Oscillations in the cerebellar cortex: a prediction of their frequency bands

Cerebellar Cortex 4-12 Hz Oscillations and Unit Phase Relation in the Awake Rat

Oscillations in the granule cell layer (GCL) of the cerebellar cortex have been related to behavior and could facilitate communication with the cerebral cortex. These local field potential (LFP) oscillations, strong at 4–12 Hz in the rodent cerebellar cortex during awake immobility, should also be an indicator of an underlying influence on the patterns of the cerebellar cortex neuronal firing during rest. To address this hypothesis, cerebellar cortex LFPs and simultaneous single-neuron activity were collected during LFP oscillatory periods in the GCL of awake resting rats. During these oscillatory episodes, different types of units across the GCL and Purkinje cell layers showed variable phase-relation with the oscillatory cycles. Overall, 74% of the Golgi cell firing and 54% of the Purkinje cell simple spike (SS) firing were phase-locked with the oscillations, displaying a clear phase relationship. Despite this tendency, fewer Golgi cells (50%) and Purkinje cell’s SSs (25%) showed an oscillatory firing pattern. Oscillatory phase-locked spikes for the Golgi and Purkinje cells occurred towards the peak of the LFP cycle. GCL LFP oscillations had a strong capacity to predict the timing of Golgi cell spiking activity, indicating a strong influence of this oscillatory phenomenon over the GCL. Phase-locking was not as prominent for the Purkinje cell SS firing, indicating a weaker influence over the Purkinje cell layer, yet a similar phase relation. Overall, synaptic activity underlying GCL LFP oscillations likely exert an influence on neuronal population firing patterns in the cerebellar cortex in the awake resting state and could have a preparatory neural network shaping capacity serving as a neural baseline for upcoming cerebellar operations.

Gap Junction Modulation of Low-Frequency Oscillations in the Cerebellar Granule Cell Layer

Local field potential (LFP) oscillations in the granule cell layer (GCL) of the cerebellar cortex have been identified previously in the awake rat and monkey during immobility. These low-frequency oscillations are thought to be generated through local circuit interactions between Golgi cells and granule cells within the GCL. Golgi cells display rhythmic firing and pacemaking properties, and also are electrically coupled through gap junctions within the GCL. Here, we tested if gap junctions in the rat cerebellar cortex contribute to the generation of LFP oscillations in the GCL. We recorded LFP oscillations under urethane anesthesia, and examined the effects of local infusion of gap junction blockers on 5-15 Hz oscillations. Local infusion of the gap junction blockers carbenoxolone and mefloquine resulted in significant decreases in the power of oscillations over a 30-min period, but the power of oscillations was unchanged in control experiments following vehicle injections. In addition, infusion of gap junction blockers had no significant effect on multi-unit activity, suggesting that the attenuation of low-frequency oscillations was likely due to reductions in electrical coupling rather than a decreased excitability within the granule cell layer. Our results indicate that electrical coupling among the Golgi cell networks in the cerebellar cortex contributes to the local circuit mechanisms that promote the occurrence of GCL LFP slow oscillations in the anesthetized rat.

A realistic bi-hemispheric model of the cerebellum uncovers the purpose of the abundant granule cells during motor control

The cerebellar granule cells (GCs) have been proposed to perform lossless, adaptive spatio-temporal coding of incoming sensory/motor information required by downstream cerebellar circuits to support motor learning, motor coordination, and cognition. Here we use a physio-anatomically inspired bi-hemispheric cerebellar neuronal network (biCNN) to selectively enable/disable the output of GCs and evaluate the behavioral and neural consequences during three different control scenarios. The control scenarios are a simple direct current motor (1 degree of freedom: DOF), an unstable two-wheel balancing robot (2 DOFs), and a simulation model of a quadcopter (6 DOFs). Results showed that adequate control was maintained with a relatively small number of GCs (< 200) in all the control scenarios. However, the minimum number of GCs required to successfully govern each control plant increased with their complexity (i.e., DOFs). It was also shown that increasing the number of GCs resulted in higher robustness against changes in the initialization parameters of the biCNN model (i.e., synaptic connections and synaptic weights). Therefore, we suggest that the abundant GCs in the cerebellar cortex provide the computational power during the large repertoire of motor activities and motor plants the cerebellum is involved with, and bring robustness against changes in the cerebellar microcircuit (e.g., neuronal connections).

A bi-hemispheric neuronal network model of the cerebellum with spontaneous climbing fiber firing produces asymmetrical motor learning during robot control

To acquire and maintain precise movement controls over a lifespan, changes in the physical and physiological characteristics of muscles must be compensated for adaptively. The cerebellum plays a crucial role in such adaptation. Changes in muscle characteristics are not always symmetrical. For example, it is unlikely that muscles that bend and straighten a joint will change to the same degree. Thus, different (i.e., asymmetrical) adaptation is required for bending and straightening motions. To date, little is known about the role of the cerebellum in asymmetrical adaptation. Here, we investigate the cerebellar mechanisms required for asymmetrical adaptation using a bi-hemispheric cerebellar neuronal network model (biCNN). The bi-hemispheric structure is inspired by the observation that lesioning one hemisphere reduces motor performance asymmetrically. The biCNN model was constructed to run in real-time and used to control an unstable two-wheeled balancing robot. The load of the robot and its environment were modified to create asymmetrical perturbations. Plasticity at parallel fiber-Purkinje cell synapses in the biCNN model was driven by error signal in the climbing fiber (cf) input. This cf input was configured to increase and decrease its firing rate from its spontaneous firing rate (approximately 1 Hz) with sensory errors in the preferred and non-preferred direction of each hemisphere, as demonstrated in the monkey cerebellum. Our results showed that asymmetrical conditions were successfully handled by the biCNN model, in contrast to a single hemisphere model or a classical non-adaptive proportional and derivative controller. Further, the spontaneous activity of the cf, while relatively small, was critical for balancing the contribution of each cerebellar hemisphere to the overall motor command sent to the robot. Eliminating the spontaneous activity compromised the asymmetrical learning capabilities of the biCNN model. Thus, we conclude that a bi-hemispheric structure and adequate spontaneous activity of cf inputs are critical for cerebellar asymmetrical motor learning.

Subcellular structural plasticity caused by the absence of the fast Ca(2+) buffer calbindin D-28k in recurrent collaterals of cerebellar Purkinje neurons

Purkinje cells (PC) control spike timing of neighboring PC by their recurrent axon collaterals. These synapses underlie fast cerebellar oscillations and are characterized by a strong facilitation within a time window of <20 ms during paired-pulse protocols. PC express high levels of the fast Ca(2+) buffer protein calbindin D-28k (CB). As expected from the absence of a fast Ca(2+) buffer, presynaptic action potential-evoked [Ca(2+)]i transients were previously shown to be bigger in PC boutons of young (second postnatal week) CB-/- mice, yet IPSC mean amplitudes remained unaltered in connected CB-/- PC. Since PC spine morphology is altered in adult CB-/- mice (longer necks, larger spine head volume), we summoned that morphological compensation/adaptation mechanisms might also be induced in CB-/- PC axon collaterals including boutons. In these mice, biocytin-filled PC reconstructions revealed that the number of axonal varicosities per PC axon collateral was augmented, mostly confined to the granule cell layer. Additionally, the volume of individual boutons was increased, evidenced from z-stacks of confocal images. EM analysis of PC-PC synapses revealed an enhancement in active zone (AZ) length by approximately 23%, paralleled by a higher number of docked vesicles per AZ in CB-/- boutons. Moreover, synaptic cleft width was larger in CB-/- (23.8 ± 0.43 nm) compared to wild type (21.17 ± 0.39 nm) synapses. We propose that the morphological changes, i.e., the larger bouton volume, the enhanced AZ length and the higher number of docked vesicles, in combination with the increase in synaptic cleft width likely modifies the GABA release properties at this synapse in CB-/- mice. We view these changes as adaptation/homeostatic mechanisms to likely maintain characteristics of synaptic transmission in the absence of the fast Ca(2+) buffer CB. Our study provides further evidence on the functioning of the Ca(2+) homeostasome.

Structured connectivity in cerebellar inhibitory networks

Defining the rules governing synaptic connectivity is key to formulating theories of neural circuit function. Interneurons can be connected by both electrical and chemical synapses, but the organization and interaction of these two complementary microcircuits is unknown. By recording from multiple molecular layer interneurons in the cerebellar cortex, we reveal specific, nonrandom connectivity patterns in both GABAergic chemical and electrical interneuron networks. Both networks contain clustered motifs and show specific overlap between them. Chemical connections exhibit a preference for transitive patterns, such as feedforward triplet motifs. This structured connectivity is supported by a characteristic spatial organization: transitivity of chemical connectivity is directed vertically in the sagittal plane, and electrical synapses appear strictly confined to the sagittal plane. The specific, highly structured connectivity rules suggest that these motifs are essential for the function of the cerebellar network.

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.

An integrator circuit in cerebellar cortex

The brain builds dynamic models of the body and the outside world to predict the consequences of actions and stimuli. A well-known example is the oculomotor integrator, which anticipates the position-dependent elasticity forces acting on the eye ball by mathematically integrating over time oculomotor velocity commands. Many models of neural integration have been proposed, based on feedback excitation, lateral inhibition or intrinsic neuronal nonlinearities. We report here that a computational model of the cerebellar cortex, a structure thought to implement dynamic models, reveals a hitherto unrecognized integrator circuit. In this model, comprising Purkinje cells, molecular layer interneurons and parallel fibres, Purkinje cells were able to generate responses lasting more than 10 s, to which both neuronal and network mechanisms contributed. Activation of the somatic fast sodium current by subthreshold voltage fluctuations was able to maintain pulse-evoked graded persistent activity, whereas lateral inhibition among Purkinje cells via recurrent axon collaterals further prolonged the responses to step and sine wave stimulation. The responses of Purkinje cells decayed with a time-constant whose value depended on their baseline spike rate, with integration vanishing at low (< 1 per s) and high rates (> 30 per s). The model predicts that the apparently fast circuit of the cerebellar cortex may control the timing of slow processes without having to rely on sensory feedback. Thus, the cerebellar cortex may contain an adaptive temporal integrator, with the sensitivity of integration to the baseline spike rate offering a potential mechanism of plasticity of the response time-constant.

The cerebellar Golgi cell and spatiotemporal organization of granular layer activity

The cerebellar granular layer has been suggested to perform a complex spatiotemporal reconfiguration of incoming mossy fiber signals. Central to this role is the inhibitory action exerted by Golgi cells over granule cells: Golgi cells inhibit granule cells through both feedforward and feedback inhibitory loops and generate a broad lateral inhibition that extends beyond the afferent synaptic field. This characteristic connectivity has recently been investigated in great detail and been correlated with specific functional properties of these neurons. These include theta-frequency pacemaking, network entrainment into coherent oscillations and phase resetting. Important advances have also been made in terms of determining the membrane and synaptic properties of the neuron, and clarifying the mechanisms of activation by input bursts. Moreover, voltage sensitive dye imaging and multi-electrode array (MEA) recordings, combined with mathematical simulations based on realistic computational models, have improved our understanding of the impact of Golgi cell activity on granular layer circuit computations. These investigations have highlighted the critical role of Golgi cells in: generating dense clusters of granule cell activity organized in center-surround structures, implementing combinatorial operations on multiple mossy fiber inputs, regulating transmission gain, and cut-off frequency, controlling spike timing and burst transmission, and determining the sign, intensity and duration of long-term synaptic plasticity at the mossy fiber-granule cell relay. This review considers recent advances in the field, highlighting the functional implications of Golgi cells for granular layer network computation and indicating new challenges for cerebellar research.

Ethanol increases GABAergic transmission and excitability in cerebellar molecular layer interneurons from GAD67-GFP knock-in mice

AIMS

This study assessed the acute effect of ethanol on GABAergic transmission at molecular layer interneurons (MLIs; i.e. basket and stellate cells) in the cerebellar cortex. The actions of ethanol on spontaneous firing of these pacemaker neurons were also measured.

METHODS

Transgenic mice (glutamic acid-decarboxylase 67-green fluorescent protein knock-in mice) that express green fluorescence protein in GABAergic interneurons were used to aid in the identification of MLIs. Parasagittal cerebellar slices were prepared and whole-cell patch-clamp electrophysiological techniques were used to measure GABA(A) receptor-mediated spontaneous and miniature inhibitory postsynaptic currents (sIPSCs and mIPSCs). Loose-seal cell-attached recordings were used to measure spontaneous action potential firing.

RESULTS

Stellate cells received spontaneous GABAergic input in the form of a mixture of action potential-dependent events (sIPSCs) and quantal events (mIPSCs); ethanol increased sIPSC frequency to a greater extent than mIPSC frequency. Ethanol increased spontaneous action potential firing of MLIs, which could explain the increase in sIPSC frequency in stellate cells. Basket cells received GABAergic input in the form of quantal events only. Ethanol significantly increased the frequency of these events, which may be mediated by a different type of interneuron (perhaps, the Lugaro cell) or Purkinje cell collaterals.

CONCLUSIONS

Ethanol exposure differentially increases GABA release at stellate cell vs. basket cell-to-Purkinje cell synapses. This effect may contribute to the abnormalities in cerebellar function associated with alcohol intoxication.

Excitation of rat cerebellar Golgi cells by ethanol: further characterization of the mechanism

BACKGROUND

Studies with rodents suggest that acute ethanol exposure impairs information flow through the cerebellar cortex, in part, by increasing GABAergic input to granule cells. Experiments suggest that an increase in the excitability of specialized GABAergic interneurons that regulate granule cell activity (i.e., Golgi cells [GoCs]) contributes to this effect. In GoCs, ethanol increases spontaneous action potential firing frequency, decreases the afterhyperpolarization amplitude, and depolarizes the membrane potential. Studies suggest that these effects could be mediated by inhibition of the Na(+)/K(+) ATPase. The purpose of this study was to characterize the potential role of other GoC conductances in the mechanism of action of ethanol.

METHODS

Computer modeling techniques and patch-clamp electrophysiological recordings with acute slices from rat cerebella were used for these studies.

RESULTS

Computer modeling suggested that modulation of subthreshold Na(+) channels, hyperpolarization-activated currents, and several K(+) conductances could explain some but not all actions of ethanol on GoCs. Electrophysiological studies did not find evidence consistent with a contribution of these conductances. Quinidine, a nonselective blocker of several types of channels (including several K(+) channels) that also antagonizes the Na(+)/K(+) ATPase, reduced the effect of ethanol on GoC firing.

CONCLUSIONS

These findings further support that ethanol increases GoC excitability via modulation of the Na(+)/K(+) ATPase and suggest that a quinidine-sensitive K(+) channel may also play a role in the mechanism of action of ethanol.

Neural circuit and its functional roles in cerebellar cortex

OBJECTIVE

To investigate the spike activities of cerebellar cortical cells in a computational network model constructed based on the anatomical structure of cerebellar cortex.

METHODS AND RESULTS

The multicompartment model of neuron and NEURON software were used to study the external influences on cerebellar cortical cells. Various potential spike patterns in these cells were obtained. By analyzing the impacts of different incoming stimuli on the potential spike of Purkinje cell, temporal focusing caused by the granule cell-golgi cell feedback inhibitory loop to Purkinje cell and spatial focusing caused by the parallel fiber-basket/stellate cell local inhibitory loop to Purkinje cell were discussed. Finally, the motor learning process of rabbit eye blink conditioned reflex was demonstrated in this model. The simulation results showed that when the afferent from climbing fiber existed, rabbit adaptation to eye blinking gradually became stable under the Spike Timing-Dependent Plasticity (STDP) learning rule.

CONCLUSION

The constructed cerebellar cortex network is a reliable and feasible model. The model simulation results confirmed the output signal stability of cerebellar cortex after STDP learning and the network can execute the function of spatial and temporal focusing.

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.

Robustness effect of gap junctions between Golgi cells on cerebellar cortex oscillations

Background

Previous one-dimensional network modeling of the cerebellar granular layer has been successfully linked with a range of cerebellar cortex oscillations observed in vivo. However, the recent discovery of gap junctions between Golgi cells (GoCs), which may cause oscillations by themselves, has raised the question of how gap-junction coupling affects GoC and granular-layer oscillations. To investigate this question, we developed a novel two-dimensional computational model of the GoC-granule cell (GC) circuit with and without gap junctions between GoCs.

Results

Isolated GoCs coupled by gap junctions had a strong tendency to generate spontaneous oscillations without affecting their mean firing frequencies in response to distributed mossy fiber input. Conversely, when GoCs were synaptically connected in the granular layer, gap junctions increased the power of the oscillations, but the oscillations were primarily driven by the synaptic feedback loop between GoCs and GCs, and the gap junctions did not change oscillation frequency or the mean firing rate of either GoCs or GCs.

Conclusion

Our modeling results suggest that gap junctions between GoCs increase the robustness of cerebellar cortex oscillations that are primarily driven by the feedback loop between GoCs and GCs. The robustness effect of gap junctions on synaptically driven oscillations observed in our model may be a general mechanism, also present in other regions of the brain.

A unified description of cerebellar inter-spike interval distributions and variabilities using summation of Gaussians

Neuronal inter-spike intervals (ISIs) have previously been described as Poisson, Gamma, inverse Gaussian or other unimodal distributions. We analyzed ISIs of rhythmic and arrhythmic neuronal spike trains in cerebellum recorded from freely behaving rats, and found that their distributions can be described as the summation or integration of multiple Gaussian distributions. The ISIs of rhythmic cerebellar Purkinje cells have a main Gaussian peak at a basic firing interval and exponentially reduced peaks at multiples of this firing period. ISIs of arrhythmic Purkinje cells can be modeled as the integration of multiple Gaussian distributions centered at continuous intervals with exponentially reduced peak amplitudes. The sources of variability are directly related to the relative timing of action potentials between neighboring cells since we show that irregularities of discharge in one cell are associated with the previous history of its discharge in time relative to another cell. Through relative phase analyses, we demonstrate that the shape and the mathematical form of the ISI distributions in cerebellum are direct result of dynamic interactions in the nearby neuronal network, in addition to intrinsic firing properties. The analysis in this paper provides a unified description of cerebellar inter-spike interval distributions which deviate from the usual Poisson assumptions. Our results suggest the existence of an intrinsic rhythmicity in cells exhibiting arrhythmic spike trains in cerebellum, and may identify an important source of variability in neuronal firing patterns that is relevant to the mechanism of neural computation in cerebellum.

Quantitative organization of GABAergic synapses in the molecular layer of the mouse cerebellar cortex

In the cerebellar cortex, interneurons of the molecular layer (stellate and basket cells) provide GABAergic input to Purkinje cells, as well as to each other and possibly to other interneurons. GABAergic inhibition in the molecular layer has mainly been investigated at the interneuron to Purkinje cell synapse. In this study, we used complementary subtractive strategies to quantitatively assess the ratio of GABAergic synapses on Purkinje cell dendrites versus those on interneurons. We generated a mouse model in which the GABA_A receptor α1 subunit (GABA_ARα1) was selectively removed from Purkinje cells using the Cre/loxP system. Deletion of the α1 subunit resulted in a complete loss of GABA_AR aggregates from Purkinje cells, allowing us to determine the density of GABA_AR clusters in interneurons. In a complementary approach, we determined the density of GABA synapses impinging on Purkinje cells using α-dystroglycan as a specific marker of inhibitory postsynaptic sites. Combining these inverse approaches, we found that synapses received by interneurons represent approximately 40% of all GABAergic synapses in the molecular layer. Notably, this proportion was stable during postnatal development, indicating synchronized synaptogenesis. Based on the pure quantity of GABAergic synapses onto interneurons, we propose that mutual inhibition must play an important, yet largely neglected, computational role in the cerebellar cortex.

Alcohol excites cerebellar Golgi cells by inhibiting the Na+/K+ ATPase

Alcohol-induced alterations of cerebellar function cause motor coordination impairments that are responsible for millions of injuries and deaths worldwide. Cognitive deficits associated with alcoholism are also a consequence of cerebellar dysfunction. The mechanisms responsible for these effects of ethanol are poorly understood. Recent studies have identified neurons in the input layer of the cerebellar cortex as important ethanol targets. In this layer, granule cells (GrCs) receive the majority of sensory inputs to the cerebellum through the mossy fibers. Information flow at these neurons is gated by a specialized pacemaker interneuron known as the Golgi cell, which provides divergent GABAergic input to thousands of GrCs. In vivo electrophysiological experiments have previously shown that acute ethanol exposure abolishes GrC responsiveness to sensory inputs carried by mossy fibers. Slice electrophysiological studies suggest that ethanol causes this effect by potentiating GABAergic transmission at Golgi cell-to-GrC synapses through an increase in Golgi cell excitability. Using patch-clamp electrophysiological techniques in cerebellar slices and computer modeling, we show here that ethanol excites Golgi cells by inhibiting the Na(+)/K(+) ATPase. Voltage-clamp recordings of Na(+)/K(+) ATPase currents indicated that ethanol partially inhibits this pump and this effect could be mimicked by low concentrations of ouabain. Partial inhibition of Na(+)/K(+) ATPase function in a computer model of the Golgi cell reproduced these experimental findings. These results establish a novel mechanism of action of ethanol on neuronal excitability, which likely has a role in ethanol-induced cerebellar dysfunction and may also contribute to neuronal functional alterations in other brain regions.

A Signal Processing Analysis of Purkinje Cells in vitro

Cerebellar Purkinje cells in vitro fire recurrent sequences of Sodium and Calcium spikes. Here, we analyze the Purkinje cell using harmonic analysis, and our experiments reveal that its output signal is comprised of three distinct frequency bands, which are combined using Amplitude and Frequency Modulation (AM/FM). We find that the three characteristic frequencies – Sodium, Calcium and Switching – occur in various combinations in all waveforms observed using whole-cell current clamp recordings. We found that the Calcium frequency can display a frequency doubling of its frequency mode, and the Switching frequency can act as a possible generator of pauses that are typically seen in Purkinje output recordings. Using a reversibly photo-switchable kainate receptor agonist, we demonstrate the external modulation of the Calcium and Switching frequencies. These experiments and Fourier analysis suggest that the Purkinje cell can be understood as a harmonic signal oscillator, enabling a higher level of interpretation of Purkinje signaling based on modern signal processing techniques.

The first second: models of short-term memory traces in the brain

Many network models in computational neuroscience rise to the challenge of explaining behavioural phenomena ranging from microseconds to tens of seconds using components operating mostly on a time-scale of milliseconds. These models have in common that the underlying system has a memory, which implies that its output depends on its past input history. In this review we compare how such memory traces or delayed responses may be implemented in different brain areas supporting a diversity of functions.

Synchronization in primate cerebellar granule cell layer local field potentials: basic anisotropy and dynamic changes during active expectancy

The cerebellar cortex is remarkable for its organizational regularity, out of which task-related neural networks should emerge. In Purkinje cells, both complex and simple spike network patterns are evident in sensorimotor behavior. However, task-related patterns of activity in the granule cell layer (GCL) have been less studied. We recorded local field potential (LFP) activity simultaneously in pairs of GCL sites in monkeys performing an active expectancy (lever-press) task, in passive expectancy, and at rest. LFP sites were selected when they showed strong 10–25 Hz oscillations; pair orientation was in stereotaxic sagittal and coronal (mainly), and diagonal. As shown previously, LFP oscillations at each site were modulated during the lever-press task. Synchronization across LFP pairs showed an evident basic anisotropy at rest: sagittal pairs of LFPs were better synchronized (more than double the cross-correlation coefficients) than coronal pairs, and more than diagonal pairs. On the other hand, this basic anisotropy was modifiable: during the active expectancy condition, where sagittal and coronal orientations were tested, synchronization of LFP pairs would increase just preceding movement, most notably for the coronal pairs. This lateral extension of synchronization was not observed in passive expectancy. The basic pattern of synchronization at rest, favoring sagittal synchrony, thus seemed to adapt in a dynamic fashion, potentially extending laterally to include more cerebellar cortex elements. This dynamic anisotropy in LFP synchronization could underlie GCL network organization in the context of sensorimotor tasks.

Neurons that fire together also conspire together: is normal sleep circuitry hijacked to generate epilepsy?

Brain circuits oscillate during sleep. The same circuits appear to generate pathological oscillations. In this review, we discuss recent advances in our understanding of how epilepsy co-opts normal, sleep-related circuits to generate seizures.

Membrane resonance in bursting pacemaker neurons of an oscillatory network is correlated with network frequency

Network oscillations typically span a limited range of frequency. In pacemaker-driven networks, including many central pattern generators (CPGs), this frequency range is determined by the properties of bursting pacemaker neurons and their synaptic connections; thus, factors that affect the burst frequency of pacemaker neurons should play a role in determining the network frequency. We examine the role of membrane resonance of pacemaker neurons on the network frequency in the crab pyloric CPG. The pyloric oscillations (frequency of approximately 1 Hz) are generated by a group of pacemaker neurons: the anterior burster (AB) and the pyloric dilator (PD). We examine the impedance profiles of the AB and PD neurons in response to sinusoidal current injections with varying frequency and find that both neuron types exhibit membrane resonance, i.e., demonstrate maximal impedance at a given preferred frequency. The membrane resonance frequencies of the AB and PD neurons fall within the range of the pyloric network oscillation frequency. Experiments with pharmacological blockers and computational modeling show that both calcium currents I(Ca) and the hyperpolarization-activated inward current I(h) are important in producing the membrane resonance in these neurons. We then demonstrate that both the membrane resonance frequency of the PD neuron and its suprathreshold bursting frequency can be shifted in the same direction by either direct current injection or by using the dynamic-clamp technique to inject artificial conductances for I(h) or I(Ca). Together, these results suggest that membrane resonance of pacemaker neurons can be strongly correlated with the CPG oscillation frequency.

Traveling waves in developing cerebellar cortex mediated by asymmetrical Purkinje cell connectivity

Correlated network activity is important in the development of many neural circuits. Purkinje cells are among the first neurons to populate the cerebellar cortex, where they sprout exuberant axon collaterals. We used multiple patch-clamp recordings targeted with two-photon microscopy to characterize monosynaptic connections between the Purkinje cells of juvenile mice. We found that Purkinje cell axon collaterals projected asymmetrically in the sagittal plane, directed away from the lobule apex. On the basis of our anatomical and physiological characterization of this connection, we constructed a network model that robustly generated waves of activity that traveled along chains of connected Purkinje cells. Consistent with the model, we observed traveling waves of activity in Purkinje cells in sagittal slices from young mice that require GABA(A) receptor-mediated transmission and intact Purkinje cell axon collaterals. These traveling waves are absent in adult mice, suggesting they have a developmental role in wiring the cerebellar cortical microcircuit.

The critical role of Golgi cells in regulating spatio-temporal integration and plasticity at the cerebellum input stage

The discovery of the Golgi cell is bound to the foundation of the Neuron Doctrine. Recently, the excitable mechanisms of this inhibitory interneuron have been investigated with modern experimental and computational techniques raising renewed interest for the implications it might have for cerebellar circuit functions. Golgi cells are pacemakers with preferential response frequency and phase-reset in the theta-frequency band and can therefore impose specific temporal dynamics to granule cell responses. Moreover, through their connectivity, Golgi cells determine the spatio-temporal organization of cerebellar activity. Finally, Golgi cells, by controlling granule cell depolarization and NMDA channel unblock, regulate the induction of long-term synaptic plasticity at the mossy fiber – granule cell synapse. Thus, the Golgi cells can exert an extensive control on spatio-temporal signal organization and information storage in the granular layer playing a critical role for cerebellar computation.

Stochastic differential equation model for cerebellar granule cell excitability

Neurons in the brain express intrinsic dynamic behavior which is known to be stochastic in nature. A crucial question in building models of neuronal excitability is how to be able to mimic the dynamic behavior of the biological counterpart accurately and how to perform simulations in the fastest possible way. The well-established Hodgkin-Huxley formalism has formed to a large extent the basis for building biophysically and anatomically detailed models of neurons. However, the deterministic Hodgkin-Huxley formalism does not take into account the stochastic behavior of voltage-dependent ion channels. Ion channel stochasticity is shown to be important in adjusting the transmembrane voltage dynamics at or close to the threshold of action potential firing, at the very least in small neurons. In order to achieve a better understanding of the dynamic behavior of a neuron, a new modeling and simulation approach based on stochastic differential equations and Brownian motion is developed. The basis of the work is a deterministic one-compartmental multi-conductance model of the cerebellar granule cell. This model includes six different types of voltage-dependent conductances described by Hodgkin-Huxley formalism and simple calcium dynamics. A new model for the granule cell is developed by incorporating stochasticity inherently present in the ion channel function into the gating variables of conductances. With the new stochastic model, the irregular electrophysiological activity of an in vitro granule cell is reproduced accurately, with the same parameter values for which the membrane potential of the original deterministic model exhibits regular behavior. The irregular electrophysiological activity includes experimentally observed random subthreshold oscillations, occasional spontaneous spikes, and clusters of action potentials. As a conclusion, the new stochastic differential equation model of the cerebellar granule cell excitability is found to expand the range of dynamics in comparison to the original deterministic model. Inclusion of stochastic elements in the operation of voltage-dependent conductances should thus be emphasized more in modeling the dynamic behavior of small neurons. Furthermore, the presented approach is valuable in providing faster computation times compared to the Markov chain type of modeling approaches and more sophisticated theoretical analysis tools compared to previously presented stochastic modeling approaches.

Computational modeling is of importance in striving to understand the complex dynamic behavior of a neuron. In neuronal modeling, the function of the neuron's components, including the cell membrane and voltage-dependent ion channels, is typically described using deterministic ordinary differential equations that always provide the same model output when repeating computer simulations with fixed model parameter values. It is well known, however, that the behavior of neurons and voltage-dependent ion channels is stochastic in nature. A stochastic modeling approach based on probabilistically describing the transition rates of ion channels has therefore gained interest due to its ability to produce more accurate results than the deterministic approaches. These Markov chain type of models are, however, relatively time-consuming to simulate. Thus it is important to develop new modeling and simulation approaches that take into account the stochasticity inherently present in the function of ion channels. In this study, we seek new stochastic methods for modeling the dynamic behavior of neurons. We apply stochastic differential equations (SDEs) and Brownian motion that are also commonly used in the air space industry and in economics. An SDE is a differential equation in which one or more of the terms of the mathematical equation are stochastic processes. Computer simulations show that the irregular firing behavior of a small neuron, in our case the cerebellar granule cell, is reproduced more accurately in comparison to previous deterministic models. Furthermore, the computation is performed in a relatively fast manner compared to previous stochastic approaches. Additionally, the SDE method provides more sophisticated mathematical analysis tools compared to other, similar kinds of stochastic approaches. In the future, the new SDE model of the cerebellar granule cell can be used in studying the emergent behavior of cerebellar neural network circuitry.

Fast-reset of pacemaking and theta-frequency resonance patterns in cerebellar golgi cells: simulations of their impact in vivo

The Golgi cells are inhibitory interneurons of the cerebellar granular layer, which respond to afferent stimulation in vivo with a burst-pause sequence interrupting their irregular background low-frequency firing (Vos et al., 1999a. Eur. J. Neurosci. 11, 2621–2634). However, Golgi cells in vitro are regular pacemakers (Forti et al., 2006. J. Physiol. 574, 711–729), raising the question how their ionic mechanisms could impact on responses during physiological activity. Using patch-clamp recordings in cerebellar slices we show that the pacemaker cycle can be suddenly reset by spikes, making the cell highly sensitive to input variations. Moreover, the neuron resonates around the pacemaker frequency, making it specifically sensitive to patterned stimulation in the theta-frequency band. Computational analysis based on a model developed to reproduce Golgi cell pacemaking (Solinas et al., 2008Front. Neurosci., 2:2) predicted that phase-reset required spike-triggered activation of SK channels and that resonance was sustained by a slow voltage-dependent potassium current and amplified by a persistent sodium current. Adding balanced synaptic noise to mimic the irregular discharge observed in vivo, we found that pacemaking converts into spontaneous irregular discharge, that phase-reset plays an important role in generating the burst-pause pattern evoked by sensory stimulation, and that repetitive stimulation at theta-frequency enhances the time-precision of spike coding in the burst. These results suggest that Golgi cell intrinsic properties exert a profound impact on time-dependent signal processing in the cerebellar granular layer.

Recurrent axon collaterals underlie facilitating synapses between cerebellar Purkinje cells

Morphological studies have provided ample evidence for synaptic connections between cerebellar Purkinje cells (PCs), but the functional properties of these synapses remain elusive. We report on direct recordings of synaptically connected PCs in mice cerebellar slices. In PCs filled with a fluorescent dye to aid axon visualization and postsynaptic target identification, presynaptic action potentials elicited unitary inhibitory postsynaptic currents in neighboring PCs in 10% of potential connections tested. In 11 pairs, postsynaptic currents had a delay onset of 1.62 +/- 0.16 ms with respect to the presynaptic spike, a 10-90% rise time of 2.20 +/- 0.33 ms, and a monoexponential decay with a time constant of 13.3 +/- 1.7 ms. Average values for peak current and variance-to-mean ratio were 55 +/- 14 and 30 +/- 3 pA, respectively. In contrast to the depressing nature of the synapse between PCs and deep cerebellar nuclei neurons, PC-PC synapses exhibited strong facilitation operating within a time window of a few milliseconds; paired-pulse ratios for 3- and 20-ms intervals were 1.79 +/- 0.18 and 1.01 +/- 0.14, respectively (n = 6). The facilitation is of presynaptic nature because it is accompanied by a decrease in failure rate. Trains of action potentials evoked in presynaptic varicosities volume-averaged calcium transients whose peak increased 1.7-fold as the frequency increased from 50 to 166 Hz. We suggest that PC-PC synapses are tuned for high fidelity of transmission during bursts of PC activity and that their operation in the cerebellar circuit modulates synchronized PC firing.

Cerebellar circuitry as a neuronal machine

Shortly after John Eccles completed his studies of synaptic inhibition in the spinal cord, for which he was awarded the 1963 Nobel Prize in physiology/medicine, he opened another chapter of neuroscience with his work on the cerebellum. From 1963 to 1967, Eccles and his colleagues in Canberra successfully dissected the complex neuronal circuitry in the cerebellar cortex. In the 1967 monograph, "The Cerebellum as a Neuronal Machine", he, in collaboration with Masao Ito and Janos Szentágothai, presented blue-print-like wiring diagrams of the cerebellar neuronal circuitry. These stimulated worldwide discussions and experimentation on the potential operational mechanisms of the circuitry and spurred theoreticians to develop relevant network models of the machinelike function of the cerebellum. In following decades, the neuronal machine concept of the cerebellum was strengthened by additional knowledge of the modular organization of its structure and memory mechanism, the latter in the form of synaptic plasticity, in particular, long-term depression. Moreover, several types of motor control were established as model systems representing learning mechanisms of the cerebellum. More recently, both the quantitative preciseness of cerebellar analyses and overall knowledge about the cerebellum have advanced considerably at the cellular and molecular levels of analysis. Cerebellar circuitry now includes Lugaro cells and unipolar brush cells as additional unique elements. Other new revelations include the operation of the complex glomerulus structure, intricate signal transduction for synaptic plasticity, silent synapses, irregularity of spike discharges, temporal fidelity of synaptic activation, rhythm generators, a Golgi cell clock circuit, and sensory or motor representation by mossy fibers and climbing fibers. Furthermore, it has become evident that the cerebellum has cognitive functions, and probably also emotion, as well as better-known motor and autonomic functions. Further cerebellar research is required for full understanding of the cerebellum as a broad learning machine for neural control of these functions.

Synaptic pathways in neural microcircuits

The functions performed by different neural microcircuits depend on the anatomical and physiological properties of the various synaptic pathways connecting neurons. Neural microcircuits across various species and brain regions are similar in terms of their repertoire of neurotransmitters, their synaptic kinetics, their short-term and long-term plasticity, and the target-specificity of their synaptic connections. However, microcircuits can be fundamentally different in terms of the precise recurrent design used to achieve a specific functionality. In this review, which is part of the TINS Microcircuits Special Feature, we compare the connectivity designs in spinal, hippocampal, neocortical and cerebellar microcircuits, and discuss the different computational challenges that each microcircuit faces.

Microcircuits in action – from CPGs to neocortex

To understand the interface between global brain function and molecular neuroscience--that is, the microcircuit level--a major challenge. Such understanding is prerequisite if we are to account for neural function in cellular terms. Very few vertebrate microcircuits are yet understood because their analysis is demanding technically. In this review of the TINS Microcircuits Special Feature, we attempt to shed light on the problem by comparing the operation of four types of microcircuit, to identify common molecular and cellular components. Central pattern generator (CPG) networks underlying rhythmic movements and hippocampal microcircuits that generate gamma and theta rhythms are compared with the neocortical microcircuits used in cognitive tasks and a cerebellar network. The long-term goal is to identify the components of a molecular and synaptic tool kit for the design of different microcircuits.