Possible dual effect of synapses that are putatively purely excitatory or purely inhibitory: bases in stability theory and implications for neural network behavior

Depolarization of an excitable membrane has a dual effect; excitatory in that it causes rapid opening of calcium and/or sodium channels but inhibitory in that it also causes those channels to inactivate. We considered whether apparently paradoxical or dual behavior might be exhibited by excitatory and inhibitory synaptic inputs. We used the classic Hodgkin-Huxley model for voltage-gated channels plus leakage channels of appropriate selectivity for ligand-gated postsynaptic channels. We summarize a model cell's behavior by calculating elicited firing frequency as a function of reversal potential and conductance of summed synaptic inputs, using stability theory and direct simulations. Dual behavior is elicited in the model with reasonable densities of ligand-gated channels. Thus a particular synaptic input to a neuron may be either excitatory or inhibitory depending on simultaneous activity of other synaptic inputs to the cell. This input-output map may give rise to biologically realistic and rich behaviors as an element of computed neural networks, and still be computationally tractable.