Self-referential phase reset based on inferior olive oscillator dynamics

3-Acetylpyridine-induced ataxic-like motor impairments are associated with plastic changes in the Purkinje cells of the rat cerebellum

Ataxias are characterized by aberrant movement patterns closely related to cerebellar dysfunction. Purkinje cell axons are the sole outputs from the cerebellar cortex, and dysfunctional activity of Purkinje cells has been associated with ataxic movements. However, the synaptic characteristics of Purkinje cells in cases of ataxia are not yet well understood. The nicotinamide antagonist 3-acethylpyridine (3-AP) selectively destroys inferior olivary nucleus neurons so it is widely used to induce cerebellar ataxia. Five days after 3-AP treatment (65mg/kg) in adult male Sprague-Dawley rats, motor incoordination was revealed through BBB and Rotarod testing. In addition, in Purkinje cells from lobules V-VII of the cerebellar vermis studied by the Golgi method, the density of dendritic spines decreased, especially the thin and mushroom types. Western blot analysis showed a decrease in AMPA and PSD-95 content with an increase of the α-catenin protein, while GAD-67 and synaptophysin were unchanged. Findings suggest a limited capacity of Purkinje cells to acquire and consolidate afferent excitatory inputs and an aberrant, rigid profile in the movement-related output patterns of Purkinje neurons that likely contributes to the motor-related impairments characteristic of cerebellar ataxias.

Effect of the electromagnetic induction in the electrical activity of the Kazantsev model of inferior Olive Neuron model

In this paper, based on the four variables Kazantsev et al. inferior olive neuron (ION) dynamic equations, a five variables neuron model is designed to describe the effect of electromagnetic induction in ION activities. Within the new ION model, the effect of magnetic flow on membrane potential is described by imposing additive memristive current in the master block of the Kasantsev et al. neuron model. The impact of magnetic flux on the stability of equilibrium point is studied. Hopf bifurcation and bifurcation diagram indicated that, as the electromagnetic field strength parameter changes, the value of the critical point also changes. Furthermore, as the electromagnetic induction is increasing, there is appearance of bursting dynamic in the slave subsystem and an increase in the spike amplitude of the master subsystem. In addition, the analog circuit of the master block confirms the observed results from numerical simulation.

Multistable autonomous motion of fruit on a smooth hotplate

Origin of scale coupling may be clarified by the understanding of multistability, or shifts between stable points via unstable equilibrium points due to a stimulus. When placed on a glasstop hotplate, cobs of corn underwent multistable autonomous oscillation, with unsteady viscous lubrication below and transitional plumes above, where the buoyancy to inertia force ratio is close to ≥ 1.0. Subsequently, viscous wall-frictional multistability occurred in six more types of smooth fruit with nominal symmetry. Autonomous motion observed are: cobs roll, pitch and yaw; but green chillies, blueberries, tropical berries, red grapes, oblong grapes and grape tomatoes roll and yaw. The cross products of the orthogonal angular momentum produce the observed motion. The prevalence of roll and yaw motion are the most common. Lubricant film thickness h\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\propto$$\end{document}∝U/(TF), for cob mass F, tangential velocity U and temperature T. In heavier cobs, the film thins, breaking frequently, changing stability. Lighter cobs have high h, favoring positive feedback and more spinning: more T rises, more viscosity of water drops, increasing U and h more, until cooling onsets. Infrequent popping of the tender corn kernel has the same mean sound pressure level as in hard popcorn. The plume vortex jets lock-in to the autonomous rolling cob oscillation. Away from any solid surface, the hot-cold side boundary produces plumes slanted at ± 45°. Surface fencing (13–26 μm high) appears to control motion drift.

Complex Electroresponsive Dynamics in Olivocerebellar Neurons Represented With Extended-Generalized Leaky Integrate and Fire Models

The neurons of the olivocerebellar circuit exhibit complex electroresponsive dynamics, which are thought to play a fundamental role for network entraining, plasticity induction, signal processing, and noise filtering. In order to reproduce these properties in single-point neuron models, we have optimized the Extended-Generalized Leaky Integrate and Fire (E-GLIF) neuron through a multi-objective gradient-based algorithm targeting the desired input–output relationships. In this way, E-GLIF was tuned toward the unique input–output properties of Golgi cells, granule cells, Purkinje cells, molecular layer interneurons, deep cerebellar nuclei cells, and inferior olivary cells. E-GLIF proved able to simulate the complex cell-specific electroresponsive dynamics of the main olivocerebellar neurons including pacemaking, adaptation, bursting, post-inhibitory rebound excitation, subthreshold oscillations, resonance, and phase reset. The integration of these E-GLIF point-neuron models into olivocerebellar Spiking Neural Networks will allow to evaluate the impact of complex electroresponsive dynamics at the higher scales, up to motor behavior, in closed-loop simulations of sensorimotor tasks.

Quasiperiodic rhythms of the inferior olive

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

Activity of the inferior olive, transmitted via climbing fibers to the cerebellum, regulates initiation and amplitude of movements, signals unexpected sensory feedback, and directs cerebellar learning. It is characterized by widespread subthreshold oscillations and synchronization promoted by strong electrotonic coupling. In brain slices, subthreshold oscillations gate which inputs can be transmitted by inferior olivary neurons and which will not—dependent on the phase of the oscillation. We tested whether the subthreshold oscillations had a measurable impact on temporal patterning of climbing fiber activity in intact, awake mice. We did so by recording neural activity of the postsynaptic Purkinje cells, in which complex spike firing faithfully represents climbing fiber activity. For short intervals (<300 ms) many Purkinje cells showed spontaneously rhythmic complex spike activity. However, our experiments designed to evoke conditional responses indicated that complex spikes are not predominantly predicated on stimulus history. Our realistic network model of the inferior olive explains the experimental observations via continuous phase modulations of the subthreshold oscillations under the influence of synaptic fluctuations. We conclude that complex spike activity emerges from a quasiperiodic rhythm that is stabilized by electrotonic coupling between its dendrites, yet dynamically influenced by the status of their synaptic inputs.

Chaotic Resonance in Coupled Inferior Olive Neurons with the Llinás Approach Neuron Model

It is well known that cerebellar motor control is fine-tuned by the learning process adjusted according to rich error signals from inferior olive (IO) neurons. Schweighofer and colleagues proposed that these signals can be produced by chaotic irregular firing in the IO neuron assembly; such chaotic resonance (CR) was replicated in their computer demonstration of a Hodgkin-Huxley (HH)-type compartment model. In this study, we examined the response of CR to a periodic signal in the IO neuron assembly comprising the Llinás approach IO neuron model. This system involves empirically observed dynamics of the IO membrane potential and is simpler than the HH-type compartment model. We then clarified its dependence on electrical coupling strength, input signal strength, and frequency. Furthermore, we compared the physiological validity for IO neurons such as low firing rate and sustaining subthreshold oscillation between CR and conventional stochastic resonance (SR) and examined the consistency with asynchronous firings indicated by the previous model-based studies in the cerebellar learning process. In addition, the signal response of CR and SR was investigated in a large neuron assembly. As the result, we confirmed that CR was consistent with the above IO neuron's characteristics, but it was not as easy for SR.

Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback

Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator reaches a specific state, it emits a pulse, which returns after propagating through a delay line. The impact of an incoming pulse is described by the oscillator's phase reset curve (PRC). In such a system we discover an unexpected phenomenon: for a sufficiently steep slope of the PRC, a periodic regular spiking solution bifurcates with several multipliers crossing the unit circle at the same parameter value. The number of such critical multipliers increases linearly with the delay and thus may be arbitrary large. This bifurcation is accompanied by the emergence of numerous "jittering" regimes with nonequal interspike intervals (ISIs). Each of these regimes corresponds to a periodic solution of the system with a period roughly proportional to the delay. The number of different "jittering" solutions emerging at the bifurcation point increases exponentially with the delay. We describe the combinatorial mechanism that underlies the emergence of such a variety of solutions. In particular, we show how a periodic solution exhibiting several distinct ISIs can imply the existence of multiple other solutions obtained by rearranging of these ISIs. We show that the theoretical results for phase oscillators accurately predict the behavior of an experimentally implemented electronic oscillator with pulsatile feedback.

Transient visual responses reset the phase of low-frequency oscillations in the skeletomotor periphery

We recorded muscle activity from an upper limb muscle while human subjects reached towards peripheral targets. We tested the hypothesis that the transient visual response sweeps not only through the central nervous system, but also through the peripheral nervous system. Like the transient visual response in the central nervous system, stimulus-locked muscle responses (< 100 ms) were sensitive to stimulus contrast, and were temporally and spatially dissociable from voluntary orienting activity. Also, the arrival of visual responses reduced the variability of muscle activity by resetting the phase of ongoing low-frequency oscillations. This latter finding critically extends the emerging evidence that the feedforward visual sweep reduces neural variability via phase resetting. We conclude that, when sensory information is relevant to a particular effector, detailed information about the sensorimotor transformation, even from the earliest stages, is found in the peripheral nervous system.

EEG gamma-band activity during audiovisual speech comprehension in different noise environments

The presence of cross-modal stochastic resonance in different noise environments has been proved in previous behavioral and event-related potential studies, while it was still unclear whether the gamma-band oscillation study was another evidence of cross-modal stochastic resonance. The multisensory gain of gamma-band activity between the audiovisual (AV) and auditory-only conditions in different noise environments was analyzed. Videos of face motion articulating words concordant with different levels of pink noise were used as stimuli. Signal-to-noise ratios (SNRs) of 0, -4, -8, -12 and -16 dB were selected to measure the speech recognition accuracy and EEG activity for 20 healthy subjects. The power and phase of EEG gamma-band oscillations increased in a time window of 50-90 ms. The multisensory gains of evoked and total activity, as well as phase-locking factor, were greatest at the -12 dB SNR, which were consistent with the behavioral result. The multisensory gain of gamma-band activity showed an inverted U-shaped curve as a function of SNR. This finding confirmed the presence of cross-modal stochastic resonance. In addition, there was a significant correlation between evoked activity and phase-locking factor of gamma-band at five different SNRs. Gamma-band oscillation was believed to play a role in the rapid processing and information linkage strengthening of AV modalities in the early stage of cognitive processes.

Modeling how shark and dolphin skin patterns control transitional wall-turbulence vorticity patterns using spatiotemporal phase reset mechanisms

Many slow-moving biological systems like seashells and zebrafish that do not contend with wall turbulence have somewhat organized pigmentation patterns flush with their outer surfaces that are formed by underlying autonomous reaction-diffusion (RD) mechanisms. In contrast, sharks and dolphins contend with wall turbulence, are fast swimmers, and have more organized skin patterns that are proud and sometimes vibrate. A nonlinear spatiotemporal analytical model is not available that explains the mechanism underlying control of flow with such proud patterns, despite the fact that shark and dolphin skins are major targets of reverse engineering mechanisms of drag and noise reduction. Comparable to RD, a minimal self-regulation model is given for wall turbulence regeneration in the transitional regime—laterally coupled, diffusively—which, although restricted to pre-breakdown durations and to a plane close and parallel to the wall, correctly reproduces many experimentally observed spatiotemporal organizations of vorticity in both laminar-to-turbulence transitioning and very low Reynolds number but turbulent regions. We further show that the onset of vorticity disorganization is delayed if the skin organization is treated as a spatiotemporal template of olivo-cerebellar phase reset mechanism. The model shows that the adaptation mechanisms of sharks and dolphins to their fluid environment have much in common.

Cross-frequency synchronization of oscillators with time-delayed coupling

We carry out theoretical and experimental studies of cross-frequency synchronization of two pulse oscillators with time-delayed coupling. In the theoretical part of the paper we utilize the concept of phase resetting curves and analyze the system dynamics in the case of weak coupling. We construct a Poincaré map and obtain the synchronization zones in the parameter space for m:n synchronization. To challenge the theoretical results we designed an electronic circuit implementing the coupled oscillators and studied its dynamics experimentally. We show that the developed theory predicts dynamical properties of the realistic system, including location of the synchronization zones and bifurcations inside them.

Breakup and then makeup: a predictive model of how cilia self-regulate hardness for posture control

Functioning as sensors and propulsors, cilia are evolutionarily conserved organelles having a highly organized internal structure. How a paramecium's cilium produces off-propulsion-plane curvature during its return stroke for symmetry breaking and drag reduction is not known. We explain these cilium deformations by developing a torsional pendulum model of beat frequency dependence on viscosity and an olivo-cerebellar model of self-regulation of posture control. The phase dependence of cilia torsion is determined, and a bio-physical model of hardness control with predictive features is offered. Crossbridge links between the central microtubule pair harden the cilium during the power stroke; this stroke's end is a critical phase during which ATP molecules soften the crossbridge-microtubule attachment at the cilium inflection point where torsion is at its maximum. A precipitous reduction in hardness ensues, signaling the start of ATP hydrolysis that re-hardens the cilium. The cilium attractor basin could be used as reference for perturbation sensing.

The olivo-cerebellar system as a neural clock

The cerebellum, and the olivo-cerebellar system in particular, may be the central mechanism of a neural clock that provides a rhythmic neural signal used to time motor and cognitive processes. Several independent lines of evidence support this hypothesis. First, the resting membrane potential of neurons in the inferior olive oscillates at ~10 Hz and the neural input from the olive leads to rhythmic complex spikes in cerebellum Purkinje cells. Second, the repeating modular microstructure of the cerebellum is ideally suited for performing computations underlying a basic neural process such as timing. Third, damage to the cerebellum leads to deficits in the perception of time and in the production of timed movements. Fourth, functional imaging studies in human subjects have shown activation of the inferior olive specifically during time perception. However, additional data on the exact role of rhythmic cerebellar activity during basis motor and sensory processing will be necessary before the hypothesis that the cerebellum is a neural clock is more widely accepted.

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.”

Handedness helps homing in swimming and flying animals

Swimming and flying animals rely on their ability to home on mobile targets. In some fish, physiological handedness and homing correlate, and dolphins exhibit handedness in their listening response. Here, we explore theoretically whether the actuators, sensors, and controllers in these animals follow similar laws of self-regulation, and how handedness affects homing. We find that the acoustic sensor (combined hydrophone-accelerometer) response maps are similar to fin force maps—modeled by Stuart-Landau oscillators—allowing localization by transitional vortex-propelled animals. The planar trajectories of bats in a room filled with obstacles are approximately reproduced by the states of a pair of strong and weak olivo-cerebellar oscillators. The stereoscopy of handedness reduces ambiguity near a mobile target, resulting in accelerated homing compared to even-handedness. Our results demonstrate how vortex-propelled animals may be localizing each other and circumventing obstacles in changing environments. Handedness could be useful in time-critical robot-assisted rescues in hazardous environments.

STATE AND PARAMETER ESTIMATION FOR CANONIC MODELS OF NEURAL OSCILLATORS

We consider the problem of how to recover the state and parameter values of typical model neurons, such as Hindmarsh-Rose, FitzHugh-Nagumo, Morris-Lecar, from in-vitro measurements of membrane potentials. In control theory, in terms of observer design, model neurons qualify as locally observable. However, unlike most models traditionally addressed in control theory, no parameter-independent diffeomorphism exists, such that the original model equations can be transformed into adaptive canonic observer form. For a large class of model neurons, however, state and parameter reconstruction is possible nevertheless. We propose a method which, subject to mild conditions on the richness of the measured signal, allows model parameters and state variables to be reconstructed up to an equivalence class.

Bifurcation of orbits and synchrony in inferior olive neurons

Inferior olive neurons (IONs) have rich dynamics and can exhibit stable, unstable, periodic, and even chaotic trajectories. This paper presents an analysis of bifurcation of periodic orbits of an ION when its two key parameters (a, μ) are varied in a two-dimensional plane. The parameter a describes the shape of the parabolic nonlinearity in the model and μ is the extracellular stimulus. The four-dimensional ION model considered here is a cascade connection of two subsystems (S(a) and S(b)). The parameter plane (a - μ) is delineated into several subregions. The ION has distinct orbit structure and stability property in each subregion. It is shown that the subsystem S(a) or S(b) undergoes supercritical Poincare-Andronov-Hopf (PAH) bifurcation at a critical value μ(c)(a) of the extracellular stimulus and periodic orbits of the neuron are born. Based on the center manifold theory, the existence of periodic orbits in the asymptotically stable S(a), when the subsystem S(b) undergoes PAH bifurcation, is established. In such a case, both subsystems exhibit periodic orbits. Interestingly when S(b) is under PAH bifurcation and S(a) is unstable, the trajectory of S(a) exhibits periodic bursting, interrupted by periods of quiescence. The bifurcation analysis is followed by the design of (i) a linear first-order filter and (ii) a nonlinear control system for the synchronization of IONs. The first controller uses a single output of each ION, but the nonlinear control system uses two state variables for feedback. The open-loop and closed-loop responses are presented which show bifurcation of orbits and synchronization of oscillating neurons.

Role of olivocerebellar system in timing without awareness

The timing of events can be implicit or without awareness yet critical for task performance. However, the neural correlates of implicit timing are unknown. One system that has long been implicated in event timing is the olivocerebellar system, which originates exclusively from the inferior olive. By using event-related functional MRI in human subjects and a specially designed behavioral task, we examined the effect of the subjects' awareness of changes in stimulus timing on the olivocerebellar system response. Subjects were scanned while observing changes in stimulus timing that were presented near each subject's detection threshold such that subjects were aware of such changes in only approximately half the trials. The inferior olive and multiple areas within the cerebellar cortex showed a robust response to time changes regardless of whether the subjects were aware of these changes. Our findings provide support to the proposed role of the olivocerebellar system in encoding temporal information and further suggest that this system can operate independently of awareness and mediate implicit timing in a multitude of perceptual and motor operations, including classical conditioning and implicit learning.

Role of neuronal synchrony in the generation of evoked EEG/MEG responses

Evoked EEG/MEG responses are a primary real-time measure of perceptual and cognitive activity in the human brain, but their neuronal generator mechanisms are not yet fully understood. Arguments have been put forward in favor of either "phase-reset" of ongoing oscillations or "added-energy" models. Instead of advocating for one or the other model, here we show theoretically that the differentiation between these two generation mechanisms might not be possible if based solely on macroscopic EEG/MEG recordings. Using mathematical modeling, we show that a simultaneous phase reset of multiple oscillating neuronal (microscopic) sources contributing to EEG/MEG can produce evoked responses in agreement with both, the "added-energy" and the "phase-reset" model. We observe a smooth transition between the two models by just varying the strength of synchronization between the multiple microscopic sources. Consequently, because precise knowledge about the strength of microscopic ensemble synchronization is commonly not available in noninvasive EEG/MEG studies, they cannot, in principle, differentiate between the two mechanisms for macroscopic-evoked responses.

Adaptive global synchrony of inferior olive neurons

This paper treats the question of global adaptive synchronization of inferior olive neurons (IONs) based on the immersion and invariance approach. The ION exhibits a variety of orbits as the parameter (termed the bifurcation parameter), which appears in its nonlinear functions, is varied. It is seen that once the bifurcation parameter exceeds a critical value, the stability of the equilibrium point of the ION is lost, and periodic orbits are born. The size and shape of the orbits depend on the value of the bifurcation parameter. It is assumed that bifurcation parameters of the IONs are not known. The orbits of IONs beginning from arbitrary initial conditions are not synchronized. For the synchronization of the IONs, a non-certainty equivalent adaptation law is derived. The control system has a modular structure consisting of an identifier and a control module. Using the Lyapunov approach, it is shown that in the closed-loop system, global synchronization of the neurons with a prescribed relative phase is accomplished, and the estimated bifurcation parameters converge to the true parameters. Unlike the certainty-equivalent adaptive control systems, an interesting feature of the designed control system is that whenever the estimated parameters coincide with the true values, the parameter estimates remain frozen thereafter, and the closed-loop system recovers the performance of the deterministic closed-loop system. Simulation results are presented which show that in the closed-loop system, the synchrony of neurons with prescribed phases is accomplished despite the uncertainties in the bifurcation parameters.

The role of abnormal neural oscillations in the pathophysiology of co-occurring Tourette syndrome and attention-deficit/hyperactivity disorder

OBJECTIVE

To examine the role of aberrant neural oscillatory activity in the pathophysiology of co-occurring Tourette Syndrome (TS) and Attention-Deficit/Hyperactivity Disorder (ADHD).

METHOD

Neural oscillations refer to periodic variations in the recording of neural activity. The temporal synchronization of oscillations represents a mechanism of neural communication implicated in normal brain functioning as well as psychopathology. We reviewed physiological, imaging, and neuropsychological evidence that tics and symptoms of ADHD may result from abnormal oscillatory activity in the brain.

RESULTS

Structural and functional abnormalities in the cortical-striatal-thalamo-cortical circuits may result in the disruption of oscillatory activity within the basal ganglia of individuals with TS and lead to transient hyperpolarization of selected thalamocortical regions. Extended to TS plus ADHD this or similar mechanisms, in turn, would lead to the dysrhythmia of particular vulnerable cortical regions and give rise to various deficits in motor control (TS + ADHD) as well as impulsivity and attention (ADHD). Compensatory systems within the prefrontal cortex could be activated and trained to modulate the misguided striatal and thalamocortical oscillations.

CONCLUSIONS

Although it is highly likely that abnormal neural oscillations have a prominent role in co-occurrence of TS + ADHD, its final relevance in this case deserves further differentiated research (i.e. oscillatory networks disentangled from other neuropsychiatric disorders).

On the cerebello-cerebral interactions

The question of which type of information and how it is being processed by the puzzling cerebellar circuitry remains open. Numerous works have highlighted and delineated the roles of cerebellar pathways in various parameters of motor control, such as timing of motor commands. Recent anatomical and functional data on a possible genuine cerebellar contribution in the processing of 'cognitive', behavioral and emotional information have not yet generated a consensus. Despite an apparent homogeneous and uniform cytoarchitecture, the actors of the cerebellar orchestra do play different roles depending on the anatomical inputs/outputs of the cerebellar regions. The numerous interactions between the cerebellum and the cerebral cortex remain a major field of research. Fundamental questions related to the cerebro-cerebellar networks, such as the modulation of corticomotoneuronal discharges in various contexts, have not been fully addressed, or only indirectly, with recent methods. Complexity of circuitries and non optimal theoretical frameworks continue to hamper our understanding of cerebellar operations.

Dynamic geometry, brain function modeling, and consciousness

Pellionisz and Llinás proposed, years ago, a geometric interpretation towards understanding brain function. This interpretation assumes that the relation between the brain and the external world is determined by the ability of the central nervous system (CNS) to construct an internal model of the external world using an interactive geometrical relationship between sensory and motor expression. This approach opened new vistas not only in brain research but also in understanding the foundations of geometry itself. The approach named tensor network theory is sufficiently rich to allow specific computational modeling and addressed the issue of prediction, based on Taylor series expansion properties of the system, at the neuronal level, as a basic property of brain function. It was actually proposed that the evolutionary realm is the backbone for the development of an internal functional space that, while being purely representational, can interact successfully with the totally different world of the so-called "external reality". Now if the internal space or functional space is endowed with stochastic metric tensor properties, then there will be a dynamic correspondence between events in the external world and their specification in the internal space. We shall call this dynamic geometry since the minimal time resolution of the brain (10-15 ms), associated with 40 Hz oscillations of neurons and their network dynamics, is considered to be responsible for recognizing external events and generating the concept of simultaneity. The stochastic metric tensor in dynamic geometry can be written as five-dimensional space-time where the fifth dimension is a probability space as well as a metric space. This extra dimension is considered an imbedded degree of freedom. It is worth noticing that the above-mentioned 40 Hz oscillation is present both in awake and dream states where the central difference is the inability of phase resetting in the latter. This framework of dynamic geometry makes it possible to distinguish one individual from another. In this paper we shall investigate the role of dynamic geometry in brain function modeling and the neuronal basis of consciousness.

Evoked γ oscillations in human scalp EEG are test–retest reliable

OBJECTIVE

Evoked, phase-locked gamma oscillations of the electroencephalogram (EEG) have been demonstrated to be modulated by both bottom-up as well as top-down factors. However, to date the test-retest reliability of these oscillations has not been studied systematically.

METHODS

We recorded EEG activity of 12 healthy volunteers in response to stimuli of different sizes. Each participant took part in two sessions separated by two weeks in time. To obtain an estimate of the reliability of evoked gamma band responses (GBRs), we compared frequency and magnitude of phase-locked EEG oscillations between sessions.

RESULTS

In response to large stimuli magnitude and frequency of the evoked GBR yielded significant reliability. However, this was not the case for stimuli which were too small to evoke detectable GBRs.

CONCLUSIONS

The results are in accordance with studies demonstrating a dependence of gamma oscillations on stimulus parameters.

SIGNIFICANCE

The current findings suggest that using appropriate stimulation, the evoked gamma response has sufficient test-retest reliability for use in assessing clinical changes in neurophysiological status.

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.

Annotation: Tourette syndrome: a relentless drumbeat--driven by misguided brain oscillations

OBJECTIVE

This annotation reviews recent evidence that points to the likely role of aberrant neural oscillations in the pathogenesis of Tourette syndrome (TS).

METHODS

The available anatomic and electrophysiological findings in TS are reviewed in the context of an emerging picture of the crucial role that neural oscillations play in maintaining normal central nervous system (CNS) function.

RESULTS

Neurons form behavior-dependent oscillating networks of various sizes and frequencies that bias input selection and facilitate synaptic plasticity, mechanisms that cooperatively support temporal representation as well as the transfer and long-term consolidation of information. Coherent network activity is likely to modulate sensorimotor gating as well as focused motor actions. When these networks are dysrhythmic, there may be a loss of control of sensory information and motor action. The known electrophysiological effects of medications and surgical interventions used to treat TS likely have an ameliorative effect on these aberrant oscillations. Similarly, a strong case can be made that successful behavioral treatments involve the willful training regions of the prefrontal cortex to engage in tic suppression and the performance of competing motor responses to unwanted sensory urges such that these prefrontal regions become effective modulators of aberrant thalamocortical rhythms.

CONCLUSIONS

A deeper understanding of neural oscillations may illuminate the complex, challenging, enigmatic, internal world that is TS.

High frequency oscillations in the somatosensory evoked potentials (SSEP's) are mainly due to phase-resetting phenomena

A small series of high frequency oscillations (HFOs) overlapping the earliest part of the N20 wave can be observed in the somatosensory evoked potentials (SSEPs) of normal subjects. We tried to elucidate whether these high frequency components are mainly due to phase-resetting phenomena, to the emergence of new oscillations related to the stimuli, or to a combination of both. Averaged median-nerve SSEPs from seven healthy subjects were studied by means of time-frequency analysis. The presence of new oscillatory activities was evaluated by averaging the energy of the single-trial time-frequency transforms in the HFOs range (400-1000 Hz). To study phase-resetting phenomena, we measured inter-trial coherence (ITC) in the same frequency range. A marked inter-trial coherence related to the HFOs was found, whereas energy changes (related to the emergence of new oscillations) were minimal. The combination of these three different approaches suggests that the HFOs are mainly due to resettings of the ongoing EEG activity originated in response to the stimuli. The emergence of new activities does not seem to be a relevant mechanism in the formation of these components.