The Linear Computational Algorithm of Cerebellar Purkinje Cells

Walter, Joy T.; Khodakhah, Kamran

doi:10.1523/jneurosci.4507-05.2006

Cited by 80 publications

(83 citation statements)

References 67 publications

(75 reference statements)

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“…The axons of these granule cells, parallel fibers, provide Purkinje cells with asynchronous inputs dispersed throughout their dendritic tree. We reproduced this asynchronous, dispersed pattern of input by photoreleasing glutamate onto a patch of granule cells (4). The stimulated patch of granule cells was chosen to be either directly beneath the target Purkinje cell or Ͼ100 m lateral to it.…”

Section: Resultsmentioning

confidence: 99%

“…Up to a maximum firing rate of Ϸ250 spikes per second, this parameter is a good measure of the strength of granule cell synaptic input because it is linearly and directly correlated with the number of extra spikes after stimulus and also with the average firing rate after stimulus (4). With this method of stimulation, from trial to trial, photorelease of glutamate at the same location results in the activation of different combinations of granule cells.…”

Section: Resultsmentioning

confidence: 99%

“…However, encoding with pauses requires a specialized decoding mechanism such as rebound firing by neurons of the deep cerebellar nuclei, the physiological prevalence of which is under considerable debate (9). In contrast to encoding with pauses, the linear algorithm is independent of the pattern or location of synaptic input and holds even under conditions of input asynchrony and intact inhibition (4). Thus, given the simplicity of encoding/ decoding with the linear algorithm, as was done for pauses, we examined its suitability for cerebellar information processing by examining its utility in pattern recognition.…”

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The advantages of linear information processing for cerebellar computation

and

Khodakhah

2009

Proc. Natl. Acad. Sci. U.S.A.

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Purkinje cells can encode the strength of parallel fiber inputs in their firing by using 2 fundamentally different mechanisms, either as pauses or as linear increases in firing rate. It is not clear which of these 2 encoding mechanisms is used by the cerebellum. We used the pattern-recognition capacity of Purkinje cells based on the Marr-Albus-Ito theory of cerebellar learning to evaluate the suitability of the linear algorithm for cerebellar information processing. Here, we demonstrate the simplicity and versatility of pattern recognition in Purkinje cells linearly encoding the strength of parallel fiber inputs in their firing rate. In contrast to encoding patterns with pauses, Purkinje cells using the linear algorithm could recognize a large number of both synchronous and asynchronous input patterns in the presence or absence of inhibitory synaptic transmission. Under all conditions, the number of patterns recognized by Purkinje cells using the linear algorithm was greater than that achieved by encoding information in pauses. Linear encoding of information also allows neurons of deep cerebellar nuclei to use a simple averaging mechanism to significantly increase the computational capacity of the cerebellum. We propose that the virtues of the linear encoding mechanism make it well suited for cerebellar computation.cerebellum ͉ motor learning ͉ Purkinje cell P urkinje cells receive Ͼ150,000 parallel fiber synaptic inputs (1) that provide them with a vast and broad spectrum of information. These inputs are integrated with the spontaneous activity of Purkinje cells to provide the sole output of the computational circuitry of the cerebellar cortex. The mechanism by which this information is encoded by Purkinje cells is fundamental to theories of cerebellar computation. It has been recently demonstrated that Purkinje cells can encode this information by using 2 different mechanisms (2), either as pauses in their activity (3) or as linear increases in their firing rate (4) (see also Fig. 1B). Although, in principle, cerebellar computation can be based on either of these 2 encoding schemes, it is unlikely that they are used concurrently because they require fundamentally different decoding mechanisms. It has not been established whether either of these 2 mechanisms is used by the cerebellum, nor is it even known how they directly compare in their ability to encode information.Pattern recognition was proposed in a pair of seminal papers by Marr and Albus (5, 6) to be the mechanism by which cerebellar Purkinje cells learn motor tasks. Based on this theory, the more patterns the cerebellum recognizes, the higher its computational power and ability to fine-tune and learn motor tasks. Numerous attempts have been made to estimate the pattern recognition capacity of Purkinje cells (3,(5)(6)(7)(8), and recently it has been used to evaluate the suitability of an encoding mechanism in cerebellar computation (3).A recent evaluation of a detailed Purkinje cell model suggested that optimal pattern recognition capacity is obtained ...

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

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The advantages of linear information processing for cerebellar computation

and

Khodakhah

2009

Proc. Natl. Acad. Sci. U.S.A.

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“…Somatic AP firing rate progressively increased during the train ( Fig. 2A), due to the facilitation of PF transmission and summation of synaptic potentials (33). Sufficiently strong synaptic stimulation triggered dendritic spikes (Fig.…”

Section: Dendritic Spikes Triggered By Synaptic Input Bursts Suppressmentioning

confidence: 95%

Dendritic spikes mediate negative synaptic gain control in cerebellar Purkinje cells

Rancz

Häusser²

2010

Proc. Natl. Acad. Sci. U.S.A.

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Dendritic spikes appear to be a ubiquitous feature of dendritic excitability. In cortical pyramidal neurons, dendritic spikes increase the efficacy of distal synapses, providing additional inward current to enhance axonal action potential (AP) output, thus increasing synaptic gain. In cerebellar Purkinje cells, dendritic spikes can trigger synaptic plasticity, but their influence on axonal output is not well understood. We have used simultaneous somatic and dendritic patch-clamp recordings to directly assess the impact of dendritic calcium spikes on axonal AP output of Purkinje cells. Dendritic spikes evoked by parallel fiber input triggered brief bursts of somatic APs, followed by pauses in spiking, which cancelled out the extra spikes in the burst. As a result, average output firing rates during trains of input remained independent of the input strength, thus flattening synaptic gain. We demonstrate that this "clamping" of AP output by the pause following dendritic spikes is due to activation of high conductance calcium-dependent potassium channels by dendritic spikes. Dendritic spikes in Purkinje cells, in contrast to pyramidal cells, thus have differential effects on temporally coded and rate coded information: increasing the impact of transient parallel fiber input, while depressing synaptic gain for sustained parallel fiber inputs.A hallmark of active dendrites is their ability to produce regenerative events known as dendritic spikes (1-8). In pyramidal neurons, the inward currents associated with dendritic spikes provide a strong local depolarization that can boost distal synaptic inputs and enhance their effect on axonal action potential (AP) output (1-4), particularly during burst generation (5, 6). Furthermore, dendritic spikes can enhance the precision of axonal APs in hippocampal pyramidal neurons (7) as well as in neocortical pyramidal cells in vivo (8). Dendritic spikes thus have a boosting effect on the output of pyramidal cells, thus enhancing the gain of the synaptic input-output (I/O) function (9, 10). In contrast, the effect of dendritic spikes on AP output in Purkinje cells is not well understood. Purkinje cell dendritic spikes, originally discovered in alligator Purkinje cells (11, 12), can be triggered by strong parallel fiber (PF) activation (11, 13) or climbing fiber activation (14, 15) and are due solely to activation of dendritic voltage-gated calcium channels (13,(16)(17)(18), because Purkinje cells lack dendritic voltage-gated sodium channels and active backpropagation of APs (17,19). Calcium influx driven by dendritic spikes has an important role in triggering synaptic plasticity (20)(21)(22) and dendritic release of neurotransmitters and neuromodulators (13,23,24). Dendritic spikes triggered by climbing fiber input have virtually no effect on the somatic complex spike waveform, probably due to the large synaptic and intrinsic conductances activated during the complex spike (14). However, the functional role of parallel fiber-driven dendritic spikes in regulating axonal output has no...

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“…Remarkably, the readout was approximately linear for small inputs (cf. Walter and Khodakhah, 2006), corresponding to the activity of only a few presynaptic neurons. This high degree of sensitivity is related to the spontaneous firing of Purkinje neurons (Häusser and Clark, 1997;Raman and Bean, 1997).…”

Section: Sensitivity Of Spike Output To Excitatory and Inhibitory Synmentioning

confidence: 99%

Linking Synaptic Plasticity and Spike Output at Excitatory and Inhibitory Synapses onto Cerebellar Purkinje Cells

Mittmann¹,

Häusser²

2007

J. Neurosci.

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Understanding the relationship between synaptic plasticity and neuronal output is essential if we are to understand how plasticity is encoded in neural circuits. In the cerebellar cortex, motor learning is thought to be implemented by long-term depression (LTD) of excitatory parallel fiber (PF) to Purkinje cell synapses triggered by climbing fiber (CF) input. However, theories of motor learning generally neglect the contribution of plasticity of inhibitory inputs to Purkinje cells. Here we describe how CF-induced plasticity of both excitatory and inhibitory inputs is reflected in Purkinje cell spike output. We show that coactivation of the CF with PF input and interneuron input leads not only to LTD of PF synapses but also to comparable, "balanced" LTD of evoked inhibitory inputs. These two forms of plasticity have opposite effects on the spike output of Purkinje cells, with the number and timing of spikes sensitively reflecting the degree of plasticity. We used dynamic clamp to evaluate plasticity-induced changes in spike responses to sequences of excitation and feedforward inhibition of varied relative and absolute amplitude. Balanced LTD of both excitatory and inhibitory components decreased the net spike output of Purkinje cells only for inputs with small inhibitory components, whereas for inputs with a larger proportion of feedforward inhibition CF-triggered LTD resulted in an increase in the net spike output. Thus, the net effect of CF-triggered plasticity on Purkinje cell output depends on the balance of excitation and feedforward inhibition and can paradoxically increase cerebellar output, contrary to current theories of cerebellar motor learning.

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The Linear Computational Algorithm of Cerebellar Purkinje Cells

Cited by 80 publications

References 67 publications

The advantages of linear information processing for cerebellar computation

The advantages of linear information processing for cerebellar computation

Dendritic spikes mediate negative synaptic gain control in cerebellar Purkinje cells

Linking Synaptic Plasticity and Spike Output at Excitatory and Inhibitory Synapses onto Cerebellar Purkinje Cells

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