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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.

The inferior olive provides the climbing fibers to Purkinje cells in the cerebellar cortex, where they elicit all-or-none complex spikes and control major forms of plasticity. Given their important role in both short-term and long-term coordination of cerebellum-dependent behaviors, it is paramount to understand the factors that determine the output of olivary neurons. Here, we use mouse models to investigate how the inhibitory and excitatory inputs to the olivary neurons interact with each other, generating spiking patterns of olivary neurons that align with their intrinsic oscillations. Using dual color optogenetic stimulation and whole-cell recordings, we demonstrate how intervals between the inhibitory input from the cerebellar nuclei and excitatory input from the mesodiencephalic junction affect phase and gain of the olivary output at both the sub- and suprathreshold level. When the excitatory input is activated shortly (~50 ms) after the inhibitory input, the phase of the intrinsic oscillations becomes remarkably unstable and the excitatory input can hardly generate any olivary spike. Instead, when the excitatory input is activated one cycle (~150 ms) after the inhibitory input, the excitatory input can optimally drive olivary spiking, riding on top of the first cycle of the subthreshold oscillations that have been powerfully reset by the preceding inhibitory input. Simulations of a large-scale network model of the inferior olive highlight to what extent the synaptic interactions penetrate in the neuropil, generating quasi-oscillatory spiking patterns in large parts of the olivary subnuclei, the size of which also depends on the relative timing of the inhibitory and excitatory inputs.

Modern neuroscience employs in silico experimentation on ever-increasing and more detailed neural networks. The high modeling detail goes hand in hand with the need for high model reproducibility, reusability and transparency. Besides, the size of the models and the long timescales under study mandate the use of a simulation system with high computational performance, so as to provide an acceptable time to result. In this work, we present EDEN (Extensible Dynamics Engine for Networks), a new general-purpose, NeuroML-based neural simulator that achieves both high model flexibility and high computational performance, through an innovative model-analysis and code-generation technique. The simulator runs NeuroML-v2 models directly, eliminating the need for users to learn yet another simulator-specific, model-specification language. EDEN's functional correctness and computational performance were assessed through NeuroML models available on the NeuroML-DB and Open Source Brain model repositories. In qualitative experiments, the results produced by EDEN were verified against the established NEURON simulator, for a wide range of models. At the same time, computational-performance benchmarks reveal that EDEN runs from one to nearly two orders-of-magnitude faster than NEURON on a typical desktop computer, and does so without additional effort from the user. Finally, and without added user effort, EDEN has been built from scratch to scale seamlessly over multiple CPUs and across computer clusters, when available., Computer Engineering, Bio-Electronics

Modern neuroscience employs in silico experimentation on ever-increasing and more detailed neural networks. The high modeling detail goes hand in hand with the need for high model reproducibility, reusability and transparency. Besides, the size of the models and the long timescales under study mandate the use of a simulation system with high computational performance, so as to provide an acceptable time to result. In this work, we present EDEN (Extensible Dynamics Engine for Networks), a new general-purpose, NeuroML-based neural simulator that achieves both high model flexibility and high computational performance, through an innovative model-analysis and code-generation technique. The simulator runs NeuroML-v2 models directly, eliminating the need for users to learn yet another simulator-specific, model-specification language. EDEN's functional correctness and computational performance were assessed through NeuroML models available on the NeuroML-DB and Open Source Brain model repositories. In qualitative experiments, the results produced by EDEN were verified against the established NEURON simulator, for a wide range of models. At the same time, computational-performance benchmarks reveal that EDEN runs from one to nearly two orders-of-magnitude faster than NEURON on a typical desktop computer, and does so without additional effort from the user. Finally, and without added user effort, EDEN has been built from scratch to scale seamlessly over multiple CPUs and across computer clusters, when available.

The Hodgkin-Huxley (HH) neuron is one of the most biophysically-meaningful models used in computational neuroscience today. Ironically, the model's high experimental value is offset by its disproportional computational complexity. To such an extent that neuroscientists have either resorted to simpler models, losing precious neuron detail, or to using high-performance computing systems, to gain acceleration, for complex models. However, multicore/multinode CPU-based systems have proven too slow while FPGA-based ones have proven too time-consuming to (re)deploy to. Clearly, a solution that bridges user friendliness and high speedups is necessary. This paper presents flexHH, a flexible FPGA library implementing five popular, highly parameterizable variants of the HH neuron model. flexHH is the first crucial step towards making FPGA-based simulations of compute-intensive neural models available to neuroscientists without the debilitating penalty of re-engineering and re-synthesis. Through flexHH, the user can instantiate custom models and immediately take advantage of the acceleration without the mediation of an engineer, which has proven to be a major inhibitor to full adoption of FPGAs in neuroscience labs. In terms of performance, flexHH achieves speedups between 8 × - 20 × compared to sequential-C implementations, while only a small drop in real-time capabilities is observed when compared to hardcoded FPGA-based versions of the models tested., Computer Engineering, Numerical Analysis, Bio-Electronics

The cerebellum is involved in the control of voluntary and autonomic rhythmic behaviors, yet it is unclear to what extent it coordinates these in concert. We studied Purkinje cell activity during unperturbed and perturbed respiration in lobules simplex, crus 1, and crus 2. During unperturbed (eupneic) respiration, complex spike and simple spike activity encode the phase of ongoing sensorimotor processing. In contrast, when the respiratory cycle is perturbed by whisker stimulation, mice concomitantly protract their whiskers and advance their inspiration in a phase-dependent manner, preceded by increased simple spike activity. This phase advancement of respiration in response to whisker stimulation can be mimicked by optogenetic stimulation of Purkinje cells and prevented by cell-specific genetic modification of their AMPA receptors, hampering increased simple spike firing. Thus, the impact of Purkinje cell activity on respiratory control is context and phase dependent, highlighting a coordinating role for the cerebellar hemispheres in aligning autonomic and sensorimotor behaviors.

Miniaturized fluorescence microscopes (miniscopes) have been instrumental to monitor neural signals during unrestrained behavior and their open-source versions have made them affordable. Often, the footprint and weight of open-source miniscopes is sacrificed for added functionality. Here, we present NINscope: a light-weight miniscope with a small footprint that integrates a high-sensitivity image sensor, an inertial measurement unit and an LED driver for an external optogenetic probe. We use it to perform the first concurrent cellular resolution recordings from cerebellum and cerebral cortex in unrestrained mice, demonstrate its optogenetic stimulation capabilities to examine cerebello-cerebral or cortico-striatal connectivity, and replicate findings of action encoding in dorsal striatum. In combination with cross-platform control software, our miniscope is a versatile addition to the expanding toolbox of open-source miniscopes that will increase access to multi-region circuit investigations during unrestrained behavior.

Saccadic eye movements enable fast and precise scanning of the visual field, which is partially controlled by the posterior cerebellar vermis. Textbook saccades have a straight trajectory and a unimodal velocity profile, and hence have well-defined epochs of start and end. However, in practice only a fraction of saccades matches this description. One way in which a saccade can deviate from its trajectory is the presence of an overshoot or undershoot at the end of a saccadic eye movement just before fixation. This additional movement, known as a glissade, is regarded as a motor command error and was characterized decades ago but was almost never studied. Using rhesus macaques, we investigated the properties of glissades and changes to glissade kinematics following cerebellar lesions. Additionally, in monkeys with an intact cerebellum, we investigated whether the glissade amplitude can be modulated using multiple adaptation paradigms. Our results show that saccade kinematics are altered by the presence of a glissade, and that glissades do not appear to have any adaptive function as they do not bring the eye closer to the target. Quantification of these results establishes a detailed description of glissades. Further, we show that lesions to the posterior cerebellum have a deleterious effect on both saccade and glissade properties, which recovers over time. Finally, the saccadic adaptation experiments reveal that glissades cannot be modulated by this training paradigm. Together our work offers a functional study of glissades and provides new insight into the cerebellar involvement in this type of motor error.

Inferior olivary activity causes both short-term and long-term changes in cerebellar output underlying motor performance and motor learning. Many of its neurons engage in coherent subthreshold oscillations and are extensively coupled via gap junctions. Studies in reduced preparations suggest that these properties promote rhythmic, synchronized output. However, the interaction of these properties with torrential synaptic inputs in awake behaving animals is not well understood. Here we combine electrophysiological recordings in awake mice with a realistic tissue-scale computational model of the inferior olive to study the relative impact of intrinsic and extrinsic mechanisms governing its activity. Our data and model suggest that if subthreshold oscillations are present in the awake state, the period of these oscillations will be transient and variable. Accordingly, by using different temporal patterns of sensory stimulation, we found that complex spike rhythmicity was readily evoked but limited to short intervals of no more than a few hundred milliseconds and that the periodicity of this rhythmic activity was not fixed but dynamically related to the synaptic input to the inferior olive as well as to motor output. In contrast, in the long-term, the average olivary spiking activity was not affected by the strength and duration of the sensory stimulation, while the level of gap junctional coupling determined the stiffness of the rhythmic activity in the olivary network during its dynamic response to sensory modulation. Thus, interactions between intrinsic properties and extrinsic inputs can explain the variations of spiking activity of olivary neurons, providing a temporal framework for the creation of both the short-term and long-term changes in cerebellar output.

KEY POINTS: Purkinje cells in the cerebellum integrate input from sensory organs with that from premotor centres. Purkinje cells use a variety of sensory inputs relaying information from the environment to modify motor control. Here we asked to what extent the climbing fibre inputs to Purkinje cells signal mono- or multi-sensory information, and to what extent this signalling is subject to recent history of activity. We show that individual climbing fibres convey multiple types of sensory information, together providing a rich mosaic projection pattern of sensory signals across the cerebellar cortex. Moreover, firing probability of climbing fibres following sensory stimulation strongly depends on the recent history of activity, showing a tendency to homeostatic dampening.ABSTRACT: Cerebellar Purkinje cells integrate sensory information with motor efference copies to adapt movements to behavioural and environmental requirements. They produce complex spikes that are triggered by the activity of climbing fibres originating in neurons of the inferior olive. These complex spikes can shape the onset, amplitude and direction of movements and the adaptation of such movements to sensory feedback. Clusters of nearby inferior olive neurons project to parasagittally aligned stripes of Purkinje cells, referred to as 'microzones'. It is currently unclear to what extent individual Purkinje cells within a single microzone integrate climbing fibre inputs from multiple sources of different sensory origins, and to what extent sensory-evoked climbing fibre responses depend on the strength and recent history of activation. Here we imaged complex spike responses in cerebellar lobule crus 1 to various types of sensory stimulation in awake mice. We find that different sensory modalities and receptive fields have a mild, but consistent, tendency to converge on individual Purkinje cells, with climbing fibres showing some degree of input-specificity. Purkinje cells encoding the same