Hi, I’m trying to model the synapses in a fairly populated and interconnected network. My problem is that I’m not sure if I’m writing the synaptic equation for inhibitory interneurons right.
What I’ve declared for synapses originating from excitatory neurons is a Synapses function in which w : volt and on_pre="v_post += w". For synapses originating from inhibitory interneurons, however, I’ve declared a Synapses function in which w : volt and on_pre="v_post -= w". This declaration effectively reduces the voltage but doesn’t return it to a steady state or something of that sort.
Is there a better way to declare synapses originating from inhibitory neurons?
Hi. Your equations model so-called “delta synapses”, where a synaptic event instantaneously updates the membrane potential. This can be used both for excitatory and inhibitory synapses, for the latter it is only a matter of taste whether you prefer v_post -= w or use v_post += w with a negative value for w. There is nothing here which would return things to a steady state, since the effect of the synapse does only apply for an (in theory) infitesimaly short amount of time. The membrane potential will return to its resting state according to its own dynamics, though.
There are more complex synaptic models, of course. The next level of complexity would be to use an “exponential current-based synapse” as in the CUBA example where each spike increases/decreases a synaptic current, which then decays back to zero. There are variants with different “shapes” instead of an exponential. If you want to be yet more realistic, you’d have each spike increase a conductance instead of a current – the actual current then depends on the value of the membrane potential, which can be important for inhbitory synapses with their reversal potential close to the resting potential of the cell. The COBAHH example uses such a synapse model.
A previous version of the Brian simulator (“Brian 1”) had a few built-in synapse models and our documentation lists the equivalent equations in Brian 2: Library models (Brian 1 –> 2 conversion) — Brian 2 2.4.2 documentation
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