The cerebellum derives its name as a diminutive of the word “cerebrum. This is particularly explicit in German, where the cerebellum is called Kleinhin (“small brain”). This structure, present in all vertebrates, occupies a position immediately behind the tectal plate and straddles the midline as a bridge over the fourth ventricle. In addition, it is the only region of the nervous system to span the midline without interruption.
The cerebellum has undergone enormous elaboration throughout phylogeny, in fact, more so than any other region of the central nervous system (CNS), but has maintained its initial neuronal structure, almost invariant. Thus, its size but not its wiring has changed with CNS evolution. As an example, the cerebellar cortex in a frog has an area approximately \(12^2\)mm that is, 4 mm wide (in the mediolateral direction) and 3 mm long (in the rostrocaudal direction). In humans, the cerebellar cortex is a single continuous sheet with an area of \(500^2\)cm (1,000 mm long and 50 mm wide). This is 4 x \(10^3\) times more extensive than that of a frog (Braitenberg & Atwood, 1958). The increase in cortical extent has resulted in folding into very deep folia (Figure 1), allowing this enormous surface to be packed into a volume of 6 cm x 5 cm x l0 cm. Because the cerebellar cortex extends mainly rostro-caudally, most of the foldings occur in that direction. (Figure 1)
Fundamentally the cerebellum implements motor “tactics” (how to) that contextualize the motor strategies (what, where and when) generated by the forebrain. Such tactics relate mostly to movement execution timing. The basic transactions are implemented at the cerebellar nuclear level the output of which blend strategy and tactics by combining incoming ascending spinal cord information with descending motor commands initiated by sensory input and intrinsic CNS activity. Thus cerebellar function must be considered within the context of the rest of the nervous system since it is not a primary way station for sensory or motor function. Moreover its destruction does not produce sensory deficits or paralysis. Nevertheless, cerebellar lesion produces devastating inability for movement coordination and execution.
Neuronal elements and circuits
The cerebellum is part of a system that comprises four main components:
- The largest component is the cerebellar cortex, a tightly folded layer of neural tissue attached to the dorsal side of the pons, with white matter underneath.
- A set of deep cerebellar nuclei, lying within the white matter, underneath the cortex.
- The inferior olivary nucleus, a convoluted structure lying within the medulla oblongata, and sending projections known as climbing fibers to the cerebellar cortex and deep nuclei.
- A large collection of inputs known as mossy fibers, impinging on the cerebellum from various brain regions and sending projections to the cerebellar cortex and deep nuclei.
This system structure is common to all vertebrates except some types of fish, which lack a discrete set of deep cerebellar nuclei but have cells with similar connectivity distributed within the deep layers of the cerebellar cortex.
Cerebellar cortex anatomy
The cerebellar cortex is one of the least variable CNS structure with respect to its neuronal elements (Raymon y Cajal, 1904; Palay & Chan-Palay, 1974). The basic neuronal connectivity, present in all vertebrates, is composed of the Purkinje cell, the single output system of the cortex, and two inputs:
- a monosynaptic input to the Purkinje cell, the climbing fiber, and
- a disynaptic input, the mossy fiber granule cell-Purkinje cell system.
Concerning the cerebellar Purkinje cells (the largest neurons in the brain) they are the sole link between the cerebellar cortex and the cerebellar nuclei and its output is entirely inhibitory (Ito et al., 1964). The cerebellar cortex is organized in three layers the Purkinje cell layer (PC). The level peripheral to the Purkinje cell layer, known as the molecular layer (ML) and (2) the layer central to the Purkinje cells (i.e., toward the white matter), the granular layer (GL). Bellow the granular layer is the white matter, formed by the input and output nerve-fiber systems of this cortex (see Figure 2).
Five types of neurons inhabit the cerebellar cortex. Four are inhibitory (Purkinje, basket, stellate and Golgi cells) and one is excitatory (granule cells)
- Purkinje cell: are the largest neuron in the vertebrate CNS (Figure 3, PC). Their dendrites are flat (isoplanar) and stack in the cortex like pressed leaves. They receive, in humans, as many as two hundred thousand synapses. Purkinje cell axons provide the only output of the cerebellar cortex. Each cell has a large and extensive dendritic arborization, a single primary dendrite, a sphere-like soma (20-40 pm) and a long, slender axon that is myelinated when it leaves the granular layer. As the main Purkinje cell axon leaves the cortex, it gives off recurrent collaterals that ascend back through the granular layer above and below the Purkinje somata and ultimately form synapses with Golgi and basket cells.
- Basket and Stellate cells: Are interneurons present in the molecular layer (Figure 3, ML). They are both inhibitory (GABAergic) on to Purkinje cells. Their axons run in the same direction as the dendrites of the Purkinje cells (see Figure 3, PC) are electrically coupled and receive both climbing fiber collaterals as well as parallel fibers originating in the granule layer.
- Basket cells (Figure 3, BC) are found in the lower molecular layer. Their axons extend along the Purkinje cell layer at right angles to the direction of the parallel fibers. They may spread over a distance equal to 20 Purkinje cell widths and 6 deep and may contact as many as 150 Purkinje cell bodies. During its course, the horizontal segment of a basket cell axon sends off groups of collaterals that descend and embrace the Purkinje cell soma and initial segment. As many as 50 different basket cells are thought to wrap their axon terminals around each Purkinje cell soma, forming a basket-like meshwork resembling that on an old Chianti bottle (Hamori & Szentagothai, 1966). Basket cell axons also ascend to contact the Purkinje cell dendritic tree. There are about six times as many basket cells as Purkinje cells.
- Stellate cells (Figure 3, SC) are generally found in the outer two-thirds of the molecular layer. The smallest stellate cells, in the most superficial regions of the molecular layer, have 5 to 9 µm-diameter somata, a few radial dendrites, and a short axon (Figure 4, SC). Deeper stellate cells are larger, have more elaborate dendritic arborizations that radiate in all directions, and have varicose axons that can extend parallel to the Purkinje cell dendritic plane as far as 450 pm. There are about 16 times as many small stellate cells as there are Purkinje cells.
- Golgi cells (Figure 3, GC) There are two sizes of Golgi cells: (I) large ones (somata 9-16 µm in diameter), which are found mainly in the upper part of the granular cell layer, and (2) smaller ones (somata 6-l l µm in diameter), which are found in the lower half of the granular layer. They have extensive radial dendritic trees that extend through all layers of the cortex (Figure 2). They receive input from the parallel fibers in the molecular layer and from climbing and mossy fiber collaterals in the granular layer. Their axons branch repeatedly in the granular layer, where they terminate on granule cell dendrites in the cerebellar glomeruli. There are approximately as many Golgi cells as Purkinje cells.
Input systems to the cerebellar cortex
Climbing Fiber pathway. The climbing fibers establish a one to one contact with Purkinje cells generating the most powerful synaptic contact in the brain (as many as three hundred synaptic contacts per fiber) i.e. maximum convergence (Hamori & Szentagothai, 1966). They all arise from one set of two brainstem nuclei, the inferior olives. The main inputs to the inferior olive originate in the spinal cord, brainstem, cerebellar nuclei, and motor cortex. Olivary axons are long, fine (1-3 pm in diameter), and myelinated. They cross the brainstem at the level of the inferior olive, after which they course rostrally to enter the cerebellum primarily via the inferior cerebellar peduncle (a small contingent from the caudal portion of the inferior olive enters via the superior peduncle). Upon entering the cerebellar mass, they give off collaterals to the cerebellar nuclei and proceed toward the cerebellar cortex after branching into several fine fibers. Each fiber branches repeatedly to “climb” along the entire Purkinje cell dendritic tree; thus, they were named climbing fibers by Ramon y Cajal. A given inferior olivary cell axon branches to form several climbing fibers. On average, about l0.
Mossy Fiber-Parallel Fiber Pathway. The second cerebellar afferents, the mossy fibers, originate from many CNS regions, to include the vestibular nerve and nuclei, spinal cord, reticular formation, and basilar pontine nuclei as part of the cortico-ponto-cerebellar pathway one of the most massive in the brain. Mossy fibers enter through all three cerebellar peduncles (inferior, middle, and superior) and send collaterals to the deep cerebellar nuclei before branching in the white matter and synapsing on the granule cells (Shinoda et al., 1992). Thus, unlike the climbing fibers, mossy fibers do not synapse directly on Purkinje cells but rather on the small granule cells lying directly below them (Figure 3, GrC). The synapses between mossy fibers and granule cells occur as the fine branches of the mossy fibers twine through the granular layer. The contacts are made as the mossy fiber enlarges and generates tight knottings along its length. These portions of contact are called mossy fiber rosettes. One mossy fiber may have 20-30 rosettes (see Figure 3). The mossy fibers go on to activate Purkinje cells via the parallel fibers described above.
There are three cerebellar nuclei (Figure 4, CN) on each side of the midline; each receives input via Purkinje cell axons (Figure 4, PC) from the region of cortex directly above it and projects to specific brain regions. The most medial nucleus, the fastigial, receives input from the midline region of the cerebellar cortex, the vermis. It projects caudally to the pons, medulla, vestibular nuclei, and spinal cord and rostrally to the ventral thalamic nuclei. Lateral to the vermis are the newer parts of the cerebellar cortex, the paravermis, which projects to the interpositus nucleus (which itself is divided into anterior and posterior divisions), and the hemispheres, which project to the dentate nucleus. The latter two cerebellar nuclei project rostrally to the red nucleus and ventral thalamic nuclei and caudally to the pons, medulla, cervical spinal cord, and reticular formation. There is a pattern of innervation of the cerebellar nuclei within this broad radial organization whereby the rostrocaudal and mediolateral groups of Purkinje cell axons parcel each cerebellar nucleus into well-defined territories (Voogd et al., 1980).
The cells of the cerebellar nuclei belong to two distinct categories Excitatory and inhibitory the ratio is about one to one. They are either Glutamatergic or GABAergic. The former project to different regions of the neuraxis (Figure 4, ECN). The GABAergic neurons provide feedback to the inferior olive exclusively (Figure 4, ICN). The cerebellar nuclei are not simply “throughput” stations; rather, the synaptic integration that takes place here is a fulcrum for cerebellum function. Indeed, it is here that information from the cerebellar cortex is integrated with direct input from the mossy and climbing fibers. The fact that half of the cerebellar nuclear neurons are GABAergic and project to the inferior olive, as their only target, underlines the importance of decoupling at the inferior olive as a central control system for motricity (Llinas, 2009).
Electrophysiological circuit properties
There are three main neuronal circuits in the cerebellum: two in the cortex, which relate to the two afferent systems as described above, and two main circuits involving the deep nuclei. These latter, as stated above, are excitatory, relating to connectivity with the rest of the brain. The other, a re-entrant inhibitory cerebellar system, terminates in the inferior olive exclusively.
Cerebellar input systems
Mossy fiber circuit
The sequence of events that follows the stimulation of mossy fibers was first suggested by Janos Szentagothai at the Semmelweis University School of Medicine in Budapest: the stimulation of a small number of mossy fibers activates, through the granule cells and their parallel fibers, an extensive array of Purkinje cells and all three types of inhibitory interneurons (Eccles, Llinas, & Sasaki, 1966a). Subsequent interactions of the neurons tend to limit the extent and duration of the response. The activation of Purkinje cells through the parallel fibers is soon inhibited by the basket cells and the stellate cells, which are activated by the same parallel fibers (see Figure 3). Because the axons of the basket and stellate cells run at right angles to the parallel fibers, the inhibition is not confined to the activated Purkinje cells; those on each side of the beam or column of stimulated Purkinje cells are also subject to strong inhibition. The effect of the inhibitory neurons is therefore to sharpen the boundary and increase the contrast between those cells that have been activated and those that have not. At the same time, the parallel fibers and the mossy fibers activate the Golgi cells in the granular layer. The Golgi cells exert their inhibitory effect on the granule cells and thereby quench any further activity in the parallel fibers. This mechanism is one of negative feedback: through the Golgi cells, the parallel fiber extinguishes its own stimulus. The net result of these interactions is the brief firing of a relatively large but sharply defined population of Purkinje cells.
Climbing fiber circuit
In the normal adult cerebellum, a one-to-one relationship exists between a climbing fiber and a given Purkinje cell (i.e. each Purkinje cell receives one climbing fiber); however, each olivary axon branches to provide climbing fibers to approximately 10 Purkinje cells (Eccles, Llinas, & Sasaki, 1966b). The branching patterns of olivocerebellar axons are not random, but rather the branches of an individual axon predominantly remain within a relatively narrow plane that is aligned to the rostrocaudal axis (Sugihara et al., 2001). Moreover, neurons from the same region of the inferior olive tend to project to the same rostrocaudally oriented strip of cerebellar cortex. Thus, the projection pattern of the olivocerebellar pathway divides the cerebellar cortex into a series of parasagittally-oriented zones. Interestingly, the projection pattern of the olivocerebellar pathway is largely in register with corticonuclear (Purkinje cell axons to deep cerebellar nuclei) and cerebellar nucleo-olivary projections, such that a series of reentrant loops are formed. For example, climbing fibers from the principal nucleus of the inferior olive project to the lateral part of the cerebellar hemisphere and also send collaterals to the dentate nucleus. In turn, the dentate is targeted by Purkinje cells of the lateral part of the hemisphere, and its GABAergic cells project back to the principal olivary nucleus. Although climbing fibers have Purkinje cells as their primary targets, they also activate other neurons of the cerebellar cortex. For example, they activate Golgi cells, which will inhibit the input through the mossy fibers (see <figref>Cerebellum_Llinas_drawing_of_the_two_cerebellar_afferent_circuits.jpg</figref>). Thus, when climbing fibers fire, their Purkinje cells are dominated by this input. The climbing fiber input to basket and stellate cells sharpens the area of activated Purkinje cells. An additional feature of the anatomy of the olivocerebellar system is of particular note with regard to its action on the cerebellum: olivary neurons are electrotonically coupled by gap junctions (Llinas et al., 1974; Sotelo et al., 1974; Llinas & Yarom, 1981). In fact, immunoflouresccnce and mRNA studies indicate that the inferior olive has one of the highest densities of connexin 36 [Belluardo, 2000 #14198; Condorelli, 1998 #14191], the protein from which neuronal gap junctions are usually formed (Rash et al., 2000). This electrotonic coupling is thought to allow olivary neurons to synchronize their activity. Interestingly, most of these gap junctions occur between dendritic spines that are part of complex synaptic arrangements known as glomeruli. Olivary glomeruli, in addition to the gap-junction-coupled dendritic spines, contain presynaptic terminals, whose function is thought to be to control the efficacy of the electrotonic coupling.
Cerebellar cortex-deep nuclei circuit
Electrical activation of mossy fiber inputs to the cerebellar system generates an early excitation in the cerebellar nuclei because the collaterals terminate directly on the cerebellar nuclear cells (see Figure 3). The same information then proceeds to the cerebellar cortex, which in turn produces an early excitation of Purkinje cells to be translated into inhibition at the cerebellar nucleus. This inhibition is followed by a prolonged increase in excitability of the cerebellar nuclear cells. The increased excitability is the result of two actions: (1) disinhibition due to reduced Purkinje cell activity, which in turn results from the inhibitory action of basket and stellate cells after the initial activation of Purkinje cells, and (2) cerebellar nuclear cell intrinsic properties (see later). The Purkinje cell inhibition is also due indirectly to the inhibitory action of the Golgi interneuron, which, by preventing the mossy fiber input from reaching the molecular layer, reduces the excitatory drive to Purkinje cells. The cerebellar nuclear projection neurons themselves send axon collaterals to cortical inhibitory interneurons including basket cells, which thus provide recurrent inhibition of the cerebellar nuclear neurons, as seen in spinal motoneurons
As stated above the climbing fiber and the mossy fiber-granule cell-parallel fiber pathways are the two main types of afferents to the cerebellum, as a whole, and to the Purkinje cells in particular. These afferent systems differ dramatically in their interactions with the Purkinje cells. Thus the Purkinje cell and its climbing fiber afferent have a one-to-one relationship, whereas the relationship between the Purkinje cell and the mossy fiber-parallel fiber system can be characterized as many-to-many. Moreover, the directionality of the parallel fibers imparts a mediolateral orientation to Purkinje cell activation by the mossy fiber-parallel fiber system, whereas the climbing fiber system, as we shall see, is organized to produce synchronous activation of specific groupings of Purkinje cells, groupings that often have a rostrocaudal orientation. Their electrophysiological and anatomical differences lead to distinct functional roles for these two systems, which we discuss later.
Concerning the climbing fiber system, as a result of the electrotonic coupling between inferior olivary neurons and the topography of the olivocerebellar projection, this system generates synchronous (on a millisecond time scale) complex spike activity in rostrocaudal bands of Purkinje cells (Figure 4). These bands are normally only about 250 µm wide in the mediolateral direction but can be several millimeters long in the rostrocaudal direction and may extend down the walls of the cerebellar folia and across several lobules . Thus, instead of providing the primary drive for activity in the olivocerebellar system, the main role of olivary afferents is to determine the pattern of “effective” electronic coupling between olivary neurons and thereby the distribution of synchronous complex spike activity across the cerebellar cortex. This idea is supported by results showing that spontaneous climbing spike activity persists following the block of glutamatergic and GABAergic input to the inferior olive (Lang, 2001, 2002).
The activity of the cerebellar nuclei thus is regulated in three ways;
- by excitatory input from collaterals of the cerebellar afferent systems,
- by inhibitory inputs from Purkinje cells activated over the mossy fiber pathways, and
- by inputs from Purkinje cells activated by the climbing fiber system.
The effect of these inputs on cerebellar nuclear cells is shown by the intracellular recording of the response of these neurons to white matter stimulation (Figure 4, A to E) at increasing levels of stimulating intensity. The stimulus activates a variety of axons that are running through the white matter, and as a result the response of these cells has five parts as shown in the Figure 4. An initial EPSP due to antidromic activation of the mossy fiber collaterals to the nuclear cell followed by an IPSP (pink arrow), which results from direct excitation of Purkinje axons projecting to the nuclear cell and a second EPSP-IPSP sequence (red arrow) with a latency of 3-4.5 msec. These latter EPSP IPSP sequence results from climbing fiber collateral activation directly the cerebellar nuclear cells, and the IPSP is generated as a result of climbing fiber activation of Purkinje cells that in turn project onto the cerebellar nucleus. Finally, the second IPSP is terminated by a rebound response, which is due to the intrinsic membrane properties of the cerebellar nuclear cells themselves and a smaller IPSP (Figure 4, red circle). Thus, the response in Fig. 4 is a combination of the properties of the synaptic circuit and the intrinsic properties of the Purkinje and cerebellar nuclear cells.
Thus the effect of synchronous olivocerebellar activity on the output of the cerebellar nuclei generates a punctate and rather powerful synaptic EPSP-IPSP sequences are often followed by a rebound depolarization followed by a return to hyperpolarization, as seen in Figure 4 (red dot). Thus if a sufficient number of inferior olivary neurons, having a common rhythmicity, are activated synchronously, a large and equally synchronous activation of Purkinje cells will occur. This in turn produces a large IPSP followed by a rebound burst response in the cerebellar nuclear cells. (Figure 4, last set of superimposed recordings).
In contrast to the punctate nature of cerebellar activation by the olivocerebellar system, the mossy fiber-parallel fiber system provides a continuous and very delicate regulation of the excitability of the cerebellar nuclei, brought about by the tonic activation of simple spikes in Purkinje cells, which ultimately generates the fine control of movement known as motor coordination. The fact that the mossy fibers inform the cerebellar cortex of both ascending and descending messages to and from the motor centers in the spinal cord and brainstem gives us an idea of the ultimate role of the mossy fiber system: it informs the cortex of the place and rate of movement of limbs and puts the motor intentions generated by the brain into the context of the status of the body at the time the movement is to be executed. By contrast the very abrupt and power activation of Purkinje cells by the climbing fibers and the fact that the inferior olive has an intrinsic rhythmicity at 5 to 10 Hz suggest the climbing fiber input is more concerned with motor timing (Llinas, 2009, 2011).
Models of the Cerebellum
The functional significance and computational capabilities of the cerebellum has been focus of intense theoretical investigation. Motivated by the unique architectonical features of the cerebellar circuitry, models have been proposed as early as... . The multitude of models proposed possibly reflects the dissonance among theories and by extension, our understanding of cerebellar function. Arguably, many of these models can have complementary roles in explanation.
Most theories and associated models depart from observations of unique features of cerebellar anatomy, though some can have more abstract representations of the hypothesized computations.
In most models, the plastic synapse between the parallel fibers and Purkinje neurons figures in a central role. The Purkinje neuron is often assumed to play the role of a perceptron that performs linear pattern separation.
Other models emphasize the temporal aspects of the cerebellar processing, such as parallel fibers as delay lines, or the oscillatory activity of the inferior olivary nucleus.
Frequently Modeled Components
Most models assume one or more of the following components:
- Parallel Fiber - Purkinje cell synapse
- The high convergence of parallel fibers on Purkinje cell suggests that some kind of pattern recognition may be take place at this synapse.
- Climbing Fiber - Purkinje cell synapse
- This powerful synapse from a single axon from the inferior olivary nucelus delivers the complex spike. The co-ocurrence of PF EPSCs and CFs is known to cause LTD of parallel fiber synapses, and conversely, no CF results in potentiation. Thus, the CF may control the direction of plasticity.
- Large Number of Granule Cells
- The immense number of granule cells is often suggested to play a pattern separation role.
- Oscillatory Gating of the Granular Layer
- Some models suggest that the negative feedback to Golgi cells promote oscillatory gating of mossy fiber activity.
- Conduction Delays of Parallel Fibers
- Parallel fibers are unusually long, thin, unmyelianated axons, with low conduction speeds (.1m/s - 3m/s) (cite Knöpfel). This has led Eccles (cite) and later Braitenberg (cite) to suggest that PFs could act as delay lines and PNs, would respond as integrators of coincidence.
- Oscillations of the Olivary Nuclei
- The climbing fiber signal originates in a nucleus known to produce oscillatory activity in vivo, as a function of the cells being intrinsic oscillators, and heavily gap junctioned.
- Reverberatory Feedback with the Deep Cerebellar Nucleus
- It's been shown in vivo and in vitro that the disinhibition of the cerebellar nucleus caused by the climbing fiber pause may trigger rebound activity in the nucleus. This has been hypothesized to gate the output signal of the cerebellum.
The selection of relevant features to simulate/emulate is the essence of modeling. Though models of the cerebellum are many and multifarious, the first sieve
The interplay between the features of anatomy, plasticity or cellular dynamics that are taken into aare crucial for cerebellar function, with respective sets of predictions and
Phenomenological and firing rate models
Dynamical reservoir networks
Models of Error Driven Learning
Inspired by the analogy between the Purkinje neuron and the Perceptronwith the connectivities of one layer perceptrons, David Marr proposed that the cerebellum would perform error driven motor learning. Marr suggested that Purkinje Neuron. He also surmised that the granule layer would have pattern separation abilities. As the synapse
These models form a large class, and a number of hardware implementations have been attempted.
(cite: Marr J Phys)
Adaptive Filter Models
Tensor Based Models
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