Embodied bidirectional simulation of a spiking cortico-basal ganglia-cerebellar-thalamic brain model and a mouse musculoskeletal body model distributed across computers including the supercomputer Fugaku.

Embodied simulation with a digital brain model and a realistic musculoskeletal body model provides a means to understand animal behavior and behavioral change. Such simulation can be too large and complex to conduct on a single computer, and so distributed simulation across multiple computers over the Internet is necessary. In this study, we report our joint effort on developing a spiking brain model and a mouse body model, connecting over the Internet, and conducting bidirectional simulation while synchronizing them. Specifically, the brain model consisted of multiple regions including secondary motor cortex, primary motor and somatosensory cortices, basal ganglia, cerebellum and thalamus, whereas the mouse body model, provided by the Neurorobotics Platform of the Human Brain Project, had a movable forelimb with three joints and six antagonistic muscles to act in a virtual environment. Those were simulated in a distributed manner across multiple computers including the supercomputer Fugaku, which is the flagship supercomputer in Japan, while communicating via Robot Operating System (ROS). To incorporate models written in C/C++ in the distributed simulation, we developed a C++ version of the rosbridge library from scratch, which has been released under an open source license. These results provide necessary tools for distributed embodied simulation, and demonstrate its possibility and usefulness toward understanding animal behavior and behavioral change.

Discrimination and learning of temporal input sequences in a cerebellar Purkinje cell model.

Introduction: Temporal information processing is essential for sequential contraction of various muscles with the appropriate timing and amplitude for fast and smooth motor control. These functions depend on dynamics of neural circuits, which consist of simple neurons that accumulate incoming spikes and emit other spikes. However, recent studies indicate that individual neurons can perform complex information processing through the nonlinear dynamics of dendrites with complex shapes and ion channels. Although we have extensive evidence that cerebellar circuits play a vital role in motor control, studies investigating the computational ability of single Purkinje cells are few. Methods: We found, through computer simulations, that a Purkinje cell can discriminate a series of pulses in two directions (from dendrite tip to soma, and from soma to dendrite), as cortical pyramidal cells do. Such direction sensitivity was observed in whatever compartment types of dendrites (spiny, smooth, and main), although they have dierent sets of ion channels. Results: We found that the shortest and longest discriminable sequences lasted for 60 ms (6 pulses with 10 ms interval) and 4,000 ms (20 pulses with 200 ms interval), respectively. and that the ratio of discriminable sequences within the region of the interesting parameter space was, on average, 3.3% (spiny), 3.2% (smooth), and 1.0% (main). For the direction sensitivity, a T-type Ca2+ channel was necessary, in contrast with cortical pyramidal cells that have N-methyl-D-aspartate receptors (NMDARs). Furthermore, we tested whether the stimulus direction can be reversed by learning, specifically by simulated long-term depression, and obtained positive results. Discussion: Our results show that individual Purkinje cells can perform more complex information processing than is conventionally assumed for a single neuron, and suggest that Purkinje cells act as sequence discriminators, a useful role in motor control and learning.

Deploying and Optimizing Embodied Simulations of Large-Scale Spiking Neural Networks on HPC Infrastructure.

Simulating the brain-body-environment trinity in closed loop is an attractive proposal to investigate how perception, motor activity and interactions with the environment shape brain activity, and vice versa. The relevance of this embodied approach, however, hinges entirely on the modeled complexity of the various simulated phenomena. In this article, we introduce a software framework that is capable of simulating large-scale, biologically realistic networks of spiking neurons embodied in a biomechanically accurate musculoskeletal system that interacts with a physically realistic virtual environment. We deploy this framework on the high performance computing resources of the EBRAINS research infrastructure and we investigate the scaling performance by distributing computation across an increasing number of interconnected compute nodes. Our architecture is based on requested compute nodes as well as persistent virtual machines; this provides a high-performance simulation environment that is accessible to multi-domain users without expert knowledge, with a view to enable users to instantiate and control simulations at custom scale via a web-based graphical user interface. Our simulation environment, entirely open source, is based on the Neurorobotics Platform developed in the context of the Human Brain Project, and the NEST simulator. We characterize the capabilities of our parallelized architecture for large-scale embodied brain simulations through two benchmark experiments, by investigating the effects of scaling compute resources on performance defined in terms of experiment runtime, brain instantiation and simulation time. The first benchmark is based on a large-scale balanced network, while the second one is a multi-region embodied brain simulation consisting of more than a million neurons and a billion synapses. Both benchmarks clearly show how scaling compute resources improves the aforementioned performance metrics in a near-linear fashion. The second benchmark in particular is indicative of both the potential and limitations of a highly distributed simulation in terms of a trade-off between computation speed and resource cost. Our simulation architecture is being prepared to be accessible for everyone as an EBRAINS service, thereby offering a community-wide tool with a unique workflow that should provide momentum to the investigation of closed-loop embodiment within the computational neuroscience community.

Postural and visual aftereffects to a slanted floor in lying and sitting positions.

After lying on a slanted floor for a while with the eyes closed, we may perceive it to be less slanted than at the beginning. After viewing a slanted floor while lying on a flat base, we may perceive it to be more horizontal. We investigated these postural and visual adaptations and their interactions with participants lying and sitting on the floor. The participants were adapted to a floor that was posturally, visually, or jointly slanted, and were asked to estimate the test slants around the adapting slant. The estimates were described as a linear function of the test slant with a high goodness-of-fit over the adapting slant. This supported normalization, not satiation, view. Second, the slope of the function, i.e., sensitivity to slant, in the lying position was low in the postural and visual conditions but high in the joint condition, whereas the sensitivity in the sitting position was equally high in all conditions. This was explained by an increase in visual and non-visual cues to the gravitational vertical in the sitting position, and by an abnormal pattern of intracorporeal hydrostatic pressure in the lying position. Third, in both body positions, the angle at which the slant appeared horizontal, i.e., the subjective horizontal (SH), was larger in the postural condition than in the visual condition. Finally, when the postural and visual adaptations were joint, the SH in the lying position was somewhere between the postural- and visual-alone SHs, whereas the SH in the sitting position approximated the visual-alone SH.

Real-Time Simulation of a Cerebellar Scaffold Model on Graphics Processing Units.

Large-scale simulation of detailed computational models of neuronal microcircuits plays a prominent role in reproducing and predicting the dynamics of the microcircuits. To reconstruct a microcircuit, one must choose neuron and synapse models, placements, connectivity, and numerical simulation methods according to anatomical and physiological constraints. For reconstruction and refinement, it is useful to be able to replace one module easily while leaving the others as they are. One way to achieve this is via a scaffolding approach, in which a simulation code is built on independent modules for placements, connections, and network simulations. Owing to the modularity of functions, this approach enables researchers to improve the performance of the entire simulation by simply replacing a problematic module with an improved one. Casali et al. (2019) developed a spiking network model of the cerebellar microcircuit using this approach, and while it reproduces electrophysiological properties of cerebellar neurons, it takes too much computational time. Here, we followed this scaffolding approach and replaced the simulation module with an accelerated version on graphics processing units (GPUs). Our cerebellar scaffold model ran roughly 100 times faster than the original version. In fact, our model is able to run faster than real time, with good weak and strong scaling properties. To demonstrate an application of real-time simulation, we implemented synaptic plasticity mechanisms at parallel fiber-Purkinje cell synapses, and carried out simulation of behavioral experiments known as gain adaptation of optokinetic response. We confirmed that the computer simulation reproduced experimental findings while being completed in real time. Actually, a computer simulation for 2 s of the biological time completed within 750 ms. These results suggest that the scaffolding approach is a promising concept for gradual development and refactoring of simulation codes for large-scale elaborate microcircuits. Moreover, a real-time version of the cerebellar scaffold model, which is enabled by parallel computing technology owing to GPUs, may be useful for large-scale simulations and engineering applications that require real-time signal processing and motor control.

Human-scale Brain Simulation via Supercomputer: A Case Study on the Cerebellum.

Performance of supercomputers has been steadily and exponentially increasing for the past 20 years, and is expected to increase further. This unprecedented computational power enables us to build and simulate large-scale neural network models composed of tens of billions of neurons and tens of trillions of synapses with detailed anatomical connections and realistic physiological parameters. Such "human-scale" brain simulation could be considered a milestone in computational neuroscience and even in general neuroscience. Towards this milestone, it is mandatory to introduce modern high-performance computing technology into neuroscience research. In this article, we provide an introductory landscape about large-scale brain simulation on supercomputers from the viewpoints of computational neuroscience and modern high-performance computing technology for specialists in experimental as well as computational neurosciences. This introduction to modeling and simulation methods is followed by a review of various representative large-scale simulation studies conducted to date. Then, we direct our attention to the cerebellum, with a review of more simulation studies specific to that region. Furthermore, we present recent simulation results of a human-scale cerebellar network model composed of 86 billion neurons on the Japanese flagship supercomputer K (now retired). Finally, we discuss the necessity and importance of human-scale brain simulation, and suggest future directions of such large-scale brain simulation research.

Simulation of a Human-Scale Cerebellar Network Model on the K Computer.

Computer simulation of the human brain at an individual neuron resolution is an ultimate goal of computational neuroscience. The Japanese flagship supercomputer, K, provides unprecedented computational capability toward this goal. The cerebellum contains 80% of the neurons in the whole brain. Therefore, computer simulation of the human-scale cerebellum will be a challenge for modern supercomputers. In this study, we built a human-scale spiking network model of the cerebellum, composed of 68 billion spiking neurons, on the K computer. As a benchmark, we performed a computer simulation of a cerebellum-dependent eye movement task known as the optokinetic response. We succeeded in reproducing plausible neuronal activity patterns that are observed experimentally in animals. The model was built on dedicated neural network simulation software called MONET (Millefeuille-like Organization NEural neTwork), which calculates layered sheet types of neural networks with parallelization by tile partitioning. To examine the scalability of the MONET simulator, we repeatedly performed simulations while changing the number of compute nodes from 1,024 to 82,944 and measured the computational time. We observed a good weak-scaling property for our cerebellar network model. Using all 82,944 nodes, we succeeded in simulating a human-scale cerebellum for the first time, although the simulation was 578 times slower than the wall clock time. These results suggest that the K computer is already capable of creating a simulation of a human-scale cerebellar model with the aid of the MONET simulator.

Large-Scale Simulation of a Layered Cortical Sheet of Spiking Network Model Using a Tile Partitioning Method.

One of the grand challenges for computational neuroscience and high-performance computing is computer simulation of a human-scale whole brain model with spiking neurons and synaptic plasticity using supercomputers. To achieve such a simulation, the target network model must be partitioned onto a number of computational nodes, and the sub-network models are executed in parallel while communicating spike information across different nodes. However, it remains unclear how the target network model should be partitioned for efficient computing on next generation of supercomputers. Specifically, reducing the communication of spike information across compute nodes is essential, because of the relatively slower network performance than processor and memory. From the viewpoint of biological features, the cerebral cortex and cerebellum contain 99% of neurons and synapses and form layered sheet structures. Therefore, an efficient method to split the network should exploit the layered sheet structures. In this study, we indicate that a tile partitioning method leads to efficient communication. To demonstrate it, a simulation software called MONET (Millefeuille-like Organization NEural neTwork simulator) that partitions a network model as described above was developed. The MONET simulator was implemented on the Japanese flagship supercomputer K, which is composed of 82,944 computational nodes. We examined a performance of calculation, communication and memory consumption in the tile partitioning method for a cortical model with realistic anatomical and physiological parameters. The result showed that the tile partitioning method drastically reduced communication data amount by replacing network communication with DRAM access and sharing the communication data with neighboring neurons. We confirmed the scalability and efficiency of the tile partitioning method on up to 63,504 compute nodes of the K computer for the cortical model. In the companion paper by Yamaura et al., the performance for a cerebellar model was examined. These results suggest that the tile partitioning method will have advantage for a human-scale whole-brain simulation on exascale computers.

A Pathological Condition Affects Motor Modules in a Bipedal Locomotion Model.

Bipedal locomotion is a basic motor activity that requires simultaneous control of multiple muscles. Physiological experiments suggest that the nervous system controls bipedal locomotion efficiently by using motor modules of synergistic muscle activations. If these modules were merged, abnormal locomotion patterns would be realized as observed in patients with neural impairments such as chronic stroke. However, sub-acute patients have been reported not to show such merged motor modules. Therefore, in this study, we examined what conditions in the nervous system merges motor modules. we built a two-dimensional bipedal locomotion model that included a musculoskeletal model with 7 segments and 18 muscles, a neural system with a hierarchical central pattern generator (CPG), and various feedback inputs from reflex organs. The CPG generated synergistic muscle activations comprising 5 motor modules to produce locomotion phases. Our model succeeded to acquire stable locomotion by using the motor modules and reflexes. Next, we examined how a pathological condition altered motor modules. Specifically, we weakened neural inputs to muscles on one leg to simulate a stroke condition. Immediately after the simulated stroke, the model did not walk. Then, internal parameters were modified to recover stable locomotion. We refitted either (a) reflex parameters or (b) CPG parameters to compensate the locomotion by adapting (a) reflexes or (b) the controller. Stable locomotion was recovered in both conditions. However the motor modules were merged only in (b). These results suggest that light or sub-acute stroke patients, who can compensate stable locomotion by just adapting reflexes, would not show merge of motor modules, whereas severe or chronic patients, who needed to adapt the controller for compensation, would show the merge, as consistent with experimental findings.

Somatic perception of floor inclination.

We investigated somatically perceived inclination of a floor on which an observer was. In the first three experiments, using blindfolded observers, we determined the point of subjective equality (PSE) and the difference limen (DL) for horizontal floor. Orientation of the lying body relative to the axis around which the floor was rotated, distance of the lying body from the rotation axis, posture (standing, sitting, and lying), and age were varied. In the fourth experiment, effects of seeing the floor were examined. The mean PSEs were accurate within ±0.25° in all experiments. The mean DLs varied with condition: 1) The largest DLs were obtained for the blindfolded observers lying orthogonally or obliquely to the rotation axis, 2) the second largest DLs for the blindfolded observers lying parallel to the rotation axis, 3) medium DLs for the blindfolded observers sitting or standing, and 4) the smallest DLs for the standing observers with visual exposure to surroundings. In the last experiment, we determined a scale for inclination from verbally estimating apparent inclination with or without a blindfold. We concluded that the ratio of shear force to normal force was used for estimation of inclination. We discussed synergy of somatic inputs and visual inputs.

Closed Fracture Diagnosed by Bedside Ultrasonography During Hemodialysis: A Report of Seven Cases and Relevant Clinical Characteristics.

BACKGROUND: Patients undergoing dialysis have a high incidence of fracture, and early diagnosis is important. We report seven cases of closed rib or upper-limb fractures diagnosed by bedside ultrasonography during maintenance hemodialysis sessions and describe relevant clinical characteristics. CASE PRESENTATION: We identified seven patients who were injured by falls in their homes. No injuries occurred on the day of dialysis. Five of the 7 patients did not visit the emergency room. All patients complained of persistent unexplained pain during a regular hemodialysis session. Ultrasonography (US) was performed during dialysis sessions, without any reports of pain. Before US evaluation, the sensitivity of radiography for diagnosis of fracture was 25%, while the sensitivity of US was 100%. Compared with other patients in our clinic, these patients were significantly older and had lower serum albumin concentrations and lower hemodialysis efficiency as determined by Kt/V. They also had a higher incidence of diabetes and a greater need for vasopressors during dialysis. These findings were consistent with the results of previous studies of the characteristics of fractures in dialysis patients. However, blood levels of creatinine, corrected calcium, phosphate, intact parathyroid hormone, and hemoglobin, as well as bone density and blood pressure, after the previous dialysis session were not different. CONCLUSIONS: To our knowledge, this is the first report of closed fracture of superficial bone diagnosed by bedside ultrasonography during a hemodialysis session. Ultrasonography is especially useful for diagnosis in these cases because it is noninvasive and highly accurate. Doctors should determine the differential diagnosis for closed fracture in patients undergoing dialysis, especially in those who are older, have diabetes, and are malnourished, and in those with recent contusions and persistent pain.

Revisiting a theory of cerebellar cortex.

Long-term depression at parallel fiber-Purkinje cell synapses plays a principal role in learning in the cerebellum, which acts as a supervised learning machine. Recent experiments demonstrate various forms of synaptic plasticity at different sites within the cerebellum. In this article, we take into consideration synaptic plasticity at parallel fiber-molecular layer interneuron synapses as well as at parallel fiber-Purkinje cell synapses, and propose that the cerebellar cortex performs reinforcement learning, another form of learning that is more capable than supervised learning. We posit that through the use of reinforcement learning, the need for explicit teacher signals for learning in the cerebellum is eliminated; instead, learning can occur via responses from evaluative feedback. We demonstrate the learning capacity of cerebellar reinforcement learning using simple computer simulations of delay eyeblink conditioning and the cart-pole balancing task.

Utility of Ultrasonography of the Median Nerve With a High-Frequency Probe for the Diagnosis of Dialysis-Related Carpal Tunnel Syndrome.

This cross-sectional study aimed to determine the utility of ultrasonography with improved resolution using a high-frequency probe for dialysis-related carpal tunnel syndrome (CTS). This study targeted 125 hemodialysis patients at our hospital. A 12 MHz probe was placed on the carpal tunnel area to identify the median nerve. The compression rate of the nerve was calculated by measuring the smallest diameter of the compressed nerve and largest diameter of the unaffected part. To quantify CTS symptoms, we determined the presence of Tinel's sign, measured pinch strength, and used questionnaires to assess numbness and pain. The association of these clinical data with the compression rate was examined. Mean compression rate was 12.1 ± 1.1%. The compression rate cutoff value for those positive with Tinel's sign was 25%, (sensitivity and specificity were 0.80 and 0.91, respectively), and that for those with a history of CTS surgery was 25% (sensitivity and specificity were 0.67 and 0.89, respectively). Multiple regression analysis identified duration of dialysis, ß2-microglobulin(ß2-Mg) concentration, positivity for Tinel's sign, history of CTS surgery, and pinch strength as independent compression rate determinants. Notably, compression rates were significantly higher in patients with a ≥4-year duration of dialysis and a ß2-Mg level of 20 mg/L or more. The compression rate of the median nerve measured by an improved ultrasound device significantly correlated with clinical symptoms, medical history, and serological features associated with dialysis-related CTS. Because ultrasonography is non-invasive, the examination might be a simple method especially for early diagnosis of dialysis-related CTS.

Real-World-Time Simulation of Memory Consolidation in a Large-Scale Cerebellar Model.

We report development of a large-scale spiking network model of the cerebellum composed of more than 1 million neurons. The model is implemented on graphics processing units (GPUs), which are dedicated hardware for parallel computing. Using 4 GPUs simultaneously, we achieve realtime simulation, in which computer simulation of cerebellar activity for 1 s completes within 1 s in the real-world time, with temporal resolution of 1 ms. This allows us to carry out a very long-term computer simulation of cerebellar activity in a practical time with millisecond temporal resolution. Using the model, we carry out computer simulation of long-term gain adaptation of optokinetic response (OKR) eye movements for 5 days aimed to study the neural mechanisms of posttraining memory consolidation. The simulation results are consistent with animal experiments and our theory of posttraining memory consolidation. These results suggest that realtime computing provides a useful means to study a very slow neural process such as memory consolidation in the brain.

Real-Time Simulation of Passage-of-Time Encoding in Cerebellum Using a Scalable FPGA-Based System.

The cerebellum plays a critical role for sensorimotor control and learning. However, dysmetria or delays in movements' onsets consequent to damages in cerebellum cannot be cured completely at the moment. Neuroprosthesis is an emerging technology that can potentially substitute such motor control module in the brain. A pre-requisite for this to become practical is the capability to simulate the cerebellum model in real-time, with low timing distortion for proper interfacing with the biological system. In this paper, we present a frame-based network-on-chip (NoC) hardware architecture for implementing a bio-realistic cerebellum model with  âˆ¼ 100 000 neurons, which has been used for studying timing control or passage-of-time (POT) encoding mediated by the cerebellum. The simulation results verify that our implementation reproduces the POT representation by the cerebellum properly. Furthermore, our field-programmable gate array (FPGA)-based system demonstrates excellent computational speed that it can complete 1sec real world activities within 25.6 ms. It is also highly scalable such that it can maintain approximately the same computational speed even if the neuron number increases by one order of magnitude. Our design is shown to outperform three alternative approaches previously used for implementing spiking neural network model. Finally, we show a hardware electronic setup and illustrate how the silicon cerebellum can be adapted as a potential neuroprosthetic platform for future biological or clinical application.

Anisotropic perception of slant from texture gradient: Size contrast hypothesis.

When we see an optical pattern that has a gradient of the size and/or density of its texture elements, we often perceive a surface that is slanted in depth. Our inquiry was to ask whether the effect of a texture gradient depends on the direction of the gradient (ground, ceiling, and sidewall patterns) or on the position of the observer's head (upward, forward, or downward). In Experiments 1 and 2, a total of 63 observers judged the apparent slant of polka-dot, grid, or flagstone patterns; regardless of head position, the ground patterns were judged to be closer to the frontal plane than were the other patterns. This means that there is a visual anisotropy in head-centric slant perception. To explain this result, we assumed accumulated positional effects of size contrast-that is, a tendency to perceive the size of the upper part of visual space to be larger than the size of the lower part. This hypothesis was examined in two subsequent experiments by reducing the size contrast among the texture elements. When 23 observers viewed regularly arranged same-sized-dot patterns with gradients of the interdot interval and with linear perspective of the dotted lines, anisotropic effects were still detected. When 22 observers viewed dynamic random-dot patterns with gradients of velocity, the anisotropic effects mentioned above were removed in many cases, and the ceiling patterns were sometimes judged to be less slanted than the other patterns. These results partially support the size contrast hypothesis and were compared with the predictions from other hypotheses.

Modeling memory consolidation during posttraining periods in cerebellovestibular learning.

Long-term depression (LTD) at parallel fiber-Purkinje cell (PF-PC) synapses is thought to underlie memory formation in cerebellar motor learning. Recent experimental results, however, suggest that multiple plasticity mechanisms in the cerebellar cortex and cerebellar/vestibular nuclei participate in memory formation. To examine this possibility, we formulated a simple model of the cerebellum with a minimal number of components based on its known anatomy and physiology, implementing both LTD and long-term potentiation (LTP) at PF-PC synapses and mossy fiber-vestibular nuclear neuron (MF-VN) synapses. With this model, we conducted a simulation study of the gain adaptation of optokinetic response (OKR) eye movement. Our model reproduced several important aspects of previously reported experimental results in wild-type and cerebellum-related gene-manipulated mice. First, each 1-h training led to the formation of short-term memory of learned OKR gain at PF-PC synapses, which diminished throughout the day. Second, daily repetition of the training gradually formed long-term memory that was maintained for days at MF-VN synapses. We reproduced such memory formation under various learning conditions. Third, long-term memory formation occurred after training but not during training, indicating that the memory consolidation occurred during posttraining periods. Fourth, spaced training outperformed massed training in long-term memory formation. Finally, we reproduced OKR gain changes consistent with the changes in the vestibuloocular reflex (VOR) previously reported in some gene-manipulated mice.

A Model of In vitro Plasticity at the Parallel Fiber-Molecular Layer Interneuron Synapses.

Theoretical and computational models of the cerebellum typically focus on the role of parallel fiber (PF)-Purkinje cell (PKJ) synapses for learned behavior, but few emphasize the role of the molecular layer interneurons (MLIs)-the stellate and basket cells. A number of recent experimental results suggest the role of MLIs is more important than previous models put forth. We investigate learning at PF-MLI synapses and propose a mathematical model to describe plasticity at this synapse. We perform computer simulations with this form of learning using a spiking neuron model of the MLI and show that it reproduces six in vitro experimental results in addition to simulating four novel protocols. Further, we show how this plasticity model can predict the results of other experimental protocols that are not simulated. Finally, we hypothesize what the biological mechanisms are for changes in synaptic efficacy that embody the phenomenological model proposed here.

A spiking network model of cerebellar Purkinje cells and molecular layer interneurons exhibiting irregular firing.

While the anatomy of the cerebellar microcircuit is well-studied, how it implements cerebellar function is not understood. A number of models have been proposed to describe this mechanism but few emphasize the role of the vast network Purkinje cells (PKJs) form with the molecular layer interneurons (MLIs)-the stellate and basket cells. We propose a model of the MLI-PKJ network composed of simple spiking neurons incorporating the major anatomical and physiological features. In computer simulations, the model reproduces the irregular firing patterns observed in PKJs and MLIs in vitro and a shift toward faster, more regular firing patterns when inhibitory synaptic currents are blocked. In the model, the time between PKJ spikes is shown to be proportional to the amount of feedforward inhibition from an MLI on average. The two key elements of the model are: (1) spontaneously active PKJs and MLIs due to an endogenous depolarizing current, and (2) adherence to known anatomical connectivity along a parasagittal strip of cerebellar cortex. We propose this model to extend previous spiking network models of the cerebellum and for further computational investigation into the role of irregular firing and MLIs in cerebellar learning and function.

Long-term depression as a model of cerebellar plasticity.

Long-term depression (LTD) here concerned is persistent attenuation of transmission efficiency from a bundle of parallel fibers to a Purkinje cell. Uniquely, LTD is induced by conjunctive activation of the parallel fibers and the climbing fiber that innervates that Purkinje cell. Cellular and molecular processes underlying LTD occur postsynaptically. In the 1960s, LTD was conceived as a theoretical possibility and in the 1980s, substantiated experimentally. Through further investigations using various pharmacological or genetic manipulations of LTD, a concept was formed that LTD plays a major role in learning capability of the cerebellum (referred to as "Marr-Albus-Ito hypothesis"). In this chapter, following a historical overview, recent intensive investigations of LTD are reviewed. Complex signal transduction and receptor recycling processes underlying LTD are analyzed, and roles of LTD in reflexes and voluntary movements are defined. The significance of LTD is considered from viewpoints of neural network modeling. Finally, the controversy arising from the recent finding in a few studies that whereas LTD is blocked pharmacologically or genetically, motor learning in awake behaving animals remains seemingly unchanged is examined. We conjecture how this mismatch arises, either from a methodological problem or from a network nature, and how it might be resolved.