> - To me as Electrical and Computer Engineering it seems the most
> natural way to model synaptic connection as a convolution between
> the presynaptic voltage and the synaptic conductance in order to
> receive the postsynaptic current, but the usual model is
> i_synapse=g(t)*[v(t)-v_synapse] ?
I agree that this is a crucial question, because it is clear that the
behavior of neural networks will be highly sensitive on how to model
Tha alpha function is usually the way which is chosen for modeling
synaptic conductances. Although it fits reasonably well some of the
postsynaptic currents (PSC) seen experimentally, it has two problems:
1. it does not correspond to any plausible biophysical mechanism
(the kinetics on which it is based are unrealistic)
2. summation of multiple PSC's is usually provided by summating alpha
functions, which is clearly a bad approximation for train of
spikes at high frequency...
There is an alternative to alpha functions, which is based on simple
biophysical mechanisms (kinetics of transmitter binding) and which
provides a natural way of performing summation of PSP's in the correct
way. Moreover, this alternative turns out to be computationally
faster than alpha functions (it also requires less memory). We have a
paper in press in Neural Computation  which describes this
mechanism in detail.
If you are interested, I invite you to ftp it from the server:
login as anonymous, password: your email address, then look into
and retreive the file
which contains a preprint of the paper + a copy of the figures.
Hope it helps
 Destexhe, A., Mainen, Z. & Sejnowski, T.J. An Efficient Method for
Computing Synaptic Conductances Based on a Kinetic Model of Receptor
Binding. Neural Computation, in press, 1993.
PS: any feedback is welcome...