Modulation of spike and burst rate in a minimal neuronal circuit with feed-forward inhibition.

Pyramidal cells perform computations on their inputs within the context of the local network. The present computational study investigates the consequences of feed-forward inhibition for the firing rate and reliability of a typical hippocampal pyramidal neuron that can respond with single spikes as well as bursts. A simple generic inhibitory interneuron is connected in a feed-forward mode to a pyramidal cell and this minimal circuit is activated with frozen noise. The properties (reversal potential, projection site, propagation delay, fast or slow kinetics) of the connecting synapse and the coupling strength between the interneuron and the pyramidal cell are varied. All forms of inhibition considered here decrease the burst rate, but the effects on the single spike (spikes that are not part of a burst) rate are more ambiguous. Slow dendritic shunting inhibition increases the single spike rate, but fast somatic inhibition does not. When a propagation delay is included in the slow dendritic synapse, the increase of the single spike rate is smaller, an effect that could also be obtained by lowering the reversal potential of the synaptic current. Cross-correlations, reverse correlation analysis and decorrelating the interneuron and pyramidal cell activity are used to demonstrate that these effects depend critically on the exact timing of inhibition, emphasizing the relevance of spatiotemporal organization. The reliability of the firing of the pyramidal cell is quantified with the Victor-Purpura measure. When burst and spikes together or spikes alone are taken into account, feed-forward inhibition makes firing more reliable. This is not the case when the analysis is restricted to bursts. A hyperpolarization-activated, non-specific cation current (Ih) is inserted into the dendritic membrane of the pyramidal cell, where it slightly depolarizes the membrane and reduces its time constant. This dendritic h-current increases the output frequency, makes inhibition less effective and introduces spike-spike interactions at a 40-140 ms time scale. Feed-forward inhibition always decreases the burst firing rate, but the effects on the single spike rate depended on the spatiotemporal organization of inhibition. Therefore, using different connection strategies, the spike and burst rate of such a minimal circuit can be modulated independently.