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synaptic current

Bruce Parnas brp at neuron.arc.nasa.gov
Wed Sep 8 11:28:50 EST 1993

In article <2624 at diane.informatik.uni-frankfurt.de>, zeller at pix1.physik.uni-frankfurt.de (Michael Zeller) writes:
|> Hi netters, 
|> I want to set up a network out of Bonhoeffer-van der Pol
|> neurons (BVP) as introduced by Fitzhugh [1]. Therfore I need to model
|> the inward synaptic current. So my question ist: What is the usual way
|> to describe the inward synaptic current of neurons? Would it be
|> reasonable to write:
|> 	I_syn(t) = g_syn(t) * (V_presyn(t)-V_postsyn(t))
|> (with g_syn(t) = alpha function; V_presyn(t) = presynaptic potential;
|> V_postsyn(t) = postsynaptic potential)

The conductance change is a postsynaptic phenomenon, and the driving force is
the difference between a presumed ionic reversal potential and the postsynaptic
membrane potential.  The presynaptic potential causes initiation of the conductance
change, the alpha function.  There isn't really a hard-and-fast (Sodium) reversal potential
in the BVP model, but one can be reasonably inferred from the higher-potential portion
of the N-shaped nullcline for V.  Then the expression might look something like

	I_syn(t) = g_syn(t) * (V_assumed_reversal-V_postsyn(t))

|> for the current, induced from one presynaptic neuron? And do I really
|> have to take into account the time dependence of V, or is it enough to
|> calculate the voltage difference once, say at the maximum of the
|> presynaptic spike, and multiply it with the alpha function?

Since the simulation takes place in time and there is a value for the alpha function
(presumably from a look-up table) at each time step, it shouldn't cost anything
to use V_postsyn(t) at each timestep instead of V_postsyn_peak, but i don't think
the latter will affect things too much since the rise to peak is pretty rapid and the
plateau is relatively short.

I've done some wsork with an even more simplified model, one that has "pasted on" , rather
than explicit, spikes, and I simply indicate the presence of a spike and use that to
trigger input to the post-synaptic cell.  The model, except for the actual pasting of
the spike, is linear and computes relatively quickly.  The tradeoff is simplicity versus
the desire for an actual spike waveform.

/usr/local/Std.Disclaimer:  The opinions expressed here are mine and
not those of NASA, but you probably could have guessed that.

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