Sunday, 30 December 2012

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.







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