Cerebellar Purkinje Cells Generate Highly Correlated Spontaneous Slow-Rate Fluctuations

Purkinje cell models: past, present and future

The investigation of the dynamics of Purkinje cell (PC) activity is crucial to unravel the role of the cerebellum in motor control, learning and cognitive processes. Within the cerebellar cortex (CC), these neurons receive all the incoming sensory and motor information, transform it and generate the entire cerebellar output. The relatively homogenous and repetitive structure of the CC, common to all vertebrate species, suggests a single computation mechanism shared across all PCs. While PC models have been developed since the 70's, a comprehensive review of contemporary models is currently lacking. Here, we provide an overview of PC models, ranging from the ones focused on single cell intracellular PC dynamics, through complex models which include synaptic and extrasynaptic inputs. We review how PC models can reproduce physiological activity of the neuron, including firing patterns, current and multistable dynamics, plateau potentials, calcium signaling, intrinsic and synaptic plasticity and input/output computations. We consider models focusing both on somatic and on dendritic computations. Our review provides a critical performance analysis of PC models with respect to known physiological data. We expect our synthesis to be useful in guiding future development of computational models that capture real-life PC dynamics in the context of cerebellar computations.

State-dependent entrainment of cerebellar nuclear neurons to the local field potential during voluntary movements

Understanding the relationship between the local field potential (LFP) and single neurons is essential if we are to understand network dynamics and the entrainment of neuronal activity. Here, we investigated the interaction between the LFP and single neurons recorded in the rat cerebellar nuclei (CN), which are part of the sensorimotor network, in freely moving rats. During movement, the LFP displayed persistent oscillations in the theta band frequency, whereas CN neurons displayed intermittent oscillations in the same frequency band contingent on the instantaneous LFP power; the neurons oscillated primarily when the concurrent LFP power was either high or low. Quantification of the relative instantaneous frequency and phase locking showed that CN neurons exhibited phase locked rhythmic activity at a frequency similar to that of the LFP or at a shifted frequency during high and low LFP power, respectively. We suggest that this nonlinear interaction between cerebellar neurons and the LFP power, which occurs solely during movement, contributes to the shaping of cerebellar output patterns.NEW & NOTEWORTHY We studied the interaction between single neurons and the LFP in the cerebellar nuclei of freely moving rats. We show that during movement, the neurons oscillated in the theta frequency band contingent on the concurrent LFP oscillation power in the same band; the neurons oscillated primarily when the LFP power was either high or low. We are the first to demonstrate a nonlinear, state-dependent entrainment of single neurons to the LFP.

A general method to generate artificial spike train populations matching recorded neurons

We developed a general method to generate populations of artificial spike trains (ASTs) that match the statistics of recorded neurons. The method is based on computing a Gaussian local rate function of the recorded spike trains, which results in rate templates from which ASTs are drawn as gamma distributed processes with a refractory period. Multiple instances of spike trains can be sampled from the same rate templates. Importantly, we can manipulate rate-covariances between spike trains by performing simple algorithmic transformations on the rate templates, such as filtering or amplifying specific frequency bands, and adding behavior related rate modulations. The method was examined for accuracy and limitations using surrogate data such as sine wave rate templates, and was then verified for recorded spike trains from cerebellum and cerebral cortex. We found that ASTs generated with this method can closely follow the firing rate and local as well as global spike time variance and power spectrum. The method is primarily intended to generate well-controlled spike train populations as inputs for dynamic clamp studies or biophysically realistic multicompartmental models. Such inputs are essential to study detailed properties of synaptic integration with well-controlled input patterns that mimic the in vivo situation while allowing manipulation of input rate covariances at different time scales.

Coding Capacity of Purkinje Cells With Different Schemes of Morphological Reduction

The brain as a neuronal system has very complex structures with a large diversity of neuronal types. The most basic complexity is seen from the structure of neuronal morphology, which usually has a complex tree-like structure with dendritic spines distributed in branches. To simulate a large-scale network with spiking neurons, the simple point neuron, such as the integrate-and-fire neuron, is often used. However, recent experimental evidence suggests that the computational ability of a single neuron is largely enhanced by its morphological structure, in particular, by various types of dendritic dynamics. As the morphology reduction of detailed biophysical models is a classic question in systems neuroscience, much effort has been taken to simulate a neuron with a few compartments to include the interaction between the soma and dendritic spines. Yet, novel reduction methods are still needed to deal with the complex dendritic tree. Here, using 10 individual Purkinje cells of the cerebellum from three species of guinea-pig, mouse and rat, we consider four types of reduction methods and study their effects on the coding capacity of Purkinje cells in terms of firing rate, timing coding, spiking pattern, and modulated firing under different stimulation protocols. We found that there is a variation of reduction performance depending on individual cells and species, however, all reduction methods can preserve, to some degree, firing activity of the full model of Purkinje cell. Therefore, when stimulating large-scale network of neurons, one has to choose a proper type of reduced neuronal model depending on the questions addressed. Among these reduction schemes, Branch method, that preserves the geometrical volume of neurons, can achieve the best balance among different performance measures of accuracy, simplification, and computational efficiency, and reproduce various phenomena shown in the full morphology model of Purkinje cells. Altogether, these results suggest that the Branch reduction scheme seems to provide a general guideline for reducing complex morphology into a few compartments without the loss of basic characteristics of the firing properties of neurons.

Cerebellar Modules and Their Role as Operational Cerebellar Processing Units: A Consensus paper [corrected]

The compartmentalization of the cerebellum into modules is often used to discuss its function. What, exactly, can be considered a module, how do they operate, can they be subdivided and do they act individually or in concert are only some of the key questions discussed in this consensus paper. Experts studying cerebellar compartmentalization give their insights on the structure and function of cerebellar modules, with the aim of providing an up-to-date review of the extensive literature on this subject. Starting with an historical perspective indicating that the basis of the modular organization is formed by matching olivocorticonuclear connectivity, this is followed by consideration of anatomical and chemical modular boundaries, revealing a relation between anatomical, chemical, and physiological borders. In addition, the question is asked what the smallest operational unit of the cerebellum might be. Furthermore, it has become clear that chemical diversity of Purkinje cells also results in diversity of information processing between cerebellar modules. An additional important consideration is the relation between modular compartmentalization and the organization of the mossy fiber system, resulting in the concept of modular plasticity. Finally, examination of cerebellar output patterns suggesting cooperation between modules and recent work on modular aspects of emotional behavior are discussed. Despite the general consensus that the cerebellum has a modular organization, many questions remain. The authors hope that this joint review will inspire future cerebellar research so that we are better able to understand how this brain structure makes its vital contribution to behavior in its most general form.