This article explores dynamical properties of the olivo-cerebellar system that arise from the specific wiring of inferior olive (IO), cerebellar cortex, and deep cerebellar nuclei (DCN). We show that the irregularity observed in the firing pattern of the IO neurons is not necessarily produced by noise but can instead be the result of a purely deterministic network effect. We propose that this effect can serve as a dynamical working memory or as a neuronal clock with a characteristic timescale of about 100 ms that is determined by the slow calcium dynamics of IO and DCN neurons. This concept provides a novel explanation of how the cerebellum can solve timing tasks on a timescale that is two orders of magnitude longer than the millisecond timescale usually attributed to neuronal dynamics.
One of the key ingredients of our model is the observation that due to postinhibitory rebound, DCN neurons can be driven by GABAergic (“inhibitory”) input from cerebellar Purkinje cells. Topographic projections from the DCN to the IO form a closed reverberating loop with an overall synaptic transmission delay of about 100 ms that is in resonance with the intrinsic oscillatory properties of the inferior olive.
We use a simple time-discrete model based on McCulloch-Pitts neurons in order to investigate in a first step some of the fundamental properties of a network with delayed reverberating projections. The macroscopic behavior is analyzed by means of a mean-field approximation. Numerical simulations, however, show that the microscopic dynamics has a surprisingly rich structure that does not show up in a mean-field description. We have thus performed extensive numerical experiments in order to quantify the ability of the network to serve as a dynamical working memory and its vulnerability by noise. In a second step, we develop a more realistic conductance-based network model of the inferior olive consisting of about 20 multicompartment neurons that are coupled by gap junctions and receive excitatory and inhibitory synaptic input via AMPA and GABAergic synapses. The simulations show that results for the time-discrete model hold true in a time-continuous description.