Adaptive filter model of the cerebellum

The Marr-Albus model of the cerebellum has been reformulated with linear system analysis. This adaptive linear filter model of the cerebellum performs a filtering action of a phase lead-lag compensator with learning capability, and will give an account for the phenomena which have been termed cerebellar compensation. It is postulated that a Golgi cell may act as a phase lag element; for example, as a leaky integrator with time constant about several seconds. Under this assumption, a mossy fiber-granule cell-Golgi cell input network functions as a phase lead-lag compensator. Output signals from Golgi-granule cell systems, namely, parallel fiber signals, are gathered together through variable synaptic connections to form a Purkinje cell output. From a general theory of adaptive linear filters, learning principles for these modifiable connections are derived. By these learning principles, a Purkinje cell output converges to the desired response to minimize the mean square error of the performance. In a more general sense, a Purkinje cell acquires a filtering function on the basis of multiple pairs of input signals and corresponding desired output signals. The mode of convergence of the output signal is described when the input signal is sinusoidal.     

Climbing Fiber Burst Size and Olivary Sub-threshold Oscillations in a Network Setting

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

Recurrent cerebellar architecture solves the motor-error problem

Current views of cerebellar function have been heavily influenced by the models of Marr and Albus, who suggested that the climbing fibre input to the cerebellum acts as a teaching signal for motor learning. It is commonly assumed that this teaching signal must be motor error (the difference between actual and correct motor command), but this approach requires complex neural structures to estimate unobservable motor error from its observed sensory consequences. We have proposed elsewhere a recurrent decorrelation control architecture in which Marr-Albus models learn without requiring motor error. Here, we prove convergence for this architecture and demonstrate important advantages for the modular control of systems with multiple degrees of freedom. These results are illustrated by modelling adaptive plant compensation for the three-dimensional vestibular ocular reflex. This provides a functional role for recurrent cerebellar connectivity, which may be a generic anatomical feature of projections between regions of cerebral and cerebellar cortex.     

Habituation rules for a theory of the cerebellar cortex

A quantitative model of cerebellar cortical function is described with a complete formalization based on (i) the topology of cerebellar cortical neuronal network, (ii) some particular synaptic properties of cell classes in cerebellum cortex, and (iii) the dynamics of excitation in this network. For (i), a construction of functional classes around one Purkinje cell is given and their existence is discussed. For (ii), as in Marr-Albus model, the modifiability of synapses between parallel fibres and Purkinje cell is assumed. But the formalization permits to consider the consequences of such a property at the level of glomerulus (with granule cells) which is known as a complex transformation system. For (iii) habituation rules are assumed. It is shown that this method leads to some interesting properties in the functioning of cerebellar cortex. Particularly, emitting frequency along a Purkinje cell axon results from a discrimination by the system between transformed input signals and an external noise due to all other contexts, and learning could be considered as the result of a conflict between a set of patterns and the transformed input signals. This model could be a basis for future numerical simulations.     

Roles of phospholipase Cbeta4 in synapse elimination and plasticity in developing and mature cerebellum

The beta isoforms of phospholipase C (PLCbetas) are thought to mediate signals from metabotropic glutamate receptor subtype 1 (mGluR1) that is crucial for the modulation of synaptic transmission and plasticity. Among four PLCbeta isoforms, PLCbeta4 is one of the two major isoforms expressed in cerebellar Purkinje cells. The authors have studied the roles of PLCbeta4 by analyzing PLCbeta4 knockout mice, which are viable, but exhibit locomotor ataxia. Their cerebellar histology, parallel fiber synapse formation, and basic electrophysiology appear normal. However, developmental elimination of multiple climbing fiber innervation is clearly impaired in the rostral portion of the cerebellar vermis, where PLCbeta4 mRNA is predominantly expressed in the wild-type mice. In the adult, long-term depression is deficient at parallel fiber to Purkinje cell synapses in the rostral cerebellum of the PLCbeta4 knockout mice. The impairment of climbing fiber synapse elimination and the loss of long-term depression are similar to those seen in mice defective in mGluR1, Galphaq, or protein kinase C. Thus, the authors' results strongly suggest that PLCbeta4 is part of a signaling pathway, including the mGluR1, Galphaq and protein kinase C, which is crucial for both climbing fiber synapse elimination in the developing cerebellum and long-term depression induction in the mature cerebellum.     

A real-time spiking cerebellum model for learning robot control

We describe a neural network model of the cerebellum based on integrate-and-fire spiking neurons with conductance-based synapses. The neuron characteristics are derived from our earlier detailed models of the different cerebellar neurons. We tested the cerebellum model in a real-time control application with a robotic platform. Delays were introduced in the different sensorimotor pathways according to the biological system. The main plasticity in the cerebellar model is a spike-timing dependent plasticity (STDP) at the parallel fiber to Purkinje cell connections. This STDP is driven by the inferior olive (IO) activity, which encodes an error signal using a novel probabilistic low frequency model. We demonstrate the cerebellar model in a robot control system using a target-reaching task. We test whether the system learns to reach different target positions in a non-destructive way, therefore abstracting a general dynamics model. To test the system's ability to self-adapt to different dynamical situations, we present results obtained after changing the dynamics of the robotic platform significantly (its friction and load). The experimental results show that the cerebellar-based system is able to adapt dynamically to different contexts.     

A model of activity-dependent formation of cerebellar microzones

According to modern views of the cerebellum in motor control, each cerebellar functional unit, or microzone, learns how to execute predictive and coordinative control, based on long-term depression of the granule cell-Purkinje cell synapses. In the present paper, in light of recent experimental and theoretical studies on synaptic elimination and cerebellar motor learning, a model of the formation of cerebellar microzones by climbing fiber synaptic elimination is proposed. It is shown that competition for an activity-dependent supply of neurotrophic factor can reproduce the spatio-temporal characteristics of climbing fiber synaptic elimination. It is further shown that when this elimination is accurate, motor coordination can be acquired in an arm reaching task. In view of the results of the present study, several predictions are proposed. Received: 19 January 1998 / Accepted in revised form: 22 April 1998     

A computational model of four regions of the cerebellum based on feedback-error learning

We propose a computationally coherent model of cerebellar motor learning based on the feedback-error-learning scheme. We assume that climbing fiber responses represent motor-command errors generated by some of the premotor networks such as the feedback controllers at the spinal-, brain stem- and cerebral levels. Thus, in our model, climbing fiber responses are considered to convey motor errors in the motor-command coordinates rather than in the sensory coordinates. Based on the long-term depression in Purkinje cells each corticonuclear microcomplex in different regions of the cerebellum learns to execute predictive and coordinative control of different types of movements. Ultimately, it acquires an inverse model of a specific controlled object and complements crude control by the premotor networks. This general model is developed in detail as a specific neural circuit model for the lateral hemisphere. A new experiment is suggested to elucidate the coordinate frame in which climbing fiber responses are represented.     

Simulation of adaptive modification of the vestibulo-ocular reflex with an adaptive filter model of the cerebellum

An adaptive linear filter model of the cerebellum (Fujita, 1982), which functions as a phase lead or lag compensator with learning capability, is applied to a problem of the cerebellar control of the vestibuloocular reflex (VOR). Under the assumption that the cerebellar flocculus accounts for adaptive modification of dynamic characteristics of the VOR, the cerebellar model was incorporated into a linear control model of the oculomotor system. The results of a simulation study are in good agreement with experimental data on eye movement.     

Delayed reverberation through time windows as a key to cerebellar function

We present a functional model of the cerebellum comprising cerebellar cortex, inferior olive, deep cerebellar nuclei, and brain stem nuclei. The discerning feature of the model being time coding, we consistently describe the system in terms of postsynaptic potentials, synchronous action potentials, and propagation delays. We show by means of detailed single-neuron modeling that (i) Golgi cells can fulfill a gating task in that they form short and well-defined time windows within which granule cells can reach firing threshold, thus organizing neuronal activity in discrete `time slices', and that (ii) rebound firing in cerebellar nuclei cells is a robust mechanism leading to a delayed reverberation of Purkinje cell activity through cerebellar-reticular projections back to the cerebellar cortex. Computer simulations of the whole cerebellar network consisting of several thousand neurons reveal that reverberation in conjunction with long-term plasticity at the parallel fiber-Purkinje cell synapses enables the system to learn, store, and recall spatio-temporal patterns of neuronal activity. Climbing fiber spikes act both as a synchronization and as a teacher signal, not as an error signal. They are due to intrinsic oscillatory properties of inferior olivary neurons and to delayed reverberation within the network. In addition to clear experimental predictions the present theory sheds new light on a number of experimental observation such as the synchronicity of climbing fiber spikes and provides a novel explanation of how the cerebellum solves timing tasks on a time scale of several hundreds of milliseconds. Received: 23 July 1999 / Accepted in revised form: 31 August 1999     

Evaluation of affine fiber kinematics in human supraspinatus tendon using quantitative projection plot analysis

Structural constitutive modeling approaches are often based on the assumption of affine fiber kinematics, even though this assumption has rarely been evaluated experimentally. We are interested in applying mathematical models to understand the mechanisms responsible for the inhomogeneous, anisotropic, and non-linear properties of human supraspinatus tendon (SST); however, the relationship between macroscopic and fiber-level deformation in this tendon remains unknown and current methods for making this assessment are inadequate. Therefore, the purpose of this study was to develop an improved method for quantitatively assessing agreement between two distributions and to examine the affine assumption in SST by comparing experimental fiber alignment to affine model predictions using this analysis approach. Measured fiber angle values of SST samples in uniaxial tensile tests were compared with predictions of affine fiber deformation using modified projection plots, which provide a method for qualitative and quantitative comparisons of two distributions. The projection plot metrics of offset and range, which were developed in this study, are of particular benefit by providing a quantitative representation of agreement that can be subjected to statistical comparisons. For SST, offset and range values varied by tendon location and test orientation, with more affine deformation evidenced for tendon regions of higher alignment. Results suggest that non-affine fiber behavior is dependent on specific tissue, orientation of the applied stretch relative to the fiber organization, and length scale of the observation. In addition, this study has established a method for evaluating the affine assumption in other tissues.     

Tonic and spillover inhibition of granule cells control information flow through cerebellar cortex

We show that information flow through the adult cerebellar cortex, from the mossy fiber input to the Purkinje cell output, is controlled by furosemide-sensitive, diazepam- and neurosteroid-insensitive GABA(A) receptors on granule cells, which are activated both tonically and by GABA spillover from synaptic release sites. Tonic activation of these receptors contributes a 3-fold larger mean inhibitory conductance than GABA released synaptically by high-frequency stimulation. Tonic and spillover inhibition reduce the fraction of granule cells activated by mossy fiber input, generating an increase of coding sparseness, which is predicted to improve the information storage capacity of the cerebellum.     

No parallel fiber volleys in the cerebellar cortex: evidence from cross-correlation analysis between Purkinje cells in a computer model and in recordings from anesthetized rats

Purkinje cells aligned on the medio-lateral axis share a large proportion of their 175,000 parallel fiber inputs. This arrangement has led to the hypothesis that movement timing is coded in the cerebellum by beams of synchronously active parallel fibers. In computer simulations I show that such synchronous activation leads to a narrow spike cross-correlation between pairs of Purkinje cells. This peak was completely absent when shared parallel fiber input was active in an asynchronous mode. To determine the presence of synchronous parallel fiber beams {in vivo} I recorded from pairs of Purkinje cells in crus IIa of anesthetized rats. I found a complete absence of precise spike synchronization, even when both cells were strongly modulated in their spike rate by trains of air-puff stimuli to the face. These results indicate that Purkinje cell spiking is not controlled by volleys of synchronous parallel fiber inputs in the conditions examined. Instead, the data support a model by which granule cells primarily control Purkinje cell spiking via dynamic population rate changes.     

剌激中缝背核压抑大鼠小脑浦肯野细胞对苔状...

In anaesthetized and paralyzed rats, the effect of dorsal raphe (DR) conditioning stimulation on cerebellar Purkinje cell (PC) responses to mossy fiber and climbing fiber inputs were examined. The main results are as follows: (1) Stimulation of cerebral sensorimotor cortex elicits widespread activation of mossy and climbing fiber inputs to PCs in contralateral VI and VII lobules of the cerebellum and generates two kinds of evoked responses, i.e. the simple spike (SS) and the complex spike (CS) responses with respectively a latency 8-25 and 12-30 ms. (2) These PC responses could be markedly suppressed by stimulation of DR at intensities which by themselves were subthreshold for directly affecting PC's spontaneous SS and CS activities. (3) This DR-induced depressive effects on evoked PC's SS and CS excitations could be attenuated or blocked by systemic administration of 5-HT receptor blocker methysergide. These results demonstrate that serotonergic fiber input from DR can suppress the efficacy of mossy and climbing fiber synaptic action on PC, or decrease the responsiveness of PC itself to afferent synaptic action. The findings of this study also suggest that the raphe-cerebellar serotonergic fiber afferent system may be involved in some of the important neuronal processing in the cerebellum.     

Determinants of slowed diffusion in the complex space of the cerebellar glomerulus

Using analytical solutions for two- and three-dimensional (2D and 3D, respectively) and fractal 2D/3D geometry with an absorbing boundary, we modeled glutamate diffusion in a glomerulus, the structure situated around the mossy fiber (MF) terminal in the cerebellum and surrounded by a glial sheath. The model with fractal geometry gave the best fit of experimental AMPA and NMDA receptor-mediated evoked postsynaptic currents (EPSC) at the MF-granule cell synapse. A comparison of the numerically integrated glutamate concentration in an idealized model of glomerulus morphology with analytical solutions reveals that the peculiarities of glomerulus geometry can explain the better fit by the solution with fractal dimension only of experimental EPSC arising from local release, but not from spillover of glutamate. An asynchronous vesicle release only slightly influences the shape of the spillover waveform. Anomalously slow diffusion of glutamate can be an explanation of the observed discrepancy between experimental results and simulations with the 3D model. A good fit of spillover-induced EPSC obtained in the simulations that use a solution for fractional Brownian motion and a match of experimental estimations and theoretical parameters of the diffusion model confirms this assumption.Neirofiziologiya/Neurophysiology, Vol. 36, Nos. 5/6, pp. 418–431, September–December, 2004.This revised version was published online in April 2005 with a corrected cover date and copyright year.     

Host records and tissue locations for Diplostomum mordax (metacercariae) inhabiting the cranial cavity of fishes from Lake Titicaca, Peru.

Metacercariae of Diplostomum mordax were found in the cranial cavity of Orestias agasii, Orestias olivaceous, Orestias luteus, and Basilichthys bonariensis, fishes from Lake Titicaca, Peru. Metacercariae were not found in Oncorhynchus mykiss introduced into the lake during 1939 and 1940. Compression of neural tissue within and on the surface of the brain was observed in all infected fishes. Metacercariae migrating into the cerebrum and cerebellum of the piscine host caused hemorrhaging, cell necrosis, inflammation, fiber formation, and nerve fiber disruption. The presence of D. mordax in B. bonariensis and the 3 species of Orestias constitute new host records. Infections in the cerebrum and cerebellum add new information on specific parasite location.     

The zebrafish cerebellar rhombic lip is spatially patterned in producing granule cell populations of different functional compartments

The upper rhombic lip, a prominent germinal zone of the cerebellum, was recently demonstrated to generate different neuronal cell types over time from spatial subdomains. We have characterized the differentiation of the upper rhombic lip derived granule cell population in stable GFP-transgenic zebrafish in the context of zebrafish cerebellar morphogenesis. Time-lapse analysis followed by individual granule cell tracing demonstrates that the zebrafish upper rhombic lip is spatially patterned along its mediolateral axis producing different granule cell populations simultaneously. Time-lapse recordings of parallel fiber projections and retrograde labeling reveal that spatial patterning within the rhombic lip corresponds to granule cells of two different functional compartments of the mature cerebellum: the eminentia granularis and the corpus cerebelli. These cerebellar compartments in teleosts correspond to the mammalian vestibulocerebellar and non-vestibulocerebellar system serving balance and locomotion control, respectively. Given the high conservation of cerebellar development in vertebrates, spatial partitioning of the mammalian granule cell population and their corresponding earlier-produced deep nuclei by patterning within the rhombic lip may also delineate distinct functional compartments of the cerebellum. Thus, our findings offer an explanation for how specific functional cerebellar circuitries are laid down by spatio-temporal patterning of cerebellar germinal zones during early brain development.     

SPECIALIZED MEMBRANE JUNCTIONS BETWEEN NEURONS IN THE VERTEBRATE CEREBELLAR CORTEX

"Gap" junctions, the morphological correlate for low-resistance junctions, are demonstrated between some mossy fiber terminals and granule cell dendrites in some lower vertebrate cerebella (gymnotid and frog). Most of the gap junctions (GJs) seen in the gymnotid-fish cerebellum exhibit an asymmetrical configuration, the electron-opaque cytoplasmic material underlying the junction being more extensive in the dendritic than in the axonal side. In the frog cerebellum, the GJs have a symmetrical distribution of such electron-opaque material. In both species the GJs are encountered at the same synaptic interface as the conventional synaptic zone (CSZ), constituting "mixed synapses" in a morphological sense. The axonal surface covered by CSZs is larger than that covered by GJs. In mammalian cerebellum, GJs are observed only in the molecular layer, between perikarya, dendrites, or perikarya and dendrites of the inhibitory interneurons. These GJs are intermixed with attachment plates and intermediary junctions interpreted as simply adhesive. In the mammalian cerebellum, a new type of junction which resembles the septate junctions (SJs) of invertebrate epithelia is observed between axonal branches forming the tip of the brush of basket fibers around the initial segment of the Purkinje cell axon. It is suggested that such junctions may be modified forms of septate junctions. The physiological implications of the possible existence of high-resistance cross-bridges between basket cell terminals, which may compartmentalize the extracellular space and thus regulate extracellular current flow, must be considered.     

A neural network model of the cerebellar cortex performing dynamic associations

The present paper proposes a model which applies formal neural network modeling techniques to construct a theoretical representation of the cerebellar cortex and its performances in motor control. A schema that makes explicit use of propagation delays of neural signals, is introduced to describe the ability to store temporal sequences of patterns in the Golgi-granule cell system. A perceptron association is then performed on these sequences of patterns by the Purkinje cell layer. The model conforms with important biological constraints, such as the known excitatory or inhibitory nature of the various synapses. Also, as suggested by experimental evidence, the synaptic plasticity underlying the learning ability of the model, is confined to the parallel fiber — Purkinje cell synapses, and takes place under the control of the climbing fibers. The result is a neural network model, constructed according to the anatomy of the cerebellar cortex, and capable of learning and retrieval of temporal sequences of patterns. It provides a framework to represent and interpret properties of learning and control of movements by the cerebellum, and to assess the capacity of formal neural network techniques for modeling of real neural systems.