Olivo-cerebellar cluster-based universal control system

Emergent Aspects of the Integration of Sensory and Motor Functions

This article delves into the intricate mechanisms underlying sensory integration in the executive control of movement, encompassing ideomotor activity, predictive capabilities, and motor control systems. It examines the interplay between motor and sensory functions, highlighting the role of the cortical and subcortical regions of the central nervous system in enhancing environmental interaction. The acquisition of motor skills, procedural memory, and the representation of actions in the brain are discussed emphasizing the significance of mental imagery and training in motor function. The development of this aspect of sensorimotor integration control can help to advance our understanding of the interactions between executive motor control, cortical mechanisms, and consciousness. Bridging theoretical insights with practical applications, it sets the stage for future innovations in clinical rehabilitation, assistive technology, and education. The ongoing exploration of these domains promises to uncover new pathways for enhancing human capability and well-being.

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.

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.

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.

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.

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.

Loss of intrinsic organization of cerebellar networks in spinocerebellar ataxia type 1: correlates with disease severity and duration

The spinocerebellar ataxias (SCAs) are a genetically heterogeneous group of cerebellar degenerative disorders, characterized by progressive gait unsteadiness, hand incoordination, and dysarthria. The mutational mechanism in SCA1, a dominantly inherited form of SCA, consists of an expanded trinucleotide CAG repeat. In SCA1, there is loss of Purkinje cells, neuronal loss in dentate nucleus, olives, and pontine nuclei. In the present study, we sought to apply intrinsic functional connectivity analysis combined with diffusion tensor imaging to define the state of cerebellar connectivity in SCA1. Our results on the intrinsic functional connectivity in lateral cerebellum and thalamus showed progressive organizational changes in SCA1 noted as a progressive increase in the absolute value of the correlation coefficients. In the lateral cerebellum, the anatomical organization of functional clusters seen as parasagittal bands in controls is lost, changing to a patchy appearance in SCA1. Lastly, only fractional anisotropy in the superior peduncle and changes in functional organization in thalamus showed a linear dependence to duration and severity of disease. The present pilot work represents an initial effort describing connectivity biomarkers of disease progression in SCA1. The functional changes detected with intrinsic functional analysis and diffusion tensor imaging suggest that disease progression can be analyzed as a disconnection syndrome.

Reorganization of cerebral networks after stroke: new insights from neuroimaging with connectivity approaches

The motor system comprises a network of cortical and subcortical areas interacting via excitatory and inhibitory circuits, thereby governing motor behaviour. The balance within the motor network may be critically disturbed after stroke when the lesion either directly affects any of these areas or damages-related white matter tracts. A growing body of evidence suggests that abnormal interactions among cortical regions remote from the ischaemic lesion might also contribute to the motor impairment after stroke. Here, we review recent studies employing models of functional and effective connectivity on neuroimaging data to investigate how stroke influences the interaction between motor areas and how changes in connectivity relate to impaired motor behaviour and functional recovery. Based on such data, we suggest that pathological intra- and inter-hemispheric interactions among key motor regions constitute an important pathophysiological aspect of motor impairment after subcortical stroke. We also demonstrate that therapeutic interventions, such as repetitive transcranial magnetic stimulation, which aims to interfere with abnormal cortical activity, may correct pathological connectivity not only at the stimulation site but also among distant brain regions. In summary, analyses of connectivity further our understanding of the pathophysiology underlying motor symptoms after stroke, and may thus help to design hypothesis-driven treatment strategies to promote recovery of motor function in patients.

Cerebellar motor learning versus cerebellar motor timing: the climbing fibre story

Theories concerning the role of the climbing fibre system in motor learning, as opposed to those addressing the olivocerebellar system in the organization of motor timing, are briefly contrasted. The electrophysiological basis for the motor timing hypothesis in relation to the olivocerebellar system is treated in detail.

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.

Inferior olive oscillation as the temporal basis for motricity and oscillatory reset as the basis for motor error correction

The cerebellum can be viewed as supporting two distinct aspects of motor execution related to a) motor coordination and the sequence that imparts such movement temporal coherence and b) the reorganization of ongoing movement when a motor execution error occurs. The former has been referred to as "motor time binding" as it requires that the large numbers of motoneurons involved be precisely activated from a temporal perspective. By contrast, motor error correction requires the abrupt reorganization of ongoing motor sequences, on occasion sufficiently important to rescue the animal or person from potentially lethal situations. The olivo-cerebellar system plays an important role in both categories of motor control. In particular, the morphology and electrophysiology of inferior olivary neurons have been selected by evolution to execute a rather unique oscillatory pace-making function, one required for temporal sequencing and a unique oscillatory phase resetting dynamic for error correction. Thus, inferior olivary (IO) neurons are electrically coupled through gap junctions, generating synchronous subthreshold oscillations of their membrane potential at a frequency of 1-10 Hz and are capable of fast and reliable phase resetting. Here I propose to address the role of the olivocerebellar system in the context of motor timing and reset.

And the Olive Said to the Cerebellum: Organization and Functional Significance of the Olivo-Cerebellar System

What is the role of the olive in cerebellar operations? And what is the role of the cerebellum in the sensory and motor functioning of the nervous system? It is clear that the olivo-cerebellar network plays a key role in the managing of vertebrate motor control, as lesions in this network cause motor deficits in humans and animals. However, it is increasingly becoming clear that the olivo-cerebellar system is involved in the control of more than simple motor behaviors. The elegant and almost geometric organization of the olivocerebellar network lends itself to performing these complex operations. In this review, the salient anatomical, physiological, and clinical features of this system are discussed. A computer-assisted visualization system is used to illustrate some of the anatomical points. The idea that the cerebellum and the olivo-cerebellar networks are perhaps in the upper echelons of the hierarchy of brain functioning, if such a hierarchy indeed exists, is discussed. NEUROSCIENTIST 13(6):616—625, 2007. DOI: 10.1177/1073858407299286

Forced phase-locked states and information retrieval in a two-layer network of oscillatory neurons with directional connectivity

We propose two-layer architecture of associative memory oscillatory network with directional interlayer connectivity. The network is capable to store information in the form of phase-locked (in-phase and antiphase) oscillatory patterns. The first (input) layer takes an input pattern to be recognized and their units are unidirectionally connected with all units of the second (control) layer. The connection strengths are weighted using the Hebbian rule. The output (retrieved) patterns appear as forced-phase locked states of the control layer. The conditions are found and analytically expressed for pattern retrieval in response on incoming stimulus. It is shown that the system is capable to recover patterns with a certain level of distortions or noises in their profiles. The architecture is implemented with the Kuramoto phase model and using synaptically coupled neural oscillators with spikes. It is found that the spiking model is capable to retrieve patterns using the spiking phase that translates memorized patterns into the spiking phase shifts at different time scales.

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.

Estimation of coupling between oscillators from short time series via phase dynamics modeling: limitations and application to EEG data

We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D. A. Smirnov and B. P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely applicable. Namely, although the expressions for the estimators and their confidence bands are derived for linear uncoupled oscillators under the influence of independent sources of Gaussian white noise, they turn out to allow reliable characterization of coupling from relatively short time series for different properties of noise, significant phase nonlinearity of the oscillators, and nonvanishing coupling between them. We apply the estimators to analyze a two-channel human intracranial epileptic electroencephalogram (EEG) recording with the purpose of epileptic focus localization.

Detection of weak directional coupling: phase-dynamics approach versus state-space approach

We compare two conceptually different approaches to the detection of weak directional couplings between two oscillatory systems from bivariate time series. The first approach is based on the analysis of the systems' phase dynamics, whereas the other one tests for interdependencies in the reconstructed state spaces of the systems. We analyze the sensitivity of both techniques to weak couplings in numerical experiments by considering couplings between almost identical as well as between significantly different nonlinear systems. We study different degrees of phase diffusion, test the robustness of the two techniques against observational noise, and investigate the influence of the time series length. Our results show that none of the two approaches is generally superior to the other, and we conclude that it is probably the combination of both techniques that would allow the most comprehensive and reliable characterization of coupled systems.

Localization of intracellular and plasma membrane Ca2+-ATPases in the cerebellum

The sarco-endoplasmic reticulum Ca2+-ATPase and the plasma membrane Ca2+-ATPase contribute to the regulation of the intracellular Ca2+ concentration. These proteins transport Ca2+ ions into the endoplasmic reticulum and to the extracellular medium, respectively. A different localization of the two families of Ca2+-ATPases has been shown in concrete subcellular areas of Purkinje cells and in other neuronal elements from cerebellum. In the light of the actual knowledge of Ca2+-ATPases, this strict distribution suggests the existence of different demands on Ca2+ homeostasis in these cerebellar and cellular subregions.

Self-referential phase reset based on inferior olive oscillator dynamics

The olivo-cerebellar network is a key neuronal circuit that provides high-level motor control in the vertebrate CNS. Functionally, its network dynamics is organized around the oscillatory membrane potential properties of inferior olive (IO) neurons and their electrotonic connectivity. Because IO action potentials are generated at the peaks of the quasisinusoidal membrane potential oscillations, their temporal firing properties are defined by the IO rhythmicity. Excitatory inputs to these neurons can produce oscillatory phase shifts without modifying the amplitude or frequency of the oscillations, allowing well defined time-shift modulation of action potential generation. Moreover, the resulting phase is defined only by the amplitude and duration of the reset stimulus and is independent of the original oscillatory phase when the stimulus was delivered. This reset property, henceforth referred to as selfreferential phase reset, results in the generation of organized clusters of electrically coupled cells that oscillate in phase and are controlled by inhibitory feedback loops through the cerebellar nuclei and the cerebellar cortex. These clusters provide a dynamical representation of arbitrary motor intention patterns that are further mapped to the motor execution system. Being supplied with sensory inputs, the olivo-cerebellar network is capable of rearranging the clusters during the process of movement execution. Accordingly, the phase of the IO oscillators can be rapidly reset to a desired phase independently of the history of phase evolution. The goal of this article is to show how this selfreferential phase reset may be implemented into a motor control system by using a biologically based mathematical model.