A computational passage-of-time model of the cerebellar Purkinje cell in eyeblink conditioning

The cerebellar Purkinje cell controlling eyeblinks can learn, remember, and reproduce the interstimulus interval in a classical conditioning paradigm. Given temporally separated inputs, the cerebellar Purkinje cell learns to pause its tonic inhibition of a motor pathway with high temporal precision so that an overt blink occurs at the right time. Most models place the passage-of-time representation in upstream network effects. Yet, bypassing the upstream network and directly stimulating the Purkinje cell's pre-synaptic fibers during conditioning still causes acquisition of a well-timed response. Additionally, while network models are sensitive to variance in the temporal structure of probe stimulation, in vivo findings suggest that the acquired Purkinje cell response is not. Such findings motivate alternative approaches to modeling neural function. Here, we present a proof-of-principle model of the passage-of-time which is internal to the Purkinje cell and is invariant to probe structure. The model is consistent with puzzling findings, accurately recapitulates Purkinje cell firing during classical conditioning and makes testable electrophysiological predictions.