Climbing fiber inputs to Purkinje cells provide instructive signals critical for cerebellum-dependent associative learning. Studying these signals in head-fixed mice facilitates the use of imaging, electrophysiological, and optogenetic methods. Here, a low-cost behavioral platform (~$1000) was developed that allows tracking of associative learning in head-fixed mice that locomote freely on a running wheel. The platform incorporates two common associative learning paradigms: eyeblink conditioning and delayed tactile startle conditioning. Behavior is tracked using a camera and the wheel movement by a detector. We describe the components and setup and provide a detailed protocol for training and data analysis. This platform allows the incorporation of optogenetic stimulation and fluorescence imaging. The design allows a single host computer to control multiple platforms for training multiple animals simultaneously.

The cerebellum resembles a feedforward, three-layer network of neurons in which the “hidden layer” consists of Purkinje cells (P-cells) and the output layer consists of deep cerebellar nucleus (DCN) neurons. In this analogy, the output of each DCN neuron is a prediction that is compared with the actual observation, resulting in an error signal that originates in the inferior olive. Efficient learning requires that the error signal reach the DCN neurons, as well as the P-cells that project onto them. However, this basic rule of learning is violated in the cerebellum: the olivary projections to the DCN are weak, particularly in adulthood. Instead, an extraordinarily strong signal is sent from the olive to the P-cells, producing complex spikes. Curiously, P-cells are grouped into small populations that converge onto single DCN neurons. Why are the P-cells organized in this way, and what is the membership criterion of each population? Here, I apply elementary mathematics from machine learning and consider the fact that P-cells that form a population exhibit a special property: they can synchronize their complex spikes, which in turn suppress activity of DCN neuron they project to. Thus complex spikes cannot only act as a teaching signal for a P-cell, but through complex spike synchrony, a P-cell population may act as a surrogate teacher for the DCN neuron that produced the erroneous output. It appears that grouping of P-cells into small populations that share a preference for error satisfies a critical requirement of efficient learning: providing error information to the output layer neuron (DCN) that was responsible for the error, as well as the hidden layer neurons (P-cells) that contributed to it. This population coding may account for several remarkable features of behavior during learning, including multiple timescales, protection from erasure, and spontaneous recovery of memory.

Spontaneous firing, observed in many neurons, is often attributed to ion channel or network level noise. Cortical cells during slow wave sleep exhibit transitions between so called Up and Down states. In this sleep state, with limited sensory stimuli, neurons fire in the Up state. Spontaneous firing is also observed in slices of cholinergic interneurons, cerebellar Purkinje cells and even brainstem inspiratory neurons. In such in vitro preparations, where the functional relevance is long lost, neurons continue to display a rich repertoire of firing properties. It is perplexing that these neurons, instead of saving their energy during information downtime and functional irrelevance, are eager to fire. We propose that spontaneous firing is not a chance event but instead, a vital activity for the well-being of a neuron. We postulate that neurons, in anticipation of synaptic inputs, keep their ATP levels at maximum. As recovery from inputs requires most of the energy resources, neurons are ATP surplus and ADP scarce during synaptic quiescence. With ADP as the rate-limiting step, ATP production stalls in the mitochondria when ADP is low. This leads to toxic Reactive Oxygen Species (ROS) formation, which are known to disrupt many cellular processes. We hypothesize that spontaneous firing occurs at these conditions - as a release valve to spend energy and to restore ATP production, shielding the neuron against ROS. By linking a mitochondrial metabolism model to a conductance-based neuron model, we show that spontaneous firing depends on baseline ATP usage and on ATP-cost-per-spike. From our model, emerges a mitochondrial mediated homeostatic mechanism that provides a recipe for different firing patterns. Our findings, though mostly affecting intracellular dynamics, may have large knock-on effects on the nature of neural coding. Hitherto it has been thought that the neural code is optimised for energy minimisation, but this may be true only when neurons do not experience synaptic quiescence.

The electrosensory lobe (ELL) in mormyrid electric fish is a cerebellar-like structure that cancels the sensory effects of self-generated electric fields, allowing prey to be detected. Like the cerebellum, the ELL involves two stages of processing, analogous to the Purkinje cells and cells of the deep cerebellar nuclei. Through the work of Curtis Bell and others, a model was previously developed to describe the output stage of the ELL, but the role of the Purkinje-cell analogs, the medium ganglion (MG) cells, in the circuit had remained mysterious. I will present a complete, multi-layer circuit description of the ELL, developed in collaboration with Nate Sawtell and Salomon Muller, that reveals a novel role for the MG cells. The resulting model provides an example of how a biological system solves well-known problems associated with learning in multi-layer networks, and it reveals that ELL circuitry is organization on the basis of learning rather than by the response properties of neurons.