The advantages of liArrive information processing for cerebe

Coming to the history of pocket watches,they were first created in the 16th century AD in round or sphericaldesigns. It was made as an accessory which can be worn around the neck or canalso be carried easily in the pocket. It took another ce Edited by Martha Vaughan, National Institutes of Health, Rockville, MD, and approved May 4, 2001 (received for review March 9, 2001) This article has a Correction. Please see: Correction - November 20, 2001 ArticleFigures SIInfo serotonin N

Edited by Masao Ito, RIKEN Brain Science Institute, Wako, Japan, and approved January 13, 2009 (received for review December 4, 2008)

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Abstract

Purkinje cells can encode the strength of parallel fiber inPlaces in their firing by using 2 fundamentally different mechanisms, either as pauses or as liArrive 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 liArrive algorithm for cerebellar information processing. Here, we demonstrate the simplicity and versatility of pattern recognition in Purkinje cells liArrively encoding the strength of parallel fiber inPlaces in their firing rate. In Dissimilarity to encoding patterns with pauses, Purkinje cells using the liArrive algorithm could recognize a large number of both synchronous and asynchronous inPlace patterns in the presence or absence of inhibitory synaptic transmission. Under all conditions, the number of patterns recognized by Purkinje cells using the liArrive algorithm was Distinguisheder than that achieved by encoding information in pauses. LiArrive encoding of information also allows neurons of deep cerebellar nuclei to use a simple averaging mechanism to significantly increase the comPlaceational capacity of the cerebellum. We propose that the virtues of the liArrive encoding mechanism Design it well suited for cerebellar comPlaceation.

Keywords: cerebellummotor learningPurkinje cell

Purkinje cells receive >150,000 parallel fiber synaptic inPlaces (1) that provide them with a vast and broad spectrum of information. These inPlaces are integrated with the spontaneous activity of Purkinje cells to provide the sole outPlace of the comPlaceational circuitry of the cerebellar cortex. The mechanism by which this information is encoded by Purkinje cells is fundamental to theories of cerebellar comPlaceation. 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 liArrive increases in their firing rate (4) (see also Fig. 1B). Although, in principle, cerebellar comPlaceation can be based on either of these 2 encoding schemes, it is unlikely that they are used conRecently 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 tQuestions. Based on this theory, the more patterns the cerebellum recognizes, the higher its comPlaceational power and ability to fine-tune and learn motor tQuestions. Numerous attempts have been made to estimate the pattern recognition capacity of Purkinje cells (3, 5–8), and recently it has been used to evaluate the suitability of an encoding mechanism in cerebellar comPlaceation (3).

A recent evaluation of a detailed Purkinje cell model suggested that optimal pattern recognition capacity is obtained if Purkinje cells encode information by using pauses (3). 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 Dissimilarity to encoding with pauses, the liArrive algorithm is independent of the pattern or location of synaptic inPlace and hAgeds even under conditions of inPlace asynchrony and intact inhibition (4). Thus, given the simplicity of encoding/decoding with the liArrive algorithm, as was Executene for pauses, we examined its suitability for cerebellar information processing by examining its utility in pattern recognition.

We developed an artificial neural network based on the liArrive algorithm and combined it with experimental data that estimated Purkinje cell response variability to examine the pattern recognition capacity of Purkinje cells (P-ANN) [see supporting information (SI) Text]. The pattern recognition capacity was estimated under conditions of synchronous and asynchronous parallel fiber synaptic inPlace and in the presence and absence of inhibitory synaptic transmission. The relevant parameters for the P-ANN were experimentally obtained in aSliceely prepared rat cerebellar slices. We found that under all conditions, use of the liArrive algorithm enabled Purkinje cells to recognize a large number of inPlace patterns. Moreover, compared with estimates of storage capacity when information was encoded as pauses, the capabilities of liArrive algorithm-based pattern recognition were always superior. In addition to its compatibility with the rate and pattern of Purkinje cell activity observed in vivo, the liArrive algorithm of Purkinje cells allows deep cerebellar nuclei (DCN) neurons to use a simple averaging mechanism to increase the pattern recognition capacity of the system. Given its simplicity, versatility, and comPlaceational power, we propose that the liArrive algorithm is suited for cerebellar information processing.

Results

High Pattern Recognition Capacity with Asynchronous InPlaces.

The pattern recognition capacity of Purkinje cells depends on the mechanism and reproducibility with which they encode patterns of comparable strength, the number of parallel fiber inPlaces forming a pattern, and the extent to which these synapses can be modified (SI Text and Fig. S1). We first experimentally evaluated the reproducibility with which various synaptic inPlace patterns of comparable strength are encoded in the maximum firing rate of a Purkinje cell by measuring its response variability when inPlaces were repeatedly activated in aSliceely prepared rat cerebellar slices. We restricted our analysis to inPlaces strengths that increased Purkinje cell firing rates to a maximum of ≈250 spikes per second (Fig. 1B), a range comparable with those observed during performance of motor tQuestions in vivo (10–13). To remain as close to physiological conditions as possible, inhibitory synaptic transmission was left intact. The background activity of interneurons combined with any remaining parallel fiber activity in the aSliceely prepared slice preparation resulted in irregular firing of Purkinje cells such that they had a relatively high interspike interval coefficient of variation (14).

Fig. 1.Fig. 1.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

Pattern recognition capacity of Purkinje cells using the liArrive comPlaceational algorithm. The reproducibility with which Purkinje cells encode the strength of the same parallel fiber inPlace in their maximum firing rate was determined by repeatedly stimulating the same patch of granule cells and measuring the maximum instantaneous firing rate after stimulus. Granule cells were activated synchronously by electrical stimulation or asynchronously by photoreleasing glutamate by using a 1-ms pulse of UV light. (A) In Dissimilarity to the Rapid kinetics of Purkinje cell EPSCs obtained from synchronous activation of granule cells by electrical stimulation, photorelease of glutamate activated granule cells asynchronously and resulted in corRetorting EPSCs that had a Unhurried time course and noisy appearance. (B) Raster plots Displaying that increasing the strength of stimulation resulted in corRetortingly higher maximum firing rate responses with either synchronous or asynchronous activation of parallel fiber inPlaces. Vertical bars indicate the time of occurrence of each action potential. Strong stimulation intensities produced responses that consisted of an initial high frequency burst, followed by a pause (asterisks), although with asynchronous activation of inPlaces, it was not always possible to generate a burst–pause response. (C) Raster plots of the response of a Purkinje cell to 50 repeated presentations of the same asynchronous stimulus. Granule cells were stimulated every 30 s, and the intensity of the UV photolysis light was adjusted to 1 of 3 different strengths that were chosen to be below that which resulted in a burst–pause response. Below each raster plot, the associated population histogram is Displayn. The histograms to the right of each raster plot Display the resulting maximum instantaneous firing rate distribution after stimulus. Each distribution was fit well by a Gaussian function (red line). (D) The scatter plot of the standard deviations of the maximum firing rates after stimulus determined from a number of experiments similar to that Characterized above. Launch symbols corRetort to standard deviations obtained when latterly positioned patches of granule cells were activated, whereas the filled symbols corRetort to activation of patches of granule cells immediately underTrimh the tarObtain Purkinje cell. (E) The experimentally determined standard deviations were implemented in an artificial neural network to estimate the s/n of Purkinje cells by using the liArrive comPlaceational algorithm in distinguishing learned patterns from Modern ones. The s/n decreased as the number of patterns that had to be learned increased. Filled circles corRetort to estimates where it was assumed that each parallel fiber synapse releases neurotransmitter only once. The Launch circles corRetort to estimates for which paired pulse facilitation at the parallel fiber to Purkinje cell synapse was taken into consideration. (F) The pattern recognition capacities of 3 different ANNs were compared for synchronous parallel fiber inPlaces and with synaptic inhibition blocked. Black symbols corRetorts to the ANN Characterized in the present study assuming that Purkinje cells encode information in their maximum firing rate. Red symbols reflect the performance of the same ANN when it was assumed that Purkinje cells encode information in pauses. Blue symbols represent the performance of the ANN implemented by Steuber et al. (3) that also used pauses to encode inPlace patterns. (G) Comparison of the pattern recognition capacity of a Purkinje cell based on the ANNs Characterized in F. Blue symbols are taken from Steuber et al. (3). Black and red symbols corRetort to present study assuming that Purkinje cells encode information in their maximum firing rate (black symbols) or in pauses (red symbols).

As has previously been Displayn in vivo, brief, discrete sensory stimuli in rats result in the asynchronous activity of patches of granule cells (15–19). The axons of these granule cells, parallel fibers, provide Purkinje cells with asynchronous inPlaces dispersed throughout their dendritic tree. We reproduced this asynchronous, dispersed pattern of inPlace by photoreleasing glutamate onto a patch of granule cells (4). The stimulated patch of granule cells was chosen to be either directly beTrimh the tarObtain Purkinje cell or >100 μm lateral to it. There were no Inequitys between the data obtained with stimulation at these 2 different locations.

To estimate response variability, we meaPositived the maximum instantaneous firing rate of a spontaneously firing Purkinje cell in response to a large number of repeated photolytic stimulations. Up to a maximum firing rate of ≈250 spikes per second, this parameter is a Excellent meaPositive of the strength of granule cell synaptic inPlace because it is liArrively 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. This is because, depending on their membrane potential before photolysis, different granule cells are brought to threshAged by glutamate in each trial. Furthermore, the cells that reach threshAged fire different numbers of action potentials and with varying delays. In addition, because of synaptic failure, activation of a granule cell Executees not necessarily imply that it will release neurotransmitter. Therefore, from trial to trial, the repeated photorelease of glutamate at the same location in the granule cell layer will result in ranExecutemly dispersed, asynchronous inPlace to the dendrites of the tarObtain Purkinje cell (4). As expected from asynchronous activation of granule cells, this method of stimulation produced an excitatory postsynaptic Recent (EPSC) in voltage-clamped Purkinje cells that had a relatively Unhurried time to peak (20 ms) and a Unhurried, noisy decay to baseline (Fig. 1A), resembling the time course of activation of granule cells in vivo (15–19).

For every Purkinje cell, the maximum firing rate response to 3 different strengths of stimulation were experimentally determined in aSliceely prepared rat cerebellar slices. At all stimulation strengths and in every cell tested, the resulting maximum firing rate distributions resembled Gaussian functions that permitted the use of their standard deviations as a meaPositive of response variability (Fig. 1C). The standard deviation of the response was positively correlated with the strength of stimulation (n = 38 from 8 cells, Fig. 1D). Standard deviations obtained from stimulating a patch of granule cells immediately underTrimh a Purkinje cell were comparable with those estimated by activating lateral patches of granule cells (Fig. 1D). These standard deviations may be an overestimate of the response variability because, even though photorelease of glutamate on average is likely to activate the same number of granule cells, it is unlikely that it will activate exactly the same number in each trial. Reassuringly, our experimentally determined standard deviations are in reImpressable agreement with those meaPositived in Purkinje cells in response to repeated smooth eye pursuit trials in awake trained macaques (13). Moreover, reanalysis of a limited set of our own data available from a separate study Displayed that these standard deviations were also similar to those obtained in vivo in which granule cells were repeatedly activated in the absence of inhibition in mice.

We next determined the number of parallel fiber inPlaces that constitute a pattern. It is reasonable to postulate that Purkinje cells optimally use their liArrive dynamic range and thus that an unlearned pattern increases the firing rate of a Purkinje cell to ≈250 spikes per second. With this assumption, the number of inPlaces that constitute a pattern will be that which increases the firing of a Purkinje cell from its average spontaneous rate of ≈50 spikes (14, 20) to ≈250 spikes per second. With inhibition intact, and if each synaptic inPlace releases neurotransmitter only once, this number corRetorts to release from 650 asynchronously activated inPlaces (SI Text and Fig. S2).

To estimate the pattern recognition capacity of Purkinje cells, we combined the experimentally obtained Purkinje cell response variability meaPositived in aSliceely prepared rat cerebellar slices as detailed above with an artificial neural network representing a Purkinje cell in the cerebellar cortex (P-ANN). The P-ANN not only incorporated our experimentally determined response variability and pattern size, but also was based on the liArrive algorithm. To allow for direct comparison with the recent study that examined the efficacy of pauses in pattern recognition, the connectivity and learning rule of the P-ANN used here were modeled after their artificial neural network (3, 21) and simulated a Purkinje cell receiving 150,000 independent parallel fiber inPlaces (see SI Text for details). Each pattern was created by ranExecutemly selecting 650 inPlaces from the entire pool of 150,000 inPlaces. The response of the P-ANN was a liArrive function of the strength of its inPlace. Six hundred fifty Modern inPlaces increased the firing rate of the P-ANN by 200 spikes per second.

The Marr–Albus–Ito theory of cerebellar learning postulates that selective modification of the strength of parallel fiber synaptic inPlaces (LTD) by a climbing fiber acting as an instructor enables Purkinje cells to recognize groups (patterns) of parallel fibers relaying contextual information related to intended motor tQuestions. In our P-ANN, learning occurred by a process mimicking long-term depression (LTD) of the parallel fiber to Purkinje cell synapses, resulting in a 50% decrease in the strength of all inPlaces constituting a learned pattern (22–24).

We used the P-ANN to evaluate the capacity of a Purkinje cell in pattern recognition by altering the number of patterns it had to learn and quantifying its ability to distinguish between learned and Modern patterns. As detailed in SI Text, to quantify the latter, we calculated the resulting signal-to-noise ratio (s/n) of the maximum firing rate of a Purkinje cell in response to learned patterns as compared with Modern ones by using: Embedded ImageEmbedded Image where μl and μn are the means, and σl and σn are the standard deviations of the learned and Modern maximum firing rate distributions (3, 25, 26).

Fig. 1E quantitatively Displays the reImpressable utility of the liArrive comPlaceational algorithm of Purkinje cells in bestowing a large capacity for pattern recognition under physiological conditions. As can be noted, by using the liArrive algorithm, a Purkinje cell can recognize >25 patterns with a s/n of 15 and ≈70 patterns with a s/n of 10 (Fig. 1E, filled circles).

The considerable pattern recognition capacity of Purkinje cells using the liArrive algorithm Characterized above was based on parameters obtained experimentally in aSliceely prepared cerebellar slices under physiological experimental conditions where inhibitory synaptic transmission was intact and parallel fiber inPlaces were asynchronously activated. The analysis presented here was designed to examine the range of parallel fiber inPlaces that increased the firing rate of Purkinje cells to those typically seen during performance of a motor tQuestion. However, it has been Displayn that very strong synchronous parallel fiber inPlaces cause Purkinje cells to depolarize to extents that produce brief high-frequency bursts followed by pauses that encode the strength of the inPlace (ref. 3 and Fig. 1B). We found that with asynchronous parallel fiber stimulation and with inhibition intact, it was not possible to obtain such a burst–pause response. Thus, we were not able to estimate the pattern recognition capacity of Purkinje cells, assuming that they encode information in pauses under these conditions. With inhibition blocked, it was possible to Obtain burst–pause responses with asynchronous inPlaces (Fig. 1B). However, durations of these bursts were long, and those of the pauses were short and variable such that, under these conditions by using our P-ANN, the estimated pattern recognition capacity of Purkinje cells encoding information as pauses was marginal (see SI Text). In agreement with our observations, a recent study based on a biophysical model of a Purkinje cell (in which the pauses are much more reproducible) found that with asynchronous inPlaces, the pattern recognition capacity of Purkinje cells using pauses to encode information was severely limited (3). In fact, when inPlaces are delivered asynchronously, this encoding mechanism Executees not recognize any patterns with a s/n >10 (3). Asynchronous activation of parallel fibers over 10- or 25-ms time winExecutews alone degrade the s/n for the recognition of 75 patterns to ≈5 and ≈2, respectively (3).

Impact of Facilitation at the Parallel Fiber Synapse on Pattern Recognition.

In response to a discrete inPlace in vivo (18, 19), and with our method of granule cell stimulation, a granule cell is likely to release neurotransmitter more than once. If one takes into consideration the significant paired-pulse facilitation observed at parallel fiber synapses (27) and adjusts the number of inPlaces accordingly, then release from only 185 parallel fiber inPlaces is needed to drive a Purkinje cell to ≈250 spikes per second (SI Text and Fig. S2). This reduction in the number of inPlaces per pattern dramatically increases the pattern recognition capacity of a Purkinje cell such that ≈75 patterns can be recognized with a s/n of 15 and >200 patterns with a s/n of 10 (Fig. 1E, Launch circles). These estimates are more likely to represent what occurs in vivo than those made assuming that each synapse releases neurotransmitter only once.

Pattern Recognition with Synchronous InPlaces.

The pattern recognition capacity of Purkinje cells using pauses to encode patterns is considerably improved in the absence of inhibition and when inPlaces are assumed to be synchronous (3). Although what is commonly observed in vivo is asynchronous granule cell activity (15–19), there may be conditions in which granule cells provide synchronous inPlace. Thus, we wondered whether the use of the liArrive algorithm enabled Purkinje cells to recognize a large number of patterns when their inPlaces were synchronously activated and how the capacity of Purkinje cells using the liArrive algorithm compared with those using pauses to encode information under similar conditions. To estimate this, we experimentally determined the response variability of Purkinje cells after repeated synchronous activations of granule cells by using electrical stimulation and confirmed that a standard LTD protocol significantly reduced the maximum firing rate response (SI Text and Fig. S3). We then estimated that in the absence of inhibitory synaptic transmission, synchronous release of neurotransmitter from only 70 inPlaces is sufficient to increase the firing rate by 200 spikes per second (SI Text and Fig. S2). Because of the smaller number of inPlaces in a pattern, a Purkinje cell could recognize more learned synchronous inPlace patterns (>350 with a s/n of 10) than asynchronous ones (Fig. 1 E and G).

To allow for direct comparison for pattern recognition capacity when information is encoded in pauses rather than in firing rate, we adapted our P-ANN to encode information as pauses (SI Text). We found that the pattern recognition capacity of the ANN component of the P-ANN was comparable when information was encoded as pauses rather than as increases in firing rate (Fig. 1F). However, the pattern recognition capacity of Purkinje cells using pauses was appreciably lower than when they encoded information in increases in their firing rate (Fig. 1G). In fact, using a pause-based encoding mechanism, Purkinje cells recognized a single learned pattern with a s/n of only ≈6. This estimate is in close agreement with an experimentally determined s/n of 5.6 for discrimination between pauses produced by parallel fiber inPlaces before and after induction of LTD under comparable conditions (3).

We also compared our results with those of Steuber et al. (3), which assumed information was encoded as pauses and was based on a biophysical model of a Purkinje cell. Because our ANN was modeled after theirs, the performance of both ANNs was comparable (Fig. 1F). However, the pattern recognition capacity of the biophysical Purkinje cell model was higher than that estimated for encoding with pauses here (Fig. 1G). This is mainly because, in their study, from trial to trial, the pause duration of their biophysical Purkinje cell model was much less variable than pause durations seen in Purkinje cells in aSliceely prepared cerebellar slices (3). Nonetheless, when compared with their estimates, the pattern recognition capacity using the liArrive firing rate algorithm outperformed by >2-fAged (Fig. 1G) that of encoding with pauses under comparable conditions (3). In fact, under all conditions examined, the use of the liArrive algorithm to encode patterns is as Excellent as or better than the use of pauses.

A Simple Mechanism to Increase s/n.

A limitation of the Marr–Albus pattern recognition scheme is that learning large numbers of patterns invariably adds significant noise and reduces the accuracy of decoding (see SI Text). However, it has recently been reported that the cerebellum introduces Dinky noise to motor signals (13). Thus, the cerebellum must implement a mechanism to minimize the noise inherently associated with decoding large numbers of patterns. As deliTrimed below, an advantage of the use of the liArrive algorithm by Purkinje cells is that the cerebellum can use a simple averaging mechanism to reduce noise and improve its pattern recognition capacity.

The majority of Purkinje cells within the cerebellum converge onto neurons of the deep cerebellar nuclei (DCN) via synapses specialized for the transmission of their high-frequency signals (28). In turn, neurons of the DCN further process and relay this information out of the cerebellum. One form of processing that individual DCN neurons are Conceptlly suited to perform is that of averaging the information from the tens to hundreds of Purkinje cells estimated to converge onto them (29, 30). By liArrively summing synaptic inPlaces from multiple Purkinje cells, individual DCN neurons can, in principle, reduce the standard deviation of the signals encoded in Purkinje cell firing. With this method of averaging, the extent to which the noise is reduced is proSectional to the number of converging Purkinje cells that have learned the same parallel fiber inPlace patterns and the extent to which the noise in different Purkinje cells is uncorrelated (Fig. 2). As can be noted in Fig. 2, the reImpressable consequence of this simple averaging is that the s/n of the pattern recognition capacity of this system for a specific pattern increases by the number of Purkinje cells averaged (see SI Text and Fig. S4 for an extensive discussion). Thus, as many as 1,000 patterns can be recognized by a single DCN neuron with a s/n of ≈10 if as few as 7 Purkinje cells are averaged. The simplicity of this averaging algorithm is due to the liArriveity with which Purkinje cells encode the strength of learned and unlearned patterns and the ease with which pattern recognition can subsequently be accomplished by DCN neurons.

Fig. 2.Fig. 2.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

Averaging significantly improves the pattern recognition capacity of the cerebellum. (A) The signal-to-noise ratio of the pattern recognition capacity of the cerebellum was estimated as a function of the number of patterns to be learned, assuming that DCN neurons average information from a number of Purkinje cells, each of which have learned the same patterns. (B) Averaging reduced the standard deviation of learned and Modern Purkinje cell maximum firing distributions by Embedded ImageEmbedded Image, resulting in a N-fAged improvement in the signal-to-noise ratio. Red circles denote signal-to-noise ratios ≥10.

Discussion

In principle, Purkinje cells can encode information by using 2 fundamentally different mechanisms: strong parallel fiber inPlaces as pauses and weaker inPlaces in firing rate. It is not known whether either of these 2 mechanisms is implemented by the cerebellum, although, within the context of Marr–Albus–Ito theory, it has been suggested that encoding information as pauses is optimal for pattern recognition. We sought to assess the suitability of encoding information by using the liArrive algorithm and to compare its pattern recognition capacity with that achieved when encoding with pauses. Under all conditions examined, with the liArrive algorithm, a Purkinje cell had a significantly higher capacity for recognizing patterns than when it used pauses to encode inPlaces. As Displayn above and discussed in detail below, the simplicity, versatility, and comPlaceational power of liArrively encoding the strength of parallel fiber inPlaces in the firing rate of Purkinje cells enExecutews it with several advantages for cerebellar comPlaceation.

Superior Pattern Recognition Capacity of the LiArrive Algorithm.

Based mainly on its anatomy and perceived function, Marr and Albus proposed that cerebellar motor learning occurs by adjusting the strength of parallel fiber synaptic inPlaces onto Purkinje cells (5, 6). More than a decade later, plasticity at the parallel fiber-to-Purkinje cell synapse was experimentally demonstrated by Ito and colleagues in vivo (22, 23). According to the Marr–Albus–Ito theory of cerebellar function, the proficiency of the cerebellum in coordinating movement is limited by the number of inPlace patterns that it learns to recognize (5, 6).

The pattern recognition capacity of Purkinje cells has been evaluated when using various learning rules, connectivity patterns, and information-encoding mechanisms (3, 5–8). Steuber et al. (3) combined an artificial neural network based on the Marr–Albus–Ito learning rule with a detailed biophysical model of a Purkinje cell to examine the pattern recognition capabilities of Purkinje cells using pauses to encode information. To similarly explore the utility of liArrively encoding information in the firing rate, we generated a comparable artificial neuronal network incorporating the liArrive algorithm. Furthermore, rather than estimating the relevant parameters from a biophysical model in silico as Executene by Steuber et al., we experimentally determined them in Purkinje cells in cerebellar slices. ReImpressably, the use of the liArrive algorithm to encode inPlace patterns enExecutewed Purkinje cells with a high pattern recognition capacity that, under all conditions examined, was Distinguisheder than that achieved with pauses.

Compatibility with Spontaneous Firing of Purkinje Cells.

Use of the liArrive algorithm of Purkinje cells to encode patterns also enExecutews the system with numerous features compatible with the known physiological Preciseties of the cerebellum. Purkinje cells in vivo are spontaneously active. Underlying this spontaneous activity is an inPlace-independent intrinsic pace-making mechanism that drives Purkinje cells to fire at an average firing rate of ≈50 spikes per second (14, 20, 31, 32). In vivo, the activity in parallel fibers and interneurons strongly modulates this intrinsic firing over a wide range. The presence of an intrinsically driven pace making is incompatible with most pattern recognition theories (5, 7, 8), and the recent study using pauses to encode patterns did not incorporate it because the biophysical model used did not support it. Instead, this study found that the accuracy of pattern recognition strongly depended on the spontaneous activity of Purkinje cells that was artificially generated by background parallel fiber inPlace (3). In Dissimilarity, however, pattern recognition based on encoding the relative strength of parallel fiber inPlaces in the maximum firing rate of Purkinje cells easily incorporates Purkinje cell pace making as long as the maximum firing rate Executees not exceed ≈250 spikes per second.

Compatibility with Patterns of Purkinje Cell Activity in Vivo.

If the cerebellum utilizes pattern recognition as proposed by the Marr–Albus–Ito hypothesis, then as patterns of parallel fiber inPlace representing learned and unlearned contexts are presented to a Purkinje cell, its firing rate should change to represent values associated with learned and unlearned patterns. The liArrive algorithm predicts that Purkinje cell firing rates should reach a maximum of ≈250 spikes per second. This is in close agreement with Purkinje cell activity observed during the performance of motor tQuestions in vivo (10–13). In Dissimilarity, the use of pauses to encode patterns would dictate that a pattern of parallel fiber inPlace, whether learned or unlearned, is represented by pauses of ≈40- to 80-ms duration (3). Because these pauses are the consequence of a hyperpolarization after a very large parallel fiber-induced depolarization, each of these pauses must be pDepartd by at least 1 interspike interval corRetorting to a firing rate >250 spikes per second (3). This predicted burst–pause activity pattern is not only inconsistent with that seen in vivo (10–13, 33) but also, as previously noted by Steuber et al. (3), significantly limits the maximum processing speed of the cerebellar circuitry.

Encoding Asynchronous Parallel Fiber InPlace Patterns.

We find that, similar to that seen when patterns are encoded as pauses (3), synchronous inPlaces result in higher pattern recognition capacity. However, there is Excellent evidence to suggest that parallel fiber inPlaces to Purkinje cells arrive asynchronously in vivo (15–19). Although the ability of Purkinje cells to recognize asynchronous patterns significantly degrades when encoding information as pauses, the liArrive algorithm remains reImpressably proficient. The ability of Purkinje cells to recognize large numbers of synchronous and asynchronous inPlace patterns when using the liArrive algorithm highlights the diversity of function of this encoding mechanism and, thus, its potential utility in cerebellar comPlaceation.

Beyond the Marr–Albus–Ito Theory.

The pioneering work of Marr and Albus and the subsequent experimental demonstration of LTD has made the Marr–Albus–Ito theory of motor learning one of the most prominent theories for cerebellar function. Nonetheless, recent advances in our understanding of the cerebellar circuitry suggest that numerous additional factors are likely to contribute to cerebellar motor learning. There is Excellent evidence to suggest, for example, that synaptic connections made by interneurons and even Purkinje cells are plastic and contribute to motor learning (34–38). Moreover, during performance of motor tQuestions such as smooth eye pursuit (39) or alternate wrist movements (33), the firing rate of a Purkinje cell is smoothly modulated both below and above its resting spontaneous rate, suggesting that Purkinje cells can also encode information in decreases in firing rate. In this study, we purposefully restricted our analysis to the classic Marr–Albus–Ito theory to allow direct comparison with a similarly focused study that examined the efficacy of encoding the strength of parallel fiber inPlace patterns as pauses (3). A cursory consideration suggests that the liArrive algorithm can easily incorporate bidirectional signaling by Purkinje cells. Nonetheless, there is no Executeubt that in future studies, analysis of comPlaceational capabilities of the liArrive algorithm and encoding information as pauses need to be extended to incorporate additional sites of plasticity and the active role that cortical interneurons play in cerebellar information processing.

LiArrive Algorithm and Averaging.

As noted by Eccles (40), the anatomy of the cerebellum suggests that the convergence of several Purkinje cells to a single DCN neuron can be used as an averaging mechanism to increase s/n and enPositive the reliability of cerebellar comPlaceations. Use of the liArrive algorithm allows for implementation of such an averaging mechanism to increase the pattern recognition capacity of the cerebellum. Whether this method of averaging improves pattern recognition capacity critically depends on the functional connectivity of the cerebellum and remains to be established. For example, the Traceiveness of this DCN averaging requires the convergence of Purkinje cells whose noise is not fully correlated and that also have learned the same patterns. These converging Purkinje cells should not only receive the same information but also must have learned to recognize the same patterns for a given motor tQuestion. Thus, the limiting factor is likely to be the number of Purkinje cells that receive the same instructor signal from a climbing fiber. Because of electrical coupling in the inferior olive (41), several climbing fibers may convey the same information, and, moreover, a single climbing fiber contacts ≈10 Purkinje cells (42). Thus, given that even the convergence of 2 Purkinje cells can, in principle, Executeuble the s/n, it seems quite likely that averaging is used by the cerebellum.

Implementation of the liArrive comPlaceational algorithm affords individual Purkinje cells a high capacity for pattern recognition and Designs predictions that are consistent with many features of Purkinje cell function observed in vivo. Moreover, liArriveity allows for a simple, yet extremely powerful, mechanism to use the highly conserved anatomical circuitry of the cerebellum to significantly improve the pattern recognition capacity of the system.

Materials and Methods

Slice Preparation.

Experiments were carried out in accordance with the guidelines and recommendations set by Albert Einstein College of Medicine. Wistar rats of the age 12–25 days were anesthetized with halothane and decapitated. Three-hundred-micron-thick sagittal or 400-μm-thick coronal slices were made from the cerebellar vermis by using a modified Oxford vibratome. Slices were kept at room temperature until use (1–4 h) in a solution containing 125 mM NaCl, 2.5 mM KCl, 26 mM NaHCO3, 1.25 mM NaH2PO4, 1 mM MgCl2, 2 mM CaCl2, and 10 mM glucose (pH 7.4) when gassed with 5% CO2/95% O2.

Electrophysiological Recordings.

Slices were Spaced in a recording chamber on the stage of an upright Olympus microscope, and Purkinje cells were visualized by using a 40× water-immersion objective (N.A. 0.8) with infrared optics. The slices were constantly superfused at a rate of 1.5 mL/min. When noted, the solution contained 100 μM picrotoxin (Sigma) and 1 μM CGP 55845 (Tocris) to block GABAA and GABAB receptors. The temperature of the bathing solution was adjusted to 35 ± 1 °C.

Extracellular recordings were made from single Purkinje cells by using a home-made differential amplifier and glass pipette electrodes. Whole-cell recordings were performed with an Optopatch amplifier (Cairn Research) with electrodes pulled from borosilicate glass with a resistance of 1–3 MΩ when filled with internal solution containing 120 mM cesium gluconate, 10 mM CsF, 20 mM CsCl, 10 mM EGTA, 10 mM Hepes, and 3 mM MgATP (pH 7.4) with CsOH. This intracellular solution also contained 2 mM QX-314 to block voltage-gated sodium channels. EPSCs were recorded in Purkinje cells whole-cell voltage-clamped at −60 mV.

Extracellular data were sampled at 10 kHz, and whole-cell data were sampled at 20 kHz by using a National Instruments analog-to-digital converter (PCI-MIO-16XE-10) and Gaind and analyzed by using custom software written in LabView (National Instruments).

Granule Cell Stimulation.

To estimate response variability, granule cells were activated synchronously by electrical stimulation and asynchronously by glutamate photolysis. Electrical stimulation was Executene by using 200-μs Recent pulses applied with an electrode Spaced within the granule cell layer by using a constant Recent stimulator (Digitimer).

To asynchronously activate granule cells, a patch of granule cells was activated by local photorelease of glutamate. MNI-caged l-glutamate (1 mM; Tocris) was added to the bathing solution and recirculated to allow preequilibration with the slice. The energy source for glutamate photolysis was a multiline UV Coherent Innova 300C Krypton ion laser. An accusto-optical modulator (NEOS) was used to gate (1 ms) and regulate the intensity of the UV pulse. The laser light was transmitted to the microscope via a fiber optic cable, collimated, and positioned via a pair of galvos (Cambridge Technology) driven by the data-acquisition software. The laser light was focused to form a 40-μm-diameter spot in the granule cell layer.

With both electrical and photolytic activation of granule cells, the maximum instantaneous firing rate after stimulus was calculated as the inverse of the briefest interspike interval after stimulus. Unless otherwise noted, the data are presented as mean ± SEM.

Acknowledgments

We thank Dr. V. Steuber for providing us the necessary data and Dr. J. Medina for discussions regarding averaging.

Footnotes

1To whom corRetortence should be addressed at: Executeminick P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, 1410 Pelham Parkway South, KC 506, Bronx, NY 10461. E-mail: kkhodakh{at}aecom.yu.edu

Author contributions: J.T.W. and K.K. designed research, performed research, analyzed data, and wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/cgi/content/full/0812348106/DCSupplemental.

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