Neuroscience · Unit 4: Motor systems

The Cerebellum

Why does damage to the cerebellum leave a person able to move but unable to move well, and on the same side as the damage? This lesson traces one repeated circuit from mossy and climbing fibres to Purkinje cells and the deep nuclei, reads the two kinds of Purkinje spike, and tests the Marr-Albus-Ito idea that climbing fibres teach by depressing parallel-fibre synapses. Afterwards you can model adaptation to prisms, design an experiment on what drives that learning, and predict the signs and side of a cerebellar lesion.

Watch first How the Cerebellum Learns from Error · 3:08

In one careful count of four adult male brains, about 69 billion of the roughly 86 billion (mean 86.1, standard deviation 8.1) neurons sat in the cerebellum (Azevedo and colleagues, 2009, using the isotropic fractionator). Damage the cerebellum and a person is not paralysed. They move, and they move badly.

The reaches overshoot, the hand shakes as it nears the cup, and walking widens and wanders. The cerebellum does not usually start movements on its own, though in trained mice its output through the thalamus is needed to trigger a cued movement; it makes them accurate, and it learns to keep them accurate when the body or the world changes.

One circuit, repeated

The cerebellum sits behind the brainstem, under the back of the cerebral hemispheres. Its cortex is a thin, deeply folded sheet, and the same small circuit repeats across it. What differs from region to region is mostly where the inputs come from and where the output goes.

Two kinds of input arrive. Mossy fibres come from many sources, among them the pontine nuclei (which relay signals from the cerebral cortex), the spinal cord and the vestibular nuclei. A nucleus, in the brain, is a cluster of neuron cell bodies. Mossy fibres excite granule cells, small neurons packed into the deepest layer of the cortex; most cerebellar neurons are granule cells. Each granule cell sends its axon up to the outer, molecular layer, where it splits and runs along the fold as a parallel fibre. Think of parallel fibres as telephone wires strung through a row of flat trees: they pass through the fan-shaped dendrites of many Purkinje cells in turn, and each Purkinje cell is contacted by a very large number of them.

The second input is the climbing fibre. Climbing fibres come from the inferior olive in the medulla, and they cross the midline, so each olive supplies the opposite half of the cerebellum. Each adult Purkinje cell receives one climbing fibre, which winds up its dendrite and makes many contacts along it. Young Purkinje cells start with several and keep one, as synapse elimination explains; how the layers form in the first place belongs to reelin and reeler.

Purkinje cells are the only output cells of the cerebellar cortex, and they release GABA. They inhibit neurons of the deep cerebellar nuclei: in humans four pairs, the fastigial, globose, emboliform and dentate nuclei, with the globose and emboliform together called the interposed nuclei. In the vestibulocerebellum some Purkinje axons skip the deep nuclei and inhibit the vestibular nuclei of the brainstem directly. The nuclear neurons also receive excitatory collaterals from mossy and climbing fibres on their way in. So the nuclei carry the output, and the cortex sculpts it by timed inhibition. Local interneurons add more inhibition: Golgi cells inhibit granule cells, and basket and stellate cells inhibit Purkinje cells. In mouse slices, Purkinje cells also inhibit a subset of interneurons in the inner molecular layer (16% of 371 sampled cells; Halverson and colleagues, 2022), so the cortex is not a strictly one-way chain.

Regions map onto jobs. The midline vermis and the fastigial nuclei serve posture, the trunk and gait. The intermediate zone and the interposed nuclei serve the limbs. The lateral hemispheres and the dentate nuclei project through the thalamus to motor and premotor cortex. The flocculonodular lobe works with the vestibular nuclei on balance and eye movements.

Two kinds of spike, two kinds of input

An electrode placed beside a Purkinje cell picks up two waveforms. Simple spikes are ordinary action potentials, fired continuously, with a rate set by the cell’s intrinsic excitability and by its excitatory and inhibitory inputs. In awake resting mice, Zhou and colleagues (2014) reported pooled mean simple-spike rates of 58.3 Hz in zebrin-positive Purkinje cells and 92.9 Hz in zebrin-negative ones. Zebrin is a protein marker that divides the cortex into stripes. Complex spikes are large spikes followed by smaller wavelets, one for each climbing-fibre event, at around one per second. After each complex spike the simple spikes pause; in adult mice the mean pause was 20.0 ms in zebrin-negative and 34.5 ms in zebrin-positive cells (Beekhof and colleagues, 2021).

Read a made-up recording. In 2 s you count 130 simple spikes and 2 complex spikes, each followed by a 25 ms gap.

rate = count / time

Simple spikes: 130 / 2 s = 65 Hz. Complex spikes: 2 / 2 s = 1 Hz. Time paused: 2 × 25 ms = 50 ms, which is 50 / 2000 = 2.5% of the record. The simple spikes are the cell’s output; the complex spikes mark when its climbing fibre fired.

Learning from error: Marr-Albus-Ito and its tests

Marr (1969) and Albus (1971) proposed that the climbing fibre is a teacher. When it fires together with a set of parallel fibres, those parallel-fibre synapses change. Albus chose weakening, and in 1982 Ito and Kano reported that pairing parallel-fibre and climbing-fibre stimulation in rabbits produced a long-lasting depression of parallel-fibre to Purkinje transmission: cerebellar long-term depression (LTD). Its calcium and protein kinase C machinery belongs to calcium signaling and PLC, IP3, DAG and PKC; LTD as a general form of plasticity is in synaptic plasticity.

Follow the sign. If the parallel fibres active just before an error are depressed, the Purkinje cell fires less in that context next time, so it inhibits its nuclear target less at that moment, and the nuclear output rises in a well-timed way. The vestibulo-ocular reflex (VOR), which turns the eyes against a head turn (see hearing and balance), is the classic test bed. Its gain is eye-speed amplitude divided by head-speed amplitude: a mouse whose eyes reach 8 degrees/s for a 10 degrees/s head turn has a gain of 0.8.

The evidence supports the idea and also limits it. Gilbert and Thach (1977) reported that complex spikes became more frequent while monkeys adapted to a changed load on a handle, with a lasting fall in simple-spike responses. Kimpo and colleagues (2014) found in two monkeys that a complex spike predicted the next trial’s output change during VOR gain-increase learning but not gain-decrease learning, and in mice that optogenetic climbing-fibre activation paired with head rotation was enough to drive gain increases only. The teacher’s effect is gated. Climbing fibres in mice trained on a rewarded task also signalled reward expectation, delivery and omission (Kostadinov and colleagues, 2019), so they carry more than movement errors. Three mouse lines with no LTD in standard slice tests learned VOR adaptation, eyeblink conditioning and a stepping task normally (Schonewille and colleagues, 2011), though modified protocols induced LTD in slices from two of these lines (Yamaguchi and colleagues, 2016), and plasticity is now thought to occur at several sites, including the nuclei. Where the VOR memory is stored, in the flocculus or in the vestibular nuclei it controls, was argued for years. Marr-Albus-Ito remains a model.

Adaptation in people

Prism goggles shift what you see to one side. Your first throws miss, later throws hit, and when the goggles come off you miss the other way. That opposite miss, the after-effect, shows that the motor command itself was recalibrated. Martin and colleagues (1996) used this throwing task and found adaptation impaired in people with damage to the olivocerebellar system.

Worked problem. This thrower is made up; the task follows Martin and colleagues. Prisms make the first throw land 20 cm right of target. Assume each throw corrects a fixed fraction k = 0.30 of the remaining error and that nothing else changes.

error after n corrections = E0 × (1 − k)^n

Step 1. With E0 = 20 cm, the error after 1 to 4 corrections is 20 × 0.7 = 14.0, then 9.8, 6.86 and 4.80 cm.

Step 2. To get below 2 cm, you need 0.7^n < 0.1. Take logs: n > ln 0.1 / ln 0.7 = (−2.303) / (−0.357) = 6.46, so 7 corrections, leaving 20 × 0.7^7 = 1.65 cm.

Step 3. The learned correction is 20 − 1.65 = 18.35 cm leftward. Remove the prisms and that correction is applied to an unshifted world, so the first throw lands about 18.4 cm left. That is the after-effect.

Step 4. Now suppose an illustrative patient with k = 0.05. After 7 corrections the error is 20 × 0.95^7 = 20 × 0.698 = 14.0 cm, and the after-effect is only 20 − 14.0 = 6.0 cm.

Prism throwing — error, correction and after-effect⚙ original · interactive
Error after n corrections, E0 × (1 − k)n
Corrections needed to get below 2 cm
Learned correction, E0 − error
After-effect: first throw, prisms off (unshifted world)

In this sketch: a made-up thrower, a fixed fraction k of the remaining error corrected per throw, nothing else changing. Right of the target is positive (the thrower’s right).

Rule to keep: the miss shrinks by the same fraction each correction, so slow learning shows twice, in a large error that remains and in a small after-effect; the after-effect shows that the motor command itself was recalibrated. This is a made-up thrower in the design of Martin and colleagues (1996), not a model of any synapse.

Split-belt walking separates two timescales. Morton and Bastian (2006) drove one leg faster than the other. People with cerebellar damage kept the quick, reactive adjustments within each step but showed disrupted predictive, feedforward adaptation, the kind that leaves an after-effect when the belts are equalized. The cerebellum seems needed for predicting, more than for reacting.

Design problem

Does cerebellum-dependent adaptation learn from a sensory prediction error (the mismatch between the predicted and the observed result of a command) or from having made a corrective movement? Design conditions that tell the two apart.

One way to do it

Rotate the cursor that shows the hand, say by 30 degrees. In a shooting condition, people make fast reaches that pass through the target with no chance to correct during the movement; they see the error but make no correction. In a pointing condition, they may correct online. If making a correction is what teaches, shooting should adapt less. If prediction error teaches, both should adapt.

Test healthy people and people with cerebellar damage. Match the size and timing of the visual error across conditions, and measure after-effects with the rotation removed and feedback withheld, so the learned change is not confused with online steering.

Tseng and colleagues (2007) ran this contrast. Healthy people adapted in both conditions, and people with hereditary cerebellar ataxia adapted less than controls in both, which supports prediction error as the signal. Limits: this is behaviour in one patient group; it does not identify the synapse or show that every task uses the same signal.

Predicting a lesion: same side, by region

Ipsilateral means on the same side; contralateral means on the opposite side. Cerebellar signs are typically ipsilateral, and you can work out why. Output from the left dentate and interposed nuclei leaves through the superior cerebellar peduncle and crosses in the midbrain to the right red nucleus and the right ventrolateral thalamus, which relays to right motor and premotor cortex. The corticospinal tract from the right cortex crosses back at the pyramidal decussation in the caudal medulla to the left side of the spinal cord. Two crossings: a left cerebellar lesion disturbs the left limbs. (The olivary climbing fibres also cross, so the right inferior olive teaches the left cerebellum.)

Then use the region. Damage to an intermediate or lateral hemisphere can produce limb ataxia (deficient coordination of movement), dysmetria (overshooting or undershooting a target), dysdiadochokinesia (difficulty with fast alternating movements), intention tremor (a tremor that worsens as the limb nears its endpoint), decomposition of movement, and slurred speech (dysarthria). Damage to the vermis or flocculonodular lobe can produce an unsteady, wide-based gait ataxia and nystagmus, rhythmic involuntary eye movements.

These lesions cause incoordination, not paralysis. And intention tremor is not the rest tremor of Parkinson’s disease, which is seen when the limb is still and relaxed and comes from the basal ganglia. Cerebellar damage is not purely motor either: in 20 patients with disease confined to the cerebellum, Schmahmann and Sherman (1998) described executive, visual-spatial and affective changes, most marked with lesions of the posterior lobe and vermis. Eyeblink conditioning, a cerebellum-dependent form of learning, returns in memory systems.

How we measure it

Single-unit extracellular recording

A fine electrode placed near one Purkinje cell picks up its spikes without entering it. Simple spikes and complex spikes have different shapes, so one record gives you both the cell's ongoing output and each climbing-fibre event it received.

Motor adaptation paradigms

You perturb a movement in a controlled way (prism goggles, a rotated cursor, treadmill belts at two speeds) and measure the error trial by trial, then remove the perturbation and measure the after-effect. The after-effect is evidence that the motor command itself was recalibrated.

Optogenetic stimulation

Neurons made to express a light-gated ion channel are driven with light at chosen moments. Pairing climbing-fibre activation with a movement tests whether that input is sufficient to cause learning in the tested protocol; it does not show that the input is necessary.

Clinical lesion studies

People with damage confined to known parts of the cerebellum are examined and tested against healthy controls. These studies show what the damaged tissue is needed for, within the limits of lesions that are rarely clean and of a small number of patients.

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GABA — the transmitter of Purkinje-cell output
GABA — the transmitter of Purkinje-cell output ● LIVE · PubChem CID 119
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Every Purkinje-cell synapse onto the deep or vestibular nuclei releases this molecule, so the only output of the cerebellar cortex is inhibition.

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GluA2 AMPA receptor — the receptor whose removal underlies cerebellar LTD
GluA2 AMPA receptor — the receptor whose removal underlies cerebellar LTD ● LIVE · RCSB PDB 3KG2
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Parallel-fibre synapses use AMPA receptors like this one. Long-term depression at those synapses is thought to involve taking such receptors out of the membrane.

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David Marr

David Marr

Proposed in 1969 that each Purkinje cell learns to recognise patterns of parallel-fibre activity, with its single climbing fibre acting as the teacher that changes the active parallel-fibre synapses.

By the late 1960s anatomists had drawn the cerebellar cortex in detail: granule cells beyond counting, parallel fibres crossing the flat Purkinje dendrites, and one climbing fibre wrapped around each Purkinje cell. Marr asked what such a circuit could compute. His answer, published in the Journal of Physiology in 1969, treated the granule-cell layer as a stage that recodes mossy-fibre input into a very large number of sparse combinations, and treated each Purkinje cell as a unit that learns which of those combinations go with a particular climbing-fibre signal. In his scheme, when a climbing fibre fired at the same time as a set of parallel fibres, those parallel-fibre synapses would be strengthened, so that the context alone would later drive the Purkinje cell. The sign turned out to be wrong; later experiments found depression. The structure of the idea survived: a cortex with an input that carries context, an input that carries instruction, and a synapse where the two meet. The theory gave experimenters a specific synapse to test, and it remains the reference point for models of cerebellar learning.

✓ verbatim Marr, A theory of cerebellar cortex, J. Physiol. 202:437–470 (1969).
James Albus

James Albus

Proposed in 1971 a theory of cerebellar function in which climbing-fibre input paired with parallel-fibre input weakens those parallel-fibre synapses, the sign later found in experiments.

Albus approached the cerebellum as an engineer interested in how a machine could learn to control movement. His 1971 paper in Mathematical Biosciences, written independently of Marr's, shared the core arrangement: parallel fibres supply a rich description of the current situation, and a climbing fibre tells a Purkinje cell when that situation needs a different output. Albus argued that the change should be a weakening. Because Purkinje cells inhibit their targets, weakening the parallel-fibre drive to a Purkinje cell at the right moment would release the nuclear cells beneath it from inhibition at that moment. His version also framed the circuit as a pattern classifier of the kind engineers were then building, and he later developed cerebellum-inspired controllers for robots at the National Bureau of Standards, now the National Institute of Standards and Technology. Experiments in the following decade reported depression at the parallel-fibre synapse when the two inputs were paired, which is why the proposal is now usually called the Marr-Albus-Ito model. His paper showed that the same circuit could be read as a learning machine for control.

✓ verbatim Albus, A theory of cerebellar function, Math. Biosci. 10:25–61 (1971); NIST publication record for the 1971 theory.
Masao Ito

Masao Ito

With Masanobu Kano, reported in 1982 that pairing parallel-fibre and climbing-fibre stimulation in the rabbit cerebellum produced a long-lasting depression of parallel-fibre to Purkinje-cell transmission, the cerebellar long-term depression that Albus's theory had predicted.

Ito's laboratory in Tokyo worked on the cerebellum for decades, and earlier work from that laboratory had shown that Purkinje cells inhibit the brainstem neurons they contact. That made the theories of Marr and Albus testable in a concrete way: if Purkinje output is inhibitory, then depressing its excitatory input would raise the activity of the nuclei at the moment the depression applied. Ito proposed that the flocculus, the part of the cerebellum that receives head-motion signals and projects to the vestibular nuclei, tunes the vestibulo-ocular reflex in this way. With Masanobu Kano he stimulated parallel fibres together with the climbing-fibre input in rabbits and reported that the field potential evoked by parallel-fibre stimulation, which reflects excitation of Purkinje-cell and other cortical dendrites, stayed depressed for at least an hour, while stimulating either input alone did not have that effect. The 1982 paper named a cellular change that the theories needed, and it opened the search for the molecular steps of cerebellar long-term depression.

✓ verbatim Ito & Kano, Neurosci. Lett. 33:253–258 (1982); Ito, The Cerebellum and Neural Control (Raven Press).
Amy Bastian

Amy Bastian

With colleagues, measured how people with cerebellar damage adapt their walking and reaching, separating reactive from predictive adjustment and testing which error signal drives cerebellum-dependent learning.

Bastian's group, at the Kennedy Krieger Institute and Johns Hopkins, studies what people with cerebellar damage can and cannot learn about their own movements. With Susanne Morton she used a split-belt treadmill, on which one leg is driven faster than the other. Healthy walkers make two kinds of change: quick reactive adjustments within each step, and a slower predictive recalibration that shows up as an after-effect when the belts return to the same speed. In the 2006 study, people with cerebellar damage kept the reactive adjustments but did not show normal predictive adaptation. With Ya-weng Tseng, Jörn Diedrichsen, John Krakauer and Reza Shadmehr she then asked what the cerebellum learns from. People with hereditary cerebellar ataxia adapted less well than controls whether or not the reaches could be corrected during the movement. The pair of studies turned a clinical observation, poor coordination, into a measurable statement about prediction.

✓ verbatim Morton & Bastian, J. Neurosci. 26:9107–9116 (2006); Tseng, Diedrichsen, Krakauer, Shadmehr & Bastian, J. Neurophysiol. 98:54–62 (2007).
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Which cells carry the output of the cerebellar cortex, and what is the sign of that output?
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Molecular structures live data

  • GluA2 AMPA receptor — the receptor whose removal underlies cerebellar LTD — RCSB PDB 3KG2 · coordinates CC0 · Rat GluA2 homotetramer, X-ray crystal structure (Sobolevsky, Rosconi & Gouaux, Nature, 2009)
  • GABA — the transmitter of Purkinje-cell output — PubChem CID 119 · gamma-aminobutyric acid, PubChem compound record

Simulations

  • Adapting to prisms · Original interactive — Biochemistrypedia (Deppmann Lab).

Scientist profiles & quotes

  • David Marr — Marr, A theory of cerebellar cortex, J. Physiol. 202:437–470 (1969).
  • James Albus — Albus, A theory of cerebellar function, Math. Biosci. 10:25–61 (1971); NIST publication record for the 1971 theory.
  • Masao Ito — Ito & Kano, Neurosci. Lett. 33:253–258 (1982); Ito, The Cerebellum and Neural Control (Raven Press).
  • Amy Bastian — Morton & Bastian, J. Neurosci. 26:9107–9116 (2006); Tseng, Diedrichsen, Krakauer, Shadmehr & Bastian, J. Neurophysiol. 98:54–62 (2007).

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How the Cerebellum Learns from Error · narration: an AI narrator voice (Gemini, Charon) reading narration written from this lesson's text · animation: AI-generated in code (Manim) by Claude, a schematic with no drawn molecular structures, plots computed from their equations · captions from the narration script.

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Like I'm five

The cerebellum is a part of your brain at the back, under the big wrinkly part. It does not decide what to do. It helps you do it smoothly. When you throw a ball and miss, it notices the miss and changes your next throw a little. If it is hurt, you can still move, but your movements wobble and miss.
High school

The cerebellum receives copies of movement commands and of what the body senses, and adjusts the commands so movements land where they should. It learns from mistakes: wear goggles that shift your view and your throws miss at first, then improve, and when the goggles come off you miss the other way for a while. Damage to one side of the cerebellum makes movements on the same side of the body clumsy, shaky near the target, and badly timed.
College

Mossy fibres excite granule cells, whose parallel fibres excite Purkinje cells; each adult Purkinje cell also receives one climbing fibre from the contralateral inferior olive, and each climbing-fibre event produces a complex spike. Purkinje cells are the only output of the cortex and inhibit the deep or vestibular nuclei, which also receive excitatory collaterals and carry the output. In the Marr-Albus-Ito model the climbing fibre signals an error and depresses the parallel-fibre synapses active at that moment, so the Purkinje cell inhibits its nuclear target less at that time. Lesion signs are ipsilateral because output crosses to the red nucleus and thalamus and the corticospinal tract crosses back.
Graduate

The cerebellum behaves like an adaptive predictor that learns from sensory prediction error: in people with cerebellar ataxia, reaching adaptation was impaired whether or not corrective movements were allowed (Tseng and colleagues, 2007), and split-belt walking separated preserved reactive adjustments from impaired predictive ones (Morton and Bastian, 2006). The classical cellular account, climbing-fibre-gated LTD at parallel-fibre synapses, is supported by conjunctive-stimulation experiments in rabbits and by trial-by-trial complex-spike effects during VOR gain-increase learning in monkeys, but the climbing fibre's teaching effect is gated by context (Kimpo and colleagues, 2014), climbing fibres in mice also signal reward expectation and omission (Kostadinov and colleagues, 2019), and three LTD-deficient mouse lines learned the tested tasks (Schonewille and colleagues, 2011).

An open question is how plasticity is divided among sites (granule layer, molecular-layer interneurons, Purkinje cells, nuclei) and over which timescales, and whether one error signal serves every cerebellar module, given that modules defined by zebrin fire at different rates.
Two theories, opposite signs

Marr and Albus arrived independently at the same arrangement: parallel fibres carry the context, the climbing fibre carries the instruction, and the synapse between parallel fibre and Purkinje cell is where the two meet and learning is stored. They disagreed on the sign. Marr proposed that pairing would strengthen the parallel-fibre synapse; Albus proposed that it would weaken it. When Ito and Kano paired the two inputs in the rabbit cerebellum, the parallel-fibre response was depressed, the sign Albus had chosen.

— Marr, J. Physiol. 202:437–470 (1969); Albus, Math. Biosci. 10:25–61 (1971); Ito & Kano, Neurosci. Lett. 33:253–258 (1982).
The teacher does not always teach

Recording from floccular Purkinje cells in two rhesus monkeys, Kimpo and colleagues found that a complex spike predicted a change in the cell's output on the next trial while the animals were learning to increase the gain of the vestibulo-ocular reflex, but not while they were learning to decrease it. In separate mice, pairing optogenetic climbing-fibre activation with head rotation was sufficient to drive gain-increase learning, and the tested pairing did not drive gain-decrease learning. The same signal taught in one context and not in another.

— Kimpo, Rinaldi, Kim, Payne & Raymond, eLife 3:e02076 (2014).
Learning without the famous synapse change

Schonewille and colleagues tested three mouse lines with mutations that block the removal of AMPA receptors from parallel-fibre synapses, a step thought to be needed for cerebellar LTD. The mice adapted their vestibulo-ocular reflex, learned eyeblink conditioning and learned to step on a ladder-like apparatus about as well as controls. The result does not rule out a role for LTD where it is intact, since other synapses may compensate, but it showed that this one change was not required for those tasks.

— Schonewille and colleagues, Neuron 70:43–50 (2011).

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