Sunday, 30 December 2012

Too many cooks? intrinsic and synaptic homoeostatic mechanisms in cortical circuit refinement by Turrigiano

Brains use classic homoeostatic negative feedback mechanisms. These allows neurons and/or circuits sense how active they are and adjust their excitability to keep activity in range.  Neurons must sense activity. When this measure deviates from a target value, force must be generated to adjust excitability to move neuronal activity back to target. If individual neurons can stabilise own firing then overall network activity can be stabilised.

There are 2 different ways neurons could homeostatically regulate excitability. 1) they can adjust synaptic strengths up or down in right direction to stabilise average neuronal firing rates.  2) Instead of regulating synaptic strength they could modulate intrinsic excitability to shift relationship between synaptic input and firing rate.

Neuron activity is determined by strength of excitatory and inhibitory synaptic inputs and by balance of inward and outward voltage-dependent conductances that regulate intrinsic excitability.

Neurons can compensate for reduced sensory drive by using synaptic mechanisms to modify balance between excitatory and inhibitory inputs or by using intrinsic mechanisms to modify balance of inward and outward voltage-dependent currents.

Homeostatic regulation of neuronal firing
Circuit activity is homeostatically regulated to maintain firing rates and/or firing patterns in boundaries.  Central neurons in dissociated cultures can maintain average firing rates around a homeostatic set point.  When cortical or hippocampal neurons are induced to fire more than normal over hours, firing returns to basline levels. If firing is reduced over time neurons compensate. Firing is restored to basline. Most homeostatic compensation in central neurons are slow and take hours to adys. This may prevent interference with info transfer.

Synaptic homeostasis
In most networks, small changes in balance between excitation and ihbition (E/I balance) can affect ongoing activity. E/I balance appears to be tightly regulated. It is required that excitatory and inhibitory syanptic strengths are adjusted in a cell-type-specific manner.

Synaptic scaling of excitatory synapses
Several forms of homeostatic plasticity of excitatory synapses. Global mechanisms include synaptic scaling. It operates on all a neuron's synapses. Local mechanisms act on individual or small groups of synapses.

Some synaptic homeostasis involves persynaptic and others postsynaptic change in function.

Synaptic scaling was identified in cultured neocortical neurons. Pharmacological manipulations of activity induced compensatory and bidirectional changes in unit strength of glutamatergic synapses. By measuring miniature EPSCs mediated by AMPA and NMDAR, it was found that modulating network activity induced uniform increases or decreases in entire mini amplitude distribution. This scales postsynaptic strength up and down. Change in mini amplitude change amplitude of evoked transmission with little or no change in short-term synaptic dynamics.

This may stabilised activity without changing relative strength of synaptic inputs. Does not disrupt info-storage mechanisms that rely on differences in synaptic weights.

How do neurons sense perturbations in activity during synaptic scaling? Studies show that synaptic scaling is cell-autonomous. Neurons sense changes in own activity through changes in firing/depolarisation and Ca2+ influx. Selectively blocking firing in an individual cortical pyramidal neuron scales up that neurons' synaptic strengths to same degree as blockade of network activity. This process requires a drop in somatic Ca2+ influx reduced activation of CamKK and CaMKIV and transcription.

Signalling pathway causes increases accumulation of AMPAR in postsynaptic membrane at all excitatory synapses. This scales up mini amplitude and enhances evoked transmission. Global enhancement of AMPAR abundance in response to activity blockade requires sequences on C-terminal of GluR2 subunit on AMPAR. This distinguishes synaptic scaling from other forms of synaptic enhancement such as LTP that requires sequences on GluR1 subunit. Synaptic scaling up is different from LTP. It takes longer time (hours) and wider spatial scale (global). It uses trafficking steps that target GluR2 subunit to enhance AMPAR abundance at synapses.

Scaling down in hippocampal slice cultures responds to enhanced activity (using channel rhodopsin and optical stimulation). It can be induced by cell-autonomous changes in Ca2+ influx. This involves CamKK/CaMKIV signalling and transcription. It requires the GluR2 subunit for its expression. Unlike CaMKK, CaMKIV is required but not sufficient to trigger reduction in synaptic strength. CamKK may activate signalling pathways that reduce synaptic strength. In hippocampal neurons driving individual neurons to fire induces synapse loss and reduced quantal amplitude.

Several molecules are involved in synaptic scaling. They regulate AMPAR trafficking. Arc (an immediate early gene) interacts with endocytic machinery to remove AMPAR from membrane.  TNFα increases synaptic AMPAR accumulation.   Beta3 integrins regulate AMPAR surface expression.

Synapse-type specificity of excitatory synaptic scaling
Rules for scaling excitatory synapses are cell-type specific. In cultured cortical and hippocampal neurons, excitatory synapses onto pyramidal neurons are scaled up by activity blockade. Excitatory synapses onto GABA-ergic interneurons are unaffected or reduced. Enhancing network activity increases excitatory transmission onto GABAergic interneurons. This involves the activity-dependent regulation of the immediate early gene Narp. Narp seems to be secreted by presynaptic pyramidal neurons. It accumulates preferentially at excitatory synapses into parvalbumin-positive interneurons.

Not all excitatory neurons express synaptic scaling at all times during development. Activating blockade in hippocampal networks scales up CA1 but not CA3 excitatory synapses. This suggests that the rules for expression of scaling in hippocampus are cell-type specific. Probably synaptic scaling is specifically expressed when and where it is needed.

It is not known whether a postsynaptic neuron can preferentially scale one subtype of excitatory synapse without affecting others. As mini amplitude distribution is scaled up or down proportionally, it is thought all excitatory synapses are affected equally during synaptic scaling in response to activity drop. If a synapse type that is a small fraction of a neuron's synapses was not affected, not sensitive enough to detect deviation.

Homoeostatic regulation of inhibitory synapses
To stabilise network activity, reciprocally regulate relative strengths of excitatory and inhibitory synapses. Inhibition is regulated by long-lasting changes in activity and/or sensory drive.

Visual deprivation or inhibition of retinal activity with tetrodotoxin decreased immunoreactivity for GABA. It reduced inhibition and inhibitory synapse number in cortical and hippocampal cultures.

Amplitude of miniature inhibitory postsynaptic currents are scaled down. This can involve changes in accumulation of postsynaptic GABAAR and reduced presynpaptic GABAergic markers. Studies show homoeostatic regulation of inhibition can occur by changes in postsynaptic strength, synapse number, and GABA packaging and release in combinations.

Is regulation of inhibition is due to presynaptic inhbitory neuron or postsynpatic inhibitory neuron.  In hippocampal cultures, firing was prevented in either postsnypatic pyramidal neuron or presyntaptic inhibitory neuron  while measuring inhibitory synapses onto pyramidal neuron. Neither was enough to mimic effects of blocking network firing. unlike synaptic scaling of excitatory synapses, homeostatic regulation of inhibition if non-cell-autonomous process. It requires changes in both pre and postynaptic activity simultaneously or is triggered by global changes in network activity.

Homeostasis of intrinsic excitability
Changes in intrinsic excitability that alter a neurons' input-output function can affect network behaviour. Intrinsic plasticity can be destabilising or homeostatic.

Learning and memory

Synaptic plasticity (Wikipedia)
In neurosciencesynaptic plasticity is the ability of the connection, or synapse, between two neurons to change in strength in response to either use or disuse of transmission over synaptic pathways.[1] Plastic change also results from the alteration of the number of receptors located on a synapse.[2] There are several underlying mechanisms that cooperate to achieve synaptic plasticity, including changes in the quantity of neurotransmitters released into a synapse and changes in how effectively cells respond to those neurotransmitters.[3] Synaptic plasticity in both excitatory and inhibitory synapses has been found to be dependent upon calcium.[2] Since memories are postulated to be represented by vastly interconnected networks of synapses in the brain, synaptic plasticity is one of the important neurochemical foundations of learning and memory (see Hebbian theory).

Biochemical mechanisms

Two molecular mechanisms for synaptic plasticity (researched by the Eric Kandel laboratories) involve the NMDA and AMPA glutamate receptors. NMDA channel opening (related to level of cellular depolarisation) increases post-synaptic Ca2+ concentration. This is linked to LTP and protein kinase activation. Strong depolarisation of postsynaptic cell completely displacces Mg2+ blocking NMDA ion channels. This allows Ca2+ to enter cell. THis may cause LTP. Weaker depolarisation only partially displaces Mg2+. This causes less Ca2+ entering postsynaptic neuron and lower intracellular Ca2+ concentrations (which activate protein phosphatases and induce long-term depression.
These activated protein kinases serve to phosphorylate post-synaptic excitatory receptors (e.g. AMPA receptors), improving cation conduction, and thereby potentiating the synapse. Also, this signals recruitment of additional receptors into the post-synaptic membrane, and stimulates the production of a modified receptor type, thereby facilitating an influx of calcium. This in turn increases post-synaptic excitation by a given pre-synaptic stimulus. This process can be reversed via the activity of protein phosphatases, which act to dephosphorylate these cation channels.[5]
The second mechanism depends on a second messenger cascade regulating gene transcription and changes in the levels of key proteins at synapses such as CaMKII and PKAII. Activation of the second messenger pathway leads to increased levels of CaMKII and PKAII within the dendritic spine. These protein kinases have been linked to growth in dendritic spine volume and LTP processes such as the addition of AMPA receptors to the plasma membrane and phosphorylation of ion channels for enhanced permeability.[6] Localization or compartmentalization of activated proteins occurs in the presence of their given stimulus which creates local effects in the dendritic spine. Calcium influx from NMDA receptors is necessary for the activation of CaMKII. This activation is localized to spines with focal stimulation and is inactivated before spreading to adjacent spines or the shaft, indicating an important mechanism of LTP in that particular changes in protein activation can be localized or compartmentalized to enhance the responsivity of single dendritic spines. Individual dendritic spines are capable of forming unique responses to presynaptic cells.[7] This second mechanism can be triggered by protein phosphorylation but takes longer and lasts longer, providing the mechanism for long-lasting memory storage. The duration of the LTP can be regulated by breakdown of these second messengersPhosphodiesterase, for example, breaks down the secondary messenger cAMP, which has been implicated in increased AMPA receptor synthesis in the post-synaptic neuron[citation needed].
Long-lasting changes in the efficacy of synaptic connections (long-term potentiation, or LTP) between two neurons can involve the making and breaking of synaptic contacts. Genes such as activin ß-A, which encodes a subunit of activin A, are up-regulated during early stage LTP. The activin molecule modulates the actin dynamics in dendritic spines through the MAP kinase pathway. By changing the F-actin cytoskeletal structure of dendritic spines, spines are lengthened and the chance that they make synaptic contacts with the axonal terminals of the presynaptic cell is increased. The end result is long term maintenance of LTP.[8]
The number of ion channels on the post-synaptic membrane affects the strength of the synapse.[9] Research suggests that the density of receptors on post-synaptic membranes changes, affecting the neuron’s excitability in response to stimuli. In a dynamic process that is maintained in equilibrium, N-methyl D-aspartate receptor (NMDA receptor) and AMPA receptors are added to the membrane by exocytosis and removed by endocytosis.[10][11][12] These processes, and by extension the number of receptors on the membrane, can be altered by synaptic activity.[10][12]Experiments have shown that AMPA receptors are delivered to the synapse through vesicular membrane fusion with the postsynaptic membrane via the protein kinase CaMKII, which is activated by the influx of calcium through NMDA receptors. CaMKII also improves AMPA ionic conductance through phosphorylation.[13] When there is high-frequency NMDA receptor activation, there is an increase in the expression of a protein PSD-95 that increases synaptic capacity for AMPA receptors. This is what leads to a long-term increase in AMPA receptors and thus synaptic strength and plasticity.
If the strength of a synapse is only reinforced by stimulation or weakened by its lack, a positive feedback loop will develop, causing some cells never to fire and some to fire too much. But two regulatory forms of plasticity, called scaling and metaplasticity, also exist to provide negative feedback.[12] Synaptic scaling is a primary mechanism by which a neuron is able to stabilize firing rates up or down.[14]
Synaptic scaling serves to maintain the strengths of synapses relative to each other, lowering amplitudes of small excitatory postsynaptic potentials in response to continual excitation and raising them after prolonged blockage or inhibition.[12] This effect occurs gradually over hours or days, by changing the numbers of NMDA receptors at the synapse (Pérez-Otaño and Ehlers, 2005).Metaplasticity varies the threshold level at which plasticity occurs, allowing integrated responses to synaptic activity spaced over time and preventing saturated states of LTP and LTD. Since LTP and LTD (long-term depression) rely on the influx of Ca2+ through NMDA channels, metaplasticity may be due to changes in NMDA receptors, altered calcium buffering, altered states of kinases or phosphatases and a priming of protein synthesis machinery.[15] Synaptic scaling is a primary mechanism by which a neuron to be selective to its varying inputs.[16] The neuronal circuitry affected by LTP/LTD and modified by scaling and metaplasticity leads to reverberatory neural circuit development and regulation in a Hebbian manner which is manifested as memory, whereas the changes in neural circuitry, which begin at the level of the synapse, are an integral part in the ability of an organism to learn.[17]
There is also a specificity element of biochemical interactions to create synaptic plasticity, namely the importance of location. Processes occur at microdomains – such as exocytosis of AMPA receptors is spatially regulated by the t-SNARE Stx4.[18] Specificity is also an important aspect of CAMKII signaling involving nanodomain calcium.[19] The spatial gradient of PKA between dendritic spines and shafts is also important for the strength and regulation of synaptic plasticity.[6] It is important to remember that the biochemical mechanisms altering synaptic plasticity occur at the level of individual synapses of a neuron. Since the biochemical mechanisms are confined to these "microdomains," the resulting synaptic plasticity affects only the specific synapse at which it took place.

Short-term plasticity

Plasticity can be categorized as short-term, lasting a few seconds or less, or long-term, which lasts from minutes to hours. Short-term synaptic enhancement results from an increase in the probability that synaptic terminals will release transmitters in response to pre-synaptic action potentials. Synapses will strengthen for a short time because of either an increase in size of the readily releasable pool of packaged transmitter or an increase in the amount of packaged transmitter released in response to each action potential.[21] Types of short term plasticity include synaptic augmentation, depression, facilitation, or neural facilitation, and post-tetanic potentiation.

[edit]Synaptic augmentation

Synaptic augmentation is the increased efficacy of synapse lasting in the order of seconds (7 s often quoted). It has been found to be associated with increased efficiency with which action potentials cause release of vesicles containing transmitters.

[edit]Synaptic depression

Synaptic fatigue or depression is usually attributed to the depletion of the readily releasable vesicles. Depression can also arise from post-synaptic processes and from feedback activation of presynaptic receptors.[22] Heterosynaptic depression is thought to be linked to the release of adenosine triphosphate (ATP) from astrocytes.[23]
Stably maintained dendritic spines are associated with lfelong memories by Yang et al
Study on mouse cortex shows that learning and novel sensory experience lead to spine formation and elmination by a protracted process. Extent of spine remodelling correlated with behavioural improvement after learning. A small fraction of new spines induced by novel experience with most psines formed early in development, are preserved and provide structural basis for memory retention. Learning and memory experience leave permanent marks on cortical connections. Sugggests lifelong memories are stored in stable synaptic networks.

Spine dynamics were examined in primary motor cortex after skill learning on an accelerated rotarod. Animals changed gait pattern and learned specific movemements. In forelimb area of motor cortex, increase in dendritic spines in young and adult mice.  Increase not observed in mice running similar distances on slowly moving rotarod and was region specific. Occured in forelimb motor cortex but not barrel cortex. After being trained for 2 days, spien formation is higher if trained with different motor task than if subjected to same training. Motor learning formation not just physical exercise causes spine formation.
a, Transcranial two-photon imaging of spines before and after rotarod training or sensory enrichment. b, CCD camera view of the vasculature of the motor cortex. c, Two-photon image of apical dendrites from the boxed region in b. A higher magnification view of a dendritic segment in c is shown in d. d, e, Repeated imaging of a dendritic branch before (d) and after rotarod training (e). Arrowheads indicate new spines formed over 2 days. f, The percentage of new spines formed within 2 days in the motor cortex was significantly higher in young or adult mice after training as compared with controls with no training or running on a non-accelerated rotarod. No increase in spine formation was found in the barrel cortex after training. g, After previous 2-day training, only a new training regime (reverse running) caused a significant increase in spine formation. h, EE increased spine formation over 2 days in the barrel cortex in both young and adult animals. No significant increase in spine formation was found under EE when the whiskers were trimmed. i, After previous 2-day EE, animals switched to a different EE showed a higher rate of spine formation than those returned to SE. Data are presented as mean ± s.d. *P < 0.005. See Supplementary Table for the number of animals in each group.

Mechanisms of long-term plasticity
Synaptic plasticity, memory and hippocampus: a neural newtork approach to causality by Kerchner and Nicholls
Patient HM suffered from intractable epilepsy. Bilateral removal of medial temporal love and large parts of both hippocampi. He could not form new episodic memories (anterograde amnesia) and loss of old memories (retrograde amnesia).  Hippocampus is essential to form new episodic memories. May have role in longterm storage.

Damage in CA1 region of hippocampus causes anterograde memory impairment in RB. GD became amnesic after bilateral damage in Ca1 region. Medial temporal lobe required to form permanent and usable long-term  memory.

Activation of CaMKII in single dendritic 
spines during long-term potentiation
CaMKII is important in LTP. Lee et al (2009) monitored spatiotemporal dynamics of CAMKII in dendritic spines during LTP.

Silent synapses and the emergence of a postsynaptic mechanism for LTP
A silent synapse is a synapse in which an EPSC is absent at resting membrane potential but becomes apparent on depolarisation. Silent synapses are thought to reflect functional presence of NMDARs but not AMPARs.  As only AMPARs can conudct current at resting membrane potential, absence of functional postsynaptic AMPAs renders a synapse silent. It cannot mediate synpatic transmission under physiological conditions.

It was shown that manipulations used to trigger LTP in hippocampus could also unsilence silent CA1 synapses.

Discovery of silent synapses
A silent synapse is defined as a synapse in which an excitatory postsynaptic current (EPSC) is absent at the resting membrane potential but becomes apparent on depolarization. The traces here were obtained during whole-cell recordings from CA1 pyramidal neurons from acute rat hippocampal slices. a | (From left to right.) High-intensity stimulation evoked a fast, AMPAR-mediated EPSC at a holding potential of -60 mV. When the stimulus intensity was reduced to below the threshold for triggering EPSCs, as shown in a series of superimposed traces from repeated trials, no evoked current appeared at -60 mV. However, using the same stimulus intensity, a slow EPSC did appear at a holding potential of +30 mV; this EPSC disappeared on application of the NMDAR antagonist D-APV, indicating that it was purely mediated by NMDARs. On returning the holding potential to -60 mV, the lower-intensity stimulus again did not evoke a current. The flat traces in this series indicate failures (see Box 2). b | The left-hand panel shows an EPSC appearing at baseline at a holding potential of +55 mV but not at -65 mV. However, after a long-term potentiation protocol, in which stimulation was paired with postsynaptic depolarization to 0 mV, EPSCs appeared at -65 mV (middle panel). As illustrated in the time course graph (right-hand panel), the number of failures diminished markedly after pairing. Part a reproduced, with permission, from Ref. 3 © (1995) Elsevier Science. Part b reproduced, with permission, from Ref. 2 © (1995) Macmillan Publishers Ltd. All rights reserved.

Silent synapsis activation is a proposed mechanism for rapid increases in synaptic efficacy eg  LTP.

Wall and Merrill discovered that some presynaptic stimuli could not trigger postsynaptic firing in spinal cord neurons.

Faber et al studied silent synapses on goldfish Mauthner cell. These giant brainstem neurons mediate escape reflex in fish. They receive inhibitory input from local glycinergic interneurons and excitatory inputs from VIIIth nerve afferent fibres.  Paired recordings from presynaptic interneurons and postsynaptic Mauthner cells showed transmission did not occur in large percentage of cases. Although synapses formed between recorded cells. This may be due to silent synapses.

After postsnyaptic injection of cyclic AMP, synapse unsilencing occurred.  Not in response to direct stimulation of presynaptic fibres by injection of Ca2+ or K+ channel antagonist.

This suggests that glycinergic silent synapses comprise a functional presynaptic bouton and a nonfuntional postsynaptic membrane.

Many VIIIth nerve excitatory synapses onto Mauther cells were silent. Presynaptic injection of K+ channel antaonists unsilenced these synapses. Possibly by enhacing Ca2+ and amplifying triggers for vesicle release. This indicates that in contrast to postynaptiaclly silent glycinergic synapses, these glutamatergic synapses were presynaptically silent.

Although silent synapses are common among different species and different areas of nervous system, mechanisms underlying synaptic silence may vary. Synaptic acitvity triggers unsilencing.

LTP and silent synapses in the hippocampus

Silent synapses was discovered in hippocampal CA1 pyramidal neurons. It was debated whether locus of LTP expression is pre- or postsynaptic. LTP is prototypical model of synaptic plasticity. Coincident presynaptic activity and postsynaptic depolarisation trigger enhanced synaptic transmission. It may be caused by presynaptic increase in glutamate releas or postynaptic increse in responsiveness to glutamate.

Many researchers observed in LTP, AMPAR-mediated EPSC (A-EPSCs) invreased. Little or no increase in NMDAR-mediated EPSCs (N-EPSCs)/

As both receptors colocalise at postsynaptic membrane and bind synaptic glutmate, it is indicated that postsynaptic modification favouring AMPAR activation underlies LTP.

However, theoretically weak presynaptic glutamate release should engage only NMDARs as they bind glutamate with higher affinity than AMPARs. Whereas a more robust signal should activate both types of receptor. Synaptic glutamate concentration peaks quickly after vesicle release. By the time glutamate dissipates by diffusion and uptake, it has not had time to achieve equilibrium with postsynaptic receptors.

Considering NMDARs have slower activation kinetics than AMPARs, apparently affinities of these receptor types converge in these non-equilibrium conditions. It is less likely that glutamate activates NMDARs without a trace of AMPAR activation.

Manipulations that selectively affect presynaptic activity (eg increasing stimulus intensity or applying GABAGB against baclofen, the adenosine antagonist theophylline or phorbol esters, parallel changes in A-EPSCs and N-EPSCS over range of amplitudes broader that amplitudes typical in LTP. LTP did not trigger change in paired pulse facilitation.  Did not seem to involve any change in probability of transmitter release (p).
The minimal magnitude of neurotransmission that can occur at a synapse is the release of a single vesicle of neurotransmitter. Because the amount of neurotransmitter (for example, glutamate) is roughly the same from vesicle to vesicle, the postsynaptic response is graded by quantal steps, the biological principle on which 'quantal analysis' is based. Quantal analysis can be performed most directly by isolating the postsynaptic response to a single quantum of neurotransmitter, typically by blocking action-potential firing with tetrodotoxin (TTX) and waiting for spontaneous, non-action-potential-initiated vesicle release to occur onto a recorded neuron. In this scenario the amplitude, or quantal size (q), of a so-called miniature excitatory postsynaptic current (mEPSC) corresponds to the glutamate sensitivity of the postsynaptic membrane (that is, the number and conductance of its AMPARs), whereas the frequency with which mEPSCs occur is thought to reflect the probability of vesicle release from the presynaptic terminal (p) and the number of release sites (n). (n is probably equivalent to the number of synapses, because most central synapses contain only one release site each.) Quantal content, or ndotp, should represent the total presynaptic output.
Quantal analysis can also be performed on stimulus-evoked EPSCs in the absence of TTX, on the premise that the EPSC is the summation of multiple quanta. If trial-to-trial fluctuations in EPSC amplitude reflect stochastic differences in the number of quanta that are released, then these amplitudes should distribute in a multimodal, quantal manner. According to this simple model, the coefficient of variation (CV) (which is the standard deviation of the EPSC amplitudes normalized to the mean amplitude) varies oppositely with quantal content, and the inverse square, CV-2, is directly proportional to quantal content. As discussed in the text, quantal theory was originally developed in studies of the neuromuscular junction. Because central synapses differ from those at the neuromuscular junction in a number of fundamental ways that go beyond the scope of this Review, some of the assumptions on which quantal theory is based might not apply to glutamatergic synapses (see the references cited in the main text).
At CA1 synapses transmission is quite unreliable, with a p of approximately 0.3; this means that most action potentials do not result in glutamate release (they are 'synaptic failures') and that the ones that are successful rarely result in the release of more than one vesicle. Paired pulse facilitation occurs, in theory, when the Ca2+ influx at a presynaptic bouton has not entirely cleared before the next action potential arrives, resulting in a higher peak presynaptic Ca2+ concentration after this second stimulus than was achieved by the first; a higher Ca2+ concentration increases p and results in the facilitation of the EPSC. Presynaptic Ca2+concentrations quickly return to baseline values, accounting for the limited time window between the first and second stimulus during which paired pulse facilitation can be observed.
Quantal content provides a direct read-out of p in the simplest experimental scenario, in which only one synapse is activated and n = 1 (see figure). But quantal content is not always a faithful presynaptic parameter: in a scenario in which more synapses are sampled in one phase of an experiment than in another (for example, after synapse unsilencing by a long-term potentiation protocol), n will seem to rise, resulting in an increased quantal content even if p remains constant. This increase in n could reflect a true increase in the number of release sites (presynaptic unsilencing) or an increase in the number of functional postsynaptic units that respond to a constant number of release sites (postsynaptic unsilencing); because n does not distinguish between these two possibilities, a change in quantal content — and consequently in CV-2 — cannot be used in isolation as a means to determine whether a change in synaptic strength has a pre- or postsynaptic locus. To take this reasoning one step further, in the scenario in which multiple synapses are activated, some containing both AMPARs and NMDARs and some containing only NMDARs, the quantal content (and thus the CV-2) for AMPAR-mediated EPSCs will seem to be smaller than that for NMDAR-mediated EPSCs21 — a result that would be confusing if these variables were wrongly assumed to reflect only the state of the presynaptic terminal.
On the other hand, it was observed that trial-to-trial variance of EPSC amplitudes declined after LTP. This suggests a presynaptic LTP mechanism. Quantal theory states this reduced variance manifested as decrease in frequency of synaptic failures. (when stimulation does not cause transmission)  and increase in index CV-2 (inverse square of coefficient of variation of EPSC amplitudes).  This reduced variance should correlate with presynaptic changes but not with postsynaptic sensitivity.

Others observed LTP-triggered increases in quantal content (n.p) alone or in concert with increases in quantal size (q).

Contradiction: CV-2 increased after LTP in same experiments in which paired pulse facilitation remained constant. CV-2 seemed to change for A-EPSCs but not N-EPSCs.

Silent synapses is an explanation. By increasing number of active synapses that contribute to EPSCs after LTP has been triggered, synapse unsilencing mimics an increase in n, causing an apparent increase in quantal content and decrease in failure rate. Rise in quantal content would occur with no change in p. This accounts for absence of any change in paired pulse facilitation.

For decades the hippocampus has been a favourite brain structure of neurophysiologists. In part this is because of its central role in the consolidation of new episodic memories, and the hope that studying it will reveal the cellular and molecular mechanisms that underlie learning and memory. Another attractive feature of the hippocampus is its simple, consistent circuitry. Santiago Ramón y Cajal revealed some details of this circuitry in his classic drawing, pictured here in part a of the figure121.
There are three main types of excitatory neurons in the hippocampus: dentate gyrus (DG) granule cells project their axons (mossy fibres) to CA3 pyramidal cells. These CA3 neurons synapse recurrently onto other CA3 neurons and project axons (Schaffer collaterals) to the CA1, where they synapse onto the pyramidal cells there. These CA1 neurons convey the main output of the hippocampus proper.
Nowhere else in the brain has excitatory neurotransmission been more thoroughly described than at the synapses between Schaffer collaterals and the apical dendrites of CA1 pyramidal neurons. At these synapses, multiple types of glutamate receptors coexist (see figure, part b, upper panels), including AMPARs and NMDARs. Both are permeable to Na+ and K+, with reversal potentials close to 0 mV. NMDARs additionally exhibit important interactions with divalent cations: whereas Ca2+ is highly permeant, mediating the important signalling functions of these receptors, Mg2+ gets stuck in the pore, producing voltage-dependent NMDAR blockade at negative membrane potentials (see figure, part b, blue trace in bottom left panel). Thus, at the resting membrane potential (left-hand panels in part b), synaptic glutamate will evoke an excitatory postsynaptic current (EPSC) that is mediated almost entirely by AMPARs (bottom left panel in part b, red trace). Depolarized potentials will relieve the Mg2+ blockade, and EPSCs will subsequently contain contributions from both AMPARs and NMDARs (bottom right panel in partb, black trace). Using selective antagonists to one or the other receptor, these components can be isolated: the AMPAR component is represented by the red trace in the bottom right panel of part b; the NMDAR component is represented by the blue trace in this panel. These traces also highlight the important kinetic differences between the two receptor subtypes: whereas AMPAR-mediated currents activate quickly and decay within milliseconds, NMDAR-mediated currents activate more slowly and decay over hundreds of milliseconds. It should be noted that under physiological conditions the membrane potential of these dendritic spines never reaches positive values. Part a of the figure modified from Ref. 121.
Postsynaptic silence models
Evidence suggests that main mode of synaptic silence is due to absence of postsynaptic AMPARs than impaired presynaptic glutamate release. Pyramidal cell contains a mixture of synapses, some silent and some not, causing lack of control. This might misinterpret data.

Montgomery et al made paired recordings from synaptically connected CA3 neurons. Recuurent CA3 synapses seem to be functionally identical to CA3-CA1 synapses. Authors studied only EPSCs elicited by current injection and action potential generation in presynaptic neuron. This isolated a single defined population of synapses.  

Recordings from some cell pairs showed all-silent synapses that became unsilenced after a pairing protocol. Raising temprature, delivering paired pulses and applying cyclothiazide (positive modulator of AMPAR) did not reveal A-EPSCs at silent synapses.  Each manipulation facilitated A-EPSCs at functional synapses.  N-EPSCs were identical before and after pairing. This indicates unsilencing was not associated in change in glutamate concentration or in speed of glutamate diffusion.  Shows lack of functional postsynaptic AMPARs at silent synapses. Refutes presynaptic mechanism. 

If a large population of hippocampal synapses expresses postynaptic NMDARs but not AMPAR, it could be visualised. Surface AMPARs are absent at some spines. In studies of cultured neurons, a subpopulation of synaptic spines was immunopositive for surface NMDARs but not AMPARs.  Activity triggered rapid appearance of AMPAR immunoreactivity at such spines in an NMDAR-dependent manner. This indicates that synaptic silencing involves physical recruitment of AMPAr.  Electron microscopy of intact tissue showed CA1 spines with immunogold labelling for NMDARs but not AMPARs. Evidence indicates that silent synapses lack AMPARs and that synaptic silencing occurs when AMPARs arrive. 
In hippocampal tissue obtained from young rats, postembedding immunogold labelling was performed using an antibody raised against the carboxyl terminus of the AMPAR subunit GluR1 (a,d,g) or using antibodies that bind to both the GluR2 and the GluR3 subunits (b,c,e,f,h,i); both GluR1 and GluR2 contribute to virtually every tetrameric AMPAR complex in CA1 pyramidal cells. The age at which the tissue was obtained increases from left to right, from postnatal day 2 (P2) to 5 weeks. In each part of the figure, the presynaptic terminals, with glutamate-containing vesicles, are labelled p; opposite each of these terminals is the postsynaptic membrane, marked by the presence of an electron-dense band (the postsynaptic density) where glutamate receptors (black dots) crowd alongside associated anchoring and signalling proteins. A large increase in AMPAR-subunit labelling, relative to the postnatal period, is evident at 5 weeks. Figure reproduced, with permission, from Ref. 96 © (1999) Macmillan Publishers Ltd. All rights reserved.

Silencing the debate
Proof of postsynaptic silencing : preparation is bathed with an inert caged clutamate derivative. One or two-photon laser stimulation is focused on a dendritic spine in a fluorescently labelled nruon. It uncages glutamate. This evokes a single-synapse uncaging-evoked EPSC (uEPSC).

Gluatmate uncaging was used to trigger uEPSCs and thus bypass presynaptic terminal. This paper demonstrated that silent synapses express no functional AMPARs in postsynaptic membrane (Busetto et al 2008).  In acute slices of neonatal rate somatosensory cortex, some spines showed N-uEPSCs but not A-uEPSCs in response to glutamate uncaging. Hypertonic solution applied to such silent spines triggered vesicle fusion at associated presynaptic bouton.This revealed N-EPSCs but not A-EPSCs. AMPAR-silent postynaptic membrane is opposite a fully competent presynaptic terminal.

A CA1 pyramidal neuron projects its large apical dendrite down into the stratum radiatum, where Schaffer collateral axons make en passant synapses onto dendritic spines. The spine pictured on the left is mature, with a full complement of both AMPARs and NMDARs. By contrast, the spine on the right possesses only NMDARs and therefore cannot conduct current in response to presynaptic glutamate release. The expanded view of this silent synapse illustrates how an LTP-induction protocol will cause AMPARs to migrate towards the postsynaptic density, either through lateral diffusion along the synaptic membrane107 or through the fusion of AMPAR-containing endosome
Activation of CaMKII in single dendritic spines during long term potentiation by Lee et al
CaMKII plays a central role in LTP.  Using two-photon fluorescence lifetime imaging microscopy spatiotemporal dynamics of CaMKII was monitored. LTP induction and associated spine enlargement in single spines triggered transient CaMKII activation restricted to stimulated spines. CaMKII in spines was activated by NMDA receptors and L-type voltage sensitive calcium channels by Ca2+ near channels, in response to glutamate uncaging and depolarisation respectively.
Modulation of AMPA receptor unitary conductance by synaptic activity by Benke et al
Benke et al observed that LTP is associated with increase in AMPAR single channel conductance.  Increase in single channel conductance is specific to  LTP. EPSCs were measured.

This may be caused by Ca2+ permeation through NMDA channels, activating kinases and causing incorporation of new repceotrs or modifiction of conductance properties of existing ones. The correlation between the increase in gamma and the baseline gamma indicates that the initial state of the AMPA receptors may determine how synaptic efficiency is altered.
 "The finding that synaptic activity can modify the single channel conductance properties of the AMPA-receptor complement provides a fundamental mechanism for the alteration of synaptic efficiency."
a, Mean EPSCs during baseline and LTP superimposed (left) and scaled (right; expanded timescale). b, All EPSC amplitudes during this experiment. c, Current–variance relationships from baseline (filled circles) and during LTP (open circles) for this cell. Solid lines represent the data fit from which gamma was estimated (for this and all following figures). d, Rise times (20–80%, open circles) and decay times (62%, filled circles) for all EPSCs used for non-SFA. There was no significant change in the variance of rise times and decay times following the induction of LTP (n = 21).
Subunit specific rules governing AMPA receptor trafficking to synapses in hippocampal pyramidal neurons by Shi et al
A change in AMPA-R-mediated transmission underlies several developmental and adult forms of synaptic plasticity [Bear 1999], [Bliss and Collingridge 1993], [Cline et al. 1996], [Linden and Connor 1995] and [Nicoll and Malenka 1995] that may play important roles in learning and memory (Martin et al., 2000). One proposed mechanism involves an activity-controlled trafficking of AMPA-Rs from nonsynaptic to synaptic sites [Lüscher et al. 2000], [Lynch and Baudry 1984] and [Malinow et al. 2000].
AMPA-Rs are hetero-oligomeric complexes composed of different combinations of four subunits, GluR1 to GluR4 (also referred as GluRA to GluRD) [Dingledine et al. 1999], [Hollmann and Heinemann 1994] and [Seeburg 1993]. Each subunit contains a large extracellular and four membrane-associated domains showing considerable homology among different subunits. In contrast, the cytoplasmic carboxyl termini of these subunits are either long (e.g., GluR1 and GluR4) or short (e.g., GluR2 and GluR3) (Köhler et al., 1994)(Figure 1A). In hippocampus, GluR4 is mainly expressed early in development while GluR1 to GluR3 expression increases with development (Zhu et al., 2000). In adult hippocampus, these three AMPA-R subunits combine to form two distinct populations, GluR1/GluR2 and GluR2/GluR3 (Wenthold et al., 1996). The functional distinction of these two AMPA-R populations or the role played by different carboxyl termini has not been clarified.
Long-term in vivo imaging of experience-dependent snyaptic plasticity in adult cortex
Trachtenberg observed with in vivo omaging that new spines form synapses.
RApid dendritic morphogenesis in CA1 hippocampal dendrites induced by Synpatic plasticity
Activity shapes the structure of neurons and their circuits. Two-photon imaging of CA1 neurons expressing enhanced green fluorescent protein in developing hippocampal slices from rat brains was used to characterize dendritic morphogenesis in response to synaptic activity. High-frequency focal synaptic stimulation induced a period (longer than 30 minutes) of enhanced growth of small filopodia-like protrusions (typically less than 5 micrometers long). Synaptically evoked growth was long-lasting and localized to dendritic regions close (less than 50 micrometers) to the stimulating electrode and was prevented by blockade of N-methyl-d-aspartate receptors. Thus, synaptic activation can produce rapid input-specific changes in dendritic structure. Such persistent structural changes could contribute to the development of neural circuitry.
Dendritic spine changes associated with hippocampal long-term synaptic plasticity by Engert
 Here we combined a local superfusion technique2,3 with two-photon imaging4, which allowed us to scrutinize specific regions of the postsynaptic dendrite where we knew that the synaptic changes had to occur. We show that after induction of long-lasting (but not short-lasting) functional enhancement of synapses in area CA1, new spines appear on the postsynaptic dendrite, whereas in control regions on the same dendrite or in slices where long-term potentiation was blocked, no significant spine growth occurred.
Rapid formation and selective stabilisation of synapses for enduring motor memories by Xu et al
Novel motor skills are learned through repetitive practice and, once acquired, persist long after training stops1, 2. Earlier studies have shown that such learning induces an increase in the efficacy of synapses in the primary motor cortex, the persistence of which is associated with retention of the task3, 4, 5. However, how motor learning affects neuronal circuitry at the level of individual synapses and how long-lasting memory is structurally encoded in the intact brain remain unknown. Here we show that synaptic connections in the living mouse brain rapidly respond to motor-skill learning and permanently rewire. Training in a forelimb reaching task leads to rapid (within an hour) formation of postsynaptic dendritic spines on the output pyramidal neurons in the contralateral motor cortex. Although selective elimination of spines that existed before training gradually returns the overall spine density back to the original level, the new spines induced during learning are preferentially stabilized during subsequent training and endure long after training stops. Furthermore, we show that different motor skills are encoded by different sets of synapses. Practice of novel, but not previously learned, tasks further promotes dendritic spine formation in adulthood. Our findings reveal that rapid, but long-lasting, synaptic reorganization is closely associated with motor learning. The data also suggest that stabilized neuronal connections are the foundation of durable motor memory.

Adaptive regulation of neuronal excitability by a voltage- independent potassium conductance by Brickley et al
Many neurons receive a continuous, or 'tonic', synaptic input, which increases their membrane conductance, and so modifies the spatial and temporal integration of excitatory signals1, 2, 3. In cerebellar granule cells, although the frequency of inhibitory synaptic currents is relatively low, the spillover of synaptically released GABA (gamma-aminobutyric acid)4 gives rise to a persistent conductance mediated by the GABAA receptor5, 6, 7 that also modifies the excitability of granule cells8. Here we show that this tonic conductance is absent in granule cells that lack the alpha6 and delta-subunits of the GABAA receptor. The response of these granule cells to excitatory synaptic input remains unaltered, owing to an increase in a 'leak' conductance, which is present at rest, with properties characteristic of the two-pore-domain K+ channel TASK-1 (refs 9,10,11,12). Our results highlight the importance of tonic inhibition mediated by GABAA receptors, loss of which triggers a form of homeostatic plasticity leading to a change in the magnitude of a voltage-independent K+ conductance that maintains normal neuronal behaviour.

Cerebellar microcircuit as an adaptive filter

Purkinje cells provide sole output of Cerebellar cortex. They receive 2 types in input. Each PC is contacted directly by 1 climbing fibre and thousands of mossy fibres.

MFs convey info from diff sources. They contact granule cells. Granule cells have direct excitatory projections to PCs through parallel fibres. 

CFs arise solely from inferior olive. They project to PC. They dicide CC into zones which are subdivided into microzones.

A microzone is a strip of C where PCs receive CFs drive by sample inputs.  Microzone is minimal functional unit of CC.

Input from MFs and CFs have diff electrophysiological efects in PCs . PCs fire 2 diff types of spoke. Simple spikes are normal APs. May be modulated by PFs that contact PC. Complex spikes are unique to PCs. Complex spokes occur only when CF fires. 

Marr and Albus microcircuit modelling: Cerebellum function was assumed to be motor- control. PC outputs are related by motor commands.  Commands are conveyed by simple spikes fired by PCs. Comles spikes are assumed to fire at too low a rate (1 spike a second) to influence cerebellar output significantly. They might act as error or teaching signal for PC. Function of circuit might be motor learning.

Marr Albus models were applied to vestibulo-ocular reflex etc.

Marr Albus models have traits of adaptive filter.

f the two main afferents to the cerebellar cortex (see the figure, part a), climbing fibres (CFs), which are the thick ramifications of the olivocerebellar axons, make direct excitatory contact with Purkinje cells (PCs), and mossy fibres (MFs) make excitatory synaptic contacts with granule cells (and with Golgi cells (not shown)). Each ascending axon of a granule cell branches in a T to form the two ends of a parallel fibre (PF), which in turn make excitatory synaptic contacts with PCs and with the molecular layer interneurons (that is, stellate and basket cells) and Golgi cells. PFs extend for several millimetres along individual cerebellar folia. CFs and MFs also provide collaterals to the cerebellar nuclei en route to the cerebellar cortex (not shown). With the exception of granule cells, all cerebellar cortical neurons, including PCs, make inhibitory synaptic connections with their target neurons.
Connectivity of the cerebellar cortical microcircuitry
In the late 1990s, all of the above microcircuitry features were known. However, as shown, this view offered no explanation of how incoming information was channelled through the microcircuitry, so the specific processing carried out by the microcircuit was essentially unknown. In the figure, part b, inputs are colour-coded to signify the type of information (somatosensory, auditory and so on) that is conveyed. A mix of colours (for example, in granule and Golgi cells) indicates that the cell or synapse was thought to sample different types of information. In PCs and interneurons, the 'mix of mixes' illustrates that they were thought to receive mixed granule cell input. Also, interneurons were considered to provide inhibition to PCs in a non-patterned fashion in the form of feedforward and/or lateral inhibition. PCs were generally thought to be the sole recipient of CF input.
Also by the late 1990s new information had emerged about patterns of connectivity between specific areas of cerebellar cortex and their CF inputs and deep cerebellar nuclear outputs. The high degree of organization of these connections formed the basis for the concept of the microzone. Microzones seem to constitute the basic functional subunit of the cerebellum and are subdivisions of the previously established sagittal zones (for reviews see Refs 148149). Microzones are defined as a coherent strip of cortex in which the PCs are activated by essentially identical CF inputs (the figure illustrates PCs in two different microzones, which receive different inputs, as indicated by the colour code of the CFs). Because all the PCs in a microzone have a common innervation territory in the deep cerebellar nuclei, they have a specific output effect — that is, they control one specific movement component or target one specific region in the downstream cerebral cortical areas or brainstem nuclei. A rough estimate of the number of microzones in the cerebellum can be obtained as follows: based on a microzone width of ~5 PCs (50–100 μm) in the C3 zone of the cat3, a microzone length of ~15 mm, and the sagittal extent of a PC dendritic tree of ~0.3 mm, we arrive at around 200 PCs for a microzone. If the total number of PCs in the cat is ~1,000,000 (Ref. 150), then the total number of microzones in the cerebellar cortex would be ~5,000. The concept of the microzones is an important frame of reference for characterizing how incoming information is channelled through the microcircuitry. These figures do not show the unipolar brush cells, which are preferentially located in cerebellar areas with vestibular input151, or Lugaro cells.

Properties of Purkinje cell (PC) spikes from intracellular whole-cell recordings in vivo
PCs fire simple spikes (see the figure, part a, top) at ~40 spikes per second on average. They are standard action potentials typical of neuronal firing throughout the nervous system. By contrast, complex spikes (see the figure, part a, bottom), which are characterized by multiple after-discharges and appear at ~1 spike per second on average, are unique to PCs. Complex spikes are generated as a result of the activation of most or all of the PC dendritic tree by the uniquely powerful climbing fibre (CF) synapse (see main text). CF discharge, in turn, is derived from the firing of neurons in the inferior olive. Simple spikes, which do not backpropagate into the PC dendritic tree152, fire spontaneously in the absence of afferent input. The spontaneous firing rate of simple spikes can be modulated in both excitatory and inhibitory directions by specific inputs (see the figure, part b), in a manner consistent with their generation by excitatory parallel fibre (PF) and inhibitory interneuronal inputs, respectively72, 76, 85, and with these inputs being summed primarily in a linear fashion153 (note, though, that other in vitro work indicates that PCs use nonlinear summation154). The origin of simple spike modulation is still the subject of controversy, particularly concerning the relative roles of PFs and the ascending part of the granule cell axon and whether PC simple spikes operate in a bistable fashion.
PF synapses versus ascending granule cell axon synapses
In recordings from the C3 zone, as shown above, the mossy fibres and granule cells that convey input from the red skin area, which provides excitatory drive to the simple spike activity (see the figure, part b), are not located beneath the PCs72, 76. It is hence clear that the PFs, rather than the ascending granule cell axon, carry most of the excitatory input. This contrasts with the view that the ascending granule cell axon might be a dominating input in PCs, an idea that has received some experimental support155. However, many of the supporting experiments in vivo were made in anaesthetized animals, and anaesthesia can severely depress the transmission of spiking activity from the granule cell to the PF (also discussed in Refs 85156). It has also been reported that the synapses made by the ascending axon and by the PFs differ in their susceptibility to long-term depression in PCs in vitro157, but this does not seem to be a prominent trait in PCs in vivo, where inputs from granule cells located beneath and from granule cells not located beneath the PC seem equally susceptible to potentiation and depression72. Furthermore, a recent in vitro study of ascending and PF inputs to PCs using optical stimulation indicates that the two inputs are functionally equivalent158.
PC bistability
Results from in vitro and anaesthetized preparations have led to suggestions that PCs have two states, an up state and a down state, and that the simple spike output of the PC depends mainly on the current state159. In this view, CF activation works as a switch between the two states, and the PC essentially becomes a binary element. However, the functional relevance of this bistability has been challenged by the claim that it is rarely observed in awake animals160 and in studies in which the PC simple-spike firing is related to behavioural parameters in activities such as smooth-pursuit eye movements (for example, see Refs 40136161,162163164165166167168169).
There is recent evidence that in awake cats, around half of PCs show frequent long pauses (mean ~700 ms), and that the transition between pauses and modulated simple spike firing is sometimes (25% of the time) associated with complex spikes170. These data are consistent with bistability. However, the issue of functional significance is still unclear. The animals were not engaged in a specific behavioural task (other than sitting quietly), and the occurrence of pauses was not related to behavioural events. The contrast between these findings and those that report correlations between simple-spike modulation and behaviour in awake animals is striking and unexplained.

Adaptive filter models
Simplified adaptive filter: MF filter inputs are analysed into PF component signals. Signals are weighted (PF-PC synapses) and recombined to form filter (PC simple spike) output.

Filter is adaptive. Its weights are adjusted by a teaching or error signal (CF input) suing covariance learning rule.  According to rule, PF signal positively correlated with an error signal has its weight reduced through long term depression. A signal negatively correlated with an error signal has it weight increased through long term potentiation. Reducing impact of PF signals correlated with an error signal reduces error itself.

Using core computational featires of adaptive filter leads to predictions that symmetrical LTP and LTD, dual pathway plasticity, silent synapses and recurrent architecture occur in microcircuitry.

| A mossy fibre (MF) input signal is distributed over many granule cells, the axons of which form parallel fibres (PFs) that synapse on Purkinje cells (PCs). In Marr–Albus-type models, correlated firing of a PF and the single climbing fibre (CF) that winds around the PC alters the strength of the PF–PC synapse. Note that this figure omits a number of the microcircuit features shown in Box 1, in particular the inhibitory projection from granule cells to PCs via stellate and basket cells. Plasticity in this projection is only rarely included in adaptive-filter models of cerebellar function8b | The structure of this microcircuit can be identified with that of an adaptive filter as follows: the processing of a sensory input or motor signal input by the granule cell layer is interpreted as analysis by a bank of filters. PC output is modelled as a weighted sum of these PF inputs, with the weights corresponding to synaptic efficiencies. The CF input is interpreted as a teaching signal that adapts synaptic weights using the covariance learning rule48. Formally, the filter weights wi are adjusted using by δwi = − β(epi), where δwiis the change in weight, e is the teaching signal, Pi is the signal to the weight and (epi) denotes the covariance of e and Pi. The teaching signal e is often performance error, and is in that case referred to as an error signal. The learning rule can then be shown theoretically to minimize mean square performance error (e2) and is usually called the least mean square rule in artificial systems. c | Forward and recurrent architectures illustrated for horizontal vestibulo-ocular reflex (VOR) adaptation. The task of the VOR is to convert the vestibular signal vhead into motor commands m to the oculomotor plant P that move the eye so as to exactly compensate for head movements: veye = vhead. This adaptable reflex is mediated by a direct pathway through the brainstem B, supplemented by forward and recurrent adaptable pathways through the floccular region of the cerebellum C that carry mainly vestibular information (processed in V) and a motor efference copy, respectively. It has been argued17 that VOR plant compensation (changes in the adaptive filter C in response to changes in the motor plant P) depend mainly on the recurrent pathway through C. This formulation has the advantage that the required teaching signal is sensory error (retinal slip e) as shown. In more general adaptation problems both forward and recurrent pathways are necessary, with the former used for vestibular compensation (that is, adaptation to changes in V) and the latter for plant compensation20. Previous schemes for plant adaptation have used only the forward pathway in a feedback error learning architecture179. The advantages of the recurrent architecture for control of nonlinear and redundant systems are discussed in Ref. 54. Parts aand b are reproduced, with permission, from Ref. 18 © (2004) The Royal Society. Part c is reproduced from Ref. 58.

In signal processing terms a filter is a process that transforms an input signal into an output signal. For example, a reflex arc that converts a sensory stimulus into a motor command can usefully be modelled as a filter (see the figure, part a). When the filter is linear it can be completely described by its response to a spike input, called its impulse response. Note that although the emphasis here is on temporal transformations, similar considerations apply to spatiotemporal transformations.
An adaptive filter has parameters that can be varied to affect the form of the output. For example, a filter might have an adjustable time constant, so that a spike input produces a prolonged response with an adjustable decay time or an adjustable gain, which varies the amplitude of the response (see the figure, part b). The parameters of an adaptive filter can be varied to suit a given task, for example in the case of a reflex to convert an aversive sensory signal into a motor signal that will produce a fast, safe withdrawal movement.
Analysis–synthesis filters form a flexible class of adaptive filters that work by analysing the input into component signals using a bank of fixed filters. In engineering systems these filters might be bandpass filters, which split the input into its various frequency components, or tapped delay lines, which delay the input signal by varying amounts. In biological systems leaky integrators, providing components that are increasingly prolonged over time, provide a plausible analysis method. The components are then recombined to form the output signal, the amount of each component being controlled by adjustable weights (see the figure, part c). These are often called linear-in-weights filters; however, the analysis–synthesis input–output relationship does not have to be linear. Nonlinear problems can be solved by including nonlinear operations, such as products of linear filters, or by including more complex filters (such as echo state networks) in the bank of fixed filters.
An important characteristic of the adaptive-filter interpretation is its computational sufficiency. If the cerebellar microcircuit could be shown to implement an adaptive filter, its usefulness for sensory processing and motor control would be clear. Adaptive filters are not just theoretically powerful, they have also been shown to be useful in an enormous range of applications ranging from process control to adaptive noise cancellation in headphones. A particularly relevant application area is the control of humanoid robots40; for example, cerebellum-inspired adaptive controllers were extensively used in the ERATO humanoid robot project171.
Symmetrical LTD and LTP and the covariance rule
Paired stimulation of PFs and CFs induced LTD at synapses between PFs and PCs (PF-LTD).

Studies show PF-LTP reverses CF-induced PF-LTD in PCs.  In vivo, PF activation in a protocol mimicking PF-LTD protocol omitting CF activation causes receptive field expansion in PCs. Indicates LTP occurred. Whether a given PF input causes synaptic depression or potentiation depends on whether a CF input is present.

Learning rule predicts that temporal coincidence of PF and CF firing produces LTD. PF firing without CF firing produces LTP. Pronounced LTD occurs for spikes coinciding at time window of 100-200ms. Much weaker LTP for noncoincident spikes.

Simple adaptive filter models have weights that can switch between positive and negative values. Real synapses are either excitatory or inhibitory. So include a parallel apthway from granule cells to PCsvia inhibitory interneurons. Synaptic weights between PFs and internurons would behave as though  they were negative weights between PFs and PCs. Weights would show plasticity.

Dual plasticity pathway
For molecular layer interneurons tohelp implement covariance learning rule in CC 3 criteria must be fulfilled.

First, CFs must control plasticity at PF-interneuron synapses as they do at PF-PC synpases. CFs must communicate with interneurons.

2nd, plasticity at PF-interneuron synpases must have reverse signto that of PF-to-PC input as both path ways affect cerebellar output in opposite directions.

3rd, interneurons that receive CF input from on microzone must target PCs in same microzone. Otherwise specificty of learning rule would be lost.

Studies show that CFs contact interneurons and can evoke electrical response in interneurons. This seems to be generated by extrasynaptic activation of AMPA and NMDA receptors/  PF-interneuron synapses are highly plastic in vitro.

studies in vivo show that cuatneuous PF receptive fields of interneurons almost  matched receptive fiels of local CFs. As individual MFs havesmall receptor fields, it is possible that interneurons receive active syanpses only from subset of PFs that receive input from sameskin area as CD. Whereas interneuorns' synpases with all other PFs were rendered silent. PF input onto interneurons may be controlled by CF.  In  vivo study combined PF and CF stumulation while recording location of very small PF input from skin. Combined stumulation caused marked increses in receptive field of interneuron, which is associated with increase in number of active PF synapses onto intenrueon. PF activation without CF activation reduced interneuron's receptive field size, compatible with decrease in number of effective PF ynaptic inputs. Receptive field changes were opposite of those recorded in PCs. Indicate that plasticity at internruon-p
C synapses must have opposite sign to plasticity at PF-PC syanpse.

In vitro studies show that CFs control plasticity at PF-internruon s\ynpases. LTP at these synpases depends on activation of NMDA receptors. Interneurons have only extrasynpatic NMDA receptors. Normal low intensity activation of PF does not activatethem. One CF activation can activate NMDA receptors on interneuons. CF input required to elicity LTP at PF-interneuron synapse was observed, this means only Cf inputs activate NMDA receptors.

CF responses have a fast onset and long duration. Diffusion signalling is effective only at short distances. Glutamate that spills over to an interneuron must be from nearest neighbouring CF-PC synpasesor nearest CF terminals. An interneurons can receive input from 2 diff CFs, each of which contacts up to 10 PCs. A microzone is 10 PCs wide. So CFS tat provide input to an interneuron is in same microzone as interneuron.

Microzone-spec inhibition of PCs (3rd criterion for inhibitory pathway to PCs for covariance learning rule). All interneurons in a microzone have same receptive field. It is same as receptive fields of CFs and inhibitory receptive fields of PCs in that microzone.  Study of vestibulocerebellum shows that interneurons of molecular layer are drive in phase with local CFs on same microzone. Compatible that they are driven by same inputs as CFs.  Neighbouring PCs were driven out of phase but inhibited in phase with CFs and interneurons.  In phase depression of PC activity could be explained if these PCS were inhibited by interneurons that were driven in phase with CF (amd thus in same microzone).  Opticmal imaging shows inhibition of PCs by interneurons is parasagitally organised (organised as mirozones).  

Silent synapses in the cerebellum
98% PF synapses may be silent.

Silent PF-PC synapses was shown by recording synaptic currents evoked in PCs by stimulating single granule cells in vitro. Granule cells formed PF synapses on PCs but controlled actiavtion on granule cells mainly failed to elicit excitatory response at PF-PC synapse. In vivo circuitry analyss using receptive field mapping in C3 zone showed that cutaneous recetive fields of individual MFs and granuel cells are very small but PFs that innverate one PC carry a complete representation of skin. Only a fraction of available skin inputs and PF inputs provide input that activates PCs. Most inputs must be silent or noneffective.

When receptive fields of PFs and interneurons' silent synapses are made active: LTP protocols applied to PFs increase receptive field by thousands percent in PCs and interneurons. Activated population of previously silent PF synapses carried representation of entire human skin.

High proportion of PFs carry signals irrelevant to learning task (noise). Silent synapses are caused by covariance learning rule.

A PC driven by single PF with a synaptic weight.  Learning rule adjusts value of synaptic weight until it minimises error signal. If PF firing represents noise,  it can produce only erroneous output. PF input will contunuously drive CF activation until synaptic weight becomes zero and synapses becomes silent  Any noise reflected in cerbellar output produces errors. PF discharge positively correlates with error as signalled by CF spikes. Positive correlation produces LTD through covariance learning rule. This drives synaptic weights on PFs that convey a weakly relevant signal to small values and on those with no relevant signal to zero.

Covariance rules predicts that parallel inhibitory pathway has silent synapses because PF-interneuron synapses in his pathway are also plastic. Noise signal transmitted from PF to PC through inhibitory interneuron has opposite sign to noise signal transmitted to PC through direct pathway.  Pf discharge transmitted through indirect pathway is negatively correlated with error. Indirect pathway has learing rule opposite to direct pathway so negative correlation produces LTD. This dirves PF-interneuron synapse to silence.  If both Pf-Pc and PF-interneuron synapses are nonzero, covariance rule produces LTD in larger of 2 weights and LTP in smaller. This drives weights to equal intermediate values so that opposite effects of 2 pathways cancel each other out.  Covariance learning rule predicts this balance in unstable.  Intrinsic noise in each partway will drive both weights to zero.  Only correlated noise in PF and CF discharges drives weights to zero. Uncorrelated spontaneous Pf discharges do not have this effect.

Silent synapses shows why parallel inhibitory pathway from granule cells to PCs is require for covariance learningr ule. Without it, silent synapses could not be used for learning tat requires a decrease in PC output (which involves active inhibitory process). Dual pathway plasticity is required by adpative filter with noisy inputs and weights restricted to positive or negative values.

Recurrent architecture
Flocculus in cerebellum is involved with eye movement. It receives MF input related to eye movement commands. It receives through CF input an error signal related to image slip across retina.  Applying covariance learning rule, synaptic weights cease to change when there are no longer any correlation between PF inputs and CF error signal.  Adaptive filter continues to learn until this state is achieved  Its function is to decorrelate its inputs.

In systems with recurrent architecture  sensory effects of inaccurate comnmands eg movement of image across retina in VOR can be used as error signal. Solves motor error problem.