Two functionally distinct Purkinje cell populations implement an internal model within a single olivo-cerebellar loop

Olivo-cerebellar loops, where anatomical patches of the cerebellar cortex and inferior olive project one onto the other, form an anatomical unit of cerebellar computation. Here, we investigated how successive computational steps map onto olivo-cerebellar loops. Lobules IX-X of the cerebellar vermis, i.e. the nodulus and uvula, implement an internal model of the inner ears graviceptor, the otolith organs. We have previously identified two populations of Purkinje cells that participate in this computation: Tilt-selective cells transform egocentric rotation signals into allocentric tilt velocity signals, to track head motion relative to gravity, and translation-selective cells encode otolith prediction error. Here we show that, despite very distinct simple spike response properties, both types of Purkinje cells emit complex spikes that are proportional to sensory prediction error. This indicates that both cell populations comprise a single olivo-cerebellar loop, in which only translation-selective cells project to the inferior olive. We propose a neural network model where sensory prediction errors computed by translation-selective cells are used as a teaching signal for both populations, and demonstrate that this network can learn to implement an internal model of the otoliths.