The cerebellum has the most well-described structure (colour me) but the most elusive function of any brain region. Some electric fish have gigantic cerebella that overshadow all other parts of the brain, suggesting a connection between cerebellar function and the record-setting abilities of electric fish (such as common mode rejection and extraordinary time analysis).

Why study electric fish?
1. Because they illuminate cerebellar function (apart from being neat animals):
    analysis of small time intervals and common mode rejection are both accomplishments of electric fish, and  both seem to be a forte of cerebellum
2. One then joins the large and friendly group of neuroethologists who have made this their model system.
3. Like bird song, microbat echolocation and owl prey capture, the electric fish model system is characterised by a high level of understanding of neural mechanisms at all levels, from sensory processing to motor output.
4. Jamming-avoidance Response (JAR): When two electric fish "meet", they adjust the frequency of electrical discharge so that it does not suffer interference from the other signal. By varying the frequency difference needed to elicit the JAR , one can show that the best species when it comes to timing, Gymnarchus, can detect a 100 nanosec time difference! The huge size of the cerebellum matches this feat.

click here for pictures of electric fish

Nature of the fish's task: How to detect minute electrical stimuli generated by prey in the water, when these signals are thousands of times smaller than the electrical stimuli generated by the movements of the fish itself?
A: One must somehow subtract the self-induced signal so that the real world signal is left behind. This process of subtraction is called efference copy (and is related to the concept of  reafference, which are the expected sensory consequences of our making a movement, that have to be subtracted if we are to distinguish between real movement  in the world and movement that was self-induced).

This complex calculation must be fast, so that it can operate in real time, in sync with the other brain operations such as movement commands and sesnory processing. While efference copy signals have been recorded at different sites in the brain, including the thalamo-cortical system, it is widely recognised that efference copy is the job of the cerebellum. Part of this recognition comes from the superb timimg accomplished by the cerebella of electric fish, along with the extreme importance of the high-levels of processing required to achieve effective efference copy in electric fish, where the real-world signals are in such danger of being swamped by the self-induced ones.

Efference copy (reafference):
The concept was widely popularised by Mittelstaedt. It is a ticklish balance, since a crude mechanism will blunt small stimuli and a poorly-tuned mechanism may lead to the conclusion that stimuli are present when they are not (Hallucinations). In humans there is a particular problem since the enormous resources of the human brain can reconstruct the world with a few hints from memory. How does one draw the fine line between the world of sense data and the reconstructed world of dreams and imagination? Knowing as much as possible about the reconstruction process and having an "efference copy" of that process will help to distinguish its products from those derived more directly from sense data.

Auditory Hallucinations in humans: Vocalisations with poorly-tuned efference copy.
Colin Frith's experiments show inuadible low level vocalisations, or sub-threshold muscle potentials, by recording from the larynx of hallucinating subjects. These subjects are therefore misattributing their own "internal conversations" to outside sources, presumably because of a some failure in the efference copy mechanism that would normally accompany speech, whether vocal or sub-vocal.
 

An experiment on efference copy: After Helmholtz:
1. Cover one eye and move the other eye vigorously across the whole scene. Note the stability of the scene.
2. Look to the other side and up a little with the open eye (e.g. look to the left and up with your right eye). Push, through your lower eyelid, gently on the open eye. Notice that the world moves with each push.
3. Have someone discharge a flash gun or flash on their camera while you look it. Observe the after-image.
4. Now repeat experiments 1 & 2 (best in a dark place to see the after image most clearly) while you observe the after image. Note that the image moves wildly when you move your eyes, despite the fact that it is absolutely fixed on the retina, but that passive eye movements generated by pushing on the eye have no effect.  Efference Copy!

How does efference copy work? One known mechanism is Anti-Hebbian Synapses in the Cerebellum: LTD
Pain as discrepancy:
Thong len: meditating away discrepancy

Electrophysiology of the torus (looks very like the cerebellum with the same kinds of neurons and connections): Anti-Hebbian plasticity

Human cerebellum
Cerebellar plasticity:
In contrast to the associative process of the forebrain's declarative memory, where related inputs are connected via LTP, the cerebellum appears to work by sculpting away, or removing, the unwanted inputs to leave behind the final set....like  David'sform, released from the marble by Michelangelo's blows. This synaptic removal or punishment called LTD, is supervised by the climbing fibre, whose activity indicates that currrently active parallel fibre synapses are, by definition, unwanted, since they are associated in time with the motor error that the climbing fibre is wired to detect.

Take the VOR example of owl flying on a wet night, whose head is heavier and therefore requires a greater motor output from the stabilising reflex to keep it steady. The decreased stability will be evident as slippage of the visual world on the retina, with firing of previously quiet DS ganglion cells and, therefore, of climbing fibres projecting to the vestibulo-cerebellum. In this scenario, parallel fibres that are active simultaneously with the retinal slip will be "punished" by the simultaneous climbing fibre activity, so diminishing the input to teh Purkinje cell and increasing the gain of the VOR. After many repetitions of turns with associated climbing fibre (error) activity, the "offending" parallel fibre synapses will have been eliminated and the reflex will have a perfect gain (by definition, since climbing fibre activity will not now be occurring). A feature of the cerebellar system pointed out in calculations by the late David Marr is that the Purkinje cells can learn many different contexts in which it must modify its firing, without confusing any of them. In other words, the scenario of the rainy night/wet head is not the only one that our Purkinje cell can learn without confusion.

In the case of the adaptation of the gain of the vestibulo-ocular reflex, the firing of a climbing fibre signals that there is retinal instability, since the climbing fibre is driven by large field direction selective ganglion cells that are driven by whole-field motion. Over many trials, the parallel fibre synapses that are associated with the error are eliminated until there is no longer any error and therefore no further need for the climbing to fire. (see diagram)

Coincidence Detection in the Cerebellum:
Simultaneously active synapses in cerebellum are modified as they are in the neocortex, but note that the principal effect is depression, rather than potentiation. Coincidence between an active climbing fibres and an active parallel fibre-spine synapses leads to a "punishment" of the parallel fibre, with subsequent LTD.

Harris AJ 1999 Cortical origin of pathological pain   LANCET 354: (9188) 1464-1466

click here for "Colour Me" cerebellar circuit.
click here for Vestibulo-ocular reflex circuit.