A local inhibitory plasticity rule for control of neuronal firing rate and supralinear dendritic integration

Inhibitory synapses can control a neuron’s firing rate and also control supralinear dendritic integration. It is not known how inhibitory synapses can learn to perform these functions using only signals available locally at the synaptic site. We study an inhibitory plasticity rule based on the Bienenstock-Cooper-Munro theory in multicompartment models of striatal projection neurons, and show that it can perform these two functions. The rule uses local voltage-gated calcium concentration in the dendrites to regulate inhibitory synaptic strength. We show that, for rate-coded inputs, the rule can achieve precise control of neuronal firing rate after changes in excitatory input rate or excitatory synaptic strength. Additionally, for sparsely-coded inputs that activate localized synaptic clusters in a single dendrite, the rule can either allow or inhibit the evoked evoked supralinear dendritic responses, or equalize their amplitude. Finally, we demonstrate the use of learning to inhibit supralinear dendritic integration for solving the nonlinear feature binding problem (NFBP), in tandem with a simple excitatory plasticity rule. We conclude by discussing why the collateral inhibitory synapses between striatal projection neurons could contribute to solving the NFBP with this plasticity rule.