UC San Diego

We join the efforts of over a century of modern scientific inquiry to understand what the cerebellum does and how the cerebellum implements its function. A myriad of anatomical and physiological facts about the cerebellum exist and have been woven into theories of cerebellar computation, but most of these theories ignore the role of a certain neuron type in the cerebellar cortex -- the molecular layer interneurons (MLIs). In this body of work, we propose mathematical models for the anatomy, physiology and synaptic plasticity of these neurons in order to characterize their role in cerebellar function. First, we introduce a simple model of the physiology of the MLI which exhibits spontaneous firing as observed in vivo. Further, we model the synaptic connectivity of MLIs with other MLIs and with Purkinje cells (PKJs). We validate the model by simulating the network of MLIs and PKJs and show that it reproduces the irregular firing activity of MLIs and PKJs as observed in vitro. Second, we introduce a phenomenological model of plasticity at parallel fiber (PF) - MLI synapses. We show via computer simulation that this model reproduces the changes in synaptic efficacy observed in vitro under a number of experimental protocols. Further, we hypothesize what biological mechanisms govern plasticity at this synapse and give rise to the model we introduce. Finally, we show analytically that the model of plasticity at PF-MLI synapses can implement temporal difference learning at these synapses under certain assumptions about the function of cerebellar cortical circuitry. This result supports the idea that reinforcement learning is the method of learning used by the cerebellum