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

Abstract

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.

Stimulus-Dependent State Transition between Synchronized Oscillation and Randomly Repetitive Burst in a Model Cerebellar Granular Layer

“…The emergence of the synchronized oscillation in the grcs and Gocs is consistent with the findings of Maex and De Schutter [7]. For the successive 2 s, in which a large current was injected to the grcs, the model grcs exhibited random alternation between burst and silent modes, consistent with the findings of Yamazaki and Tanaka [3]. After the current amplitude was decreased to that for the first 2 s, the network quickly returned to the oscillatory state at 9 Hz.…”

“… monotonically decreased as | τ | increased with the POT-representation index PI  = 0.923. This indicates that the population of active grcs changed gradually with time from the onset of a large current injection without the recurrence of active grc populations, as reported by Yamazaki and Tanaka [3]. The NAC ( τ ) and for model Gocs were similar to those for model grcs (Fig.…”

A Computational Mechanism for Unified Gain and Timing Control in the Cerebellum

“…In our previous modeling study [25], we reported that such a sequence could be generated in response to sustained MF inputs in which the firing rate is constant at 30 spikes/s. In the present study, we suggested that a similar sequence can be generated even for the sinusoidally oscillating MF inputs at 0.5 Hz (Fig.…”

A neural model for the adaptive control of saccadic eye movements

“…Hence, the cerebellar VPFL is a strong candidate for the neural controller of our model. More specifically, we can consider the neural delay line structure as a model of the granular layer and the read-out neuron as a P-cell, in accordance with the cerebellar models which assume the granular layer as a basis for the spatio-temporal representation of the input signals and the P-cell layer as a layer that receives weighted projections from the granular layer [26] [27].…”