Hi everyone,
I am presently struggling a bit to make sense of David&Friston2003,
David et al. 2005 and David et al. 2006.
Specifically I am a little uncertain about the meaning of the
state-variables (x_0 -- x_8) in David et al 2006. And also the relation
between the notation in David&Friston 2003 and David et al 2006.
I am assuming that v_1 of David 2003 (stellate cells membrane potential)
correspond to x_1 in David 2006. Likewise v_2 should correspond to x_7,
right?
Also the trans-membrane currents x_1 and x_2 of David 2003 corresponds
to x_4 and x_8 of David 2006, right?
But then it gets tricky (in David et al. 2006). I am assuming x_0 is the
membrane potential of the pyramidal cells, but this seems to be affected
by 2 distinct trans-membrane currents (x_5 and x_6) with opposite
directions. Apparently corresponding to two distinct trans-membrane
potentials x_2 and x_3.
In the text it is said that "The depolarisation of pyramidal cells
x_0=x_2-x_3 represents a mixture of excitatory and inhibitory ...
currents, respectively".
Why is it modelled like this. I would assume there can be only 1 (mean)
membrane potential and 1 trans-membrane current associated with a given
population of neurons. It also seems these sources have different "decay
times" as determined by tau_i and tau_e (aren't these related to the
capacitance of the neurons, so how can there be two for a given
population of neurons?)? Does this represent different neuronal
subpopulations? Does it represent different ion-channels?
Also (maybe nitty-gritty) in David 2003 the decay of the inhibitory
interneurons were given by tau_i, whereas in David 2006 it is given by
tau_e?
I'd be immensly grateful if anyone hasn't yet left for QL and takes
his/her time to explain this to me.
Puss Jesper
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