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

Abstract 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 dendrites, the rule can either allow or inhibit the supralinear dendritic response evoked by the clustered excitatory synapses, or equalize the dendritic response arising from different clusters. 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. Author summary Neurons are the main cells in the nervous system that process information. They receive signals from the body’s senses—both external and internal—and use them to guide actions such as muscle movement and the regulation of bodily functions. A neuron becomes active when incoming signals excite it strongly enough. But for neurons to work timely, precisely, and reliably, their activity needs to be shaped, modified and controlled. This is done by inhibition, which comes from specialized inhibitory neurons. In this article we study how inhibition can learn to do two of its most basic roles in the nervous system. The first is to help neurons stay responsive across a wide range of input strengths—from very weak to very strong stimulation. For example, neurons in the retina allow vision both in dim starlight and in bright sunlight, even though these conditions differ in brightness by a trillion-fold. Inhibition contributes to handling this huge range by preventing overstimulation of the neurons in bright light. The second role of inhibition is to control strong, local excitations that occur on specific dendritic branches of a neuron. These local excitations can suddenly push a neuron into activity, and inhibition controls whether such excitations are allowed or suppressed. We use a learning mechanism that is already known to exist for excitatory synapses, but here we apply it to inhibition to explore what it could achieve. The results show that if inhibitory synapses used this same learning rule, they could support the two fundamental roles of inhibition in the nervous system described above.