  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 relegate the Purkinje cell's
passage-of-time representation to afferent granule cells, a subpopulation of
which is supposedly selected for synaptic depression in order to make the
Purkinje cell pause. However, granule cell models have recently faced two
crucial challenges: 1) bypassing granule cells and directly stimulating the
Purkinje cell's pre-synaptic fibers during training still produces a well-timed
pause, and 2) the Purkinje cell can reproduce the learned pause, invariant to
the temporal structure of probe stimulation. Here, we present a passage-of-time
model which is internal to the Purkinje cell and is invariant to probe
structure. The model accurately simulates the Purkinje cell learning mechanism
and makes testable electrophysiological predictions. Importantly, the model is
a numerical proof-of-principle for a biological learning mechanism which does
not rely on changes of synaptic strength.
