak) ~ 0.3 - 1 ms
> NMDA: g(peak) ~ 0.05 - 0.5 ns, t(peak) ~ 5 - 50 ms
> 
> Inhibitory
> GABAa: g(peak) ~ 0.4 - 1 ns, t(peak) ~ 0.2 - 1.2 ms
> GABAb: g(peak) ~ 0.1 - 0.3 ns, t(peak) ~ 40 - 150 ms
> 
> [The Handbook of Brain Theory and Neural Networks (Arbib, 1995), "Dendridic
> Processing" (Segev), Table 1]


Those numbers look roughly OK to me.  Obviously these values will vary
a lot between cell types, with temperature, etc.  You should check
whether the authors are quoting values for miniature- synaptic
currents (i.e., due to release of a single vesicle) or rather in
response to an action potential which invades -all- of the axon
terminals at once. In that case,  the effective synaptic conductance
will be the sum of several miniature conductances.



> 
> 1) Easy question: What is an 'ns'? It's not just 1/giga-ohms, is it?

A "ns" (should be "nS") is a nanoSiemen. 1 Siemen = 1/Ohm, so yes, 1
nS = 1/1GOhm.


> 2) Harder question: I'm trying to calculate the range of ratios between the
> AMPA and NMDA (and GABAa and GABAb) time-summed currents. I am, of course,
> applying a membrane decay convolution function to the beta functions I'm
> using to approximate the currents, with Tm ~ 7 - 50 ms. 


I'm not sure what you mean by membrane decay convolution. Is this in
order to convert the conductance into a current under conditions of
changing membrane potential?  If so, I think I would agree with
Christian Wilms' post  that the best thing would be to explicitly
simulate the currents and membrane potential, including
voltage-dependence of NMDA (but this gets costly of course).  If it is
really currents you're interested in, these will always depend on
membrane potential, which will be fluctuating in complex ways during a
network simulation.

If you're trying to simplify the complicated current waveforms into
simple ratios, so that you can use a "mean field" approximation in
your modeling, then at the very least I would explicitly simulate the
changing NMDA current in response to a randomly fluctuating voltage,
and average and convolve over that instead of the raw beta function.
It would be a big mistake to ignore the voltage dependence of NMDA
current.

But maybe I'm not understanding the problem correctly.


Clearly I could use
> the maximum AMPA and the minimum NMDA conductances for one limit of the
> ratios, and the opposite conductances for the other limit, as this would be
> inclusive. 

This actually seems pretty reasonable to me.

However, I suspect that individual synapses (containing both AMPA
> and NMDA receptors) maintain some sort of relationship between the numbers
> of each type of receptor - 

Right, this seems reasonable too. For a long time, there were some
"average ratios" that people could depend on. Try looking up papers
from about 10 years ago that have both 1) "Rosenmund" and "Westbrook"
or 2)  "Bekkers" and "Stevens" on the authorlist.

Unfortunately, these days, these "average ratios" are no longer in
vogue, thanks to a recent phenomenon known as "silent synapses". So
you're following statement is no longer as accurate as it was 5 years
ago:

I don't believe that a synapse would have no AMPA
> receptors while also having a plethora of NMDA receptors, or vice-versa.
> 
> Does anyone know of research that might reveal such a relationship?


See the authors I mentioned above for evidence in support of such a
relationship.

Do a medline search for "silent synapses" to get a more recent view in
which the ratio of AMPA/NMDA is in almost perpetual flux.  Silent
synapses refers to a form of plasticity in which this ratio is the key
element in the learning rule for adjustment of synaptic weight, to put
it in neural net-speak.

Good luck,

Matt 








> 
> Thanks you,
> 
> Bryan Price
> 
> [ Also posted to comp.ai.neural-nets ]



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