A spiking network model for passage-of-time representation in the cerebellum

In Pavlovian delay eyeblink conditioning, the cerebellum represents the passage-of-time (POT) between onsets of conditioned and unconditioned stimuli (CS and US, respectively). To study possible computational mechanisms of the POT representation we built a large-scale spiking network model of the cerebellum. Consistent with our previous rate-coding model, we found two conditions necessary for the present model to represent the POT with a dynamic population of active granule cells: (i) long temporal integration of input signals; and (ii) random recurrent connections between granule and Golgi cells. When these conditions were satisfied, a nonrecurrent sequence of active granule cell populations was generated in response to a CS and, conversely, the POT from the CS onset was able to be read out from the sequence. Specifically, simulated N-methyl-D-aspartate (NMDA) channels with a long decay time constant at granule and Golgi cells were responsible for the long temporal integration. Thus, blocking the NMDA channels or ablating Golgi cells impaired the POT representation. Simulated glomerulus structure made POT representation robust against noise in mossy fibre inputs. Long-term potentiation induced at mossy fibre synapses on granule cells also served to enhance the robustness. We reproduced some experimental results of Pavlovian delay eyeblink conditioning using the present model. These results suggest that the recurrent network in the granular layer and NMDA channels in granule and Golgi cells play an essential role in the timing mechanisms in the cerebellum, whereas the glomerulus serves to realize a robust representation of time.