Substantial evidence has established that the cerebellum plays an important role in the generation of movements. An important aspect of motor output is its timing in relation to external stimuli or to other components of a movement. Previous studies suggest that the cerebellum plays a role in the timing of movements. Here we describe a neural network model based on the synaptic organization of the cerebellum that can generate timed responses in the range of tens of milliseconds to seconds. In contrast to previous models, temporal coding emerges from the dynamics of the cerebellar circuitry and depends neither on conduction delays, arrays of elements with different time constants, nor populations of elements oscillating at different frequencies. Instead, time is extracted from the instantaneous granule cell population vector. The subset of active granule cells is time-varying due to the granule—Golgi—granule cell negative feedback. We demonstrate that the population vector of simulated granule cell activity exhibits dynamic, nonperiodic trajectories in response to a periodic input. With time encoded in this manner, the output of the network at a particular interval following the onset of a stimulus can be altered selectively by changing the strength of granule → Purkinje cell connections for those granule cells that are active during the target time window. The memory of the reinforcement at that interval is subsequently expressed as a change in Purkinje cell activity that is appropriately timed with respect to stimulus onset. Thus, the present model demonstrates that a network based on cerebellar circuitry can learn appropriately timed responses by encoding time as the population vector of granule cell activity.

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