Adaptive-filter models of the cerebellum: computational analysis

Interactions between circuit architecture and plasticity in a closed-loop cerebellar system

Determining the sites and directions of plasticity underlying changes in neural activity and behavior is critical for understanding mechanisms of learning. Identifying such plasticity from neural recording data can be challenging due to feedback pathways that impede reasoning about cause and effect. We studied interactions between feedback, neural activity, and plasticity in the context of a closed-loop motor learning task for which there is disagreement about the loci and directions of plasticity: vestibulo-ocular reflex learning. We constructed a set of circuit models that differed in the strength of their recurrent feedback, from no feedback to very strong feedback. Despite these differences, each model successfully fit a large set of neural and behavioral data. However, the patterns of plasticity predicted by the models fundamentally differed, with the direction of plasticity at a key site changing from depression to potentiation as feedback strength increased. Guided by our analysis, we suggest how such models can be experimentally disambiguated. Our results address a long-standing debate regarding cerebellum-dependent motor learning, suggesting a reconciliation in which learning-related changes in the strength of synaptic inputs to Purkinje cells are compatible with seemingly oppositely directed changes in Purkinje cell spiking activity. More broadly, these results demonstrate how changes in neural activity over learning can appear to contradict the sign of the underlying plasticity when either internal feedback or feedback through the environment is present.

An emergent temporal basis set robustly supports cerebellar time-series learning

The cerebellum is considered a "learning machine" essential for time interval estimation underlying motor coordination and other behaviors. Theoretical work has proposed that the cerebellum's input recipient structure, the granule cell layer (GCL), performs pattern separation of inputs that facilitates learning in Purkinje cells (P-cells). However, the relationship between input reformatting and learning has remained debated, with roles emphasized for pattern separation features from sparsification to decorrelation. We took a novel approach by training a minimalist model of the cerebellar cortex to learn complex time-series data from time-varying inputs, typical during movements. The model robustly produced temporal basis sets from these inputs, and the resultant GCL output supported better learning of temporally complex target functions than mossy fibers alone. Learning was optimized at intermediate threshold levels, supporting relatively dense granule cell activity, yet the key statistical features in GCL population activity that drove learning differed from those seen previously for classification tasks. These findings advance testable hypotheses for mechanisms of temporal basis set formation and predict that moderately dense population activity optimizes learning.NEW & NOTEWORTHY During movement, mossy fiber inputs to the cerebellum relay time-varying information with strong intrinsic relationships to ongoing movement. Are such mossy fibers signals sufficient to support Purkinje signals and learning? In a model, we show how the GCL greatly improves Purkinje learning of complex, temporally dynamic signals relative to mossy fibers alone. Learning-optimized GCL population activity was moderately dense, which retained intrinsic input variance while also performing pattern separation.

Dual STDP processes at Purkinje cells contribute to distinct improvements in accuracy and speed of saccadic eye movements

Saccadic eye-movements play a crucial role in visuo-motor control by allowing rapid foveation onto new targets. However, the neural processes governing saccades adaptation are not fully understood. Saccades, due to the short-time of execution (20-100 ms) and the absence of sensory information for online feedback control, must be controlled in a ballistic manner. Incomplete measurements of the movement trajectory, such as the visual endpoint error, are supposedly used to form internal predictions about the movement kinematics resulting in predictive control. In order to characterize the synaptic and neural circuit mechanisms underlying predictive saccadic control, we have reconstructed the saccadic system in a digital controller embedding a spiking neural network of the cerebellum with spike timing-dependent plasticity (STDP) rules driving parallel fiber-Purkinje cell long-term potentiation and depression (LTP and LTD). This model implements a control policy based on a dual plasticity mechanism, resulting in the identification of the roles of LTP and LTD in regulating the overall quality of saccade kinematics: it turns out that LTD increases the accuracy by decreasing visual error and LTP increases the peak speed. The control policy also required cerebellar PCs to be divided into two subpopulations, characterized by burst or pause responses. To our knowledge, this is the first model that explains in mechanistic terms the visual error and peak speed regulation of ballistic eye movements in forward mode exploiting spike-timing to regulate firing in different populations of the neuronal network. This elementary model of saccades could be extended and applied to other more complex cases in which single jerks are concatenated to compose articulated and coordinated movements.

A differential Hebbian framework for biologically-plausible motor control

In this paper we explore a neural control architecture that is both biologically plausible, and capable of fully autonomous learning. It consists of feedback controllers that learn to achieve a desired state by selecting the errors that should drive them. This selection happens through a family of differential Hebbian learning rules that, through interaction with the environment, can learn to control systems where the error responds monotonically to the control signal. We next show that in a more general case, neural reinforcement learning can be coupled with a feedback controller to reduce errors that arise non-monotonically from the control signal. The use of feedback control can reduce the complexity of the reinforcement learning problem, because only a desired value must be learned, with the controller handling the details of how it is reached. This makes the function to be learned simpler, potentially allowing learning of more complex actions. We use simple examples to illustrate our approach, and discuss how it could be extended to hierarchical architectures.

Interactions Between Purkinje Cells and Granule Cells Coordinate the Development of Functional Cerebellar Circuits

Cerebellar development has a remarkably protracted morphogenetic timeline that is coordinated by multiple cell types. Here, we discuss the intriguing cellular consequences of interactions between inhibitory Purkinje cells and excitatory granule cells during embryonic and postnatal development. Purkinje cells are central to all cerebellar circuits, they are the first cerebellar cortical neurons to be born, and based on their cellular and molecular signaling, they are considered the master regulators of cerebellar development. Although rudimentary Purkinje cell circuits are already present at birth, their connectivity is morphologically and functionally distinct from their mature counterparts. The establishment of the Purkinje cell circuit with its mature firing properties has a temporal dependence on cues provided by granule cells. Granule cells are the latest born, yet most populous, neuronal type in the cerebellar cortex. They provide a combination of mechanical, molecular and activity-based cues that shape the maturation of Purkinje cell structure, connectivity and function. We propose that the wiring of Purkinje cells for function falls into two developmental phases: an initial phase that is guided by intrinsic mechanisms and a later phase that is guided by dynamically-acting cues, some of which are provided by granule cells. In this review, we highlight the mechanisms that granule cells use to help establish the unique properties of Purkinje cell firing.

Cellular-resolution mapping uncovers spatial adaptive filtering at the rat cerebellum input stage

Long-term synaptic plasticity is thought to provide the substrate for adaptive computation in brain circuits but very little is known about its spatiotemporal organization. Here, we combined multi-spot two-photon laser microscopy in rat cerebellar slices with realistic modeling to map the distribution of plasticity in multi-neuronal units of the cerebellar granular layer. The units, composed by ~300 neurons activated by ~50 mossy fiber glomeruli, showed long-term potentiation concentrated in the core and long-term depression in the periphery. This plasticity was effectively accounted for by an NMDA receptor and calcium-dependent induction rule and was regulated by the inhibitory Golgi cell loops. Long-term synaptic plasticity created effective spatial filters tuning the time-delay and gain of spike retransmission at the cerebellum input stage and provided a plausible basis for the spatiotemporal recoding of input spike patterns anticipated by the motor learning theory.

Casali, Tognolina et al. use two-photon laser microscopy to spatially map long-term synaptic plasticity in rat cerebellar granular cells following stimulation of mossy fibers. Their data allow them to apply realistic modeling to test hypotheses about the synaptic spiking dynamics and reveal the importance of synaptic inhibition to defining these microcircuits.

Draculab: A Python Simulator for Firing Rate Neural Networks With Delayed Adaptive Connections

Draculab is a neural simulator with a particular use scenario: firing rate units with delayed connections, using custom-made unit and synapse models, possibly controlling simulated physical systems. Draculab also has a particular design philosophy. It aims to blur the line between users and developers. Three factors help to achieve this: a simple design using Python's data structures, extensive use of standard libraries, and profusely commented source code. This paper is an introduction to Draculab's architecture and philosophy. After presenting some example networks it explains basic algorithms and data structures that constitute the essence of this approach. The relation with other simulators is discussed, as well as the reasons why connection delays and interaction with simulated physical systems are emphasized.

Integrating Brain and Biomechanical Models-A New Paradigm for Understanding Neuro-muscular Control

To date, realistic models of how the central nervous system governs behavior have been restricted in scope to the brain, brainstem or spinal column, as if these existed as disembodied organs. Further, the model is often exercised in relation to an in vivo physiological experiment with input comprising an impulse, a periodic signal or constant activation, and output as a pattern of neural activity in one or more neural populations. Any link to behavior is inferred only indirectly via these activity patterns. We argue that to discover the principles of operation of neural systems, it is necessary to express their behavior in terms of physical movements of a realistic motor system, and to supply inputs that mimic sensory experience. To do this with confidence, we must connect our brain models to neuro-muscular models and provide relevant visual and proprioceptive feedback signals, thereby closing the loop of the simulation. This paper describes an effort to develop just such an integrated brain and biomechanical system using a number of pre-existing models. It describes a model of the saccadic oculomotor system incorporating a neuromuscular model of the eye and its six extraocular muscles. The position of the eye determines how illumination of a retinotopic input population projects information about the location of a saccade target into the system. A pre-existing saccadic burst generator model was incorporated into the system, which generated motoneuron activity patterns suitable for driving the biomechanical eye. The model was demonstrated to make accurate saccades to a target luminance under a set of environmental constraints. Challenges encountered in the development of this model showed the importance of this integrated modeling approach. Thus, we exposed shortcomings in individual model components which were only apparent when these were supplied with the more plausible inputs available in a closed loop design. Consequently we were able to suggest missing functionality which the system would require to reproduce more realistic behavior. The construction of such closed-loop animal models constitutes a new paradigm of computational neurobehavior and promises a more thoroughgoing approach to our understanding of the brain's function as a controller for movement and behavior.

Computational Theory Underlying Acute Vestibulo-ocular Reflex Motor Learning with Cerebellar Long-Term Depression and Long-Term Potentiation

The vestibulo-ocular reflex (VOR) can be viewed as an adaptive control system that maintains compensatory eye movements during head motion. As the cerebellar flocculus is intimately involved in this adaptive motor control of the VOR, the VOR has been a popular model system for investigating cerebellar motor learning. Long-term depression (LTD) and long-term potentiation (LTP) at the parallel fiber-Purkinje cell synapses are considered to play major roles in cerebellar motor learning. A recent study using mutant mice demonstrated cerebellar motor learning with hampered LTD; the study concluded that the parallel fiber-Purkinje cell LTD is not essential. More recently, multiple forms of plasticity have been found in the cerebellum, and they are believed to contribute to cerebellar motor learning. However, it is still unclear how synaptic plasticity modifies the signal processing that underlies motor learning in the flocculus. A computational simulation suggested that the plasticity present in mossy fiber-granule cell synapses improves VOR-related sensory-motor information transferred into granule cells, whereas the plasticity in the molecular layer stores this information as a memory under guidance from climbing fiber teaching signals. Thus, motor learning and memory are thought to be induced mainly by LTD and LTP at parallel fiber-Purkinje cell synapses and by rebound potentiation at molecular interneuron-Purkinje cell synapses among the multiple forms of plasticity in the cerebellum. In this study, we focused on the LTD and LTP at parallel fiber-Purkinje cell synapses. Based on our simulation, we propose that acute VOR motor learning accomplishes by simultaneous enhancement of eye movement signals via LTP and suppression of vestibular signals via LTD to increase VOR gain (gain-up learning). To decrease VOR gain (gain-down learning), these two signals are modified in the opposite directions; namely, LTD suppresses eye movement signals, whereas LTP enhances vestibular signals.

Population-scale organization of cerebellar granule neuron signaling during a visuomotor behavior

Granule cells at the input layer of the cerebellum comprise over half the neurons in the human brain and are thought to be critical for learning. However, little is known about granule neuron signaling at the population scale during behavior. We used calcium imaging in awake zebrafish during optokinetic behavior to record transgenically identified granule neurons throughout a cerebellar population. A significant fraction of the population was responsive at any given time. In contrast to core precerebellar populations, granule neuron responses were relatively heterogeneous, with variation in the degree of rectification and the balance of positive versus negative changes in activity. Functional correlations were strongest for nearby cells, with weak spatial gradients in the degree of rectification and the average sign of response. These data open a new window upon cerebellar function and suggest granule layer signals represent elementary building blocks under-represented in core sensorimotor pathways, thereby enabling the construction of novel patterns of activity for learning.

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

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

Redefining the cerebellar cortex as an assembly of non-uniform Purkinje cell microcircuits

The adult mammalian cerebellar cortex is generally assumed to have a uniform cytoarchitecture. Differences in cerebellar function are thought to arise primarily through distinct patterns of input and output connectivity rather than as a result of variations in cortical microcircuitry. However, evidence from anatomical, physiological and genetic studies is increasingly challenging this orthodoxy, and there are now various lines of evidence indicating that the cerebellar cortex is not uniform. Here, we develop the hypothesis that regional differences in properties of cerebellar cortical microcircuits lead to important differences in information processing.

Visual anticipation biases conscious decision making but not bottom-up visual processing

Prediction plays a key role in control of attention but it is not clear which aspects of prediction are most prominent in conscious experience. An evolving view on the brain is that it can be seen as a prediction machine that optimizes its ability to predict states of the world and the self through the top-down propagation of predictions and the bottom-up presentation of prediction errors. There are competing views though on whether prediction or prediction errors dominate the formation of conscious experience. Yet, the dynamic effects of prediction on perception, decision making and consciousness have been difficult to assess and to model. We propose a novel mathematical framework and a psychophysical paradigm that allows us to assess both the hierarchical structuring of perceptual consciousness, its content and the impact of predictions and/or errors on conscious experience, attention and decision-making. Using a displacement detection task combined with reverse correlation, we reveal signatures of the usage of prediction at three different levels of perceptual processing: bottom-up fast saccades, top-down driven slow saccades and consciousnes decisions. Our results suggest that the brain employs multiple parallel mechanism at different levels of perceptual processing in order to shape effective sensory consciousness within a predicted perceptual scene. We further observe that bottom-up sensory and top-down predictive processes can be dissociated through cognitive load. We propose a probabilistic data association model from dynamical systems theory to model the predictive multi-scale bias in perceptual processing that we observe and its role in the formation of conscious experience. We propose that these results support the hypothesis that consciousness provides a time-delayed description of a task that is used to prospectively optimize real time control structures, rather than being engaged in the real-time control of behavior itself.

Computational modeling predicts the ionic mechanism of late-onset responses in unipolar brush cells

Unipolar Brush Cells (UBCs) have been suggested to play a critical role in cerebellar functioning, yet the corresponding cellular mechanisms remain poorly understood. UBCs have recently been reported to generate, in addition to early-onset glutamate receptor-dependent synaptic responses, a late-onset response (LOR) composed of a slow depolarizing ramp followed by a spike burst (Locatelli et al., 2013). The LOR activates as a consequence of synaptic activity and involves an intracellular cascade modulating H- and TRP-current gating. In order to assess the LOR mechanisms, we have developed a UBC multi-compartmental model (including soma, dendrite, initial segment, and axon) incorporating biologically realistic representations of ionic currents and a cytoplasmic coupling mechanism regulating TRP and H channel gating. The model finely reproduced UBC responses to current injection, including a burst triggered by a low-threshold spike (LTS) sustained by CaLVA currents, a persistent discharge sustained by CaHVA currents, and a rebound burst following hyperpolarization sustained by H- and CaLVA-currents. Moreover, the model predicted that H- and TRP-current regulation was necessary and sufficient to generate the LOR and its dependence on the intensity and duration of mossy fiber activity. Therefore, the model showed that, using a basic set of ionic channels, UBCs generate a rich repertoire of bursts, which could effectively implement tunable delay-lines in the local microcircuit.

Consensus paper: roles of the cerebellum in motor control--the diversity of ideas on cerebellar involvement in movement

Considerable progress has been made in developing models of cerebellar function in sensorimotor control, as well as in identifying key problems that are the focus of current investigation. In this consensus paper, we discuss the literature on the role of the cerebellar circuitry in motor control, bringing together a range of different viewpoints. The following topics are covered: oculomotor control, classical conditioning (evidence in animals and in humans), cerebellar control of motor speech, control of grip forces, control of voluntary limb movements, timing, sensorimotor synchronization, control of corticomotor excitability, control of movement-related sensory data acquisition, cerebro-cerebellar interaction in visuokinesthetic perception of hand movement, functional neuroimaging studies, and magnetoencephalographic mapping of cortico-cerebellar dynamics. While the field has yet to reach a consensus on the precise role played by the cerebellum in movement control, the literature has witnessed the emergence of broad proposals that address cerebellar function at multiple levels of analysis. This paper highlights the diversity of current opinion, providing a framework for debate and discussion on the role of this quintessential vertebrate structure.

Neuroecology of cartilaginous fishes: the functional implications of brain scaling

It is a widely accepted view that neural development can reflect morphological adaptations and sensory specializations. The aim of this review is to give a broad overview of the current status of brain data available for cartilaginous fishes and examine how perspectives on allometric scaling of brain size across this group of fishes has changed within the last 50 years with the addition of new data and more rigorous statistical analyses. The current knowledge of neuroanatomy in cartilaginous fishes is reviewed and data on brain size (encephalization, n = 151) and interspecific variation in brain organization (n = 84) has been explored to ascertain scaling relationships across this clade. It is determined whether similar patterns of brain organization, termed cerebrotypes, exist in species that share certain lifestyle characteristics. Clear patterns of brain organization exist across cartilaginous fishes, irrespective of phylogenetic grouping and, although this study was not a functional analysis, it provides further evidence that chondrichthyan brain structures might have developed in conjunction with specific behaviours or enhanced cognitive capabilities. Larger brains, with well-developed telencephala and large, highly foliated cerebella are reported in species that occupy complex reef or oceanic habitats, potentially identifying a reef-associated cerebrotype. In contrast, benthic and benthopelagic demersal species comprise the group with the smallest brains, with a relatively reduced telencephalon and a smooth cerebellar corpus. There is also evidence herein of a bathyal cerebrotype; deep-sea benthopelagic sharks possess relatively small brains and show a clear relative hypertrophy of the medulla oblongata. Despite the patterns observed and documented, significant gaps in the literature have been highlighted. Brain mass data are only currently available on c. 16% of all chondrichthyan species, and only 8% of species have data available on their brain organization, with far less on subsections of major brain areas that receive distinct sensory input. The interspecific variability in brain organization further stresses the importance of performing functional studies on a greater range of species. Only an expansive data set, comprised of species that span a variety of habitats and taxonomic groups, with widely disparate behavioural repertoires, combined with further functional analyses, will help shed light on the extent to which chondrichthyan brains have evolved as a consequence of behaviour, habitat and lifestyle in addition to phylogeny.

Crossing zones in the vestibulocerebellum: a commentary

The contention of this commentary, focused on the vestibulocerebellum (particularly the flocculus), is that the great importance for our understanding of cerebellar organization in terms of climbing fiber zones, begun years ago by Voogd [1969, 2011] and Oscarsson [1969], needs to be matched by coming more to grips with the other fundamental geometrical organization of the cerebellum, the parallel fibers. The central issue is the selection of those parallel fiber signals to be transformed into Purkinje cell activity in the different zones. At present, in comparison to our knowledge of vestibulocerebellar climbing fiber inputs, the deficiencies in our knowledge of the zonal anatomy and physiology of vestibulocerebellar mossy fibers and granule cells are glaring. The recent emphasis on molecularly oriented investigations points to the need to reinvigorate pursuit of unanswered questions about cerebellar anatomy, the handmaiden of physiology.

Time course of classically conditioned Purkinje cell response is determined by initial part of conditioned stimulus

Classical conditioning of a motor response such as eyeblink is associated with the development of a pause in cerebellar Purkinje cell firing that is an important driver of the overt response. This conditioned Purkinje cell response is adaptively timed and has a specific temporal profile that probably explains the time course of the overt behavior. It is generally assumed that the temporal properties of the conditioned Purkinje cell response are determined by the temporal pattern of the parallel fiber impulses generated by the conditioned stimulus at the time of the conditioned response. We show here in the decerebrate ferret preparation that a very brief conditioned stimulus, consisting of only one or two impulses in the mossy fibers, can be sufficient to elicit a full conditioned Purkinje cell response with normal time course. The finding suggests that parallel fiber input to the Purkinje cell influences the firing rate several hundred milliseconds later. It poses a serious challenge to the standard view of the role of parallel fiber impulses in response timing.

Evaluating the adaptive-filter model of the cerebellum

The adaptive-filter model of the cerebellar microcircuit is in widespread use, combining as it does an explanation of key microcircuit features with well-specified computational power. Here we consider two methods for its evaluation. One is to test its predictions concerning relations between cerebellar inputs and outputs. Where the relevant experimental data are available, e.g. for the floccular role in image stabilization, the predictions appear to be upheld. However, for the majority of cerebellar microzones these data have yet to be obtained. The second method is to test model predictions about details of the microcircuit. We focus on features apparently incompatible with the model, in particular non-linear patterns in Purkinje cell simple-spike firing. Analysis of these patterns suggests the following three conclusions. (i) It is important to establish whether they can be observed during task-related behaviour. (ii) Highly non-linear models based on these patterns are unlikely to be universal, because they would be incompatible with the (approximately) linear nature of floccular function. (iii) The control tasks for which these models are computationally suited need to be identified. At present, therefore, the adaptive filter remains a candidate model of at least some cerebellar microzones, and its evaluation suggests promising lines for future enquiry.

Are mushroom bodies cerebellum-like structures?

The mushroom bodies are distinctive neuropils in the protocerebral brain segments of many protostomes. A defining feature of mushroom bodies is their intrinsic neurons, masses of cytoplasm-poor globuli cells that form a system of lobes with their densely-packed, parallel-projecting axon-like processes. In insects, the role of the mushroom bodies in olfactory processing and associative learning and memory has been studied in depth, but several lines of evidence suggest that the function of these higher brain centers cannot be restricted to these roles. The present account considers whether insight into an underlying function of mushroom bodies may be provided by cerebellum-like structures in vertebrates, which are similarly defined by the presence of masses of tiny granule cells that emit thin parallel fibers forming a dense molecular layer. In vertebrates, the shared neuroarchitecture of cerebellum-like structures has been suggested to underlie a common functional role as adaptive filters for the removal of predictable sensory elements, such as those arising from reafference, from the total sensory input. Cerebellum-like structures include the vertebrate cerebellum, the electrosensory lateral line lobe, dorsal and medial octavolateral nuclei of fish, and the dorsal cochlear nucleus of mammals. The many architectural and physiological features that the insect mushroom bodies share with cerebellum-like structures suggest that it might be fruitful to consider mushroom body function in light of a possible role as adaptive sensory filters. The present account thus presents a detailed comparison of the insect mushroom bodies with vertebrate cerebellum-like structures.

Cerebellarlike corrective model inference engine for manipulation tasks

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

Intermittent control: a computational theory of human control

The paradigm of continuous control using internal models has advanced understanding of human motor control. However, this paradigm ignores some aspects of human control, including intermittent feedback, serial ballistic control, triggered responses and refractory periods. It is shown that event-driven intermittent control provides a framework to explain the behaviour of the human operator under a wider range of conditions than continuous control. Continuous control is included as a special case, but sampling, system matched hold, an intermittent predictor and an event trigger allow serial open-loop trajectories using intermittent feedback. The implementation here may be described as "continuous observation, intermittent action". Beyond explaining unimodal regulation distributions in common with continuous control, these features naturally explain refractoriness and bimodal stabilisation distributions observed in double stimulus tracking experiments and quiet standing, respectively. Moreover, given that human control systems contain significant time delays, a biological-cybernetic rationale favours intermittent over continuous control: intermittent predictive control is computationally less demanding than continuous predictive control. A standard continuous-time predictive control model of the human operator is used as the underlying design method for an event-driven intermittent controller. It is shown that when event thresholds are small and sampling is regular, the intermittent controller can masquerade as the underlying continuous-time controller and thus, under these conditions, the continuous-time and intermittent controller cannot be distinguished. This explains why the intermittent control hypothesis is consistent with the continuous control hypothesis for certain experimental conditions.

Sensory prediction or motor control? Application of marr-albus type models of cerebellar function to classical conditioning

Marr-Albus adaptive filter models of the cerebellum have been applied successfully to a range of sensory and motor control problems. Here we analyze their properties when applied to classical conditioning of the nictitating membrane response in rabbits. We consider a system-level model of eyeblink conditioning based on the anatomy of the eyeblink circuitry, comprising an adaptive filter model of the cerebellum, a comparator model of the inferior olive and a linear dynamic model of the nictitating membrane plant. To our knowledge, this is the first model that explicitly includes all these principal components, in particular the motor plant that is vital for shaping and timing the behavioral response. Model assumptions and parameters were systematically investigated to disambiguate basic computational capacities of the model from features requiring tuning of properties and parameter values. Without such tuning, the model robustly reproduced a range of behaviors related to sensory prediction, by displaying appropriate trial-level associative learning effects for both single and multiple stimuli, including blocking and conditioned inhibition. In contrast, successful reproduction of the real-time motor behavior depended on appropriate specification of the plant, cerebellum and comparator models. Although some of these properties appear consistent with the system biology, fundamental questions remain about how the biological parameters are chosen if the cerebellar microcircuit applies a common computation to many distinct behavioral tasks. It is possible that the response profiles in classical conditioning of the eyeblink depend upon operant contingencies that have previously prevailed, for example in naturally occurring avoidance movements.

Purkinje cell-specific knockout of the protein phosphatase PP2B impairs potentiation and cerebellar motor learning

Cerebellar motor learning is required to obtain procedural skills. Studies have provided supportive evidence for a potential role of kinase-mediated long-term depression (LTD) at the parallel fiber to Purkinje cell synapse in cerebellar learning. Recently, phosphatases have been implicated in the induction of potentiation of Purkinje cell activities in vitro, but it remains to be shown whether and how phosphatase-mediated potentiation contributes to motor learning. Here, we investigated its possible role by creating and testing a Purkinje cell-specific knockout of calcium/calmodulin-activated protein-phosphatase-2B (L7-PP2B). The selective deletion of PP2B indeed abolished postsynaptic long-term potentiation in Purkinje cells and their ability to increase their excitability, whereas LTD was unaffected. The mutants showed impaired "gain-decrease" and "gain-increase" adaptation of their vestibulo-ocular reflex (VOR) as well as impaired acquisition of classical delay conditioning of their eyeblink response. Thus, our data indicate that PP2B may indeed mediate potentiation in Purkinje cells and contribute prominently to cerebellar motor learning.

Model-founded explorations of the roles of molecular layer inhibition in regulating purkinje cell responses in cerebellar cortex: more trouble for the beam hypothesis

For most of the last 50 years, the functional interpretation for inhibition in cerebellar cortical circuitry has been dominated by the relatively simple notion that excitatory and inhibitory dendritic inputs sum, and if that sum crosses threshold at the soma the Purkinje cell generates an action potential. Thus, inhibition has traditionally been relegated to a role of sculpting, restricting, or blocking excitation. At the level of networks, this relatively simply notion is manifest in mechanisms like "surround inhibition" which is purported to "shape" or "tune" excitatory neuronal responses. In the cerebellum, where all cell types except one (the granule cell) are inhibitory, these assumptions regarding the role of inhibition continue to dominate. Based on our recent series of modeling and experimental studies, we now suspect that inhibition may play a much more complex, subtle, and central role in the physiological and functional organization of cerebellar cortex. This paper outlines how model-based studies are changing our thinking about the role of feed-forward molecular layer inhibition in the cerebellar cortex. The results not only have important implications for continuing efforts to understand what the cerebellum computes, but might also reveal important features of the evolution of this large and quintessentially vertebrate brain structure.

Evaluation of image-enhanced paediatric computed tomography brain examinations

The aim of this study was to evaluate the possibility of reducing the radiation dose to paediatric patients undergoing computed tomography (CT) brain examination by using image-enhancing software. Artificial noise was added to the raw data collected from 20 patients aged between 1 and 10 y to simulate tube current reductions of 20, 40 and 60 mA. All images were created in duplicate; one set of images remained unprocessed whereas the other was processed with image-enhancing software. Three paediatric radiologists assessed the image quality based on their ability to visualise the high- and low-contrast structures and their overall impression of the diagnostic value of the image. For patients aged 6-10 y, it was found that dose reductions from 27 mGy (CTDI(vol)) to 23 mGy (15 %) in the upper brain and from 32 to 28 mGy (13 %) in the lower brain were possible for standard diagnostic CT examinations when using the image-enhancing filter. For patients 1-5 y, the results for standard diagnostics in the upper brain were inconclusive, for the lower brain no dose reductions were found possible.