Invariant phase structure of olivo-cerebellar oscillations and its putative role in temporal pattern generation

Chemical suppression of harmaline-induced body tremor yields recovery of pairwise neuronal coherence in cerebellar nuclei neurons

Neuronal oscillations occur in health and disease; however, their characteristics can differ across conditions. During voluntary movement in freely moving rats, cerebellar nuclei (CN) neurons display intermittent but coherent oscillations in the theta frequency band (4-12 Hz). However, in the rat harmaline model of essential tremor, a disorder attributed to cerebellar malfunction, CN neurons display aberrant oscillations concomitantly with the emergence of body tremor. To identify the oscillation features that may underlie the emergence of body tremor, we analyzed neuronal activity recorded chronically from the rat CN under three conditions: in freely behaving animals, in harmaline-treated animals, and during chemical suppression of the harmaline-induced body tremor. Suppression of body tremor did not restore single neuron firing characteristics such as firing rate, the global and local coefficients of variation, the likelihood of a neuron to fire in bursts or their tendency to oscillate at a variety of dominant frequencies. Similarly, the fraction of simultaneously recorded neuronal pairs oscillating at a similar dominant frequency (<1 Hz deviation) and the mean frequency deviation within pairs remained similar to the harmaline condition. Moreover, the likelihood that pairs of CN neurons would co-oscillate was not only significantly lower than that measured in freely moving animals, but was significantly worse than chance. By contrast, the chemical suppression of body tremor fully restored pairwise neuronal coherence; that is, unlike in the harmaline condition, pairs of neurons that oscillated at the same time and frequency displayed high coherence, as in the controls. We suggest that oscillation coherence in CN neurons is essential for the execution of smooth movement and its loss likely underlies the emergence of body tremor.

Cerebellar nuclei neurons display aberrant oscillations during harmaline-induced tremor

Essential tremor, a common, debilitating motor disorder, is thought to be caused by cerebellar malfunction. It has been shown that rhythmic Purkinje cell firing is both necessary and sufficient to induce body tremor. During tremor, cerebellar nuclei (CN) cells also display oscillatory activity. This study examined whether rhythmic activity in the CN characterizes the occurrence of body tremor, or alternatively, whether aberrant bursting activity underlies body tremor. Cerebellar nuclei activity was chronically recorded and analyzed in freely moving and in harmaline treated rats. CN neurons displayed rhythmic activity in both conditions, but the number of oscillatory neurons and the relative oscillation time were significantly higher under harmaline. The dominant frequencies of the oscillations were broadly distributed under harmaline and the likelihood that two simultaneously recorded neurons would co-oscillate and their oscillation coherence were significantly lower. It is argued that these alterations rather than neuronal rhythmicity per se underlie harmaline-induced body tremor.

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.

Imaging Subthreshold Voltage Oscillation With Cellular Resolution in the Inferior Olive in vitro

Voltage imaging with cellular resolution in mammalian brain slices is still a challenging task. Here, we describe and validate a method for delivery of the voltage-sensitive dye ANNINE-6plus (A6+) into tissue for voltage imaging that results in higher signal-to-noise ratio (SNR) than conventional bath application methods. The not fully dissolved dye was injected into the inferior olive (IO) 0, 1, or 7 days prior to acute slice preparation using stereotactic surgery. We find that the voltage imaging improves after an extended incubation period in vivo in terms of labeled volume, homogeneous neuropil labeling with saliently labeled somata, and SNR. Preparing acute slices 7 days after the dye injection, the SNR is high enough to allow single-trial recording of IO subthreshold oscillations using wide-field (network-level) as well as high-magnification (single-cell level) voltage imaging with a CMOS camera. This method is easily adaptable to other brain regions where genetically-encoded voltage sensors are prohibitively difficult to use and where an ultrafast, pure electrochromic sensor, like A6+, is required. Due to the long-lasting staining demonstrated here, the method can be combined, for example, with deep-brain imaging using implantable GRIN lenses.

Robust dynamical invariants in sequential neural activity

By studying different sources of temporal variability in central pattern generator (CPG) circuits, we unveil fundamental aspects of the instantaneous balance between flexibility and robustness in sequential dynamics -a property that characterizes many systems that display neural rhythms. Our analysis of the triphasic rhythm of the pyloric CPG (Carcinus maenas) shows strong robustness of transient dynamics in keeping not only the activation sequences but also specific cycle-by-cycle temporal relationships in the form of strong linear correlations between pivotal time intervals, i.e. dynamical invariants. The level of variability and coordination was characterized using intrinsic time references and intervals in long recordings of both regular and irregular rhythms. Out of the many possible combinations of time intervals studied, only two cycle-by-cycle dynamical invariants were identified, existing even outside steady states. While executing a neural sequence, dynamical invariants reflect constraints to optimize functionality by shaping the actual intervals in which activity emerges to build the sequence. Our results indicate that such boundaries to the adaptability arise from the interaction between the rich dynamics of neurons and connections. We suggest that invariant temporal sequence relationships could be present in other networks, including those shaping sequences of functional brain rhythms, and underlie rhythm programming and functionality.

Variability and directionality of inferior olive neuron dendrites revealed by detailed 3D characterization of an extensive morphological library

The inferior olive (IO) is an evolutionarily conserved brain stem structure and its output activity plays a major role in the cerebellar computation necessary for controlling the temporal accuracy of motor behavior. The precise timing and synchronization of IO network activity has been attributed to the dendro-dendritic gap junctions mediating electrical coupling within the IO nucleus. Thus, the dendritic morphology and spatial arrangement of IO neurons governs how synchronized activity emerges in this nucleus. To date, IO neuron structural properties have been characterized in few studies and with small numbers of neurons; these investigations have described IO neurons as belonging to two morphologically distinct types, “curly” and “straight”. In this work we collect a large number of individual IO neuron morphologies visualized using different labeling techniques and present a thorough examination of their morphological properties and spatial arrangement within the olivary neuropil. Our results show that the extensive heterogeneity in IO neuron dendritic morphologies occupies a continuous range between the classically described “curly” and “straight” types, and that this continuum is well represented by a relatively simple measure of “straightness”. Furthermore, we find that IO neuron dendritic trees are often directionally oriented. Combined with an examination of cell body density distributions and dendritic orientation of adjacent IO neurons, our results suggest that the IO network may be organized into groups of densely coupled neurons interspersed with areas of weaker coupling.

Conditioned climbing fiber responses in cerebellar cortex and nuclei

The eyeblink conditioning paradigm captures an elementary form of associative learning in a neural circuitry that is understood to an extraordinary degree. Cerebellar cortical Purkinje cell simple spike suppression is widely regarded as the main process underlying conditioned responses (CRs), leading to disinhibition of neurons in the cerebellar nuclei that innervate eyelid muscles downstream. However, recent work highlights the addition of a conditioned Purkinje cell complex spike response, which at the level of the interposed nucleus seems to translate to a transient spike suppression that can be followed by a rapid spike facilitation. Here, we review the characteristics of these responses at the cerebellar cortical and nuclear level, and discuss possible origins and functions.

The Errors of Our Ways: Understanding Error Representations in Cerebellar-Dependent Motor Learning

The cerebellum is essential for error-driven motor learning and is strongly implicated in detecting and correcting for motor errors. Therefore, elucidating how motor errors are represented in the cerebellum is essential in understanding cerebellar function, in general, and its role in motor learning, in particular. This review examines how motor errors are encoded in the cerebellar cortex in the context of a forward internal model that generates predictions about the upcoming movement and drives learning and adaptation. In this framework, sensory prediction errors, defined as the discrepancy between the predicted consequences of motor commands and the sensory feedback, are crucial for both on-line movement control and motor learning. While many studies support the dominant view that motor errors are encoded in the complex spike discharge of Purkinje cells, others have failed to relate complex spike activity with errors. Given these limitations, we review recent findings in the monkey showing that complex spike modulation is not necessarily required for motor learning or for simple spike adaptation. Also, new results demonstrate that the simple spike discharge provides continuous error signals that both lead and lag the actual movements in time, suggesting errors are encoded as both an internal prediction of motor commands and the actual sensory feedback. These dual error representations have opposing effects on simple spike discharge, consistent with the signals needed to generate sensory prediction errors used to update a forward internal model.

An optimized surgical approach for obtaining stable extracellular single-unit recordings from the cerebellum of head-fixed behaving mice

BACKGROUND

Electrophysiological recording approaches are essential for understanding brain function. Among these approaches are various methods of performing single-unit recordings. However, a major hurdle to overcome when recording single units in vivo is stability. Poor stability results in a low signal-to-noise ratio, which makes it challenging to isolate neuronal signals. Proper isolation is needed for differentiating a signal from neighboring cells or the noise inherent to electrophysiology. Insufficient isolation makes it impossible to analyze full action potential waveforms. A common source of instability is an inadequate surgery. Problems during surgery cause blood loss, tissue damage and poor healing of the surrounding tissue, limited access to the target brain region, and, importantly, unreliable fixation points for holding the mouse's head.

NEW METHOD

We describe an optimized surgical procedure that ensures limited tissue damage and delineate a method for implanting head plates to hold the animal firmly in place.

RESULTS

Using the cerebellum as a model, we implement an extracellular recording technique to acquire single units from Purkinje cells and cerebellar nuclear neurons in behaving mice. We validate the stability of our method by holding single units after injecting the powerful tremorgenic drug harmaline. We performed multiple structural analyses after recording.

COMPARISON WITH EXISTING METHODS

Our approach is ideal for studying neuronal function in active mice and valuable for recording single-neuron activity when considerable motion is unavoidable.

CONCLUSIONS

The surgical principles we present for accessing the cerebellum can be easily adapted to examine the function of neurons in other brain regions.

How the credit assignment problems in motor control could be solved after the cerebellum predicts increases in error

We present a cerebellar architecture with two main characteristics. The first one is that complex spikes respond to increases in sensory errors. The second one is that cerebellar modules associate particular contexts where errors have increased in the past with corrective commands that stop the increase in error. We analyze our architecture formally and computationally for the case of reaching in a 3D environment. In the case of motor control, we show that there are synergies of this architecture with the Equilibrium-Point hypothesis, leading to novel ways to solve the motor error and distal learning problems. In particular, the presence of desired equilibrium lengths for muscles provides a way to know when the error is increasing, and which corrections to apply. In the context of Threshold Control Theory and Perceptual Control Theory we show how to extend our model so it implements anticipative corrections in cascade control systems that span from muscle contractions to cognitive operations.

Neuronal oscillations in Golgi cells and Purkinje cells are accompanied by decreases in Shannon information entropy

Neuronal oscillations have been shown to contribute to the function of the cerebral cortex by coordinating the neuronal activities of distant cortical regions via a temporal synchronization of neuronal discharge patterns. This can occur regardless whether these regions are linked by cortico-cortical pathways or not. Less is known concerning the role of neuronal oscillations in the cerebellum. Golgi cells and Purkinje cells are both principal cell types in the cerebellum. Purkinje cells are the sole output cells of the cerebellar cortex while Golgi cells contribute to information processing at the input stage of the cerebellar cortex. Both cell types have large cell bodies, as well as dendritic structures, that can generate large currents. The discharge patterns of both these cell types also exhibit oscillations. In view of the massive afferent information conveyed by the mossy fiber-granule cell system to different and distant areas of the cerebellar cortex, it is relevant to inquire the role of cerebellar neuronal oscillations in information processing. In this study, we compared the discharge patterns of Golgi cells and Purkinje cells in conscious rats and in rats anesthetized with urethane. We assessed neuronal oscillations by analyzing the regularity in the timing of individual spikes within a spike train by using autocorrelograms and fast-Fourier transform. We measured the differences in neuronal oscillations and the amount of information content in a spike train (defined by Shannon entropy processed per unit time) in rats under anesthesia and in conscious, awake rats. Our findings indicated that anesthesia caused more prominent neuronal oscillations in both Golgi cells and Purkinje cells accompanied by decreases in Shannon information entropy in their spike trains.

Realistic modeling of neurons and networks: towards brain simulation

Realistic modeling is a new advanced methodology for investigating brain functions. Realistic modeling is based on a detailed biophysical description of neurons and synapses, which can be integrated into microcircuits. The latter can, in turn, be further integrated to form large-scale brain networks and eventually to reconstruct complex brain systems. Here we provide a review of the realistic simulation strategy and use the cerebellar network as an example. This network has been carefully investigated at molecular and cellular level and has been the object of intense theoretical investigation. The cerebellum is thought to lie at the core of the forward controller operations of the brain and to implement timing and sensory prediction functions. The cerebellum is well described and provides a challenging field in which one of the most advanced realistic microcircuit models has been generated. We illustrate how these models can be elaborated and embedded into robotic control systems to gain insight into how the cellular properties of cerebellar neurons emerge in integrated behaviors. Realistic network modeling opens up new perspectives for the investigation of brain pathologies and for the neurorobotic field.

Cerebellar inhibitory input to the inferior olive decreases electrical coupling and blocks subthreshold oscillations

GABAergic projection neurons in the cerebellar nuclei (CN) innervate the inferior olive (IO) that in turn is the source of climbing fibers targeting Purkinje neurons in the cerebellar cortex. Anatomical evidence suggests that CN synapses modulate electrical coupling between IO neurons. In vivo studies indicate that they are also involved in controlling synchrony and rhythmicity of IO neurons. Here, we demonstrate using virally targeted channelrhodopsin in the cerebellar nucleo-olivary neurons that synaptic input can indeed modulate both the strength and symmetry of electrical coupling between IO neurons and alter network activity. Similar synaptic modifications of electrical coupling are likely to occur in other brain regions, where rapid modification of the spatiotemporal features of the coupled networks is needed to adequately respond to behavioral demands.

Electrophysiological characterization of entopeduncular nucleus neurons in anesthetized and freely moving rats

The EntoPeduncular nucleus (EP), which is homologous to the internal segment of the Globus Pallidus (GPi) in primates, is one of the two basal ganglia (BG) output nuclei. Despite their importance in cortico-BG information processing, EP neurons have rarely been investigated in rats and there is no available electrophysiological characterization of EP neurons in vivo. We recorded and analyzed the activity of EP neurons in freely moving as well as anesthetized rats, and compared their activity patterns. Examination of neuronal firing statistics during wakefulness suggested that similar to neurons recorded in the primate GPi, EP neurons are a single population characterized by Poisson-like firing. Under isoflurane anesthesia the firing rate of EP neurons decreased substantially and their coefficient of variation and relative duration of quiescence periods increased. Investigation of the relationship between firing rate and depth of anesthesia revealed two distinct neuronal groups: one that decreased its firing rate with the increase in anesthesia level, and a second group where the firing rate was independent of anesthesia level. Post-hoc examination of the firing properties of the two groups showed that they were statistically distinct. These results may thus help reconcile in vitro studies in rats and primates which have reported two distinct neuronal populations, and in vivo studies in behaving primates indicating one homogeneous population. Our data support the existence of two distinct neuronal populations in the rat EP that can be distinguished by their characteristic firing response to anesthesia.

Linking oscillations in cerebellar circuits

In many neuroscience fields, the study of local and global rhythmicity has been receiving increasing attention. These network influences could directly impact on how neuronal groups interact together, organizing for different contexts. The cerebellar cortex harbors a variety of such local circuit rhythms, from the rhythms in the cerebellar cortex per se, or those dictated from important afferents. We present here certain cerebellar oscillatory phenomena that have been recorded in rodents and primates. Those take place in a range of frequencies: from the more known oscillations in the 4-25 Hz band, such as the olivocerebellar oscillatory activity and the granule cell layer oscillations, to the more recently reported slow (<1 Hz oscillations), and the fast (>150 Hz) activity in the Purkinje cell layer. Many of these oscillations appear spontaneously in the circuits, and are modulated by behavioral imperatives. We review here how those oscillations are recorded, some of their modulatory mechanisms, and also identify some of the cerebellar nodes where they could interact. A particular emphasis has been placed on how these oscillations could be modulated by movement and certain neuropathological manifestations. Many of those oscillations could have a definite impact on the way information is processed in the cerebellum and how it interacts with other structures in a variety of contexts.

Realistic modeling of neurons and networks: towards brain simulation

Realistic modeling is a new advanced methodology for investigating brain functions. Realistic modeling is based on a detailed biophysical description of neurons and synapses, which can be integrated into microcircuits. The latter can, in turn, be further integrated to form large-scale brain networks and eventually to reconstruct complex brain systems. Here we provide a review of the realistic simulation strategy and use the cerebellar network as an example. This network has been carefully investigated at molecular and cellular level and has been the object of intense theoretical investigation. The cerebellum is thought to lie at the core of the forward controller operations of the brain and to implement timing and sensory prediction functions. The cerebellum is well described and provides a challenging field in which one of the most advanced realistic microcircuit models has been generated. We illustrate how these models can be elaborated and embedded into robotic control systems to gain insight into how the cellular properties of cerebellar neurons emerge in integrated behaviors. Realistic network modeling opens up new perspectives for the investigation of brain pathologies and for the neurorobotic field.

Oscillatory activity, phase differences, and phase resetting in the inferior olivary nucleus

The generation of temporal patterns is one of the most fascinating functions of the brain. Unlike the response to external stimuli temporal patterns are generated within the system and recalled for a specific use. To generate temporal patterns one needs a timing machine, a “master clock” that determines the temporal framework within which temporal patterns can be generated and implemented. Here we present the concept that in this putative “master clock” phase and frequency interact to generate temporal patterns. We define the requirements for a neuronal “master clock” to be both reliable and versatile. We introduce this concept within the inferior olive nucleus which at least by some scientists is regarded as the source of timing for cerebellar function. We review the basic properties of the subthreshold oscillation recorded from olivary neurons, analyze the phase relationships between neurons and demonstrate that the phase and onset of oscillation is tightly controlled by synaptic input. These properties endowed the olivary nucleus with the ability to act as a “master clock.”

Climbing fiber burst size and olivary sub-threshold oscillations in a network setting

The inferior olivary nucleus provides one of the two main inputs to the cerebellum: the so-called climbing fibers. Activation of climbing fibers is generally believed to be related to timing of motor commands and/or motor learning. Climbing fiber spikes lead to large all-or-none action potentials in cerebellar Purkinje cells, overriding any other ongoing activity and silencing these cells for a brief period of time afterwards. Empirical evidence shows that the climbing fiber can transmit a short burst of spikes as a result of an olivary cell somatic spike, potentially increasing the information being transferred to the cerebellum per climbing fiber activation. Previously reported results from in vitro studies suggested that the information encoded in the climbing fiber burst is related to the occurrence of the spike relative to the ongoing sub-threshold membrane potential oscillation of the olivary cell, i.e. that the phase of the oscillation is reflected in the size of the climbing fiber burst. We used a detailed three-compartmental model of an inferior olivary cell to further investigate the possible factors determining the size of the climbing fiber burst. Our findings suggest that the phase-dependency of the burst size is present but limited and that charge flow between soma and dendrite is a major determinant of the climbing fiber burst. From our findings it follows that phenomena such as cell ensemble synchrony can have a big effect on the climbing fiber burst size through dendrodendritic gap-junctional coupling between olivary cells.

The inferior olive is a nucleus in the brain stem with neurons that exhibit continuous sub-threshold activity and are electrically coupled by gap junctions. It is implicated in execution and learning of motor skills and it is often assumed that it provides a teacher signal to the cerebellum. Models based on this theory generally require a continuously updated quantitative value to be sent to the cerebellum, yet the inferior olive fires spikes at a low rate of approximately 1 Hz, making reconciliation of model and biological system problematic. However, it has also been shown that olivary cells can generate an axonal burst of spikes for every somatically recorded action potential, theoretically rendering them capable of transmitting more information per event. Using a detailed neuronal model of an inferior olive cell, we examined what factors may underlie the axonal burst size. We found that leak currents between dendrite and soma and electrically coupled dendrites are major determinants. From our findings and current literature it follows that the inferior olive may be capable of adapting the speed at which motor tasks in the cerebellum are learned, depending on the synchrony of sub-threshold activity in clusters of electrically coupled cells.

Inferior olive mirrors joint dynamics to implement an inverse controller

To produce smooth and coordinated motion, our nervous systems need to generate precisely timed muscle activation patterns that, due to axonal conduction delay, must be generated in a predictive and feedforward manner. Kawato proposed that the cerebellum accomplishes this by acting as an inverse controller that modulates descending motor commands to predictively drive the spinal cord such that the musculoskeletal dynamics are canceled out. This and other cerebellar theories do not, however, account for the rich biophysical properties expressed by the olivocerebellar complex's various cell types, making these theories difficult to verify experimentally. Here we propose that a multizonal microcomplex's (MZMC) inferior olivary neurons use their subthreshold oscillations to mirror a musculoskeletal joint's underdamped dynamics, thereby achieving inverse control. We used control theory to map a joint's inverse model onto an MZMC's biophysics, and we used biophysical modeling to confirm that inferior olivary neurons can express the dynamics required to mirror biomechanical joints. We then combined both techniques to predict how experimentally injecting current into the inferior olive would affect overall motor output performance. We found that this experimental manipulation unmasked a joint's natural dynamics, as observed by motor output ringing at the joint's natural frequency, with amplitude proportional to the amount of current. These results support the proposal that the cerebellum-in particular an MZMC-is an inverse controller; the results also provide a biophysical implementation for this controller and allow one to make an experimentally testable prediction.

Globus Pallidus external segment neuron classification in freely moving rats: a comparison to primates

Globus Pallidus external segment (GPe) neurons are well-characterized in behaving primates. Based on their firing properties, these neurons are commonly divided into two distinct groups: high frequency pausers (HFP) and low frequency bursters (LFB). However, no such characterization has been made for behaving rats. The current study characterizes and categorizes extracellularly recorded GPe neurons in freely moving rats, and compares these results to those obtained by extracellular recordings in behaving primates using the same analysis methods. Analysis of our data recorded in rats revealed two distinct neuronal populations exhibiting firing-pattern characteristics that are similar to those obtained in primates. These characteristic firing patterns are conserved between species although the firing rate is significantly lower in rats than in primates. Significant differences in waveform duration and shape were insufficient to create a reliable waveform-based classification in either species. The firing pattern analogy may emphasize conserved processing properties over firing rate per-se. Given the similarity in GPe neuronal activity between human and non-human primates in different pathologies, our results encourage information transfer using complementary studies across species in the GPe to acquire a better understanding of the function of this nucleus in health and disease.

The generation of phase differences and frequency changes in a network model of inferior olive subthreshold oscillations

It is commonly accepted that the Inferior Olive (IO) provides a timing signal to the cerebellum. Stable subthreshold oscillations in the IO can facilitate accurate timing by phase-locking spikes to the peaks of the oscillation. Several theoretical models accounting for the synchronized subthreshold oscillations have been proposed, however, two experimental observations remain an enigma. The first is the observation of frequent alterations in the frequency of the oscillations. The second is the observation of constant phase differences between simultaneously recorded neurons. In order to account for these two observations we constructed a canonical network model based on anatomical and physiological data from the IO. The constructed network is characterized by clustering of neurons with similar conductance densities, and by electrical coupling between neurons. Neurons inside a cluster are densely connected with weak strengths, while neurons belonging to different clusters are sparsely connected with stronger connections. We found that this type of network can robustly display stable subthreshold oscillations. The overall frequency of the network changes with the strength of the inter-cluster connections, and phase differences occur between neurons of different clusters. Moreover, the phase differences provide a mechanistic explanation for the experimentally observed propagating waves of activity in the IO. We conclude that the architecture of the network of electrically coupled neurons in combination with modulation of the inter-cluster coupling strengths can account for the experimentally observed frequency changes and the phase differences.

There is a profound interest in the dynamics of neuronal networks and the simulation of network models is a prevalent approach to study these dynamics. Generally, network models contain neurons that are connected mostly through chemical synapses to form either a completely regular topology (such as nearest neighbor connections), a completely random topology, small-world networks or scale-free networks. We investigate the dynamics of an atypical network, inspired by the Inferior Olive (IO) network, a brain structure located at the end of the brainstem that is responsible for timely execution of motor commands. This network is atypical in the sense that it has neurons in a clustered topology, which are connected solely by electrical synapses. The dynamics in the IO are enigmatic as the membrane voltage of some neurons can oscillate at the same frequency while maintaining phase difference with other neurons. It has also been demonstrated that propagating waves of activity occur spontaneously in this network. Using computer simulations we unraveled the mechanism underlying these previously enigmatic experimental observations. In so doing, we stress the importance of investigating more realistic network topologies to explore complex brain dynamics.

Neural circuits of the cerebellum: hypothesis for function

The rapid growth of cerebellar research is going to clarify several aspects of cellular and circuit physiology. However, the concepts about cerebellar mechanisms of function are still largely related to clinical observations and to models elaborated before the last discoveries appeared. In this paper, the major issues are revisited, suggesting that previous concepts can now be refined and modified. The cerebellum is fundamentally involved in timing and in controlling the ordered and precise execution of motor sequences. The fast reaction of the cerebellum to the inputs is sustained by specific cellular mechanisms ensuring precision on the millisecond scale. These include burst-burst reconversion in the granular layer and instantaneous frequency modulation on the 100-Hz band in Purkinje and deep cerebellar nuclei cells. Precisely timed signals can be used for perceptron operations in Purkinje cells and to establish appropriate correlations with climbing fiber signals inducing learning at parallel fiber synapses. In the granular layer, plasticity turns out to be instrumental to timing, providing a conceptual solution to the discrepancy between cerebellar learning and timing. The granular layer sub-circuit can be tuned by long-term synaptic plasticity and synaptic inhibition to delay the incoming signals over a 100-ms range. For longer sequences, large circuit sections can be entrained into coherent activity in 100-ms cycles. These dynamic aspects, which have not been accounted for by original theories, could in fact represent the essence of cerebellar functioning. It is suggested that the cerebellum can, in this way, operate the realignment of temporally incongruent signals, allowing their binding and pattern recognition in Purkinje cells. The demonstration of these principles, their behavioral relevance and their relationship with internal model theories represent a challenge for future cerebellar research.

Distinct roles for I(T) and I(H) in controlling the frequency and timing of rebound spike responses

The ability for neurons to generate rebound bursts following inhibitory synaptic input relies on ion channels that respond in a unique fashion to hyperpolarization. Inward currents provided by T-type calcium channels (I(T)) and hyperpolarization-activated HCN channels (I(H)) increase in availability upon hyperpolarization, allowing for a rebound depolarization after a period of inhibition. Although rebound responses have long been recognized in deep cerebellar nuclear (DCN) neurons, the actual extent to which I(T) and I(H) contribute to rebound spike output following physiological levels of membrane hyperpolarization has not been clearly established. The current study used recordings and simulations of large diameter cells of the in vitro rat DCN slice preparation to define the roles for I(T) and I(H) in a rebound response. We find that physiological levels of hyperpolarization make only small proportions of the total I(T) and I(H) available, but that these are sufficient to make substantial contributions to a rebound response. At least 50% of the early phase of the rebound spike frequency increase is generated by an I(T)-mediated depolarization. An additional frequency increase is provided by I(H) in reducing the time constant and thus the extent of I(T) inactivation as the membrane returns from a hyperpolarized state to the resting level. An I(H)-mediated depolarization creates an inverse voltage-first spike latency relationship and produces a 35% increase in the precision of the first spike latency of a rebound. I(T) and I(H) can thus be activated by physiologically relevant stimuli and have distinct roles in the frequency, timing and precision of rebound responses.

Signals and circuits in the purkinje neuron

Purkinje neurons (PN) in the cerebellum have over 100,000 inputs organized in an orthogonal geometry, and a single output channel. As the sole output of the cerebellar cortex layer, their complex firing pattern has been associated with motor control and learning. As such they have been extensively modeled and measured using tools ranging from electrophysiology and neuroanatomy, to dynamic systems and artificial intelligence methods. However, there is an alternative approach to analyze and describe the neuronal output of these cells using concepts from electrical engineering, particularly signal processing and digital/analog circuits. By viewing the PN as an unknown circuit to be reverse-engineered, we can use the tools that provide the foundations of today’s integrated circuits and communication systems to analyze the Purkinje system at the circuit level. We use Fourier transforms to analyze and isolate the inherent frequency modes in the PN and define three unique frequency ranges associated with the cells’ output. Comparing the PN to a signal generator that can be externally modulated adds an entire level of complexity to the functional role of these neurons both in terms of data analysis and information processing, relying on Fourier analysis methods in place of statistical ones. We also re-describe some of the recent literature in the field, using the nomenclature of signal processing. Furthermore, by comparing the experimental data of the past decade with basic electronic circuitry, we can resolve the outstanding controversy in the field, by recognizing that the PN can act as a multivibrator circuit.

The mysterious microcircuitry of the cerebellar nuclei

The microcircuitry of cerebellar cortex and, in particular, the physiology of its main element, the Purkinje neuron, has been extensively investigated and described. However, activity in Purkinje neurons, either as single cells or populations, does not directly mediate the cerebellar effects on the motor effector systems. Rather, the result of the entire cerebellar cortical computation is passed to the relatively small cerebellar nuclei that act as the final, integrative processing unit in the cerebellar circuitry. The nuclei ultimately control the temporal and spatial features of the cerebellar output. Given this key role, it is striking that the internal organization and the connectivity with afferent and efferent pathways in the cerebellar nuclei are rather poorly known. In the present review, we discuss some of the many critical shortcomings in the understanding of cerebellar nuclei microcircuitry: the extent of convergence and divergence of the cerebellar cortical pathway to the various cerebellar nuclei neurons and subareas, the possible (lack of) conservation of the finely-divided topographical organization in the cerebellar cortex at the level of the nuclei, as well as the absence of knowledge of the synaptic circuitry within the cerebellar nuclei. All these issues are important for predicting the pattern-extraction and encoding capabilities of the cerebellar nuclei and, until resolved, theories and models of cerebellar motor control and learning may err considerably.

Putative cholinergic interneurons in the ventral and dorsal regions of the striatum have distinct roles in a two choice alternative association task

The striatum consists of GABAergic projection neurons and various types of interneurons. Despite their relative scarcity, these interneurons play a key role in information processing in the striatum. One such class of interneurons is the cholinergic tonically active neurons (TANs). In the dorsal striatum, TANs are traditionally considered to be responsive to events of motivational significance. However, in recent years, studies have suggested that TANs are not exclusively related to reward and reward-predicting stimuli, but may contribute to other processes, including responses to aversive stimuli, detecting the spatial location of stimuli and generating movement. Currently there is little data concerning TAN activity in the ventral striatum (VS) of behaving animals. Here, we simultaneously recorded neurons in the ventral and the dorsolateral (DLS) regions of the striatum while animals performed a two choice alternative association task. Our data show that a large percentage of the putative TANs in both regions responded around movement initiation and execution. The majority of these neurons exhibited directional selectivity which was stronger in DLS relative to VS. In addition, the preferred directions in VS were mostly contralateral to the recording site whereas the observed preferred directions in DLS were equally distributed contralaterally and ipsilaterally to the recording site. The most interesting difference between DLS and VS was that DLS TANs maintained activity alterations throughout the movement whereas TANs in VS exhibited short-lasting phasic activity alterations that were maintained throughout the movement by different neurons. Our findings suggest that coding of movement by TANs in both regions overlaps to some degree, yet the differences in response patterns support the notion that the TANs in DLS participate in the motor loop whereas TANs in VS convey event-related information such as movement initiation, movement direction, and end of movement.

Spatiotemporal firing patterns in the cerebellum

Neurons are generally considered to communicate information by increasing or decreasing their firing rate. However, in principle, they could in addition convey messages by using specific spatiotemporal patterns of spiking activities and silent intervals. Here, we review expanding lines of evidence that such spatiotemporal coding occurs in the cerebellum, and that the olivocerebellar system is optimally designed to generate and employ precise patterns of complex spikes and simple spikes during the acquisition and consolidation of motor skills. These spatiotemporal patterns may complement rate coding, thus enabling precise control of motor and cognitive processing at a high spatiotemporal resolution by fine-tuning sensorimotor integration and coordination.

Cerebellarlike corrective model inference engine for manipulation tasks

This paper presents how a simple cerebellumlike architecture can infer corrective models in the framework of a control task when manipulating objects that significantly affect the dynamics model of the system. The main motivation of this paper is to evaluate a simplified bio-mimetic approach in the framework of a manipulation task. More concretely, the paper focuses on how the model inference process takes place within a feedforward control loop based on the cerebellar structure and on how these internal models are built up by means of biologically plausible synaptic adaptation mechanisms. This kind of investigation may provide clues on how biology achieves accurate control of non-stiff-joint robot with low-power actuators which involve controlling systems with high inertial components. This paper studies how a basic temporal-correlation kernel including long-term depression (LTD) and a constant long-term potentiation (LTP) at parallel fiber-Purkinje cell synapses can effectively infer corrective models. We evaluate how this spike-timing-dependent plasticity correlates sensorimotor activity arriving through the parallel fibers with teaching signals (dependent on error estimates) arriving through the climbing fibers from the inferior olive. This paper addresses the study of how these LTD and LTP components need to be well balanced with each other to achieve accurate learning. This is of interest to evaluate the relevant role of homeostatic mechanisms in biological systems where adaptation occurs in a distributed manner. Furthermore, we illustrate how the temporal-correlation kernel can also work in the presence of transmission delays in sensorimotor pathways. We use a cerebellumlike spiking neural network which stores the corrective models as well-structured weight patterns distributed among the parallel fibers to Purkinje cell connections.

The cerebellar network: from structure to function and dynamics

Since the discoveries of Camillo Golgi and Ramón y Cajal, the precise cellular organization of the cerebellum has inspired major computational theories, which have then influenced the scientific thought not only on the cerebellar function but also on the brain as a whole. However, six major issues revealing a discrepancy between morphologically inspired hypothesis and function have emerged. (1) The cerebellar granular layer does not simply operate a simple combinatorial decorrelation of the inputs but performs more complex non-linear spatio-temporal transformations and is endowed with synaptic plasticity. (2) Transmission along the ascending axon and parallel fibers does not lead to beam formation but rather to vertical columns of activation. (3) The olivo-cerebellar loop could perform complex timing operations rather than error detection and teaching. (4) Purkinje cell firing dynamics are much more complex than for a linear integrator and include pacemaking, burst-pause discharges, and bistable states in response to mossy and climbing fiber synaptic inputs. (5) Long-term synaptic plasticity is far more complex than traditional parallel fiber LTD and involves also other cerebellar synapses. (6) Oscillation and resonance could set up coherent cycles of activity designing a functional geometry that goes far beyond pre-wired anatomical circuits. These observations clearly show that structure is not sufficient to explain function and that a precise knowledge on dynamics is critical to understand how the cerebellar circuit operates.

Implications of functional anatomy on information processing in the deep cerebellar nuclei

The cerebellum has been implicated as a major player in producing temporal acuity. Theories of cerebellar timing typically emphasize the role of the cerebellar cortex while overlooking the role of the deep cerebellar nuclei (DCN) that provide the sole output of the cerebellum. Here we review anatomical and electrophysiological studies to shed light on the DCN's ability to support temporal pattern generation in the cerebellum. Specifically, we examine data on the structure of the DCN, the biophysical properties of DCN neurons and properties of the afferent systems to evaluate their contribution to DCN firing patterns. In addition, we manipulate one of the afferent structures, the inferior olive (IO), using systemic harmaline injection to test for a network effect on activity of single DCN neurons in freely moving animals. Harmaline induces a rhythmic firing pattern of short bursts on a quiescent background at about 8 Hz. Other neurons become quiescent for long periods (seconds to minutes). The observed patterns indicate that the major effect harmaline exerts on the DCN is carried indirectly by the inhibitory Purkinje cells (PCs) activated by the IO, rather than by direct olivary excitation. Moreover, we suggest that the DCN response profile is determined primarily by the number of concurrently active PCs, their firing rate and the level of synchrony occurring in their transitions between continuous firing and quiescence. We argue that DCN neurons faithfully transfer temporal patterns resulting from strong correlations in PCs state transitions, while largely ignoring the timing of simple spikes from individual PCs. Future research should aim at quantifying the contribution of PC state transitions to DCN activity, and the interplay between the different afferent systems that drive DCN activity.