Holt, GR. Koch, C. (1997) Shunting Inhibition Does Not Have a Divisive Effect on Firing Rates. Neural Computation 9: 1001-1013.
Christof was my advisor in undergrad. He's famous for consciousness stuff as well as a bunch of computational biophysics stuff.
I was surprised there's so much in the literature about shunting inhibition not acting divisively. I'm working on a model in the leech where we use shunting inhibition divisively, and it's a pretty simple and biophysically plausible mechanism. I'll write some about that project later.
The shunting inhibition mechanism is important as we keep seeing gain control in cortex, but we have to make sure that it is being done correctly. Multiplicative inhibition is important because it can maintain a population code (the population vector points in the same direction), and keep activity in a good dynamic range. There could be additive feedback like mechanisms that are really in charge of gain control, but the simplest way would be to have a direct mechanism which would be a multiplicative synapse. Biophysically this is simply done through shunting inhibition, as shunting inhibition acts as a voltage divider. I'll discuss this more later too.
They use a fairly complex Neuron model with lots of different channel types. They also use an IF model. To simulate inhibition they change the leak conductance (this is fine).
They make a cable equation model to look at the effect of distal inhibition and proximal excitation (for some reason). They show it is still additive. I'm not sure why they didn't do this with proximal inhibition and distal excitation - perhaps because then it would be divisive...
So the key difference between my model and this one is that they put the inhibitory synapse in the same compartment as the spiking mechanism.