Computational Principles of Supervised Learning in the Cerebellum.

Supervised learning plays a key role in the operation of many biological and artificial neural networks. Analysis of the computations underlying supervised learning is facilitated by the relatively simple and uniform architecture of the cerebellum, a brain area that supports numerous motor, sensory, and cognitive functions. We highlight recent discoveries indicating that the cerebellum implements supervised learning using the following organizational principles: ( a) extensive preprocessing of input representations (i.e., feature engineering), ( b) massively recurrent circuit architecture, ( c) linear input-output computations, ( d) sophisticated instructive signals that can be regulated and are predictive, ( e) adaptive mechanisms of plasticity with multiple timescales, and ( f) task-specific hardware specializations. The principles emerging from studies of the cerebellum have striking parallels with those in other brain areas and in artificial neural networks, as well as some notable differences, which can inform future research on supervised learning and inspire next-generation machine-based algorithms.

Dendritic Inhibition by Shh Signaling-Dependent Stellate Cell Pool Is Critical for Motor Learning.

Cerebellar inhibitory interneurons are important regulators of neural circuit activity for diverse motor and nonmotor functions. The molecular layer interneurons (MLIs), consisting of basket cells (BCs) and stellate cells (SCs), provide dendritic and somatic inhibitory synapses onto Purkinje cells, respectively. They are sequentially generated in an inside-out pattern from Pax2+ immature interneurons, which migrate from the prospective white matter to the ML of the cortex. However, little is known about how MLI subtype identities and pool sizes are determined, nor are their contributions to motor learning well understood. Here, we show that GABAergic progenitors fated to generate both BCs and SCs respond to the Sonic hedgehog (Shh) signal. Conditional abrogation of Shh signaling of either sex inhibited proliferation of GABAergic progenitors and reduced the number of Pax2+ cells, whereas persistent Shh pathway activation increased their numbers. These changes, however, did not affect early born BC numbers but selectively altered the SC pool size. Moreover, genetic depletion of GABAergic progenitors when BCs are actively generated also resulted in a specific reduction of SCs, suggesting that the specification of MLI subtypes is independent of Shh signaling and their birth order and likely occurs after Pax2+ cells settle into their laminar positions in an inside-out sequence. Mutant mice with reduced SC numbers displayed decreased dendritic inhibitory synapses and neurotransmission onto Purkinje cells, resulting in an impaired acquisition of eyeblink conditioning. These findings also reveal an essential role of Shh signaling-dependent SCs in regulating inhibitory dendritic synapses and motor learning.SIGNIFICANCE STATEMENT The cerebellar circuit that enables fine motor learning involves MLIs of BCs and SCs, which provide dendritic and somatic inhibitory synapses onto Purkinje cells. Little is known about how their identities and numbers are determined, nor are their specific contributions to motor learning well understood. We show that MLI subtypes are specified independent of Shh signaling and their birth orders but appear to occur in their terminal laminar positions according to the inside-out sequence. This finding challenges the current view that MLI subtypes are specified sequentially at the progenitor level. We also demonstrate that dendritic inhibition by Shh signaling-dependent SC pool is necessary for motor learning.

P-sort: an open-source software for cerebellar neurophysiology.

Analysis of electrophysiological data from Purkinje cells (P-cells) of the cerebellum presents unique challenges to spike sorting. Complex spikes have waveforms that vary significantly from one event to the next, raising the problem of misidentification. Even when complex spikes are detected correctly, the simple spikes may belong to a different P-cell, raising the danger of misattribution. To address these identification and attribution problems, we wrote an open-source, semiautomated software called P-sort, and then tested it by analyzing data from P-cells recorded in three species: marmosets, macaques, and mice. Like other sorting software, P-sort relies on nonlinear dimensionality reduction to cluster spikes. However, it also uses the statistical relationship between simple and complex spikes to merge disparate clusters and split a single cluster. In comparison with expert manual curation, occasionally P-sort identified significantly more complex spikes, as well as prevented misattribution of clusters. Three existing automatic sorters performed less well, particularly for identification of complex spikes. To improve the development of analysis tools for the cerebellum, we provide labeled data for 313 recording sessions, as well as statistical characteristics of waveforms and firing patterns of P-cells in three species.NEW & NOTEWORTHY Algorithms that perform spike sorting depend on waveforms to cluster spikes. However, a cerebellar Purkinje-cell produces two types of spikes; simple and complex spikes. A complex spike coincides with the suppression of generating simple spikes. Here, we recorded neurophysiological data from three species and developed a spike analysis software named P-sort that relies on this statistical property to improve both the detection and the attribution of simple and complex spikes in the cerebellum.

Bidirectional short-term plasticity during single-trial learning of cerebellar-driven eyelid movements in mice.

The brain is constantly monitoring its own performance, using error signals to trigger mechanisms of plasticity that help improve future behavior. Indeed, adaptive changes in behavior have been observed after a single error trial in many learning tasks, including cerebellum-dependent eyeblink conditioning. Here, we demonstrate that the plasticity underlying single-trial learning during eyeblink conditioning in mice is bidirectionally regulated by positive and negative prediction errors, has an ephemeral effect on behavior (decays in <1 min), and can be triggered in the absence of errors in performance. We suggest that these three properties of single-trial learning may be particularly useful for driving mechanisms of motor adaptation that can achieve optimal performance in the face of environmental disturbances with a fast timescale.

Precise control of movement kinematics by optogenetic inhibition of Purkinje cell activity.

Purkinje cells (PCs) of the cerebellar cortex are necessary for controlling movement with precision, but a mechanistic explanation of how the activity of these inhibitory neurons regulates motor output is still lacking. We used an optogenetic approach in awake mice to show for the first time that transiently suppressing spontaneous activity in a population of PCs is sufficient to cause discrete movements that can be systematically modulated in size, speed, and timing depending on how much and how long PC firing is suppressed. We further demonstrate that this fine control of movement kinematics is mediated by a graded disinhibition of target neurons in the deep cerebellar nuclei. Our results prove a long-standing model of cerebellar function and provide the first demonstration that suppression of inhibitory signals can act as a powerful mechanism for the precise control of behavior.

Cerebellar-dependent expression of motor learning during eyeblink conditioning in head-fixed mice.

Eyeblink conditioning in restrained rabbits has served as an excellent model of cerebellar-dependent motor learning for many decades. In mice, the role of the cerebellum in eyeblink conditioning is less clear and remains controversial, partly because learning appears to engage fear-related circuits and lesions of the cerebellum do not abolish the learned behavior completely. Furthermore, experiments in mice are performed using freely moving systems, which lack the stability necessary for mapping out the essential neural circuitry with electrophysiological approaches. We have developed a novel apparatus for eyeblink conditioning in head-fixed mice. Here, we show that the performance of mice in our apparatus is excellent and that the learned behavior displays two hallmark features of cerebellar-dependent eyeblink conditioning in rabbits: (1) gradual acquisition; and (2) adaptive timing of conditioned movements. Furthermore, we use a combination of pharmacological inactivation, electrical stimulation, single-unit recordings, and targeted microlesions to demonstrate that the learned behavior is completely dependent on the cerebellum and to pinpoint the exact location in the deep cerebellar nuclei that is necessary. Our results pave the way for using eyeblink conditioning in head-fixed mice as a platform for applying next-generation genetic tools to address molecular and circuit-level questions about cerebellar function in health and disease.

Diversity of neural responses in the brainstem during smooth pursuit eye movements constrains the circuit mechanisms of neural integration.

Neural integration converts transient events into sustained neural activity. In the smooth pursuit eye movement system, neural integration is required to convert cerebellar output into the sustained discharge of extraocular motoneurons. We recorded the expression of integration in the time-varying firing rates of cerebellar and brainstem neurons in the monkey during pursuit of step-ramp target motion. Electrical stimulation with single shocks in the cerebellum identified brainstem neurons that are monosynaptic targets of inhibition from the cerebellar floccular complex. They discharge in relation to eye acceleration, eye velocity, and eye position, with a stronger acceleration signal than found in most other brainstem neurons. The acceleration and velocity signals can be accounted for by opponent contributions from the two sides of the cerebellum, without integration; the position signal implies participation in the integrator. Other neurons in the vestibular nucleus show a wide range of blends of signals related to eye velocity and eye position, reflecting different stages of integration. Neurons in the abducens nucleus discharge homogeneously in relation mainly to eye position, and reflect almost perfect integration of the cerebellar outputs. Average responses of neural populations and the diverse individual responses of large samples of individual neurons are reproduced by a hierarchical neural circuit based on a model suggested the anatomy and physiology of the larval zebrafish brainstem. The model uses a combination of feedforward and feedback connections to support a neural circuit basis for integration in monkeys and other species.

A deep-learning strategy to identify cell types across species from high-density extracellular recordings.

High-density probes allow electrophysiological recordings from many neurons simultaneously across entire brain circuits but don't reveal cell type. Here, we develop a strategy to identify cell types from extracellular recordings in awake animals, revealing the computational roles of neurons with distinct functional, molecular, and anatomical properties. We combine optogenetic activation and pharmacology using the cerebellum as a testbed to generate a curated ground-truth library of electrophysiological properties for Purkinje cells, molecular layer interneurons, Golgi cells, and mossy fibers. We train a semi-supervised deep-learning classifier that predicts cell types with greater than 95% accuracy based on waveform, discharge statistics, and layer of the recorded neuron. The classifier's predictions agree with expert classification on recordings using different probes, in different laboratories, from functionally distinct cerebellar regions, and across animal species. Our classifier extends the power of modern dynamical systems analyses by revealing the unique contributions of simultaneously-recorded cell types during behavior.

Somatodendritic orientation determines tDCS-induced neuromodulation of Purkinje cell activity in awake mice.

Transcranial direct-current stimulation (tDCS) of the cerebellum is a promising non-invasive neuromodulatory technique being proposed for the treatment of neurological and neuropsychiatric disorders. However, there is a lack of knowledge about how externally applied currents affect neuronal spiking activity in cerebellar circuits in vivo. In this study, we observe that tDCS induces a heterogeneous polarity-dependent modulation of the firing rate of Purkinje cells (PC) and non-PC in the mouse cerebellar cortex. Using a combination of juxtacellular labeling and high-density Neuropixels recordings, we demonstrate that the apparently heterogeneous effects of tDCS on PC activity can be explained by taking into account the somatodendritic orientation relative to the electric field. Our findings emphasize the importance of considering neuronal orientation and morphological aspects to increase the predictive power of tDCS computational models, enhance the reliability of current stimulation protocols and optimize desired effects in basic and clinical human applications.

Acquisition of neural learning in cerebellum and cerebral cortex for smooth pursuit eye movements.

We evaluated the emergence of neural learning in the frontal eye fields (FEF(SEM)) and the floccular complex of the cerebellum while monkeys learned a precisely timed change in the direction of pursuit eye movement. For each neuron, we measured the time course of changes in neural response across a learning session that comprised at least 100 repetitions of an instructive change in target direction. In both areas, the average population learning curves tracked the behavioral changes with high fidelity, consistent with possible roles in driving learning. However, the learning curves of individual neurons sometimes bore little relation to the smooth, monotonic progression of behavioral learning. In the FEF(SEM), neural learning was episodic. For individual neurons, learning appeared at different times during the learning session and sometimes disappeared by the end of the session. Different FEF(SEM) neurons expressed maximal learning at different times relative to the acquisition of behavioral learning. In the floccular complex, many Purkinje cells acquired learned simple-spike responses according to the same time course as behavioral learning and retained their learned responses throughout the learning session. A minority of Purkinje cells acquired learned responses late in the learning session, after behavioral learning had reached an asymptote. We conclude that learning in single neurons can follow a very different time course from behavioral learning. Both the FEF(SEM) and the floccular complex contain representations of multiple temporal components of learning, with different neurons contributing to learning at different times during the acquisition of a learned movement.

Action-based organization of a cerebellar module specialized for predictive control of multiple body parts.

The role of the cerebellum in predictive motor control and coordination has been thoroughly studied during movements of a single body part. In the real world, however, actions are often more complex. Here, we show that a small area in the rostral anterior interpositus nucleus (rAIN) of the mouse cerebellum is responsible for generating a predictive motor synergy that serves to protect the eye by precisely coordinating muscles of the eyelid, neck, and forelimb. Within the rAIN region, we discovered a new functional category of neurons with unique properties specialized for control of motor synergies. These neurons integrated inhibitory cutaneous inputs from multiple parts of the body, and their activity was correlated with the vigor of the defensive motor synergy on a trial-by-trial basis. We propose that some regions of the cerebellum are organized in poly-somatotopic "action maps" to reduce dimensionality and simplify motor control during ethologically relevant behaviors.

Deleting Mecp2 from the cerebellum rather than its neuronal subtypes causes a delay in motor learning in mice.

Rett syndrome is a devastating childhood neurological disorder caused by mutations in MECP2. Of the many symptoms, motor deterioration is a significant problem for patients. In mice, deleting Mecp2 from the cortex or basal ganglia causes motor dysfunction, hypoactivity, and tremor, which are abnormalities observed in patients. Little is known about the function of Mecp2 in the cerebellum, a brain region critical for motor function. Here we show that deleting Mecp2 from the cerebellum, but not from its neuronal subtypes, causes a delay in motor learning that is overcome by additional training. We observed irregular firing rates of Purkinje cells and altered heterochromatin architecture within the cerebellum of knockout mice. These findings demonstrate that the motor deficits present in Rett syndrome arise, in part, from cerebellar dysfunction. For Rett syndrome and other neurodevelopmental disorders, our results highlight the importance of understanding which brain regions contribute to disease phenotypes.

Immediate and after effects of transcranial direct-current stimulation in the mouse primary somatosensory cortex.

Transcranial direct-current stimulation (tDCS) is a non-invasive brain stimulation technique consisting in the application of weak electric currents on the scalp. Although previous studies have demonstrated the clinical value of tDCS for modulating sensory, motor, and cognitive functions, there are still huge gaps in the knowledge of the underlying physiological mechanisms. To define the immediate impact as well as the after effects of tDCS on sensory processing, we first performed electrophysiological recordings in primary somatosensory cortex (S1) of alert mice during and after administration of S1-tDCS, and followed up with immunohistochemical analysis of the stimulated brain regions. During the application of cathodal and anodal transcranial currents we observed polarity-specific bidirectional changes in the N1 component of the sensory-evoked potentials (SEPs) and associated gamma oscillations. On the other hand, 20 min of cathodal stimulation produced significant after-effects including a decreased SEP amplitude for up to 30 min, a power reduction in the 20-80 Hz range and a decrease in gamma event related synchronization (ERS). In contrast, no significant changes in SEP amplitude or power analysis were observed after anodal stimulation except for a significant increase in gamma ERS after tDCS cessation. The polarity-specific differences of these after effects were corroborated by immunohistochemical analysis, which revealed an unbalance of GAD 65-67 immunoreactivity between the stimulated versus non-stimulated S1 region only after cathodal tDCS. These results highlight the differences between immediate and after effects of tDCS, as well as the asymmetric after effects induced by anodal and cathodal stimulation.

A cerebello-olivary signal for negative prediction error is sufficient to cause extinction of associative motor learning.

The brain generates negative prediction error (NPE) signals to trigger extinction, a type of inhibitory learning that is responsible for suppressing learned behaviors when they are no longer useful. Neurons encoding NPE have been reported in multiple brain regions. Here, we use an optogenetic approach to demonstrate that GABAergic cerebello-olivary neurons can generate a powerful NPE signal, capable of causing extinction of conditioned motor responses on its own.

The representation of time for motor learning.

We have identified factors that control precise motor timing by studying learning in smooth pursuit eye movements. Monkeys tracked a target that moved horizontally for a fixed time interval before changing direction through the addition of a vertical component of motion. After repeated presentations of the same target trajectory, infrequent probe trials of purely horizontal target motion evoked a vertical eye movement around the time when the change in target direction would have occurred. The pursuit system timed the vertical eye movement by keeping track of the duration of horizontal target motion and by measuring the distance the target traveled before changing direction, but not by learning the position in space where the target changed direction. We conclude that high temporal precision in motor output relies on multiple signals whose contributions to timing vary according to task requirements.

Encoding and decoding of learned smooth-pursuit eye movements in the floccular complex of the monkey cerebellum.

We recorded the simple-spike (SS) firing of Purkinje cells (PCs) in the floccular complex both during normal pursuit caused by step-ramp target motions and after learning induced by a consistently timed change in the direction of target motion. The encoding of eye movement by the SS firing rate of individual PCs was described by a linear regression model, in which the firing rate is a sum of weighted components related to eye acceleration, velocity, and position. Although the model fit the data well for individual conditions, the regression coefficients for the learned component of firing often differed substantially from those for normal pursuit of step-ramp target motion. We suggest that the different encoding of learned versus normal pursuit responses in individual PCs reflects different amounts of learning in their inputs. The decoded output from the floccular complex, estimated by averaging responses across the population of PCs, also was fitted by the regression model. Regression coefficients were equal for the two conditions for on-direction pursuit, but differed for off-direction target motion. We conclude that the average output from the population of floccular PCs provides some, but not all, of the neural signals that drive the learned component of pursuit and that plasticity outside of the flocculus makes an important contribution.

Instructive signals for motor learning from visual cortical area MT.

Sensory error signals have long been proposed to act as instructive signals to guide motor learning. Here we have exploited the temporal specificity of learning in smooth pursuit eye movements and the well-defined anatomical structure of the neural circuit for pursuit to identify a part of sensory cortex that provides instructive signals for motor learning in monkeys. We show that electrical microstimulation in the motion-sensitive middle temporal area (MT) of extrastriate visual cortex instructs learning in smooth eye movements in a way that closely mimics the learning instructed by real visual motion. We conclude that MT provides instructive signals for motor learning in smooth pursuit eye movements under natural conditions, suggesting a similar role for sensory cortices in many kinds of learned behaviors.

Variation, signal, and noise in cerebellar sensory-motor processing for smooth-pursuit eye movements.

Neural responses are variable, yet motor performance can be quite precise. To ask how neural signal and noise are processed in the brain during sensory-motor behavior, we have evaluated the trial-by-trial variation of Purkinje cell (PC) activity in the floccular complex of the cerebellum, an intermediate stage in the neural circuit for smooth-pursuit eye movements. We find strong correlations between small trial-by-trial variations in the simple spike activity of individual PCs and the eye movements at the initiation of pursuit. The correlation is lower but still present during steady-state pursuit. Recordings from a few pairs of PCs verified the predictions of a model of the PC population, that there is a transition from highly covariant PC activity during movement initiation to more independent activity later on. Application to the data of a theoretical and computational analysis suggests that variation in pursuit initiation arises mostly from variation in visual motion signals that provide common inputs to the PC population. Variation in eye movement during steady-state pursuit can be attributed primarily to signal-dependent motor noise that arises downstream from PCs.

Using animal models to improve the design and application of transcranial electrical stimulation in humans.

PURPOSE OF REVIEW: Transcranial electrical stimulation (tES) is a non-invasive stimulation technique used for modulating brain function in humans. To help tES reach its full therapeutic potential, it is necessary to address a number of critical gaps in our knowledge. Here, we review studies that have taken advantage of animal models to provide invaluable insight about the basic science behind tES. RECENT FINDINGS: Animal studies are playing a key role in elucidating the mechanisms implicated in tES, defining safety limits, validating computational models, inspiring new stimulation protocols, enhancing brain function and exploring new therapeutic applications. SUMMARY: Animal models provide a wealth of information that can facilitate the successful utilization of tES for clinical interventions in human subjects. To this end, tES experiments in animals should be carefully designed to maximize opportunities for applying discoveries to the treatment of human disease.