Temporal integration and 1/f power scaling in a circuit model of cerebellar interneurons

Inhibitory interneurons interconnected via electrical and chemical (GABAA receptor) synapses form extensive circuits in several brain regions. They are thought to be involved in timing and synchronization through fast feed-forward control of principal neurons. Theoretical studies have shown, however, that whereas self-inhibition does indeed reduce response duration, lateral inhibition, in contrast, may generate slow response components through a process of gradual disinhibition. Here we simulated a circuit of interneurons (stellate and basket cells) of the molecular layer of the cerebellar cortex, and observed circuit time-constants that could rise, depending on the parameter values, to more than one second. The integration time scaled both with the strength of inhibition, vanishing completely when inhibition was blocked, and with the average connection distance, which determined the balance between lateral and self-inhibition. Electrical synapses could further enhance the integration time by limiting heterogeneity among the interneurons, and by introducing a slow capacitive current. The model can explain several observations, such as the slow time-course of OFF-beam inhibition, the phase lag of interneurons during vestibular rotation, or the phase lead of Purkinje cells. Interestingly, the interneuron spike trains displayed power that scaled approximately as 1/f at low frequencies. In conclusion, stellate and basket cells in cerebellar cortex, and interneuron circuits in general, may not only provide fast inhibition to principal cells, but also act as temporal integrators that build a very-short-term memory.