Computational physiology of the neural networks of the primate globus pallidus: function and dysfunction

Neuroscience 198 (2011) 171–192

REVIEW COMPUTATIONAL PHYSIOLOGY OF THE NEURAL NETWORKS OF THE PRIMATE GLOBUS PALLIDUS: FUNCTION AND DYSFUNCTION J. A. GOLDBERGa AND H. BERGMANb*

The first generation—pyramidal vs. extra pyramidal subsystems 172 The second generation—the basal ganglia is part of a cortical closed loop 172 Current models and the major anatomical constraints of the basal ganglia 173 Cellular anatomy of the pallidal network 174 The pallidal neurons 174 The synaptic input of the pallidal neurons 174 Cellular physiology of pallidal cells 175 Physiological characteristics of the main pallidal neurons 175 Ionic channels of the pallidal neurons 176 Spiking activity of neurons in the pallidal network 176 Discharge rate and the different classes of neurons in the pallidal network 176 Discharge patterns in the pallidal network 177 GPe pauses 178 Cross-correlation of spontaneous spiking activity in the pallidal network 179 Neuronal responses to behavioral events in the pallidal network 180 Similarity of encoding between pallidal neurons (signal correlation) 181 The spiking activity of the pallidal networks following dopamine depletion (Parkinson’s disease) 181 Discharge rate in the pallidal networks following dopamine depletion 182 Discharge patterns in the pallidal networks following dopamine depletion 182 Synchronization of pallidal activity following striatal dopamine depletion 182 Dynamical system characterization of basal ganglia neurons 183 Dynamical system analysis of neurons in a nutshell 183 Dynamical system analysis of the neurons of the BG main axis 184 Pallidal neurons as autonomous and weakly coupled pacemakers 185 Why in-vivo pallidal neurons may express class II excitability behavior 185 Computational physiology of the basal ganglia and their disorders 185 Discussion 186 Acknowledgments 186 References 186

a

Department of Physiology, Feinberg School of Medicine, Northwestern University, 303 East Chicago Avenue, Chicago, IL 60611, USA b Department of Medical Neurobiology (Physiology) and the Edmond and Lily Safra Center for Brain Sciences, The Hebrew University, Jerusalem, Israel

Abstract—The dorsal pallidal complex is made up of the external and internal segments of the globus pallidus (GPe and GPi respectively). It is part of the main axis of the basal ganglia (BG) that connects the thalamo-cortical networks to the BG input stages (striatum and subthalamic nucleus) and continues directly, and indirectly through the GPe, to the BG output stages (GPi and substantia nigra reticulata). Here we review the unique anatomical and physiological features of the pallidal complex and argue that they support the main computational goal of the BG main axis (actor); namely, a behavioral policy that maximizes future cumulative gains and minimizes costs. The three mono-layer competitive networks of the BG main axis flexibly extract relevant features from the current state of the thalamo-cortical activity to control current (ongoing) and future actions. We hypothesize that the striatal and the subthalamic projections neurons act as mono-stable integrators (class I excitability) and the in-vivo pallidal neurons act as bi-stable resonators (class II excitability). GPe neurons exhibit pausing behavior because their membrane potential lingers in the vicinity of an unstable equilibrium point and bi-stability, and these pauses enable a less-greedy exploratory behavioral policy. Finally, degeneration of midbrain dopaminergic neurons and striatal dopamine depletion (as in Parkinson’s disease) lead to augmentation of striatal excitability and competitive dynamics. As a consequence the pallidal network, whose elements tend to synchronize as a result of their bi-stable resonance behavior, shifts from a Poissonian-like non-correlated to synchronous oscillatory discharge mode. This article is part of a Special Issue entitled: Function and Dysfunction of the Basal Ganglia. © 2011 IBRO. Published by Elsevier Ltd. All rights reserved. Key words: basal ganglia, primate, neurons, correlations, oscillations, Parkinson’s disease. Contents Input/output organization of the basal ganglia and the pallidal network 172

The neural networks of the globus pallidus are part of the main axis of the basal ganglia (BG) that connects the cortical and thalamic networks, hippocampus and amygdala with the cortical and brainstem motor centers. The input structures of the basal ganglia—the striatum and the subthalamic nucleus (STN)—are reciprocally connected to the external segment of the globus pallidus (GPe) and these three structures (striatum, STN, and GPe) innervate the output structures of the

*Corresponding author. Tel: ⫹972-2-6757388; fax: ⫹972-2-6439736. E-mail address: [email protected] (H. Bergman). Abbreviations: BG, basal ganglia; CV, coefficient of variance; GPe, external segment of the globus pallidus; GPi, internal segment of the globus pallidus; HCN, hyperpolarization and cyclic nucleotide-gated; ISI, inter-spike-interval; MPTP, 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine; MSNs, medium spiny neurons; SNr, substantia nigra pars reticulate; STN, subthalamic nucleus.

0306-4522/11 $ - see front matter © 2011 IBRO. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.neuroscience.2011.08.068

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basal ganglia—the internal segment of the globus pallidus (GPi) and substantia nigra pars reticulata (SNr). The rodent homologue nuclei of the primate GPe and GPi are the globus pallidus (GP) and the entopeduncular nucleus (EP), respectively. To simplify this review we will use the primate terminology also for the rodent pallidum. Current computational models of the basal ganglia treat them as an actor/critic reinforcement learning network. The main axis or the actor part implements the behavioral policy or the mapping between states and actions. The neuromodulators of the basal ganglia, which include the midbrain dopaminergic neurons, striatal cholinergic interneurons and others, provide the main axis with a temporal prediction error. We recently hypothesized (Parush et al., 2011) that the computational goal of the basal ganglia is to optimize the tradeoff between the orthogonal goals of maximizing future cumulative gain and minimizing the behavioral cost. This multi-dimensional or multi-objective optimization goal naturally leads to a softmax like behavioral policy where dopamine plays a dual role. First, and as in previous models, dopamine affects the efficacy of the cortico-striatal synapses (Schultz et al., 1997). But, dopamine also acts as a pseudo-temperature soft-max parameter that controls the tradeoff between gain and cost and the continuum between exploratory (gambling) and greedy (akinetic) behavioral policies (the motor vigor, Cools et al., 2011; Niv et al., 2007). In this manuscript, we limit ourselves to the main axis of the basal ganglia. In the first section we provide a brief historical review of the evolvement of models of basal ganglia connectivity. We end up with current views of the basal ganglia that connect the thalamic and cortical networks with the cortical and brainstem motor system. In these models the GPe is the central nucleus of the basal ganglia and affects all other basal ganglia structures (Kita, 1994b, 2007). The second section is devoted to a description of the unique cellular anatomy of the pallidal neurons. Here, we emphasize the structural specificities of the long and sparsely branched dendrites of pallidal neurons that are oriented perpendicular to the afferent striatal axons (Percheron et al., 1984), and covered by 30,000 to 40,000 synapses, ⬃90% of which are GABAergic from the striatum, and only 5–10% glutamatergic from the STN (Shink and Smith, 1995a). In the third section we briefly review the field of the intracellular physiology of pallidal neurons. We confine our review to the neuronal class that probably corresponds to the in-vivo high-frequency discharge pallidal neuron. In the fourth section we summarize the main results of extracellular recording studies of single and multiple neurons (units) in awake and behaving primates. Next, we describe the changes in the discharge properties (rate, pattern and synchronization) in the pallidum following dopamine depletion and the development of Parkinsonian symptoms. These two sections correspond to the experimental paradigm of our research group, and therefore are more detailed than the previous sections. The sixth section is devoted to a dynamical system analysis of the high-frequency discharge neurons in the pallidum. Here we present our working hypothesis that pallidal neurons behave in-vivo like bi-stable resonators (class II excitability). We claim that the

linear I–f curve reported in in-vitro studies can be attributed to recordings in the soma and the lack of tonic synaptic inputs to the pallidal neurons in the anaesthetized animal and in invitro conditions. Finally, in the concluding section we show how the intrinsic (i.e. mono-stable integrators and bi-stable resonators) and the network properties of the basal ganglia enable the basal ganglia to achieve their computational goal— efficient and flexible feature extraction of the thalamocortical state.

INPUT/OUTPUT ORGANIZATION OF THE BASAL GANGLIA AND THE PALLIDAL NETWORK Perspectives on basal ganglia connectivity have evolved considerably over the years. A comprehensive historical review of this magnificent “relay race” of knowledge is far beyond the scope of this manuscript. Below, we briefly summarize our view of three generations of basal ganglia models. The first generation—pyramidal vs. extra pyramidal subsystems The motor system was classically described as consisting of two parts: the pyramidal and the extra-pyramidal subsystems. The pyramidal system starts at the motor cortices (upper motor neurons), and through the brainstem pyramids projects to spinal alpha (lower) motor neurons, innervating the distal parts of the limbs. In contrast, the extrapyramidal system originates in the basal ganglia and the cerebellum, descends parallel to the pyramidal system, and innervates the spinal circuits involved in control of automatic and postural movements. Neurology textbooks thus taught that the pyramidal system controls the execution of distal (e.g. fingers) accurate, voluntary movements whereas the extra-pyramidal system controls more axial (postural), automatic non-voluntary movements. The second generation—the basal ganglia is part of a cortical closed loop The revolution in anatomical methods during the second half of the 20th century led to changes in the way the motor system and the basal ganglia were perceived. The basal ganglia were redefined as the feed-forward part of a closed loop connecting all cortical areas sequentially through the striatum, pallidum, and thalamus back to the frontal cortex. The frontal cortex projects downstream through the cortico-spinal and cortico-brainstem pathways to the spinal level. This revised view of the basal ganglia networks assumed that there are two segregated internal basal ganglia pathways that start in the striatum and converge on the output structures of the basal ganglia (the GPi and the SNr). The so-called “direct pathway” is a direct GABAergic inhibitory pathway, whereas the “indirect pathway” is a polysynaptic dis-inhibitory pathway through the GPe and the glutamatergic (excitatory) STN. The reciprocal connections between the GPe and the STN (Carpenter et al., 1981a; Kim et al., 1976) tended to be ignored in these models, and the GPe was depicted as a relay nucleus

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Fig. 1. Schematic representation of the connectivity of the basal ganglia and the pallidal networks. (A) The main axis of the basal ganglia. Gray arrows represent afferent and efferent connections of the basal ganglia network; black arrows indicate basal ganglia connectivity. Arrow-heads are for glutamatergic-excitatory connections, and round-head arrows are for GABAergic-inhibitory connections. (B) The three layer reduced model of the main axis of the basal ganglia. Abbreviations: STN, subthalamic nucleus; GPe, globus pallidus external segment; GPi, globus pallidus internal segment; SNr, substantia nigra pars reticulata.

between the striatum and the STN (e.g. Bergman et al., 1990, Fig. 1). The projection striatal neurons in the direct pathway are medium spiny neurons (MSNs) that express D1 dopamine receptors and substance-P, whereas those in the indirect pathway express D2 dopamine receptors and enkephalin (Gerfen et al., 1990). Dopamine is believed to have differential effects on the two striato-pallidal pathways: it is thought to excite and facilitate transmission along the direct pathway via activation of D1 receptors and inhibit transmission along the indirect pathway via the D2 receptors (Albin et al., 1989; Gerfen et al., 1990). Current models and the major anatomical constraints of the basal ganglia Recently, modern anatomical studies have revealed an even more complex map of basal ganglia connectivity. Both the striatum and STN receive considerable glutamatergic inputs not only from the cortex, but also from the thalamus (Haber and Calzavara, 2008; Smith et al., 2009). The intra-laminar thalamic nuclei also project to the pallidal neurons (Smith et al., 2004; Yasukawa et al., 2004). The feedback projections from the GPe to the striatum (Bevan et al., 1998; Bolam et al., 2000; Kita and Kita, 2001; Kita et al., 1999; Spooren et al., 1996) parallel the reciprocal connections between the GPe and the STN (Carpenter et al., 1981a; Kim et al., 1976). These anatomical findings, combined with physiological evidence highlighting the importance of the (hyper) direct projections from the motor cortex to the STN (Kitai and Deniau, 1981; Nambu, 2004; Ryan and Clark, 1991) indicate that like the striatum, the STN is an input stage of the basal ganglia. The discovery of massive GPe to GPi projections (Hazrati et al., 1990a; Sato et al., 2000) strongly suggest that the GPe is not a mere relay station in the indirect pathway of the basal

ganglia. Rather, the GPe is probably a central nucleus in the basal ganglia circuitry, which is reciprocally connected to the striatum and the STN, and is a major source of innervation to the GPi and the SNr (Kita, 1994b, Fig. 1). Furthermore, the basal ganglia outputs to brainstem motor centers such as the pedunculopontine nucleus and the superior colliculus (Delwaide et al., 2000; Redgrave et al., 2010) are integrated into current models of the basal ganglia. Thus, rather than being part of a closed loop cortical network, the basal ganglia are described as connecting the diverse thalamo-cortical networks and the motor centers of the nervous system. Finally, unlike the “motor-centric” view of the first and second generation basal ganglia models, current thinking emphasizes the role of the basal ganglia in integrating the cognitive and limbic with the motor domain (Haber and Knutson, 2010). These studies usually divide the basal ganglia into three partially overlapping domains (limbic, cognitive, and motor) and indicate that the basal ganglia connectivity is characterized by substantial local heterogeneity within the large-scale order. Fig. 1A follows Fig. 1 of Kita (1994b) and schematically summarizes the current view of the complex connectivity among the basal ganglia nuclei. It is obvious that the basal ganglia are not a linear sequential network but rather contain many reciprocal and loop connections. Nevertheless, a major feature of basal ganglia connectivity is its unidirectional flow of information. The input structures of the basal ganglia receive inputs from the cortex and the thalamus but do not project back to the cortex or the thalamus. Similarly, the output structures of the basal ganglia (the GPi and the SNr) project to the thalamus and brainstem structures but do not receive massive direct back projection from their targets. Finally, the GPe receives inputs mainly from basal ganglia structures (striatum, STN, and

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GPe lateral connectivity) and projects to all basal ganglia structures, but not outside of the basal ganglia. Thus, anatomically, there is a unidirectional flow of information in the basal ganglia network from the input structures (striatum and STN), through the central networks of the GPe, to the basal ganglia outputs—the GPi and the SNr. In this chapter we simplify this to a three layer network composed of the basal ganglia input structures (striatum and STN), the GPe and the GPi (Fig. 1B). Future thinking on the basal ganglia network should include the other major parts of the basal ganglia network, such as the ventral striatum, ventral pallidum and the SNr. The other key feature of the basal ganglia that affects information flow is the dramatic decrease in tissue volume and the number of neurons down the striatum-GPe-GPi axis. In the human the volume of the dorsal striatum (caudate nucleus and putamen, 9700 mm3) is 12 times larger than that of the GPe (800 mm3) and 20 –25 times larger than that of the GPi and SNr (480 and 410 mm3 respectively, Yelnik, 2002). The smaller STN (160 mm3) can be neglected in this quantitative approach. Given the smaller size and higher density of neurons in the striatum compared to the GPe/GPi, it is not surprising that this reduction in volume is reflected in the sharp drop in the number of neurons along the basal ganglia main axis. There is at least one order of magnitude more neurons in the cortex projecting to the striatum than the number of neurons in striatum (Kincaid et al., 1998; Zheng and Wilson, 2002). In the primate, there are about 10,000,000 projection MSNs in the striatum vs. 150,000 and 50,000 neurons in the GPe and GPi respectively (Percheron et al., 1994). A similar funneling organization is seen in the rodent basal ganglia. There are 1,700,000 –2,800,000 neurons in the rodent striatum (Oorschot, 1996; Zheng and Wilson, 2002) and 46,000 and 3,200 neurons in the rodent homologues of the GPe and GPi respectively (Oorschot, 1996).

CELLULAR ANATOMY OF THE PALLIDAL NETWORK The term “globus pallidus” comes from the pale appearance of the globus pallidus in Nissl stains. This is due to the low density of neurons in this structure, which are surrounded by a massive volume of axons (white matter). The pallidal neurons The cellular morphology of the neurons in the globus pallidus is more uniform than that of most other areas in the central nervous system. The primate globus pallidus is primarily made up of relatively large cells with triangular or polygonal cell bodies that give rise to thick, sparsely spined, poorly branching dendrites (Difiglia et al., 1982; Fox et al., 1974; Francois et al., 1984; Percheron et al., 1984; Yelnik et al., 1984). The rodent cellular morphology (Iwahori and Mizuno, 1981a; Kita and Kitai, 1994; Nambu and Llinás, 1997) and that of other species (e.g. Iwahori and Mizuno, 1981b) reveals a very similar pattern. Nevertheless, there is probably more than one morphological subtype of pallidal neurons (Francois et al., 1984; Kita and

Kitai, 1994; Nambu and Llinás, 1997). The smaller ones have spiny dendrites and are considered to be local circuit neurons (Francois et al., 1984; Nambu and Llinás, 1997). Some studies describe more than a single morphological or biochemical subtype of pallidal projection neurons (Kita, 1994a; Kita and Kitai, 1994; Sadek et al., 2007). We neglect this small morphological diversity of pallidal projection neurons in the following discussion. The dendrites of the pallidal projection neurons are very long, sometimes creating dendritic radii of more than one millimeter in their principal plane. In the central areas of the primate GPe and GPi, these dendrites appear as a 1,500⫻1,000⫻250 ␮m3 disc-like territory (Yelnik et al., 1984). The flat plane of the discoidal dendritic field parallels the border between the GPe and the putamen and is oriented perpendicular to incoming striatal fibers (Kita and Kitai, 1994; Percheron et al., 1984; Yelnik et al., 1984). The synaptic input of the pallidal neurons The pallidal dendrites are densely innervated by synapses which cover the entire dendrite (Difiglia et al., 1982; Difiglia and Rafols, 1988; Fox et al., 1974). In the primate, the mean number of synapses contacting the dendrites of one pallidal neuron is estimated to be 30,000 to 40,000 (Percheron et al., 1994; Yelnik et al., 1996). The vast majority of these synapses represent striato-pallidal GABAergic terminals (Shink and Smith, 1995a). Myelinated striatal axons cross perpendicular to pallidal discoidal dendritic fields and send thin unmyelinated collaterals (“wooly fibers”) parallel to pallidal dendrites with which they repeatedly synapse (Difiglia and Rafols, 1988; Haber and Nauta, 1983). Injections of anterograde tracers to the striatum (Hazrati and Parent, 1992a, b) revealed that these axon collaterals are part of the multiple, narrow elongated bands of fibers aligned in parallel with the putamen-GPe border (or in parallel with the pallidal disks). However, a three-dimensional reconstruction of biocytin-labeled striatal axons (Yelnik et al., 1996) showed that individual axons form bifurcations devolved only to one band. The striatal axons make only a few (up to 10, but in many cases only one) contacts (boutons) with a given pallidal dendrite. This suggests that as is the case for cortico-striatal connections (Kincaid et al., 1998; Zheng and Wilson, 2002) striatopallidal connections are both divergent (distribute the same striatal information to many pallidal neurons) and convergent (a single pallidal neuron integrates information from many striatal inputs). The average number of synapses emitted in the pallidum by a single striatal neuron is estimated to be 200 –300 (Yelnik et al., 1996). Thus, even if a single striatal neuron transmitted all its contacts to a single pallidal neuron, this pallidal neuron would get information from another 100 striatal neurons (yielding a total of 100⫻300⫽30,000 synapses). In fact, a striatal neuron makes only a few synapses with a given pallidal neuron. Thus, a single pallidal neuron probably samples the neural activity of thousands (circa 3000 –10,000) of striatal neurons. The major glutamatergic and excitatory (Smith and Parent, 1988) input to GPe and GPi is derived from the

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STN (Carpenter et al., 1981a, b; Hazrati and Parent, 1992a; Nauta and Cole, 1978; Smith et al., 1990). There are many more GABAergic synapses from the striatum than STN glutamatergic synapses on the GPe and GPi neurons. Striatal input to the GPe and GPi synapse all along the thick dendrites (Shink and Smith, 1995b). Early studies claimed that the STN inputs were strategically located on the GPe soma (Parent and Hazrati, 1993). However, later studies revealed that terminals from STN intermingle with the much greater GABAergic innervation from the striatum (Shink and Smith, 1995b) and therefore are not strategically (soma) located to “drive” the pallidal activity (Kitai and Kita, 1987). Finally, voltage-gated sodium channels were found to exhibit a specific clustering at sites of excitatory synaptic inputs on the pallidal dendrites and therefore could mediate dendritic spike generation (Edgerton et al., 2010; Hanson et al., 2004). It is still not clear whether this clustering of sodium channels is the only (or chief) mechanism that counter-balances the quantitative dominance of GABAergic vs. glutamatergic synapses on pallidal neurons. In addition to the afferent input from the striatum and STN, GPe neurons receive collateral innervation from other GPe neurons and the GPi also receives input from the GPe. These pallido-pallidal connections terminate close to or on the soma (Hazrati et al., 1990b; Parent et al., 2000; Sadek et al., 2007; Shink and Smith, 1995b; Smith et al., 1998). A quantitative analysis indicated that in the rodent, GPe neurons possess on average 264 to 581 local axonal boutons, depending on their location inside the GPe (Sadek et al., 2007). In summary, the box and arrow models of the basal ganglia (Albin et al., 1989; Bergman et al., 1990) hinted at an “all-to-all” functional connectivity. However, today the BG networks (as most of brain networks) are assumed to be characterized by sparse connectivity. As noted above, a single striatal neuron innervates ⬃100 pallidal neurons (less than 0.1% of the 105 GPe or GPi neurons), and a single pallidal neuron receives information from no more than 10,000 striatal neurons (i.e. less than 0.1% of the 107 striatal projection neurons). Similarly, juxtacellular labeling of single GPe neurons and stereological analysis suggest that the GPe to STN connection is also surprisingly sparse: single GPe neurons contact less than 2% of STN neurons and single STN neurons receive input from less than 2% of the GPe neurons (Baufreton et al., 2009). We are not aware of a quantitative analysis of the number of synapses emitted by a single STN neuron, but this can be estimated from the number of STN and pallidal neurons (⬃104 and 105, respectively in the primate) and the number of STN synapses on a single GP neuron (5–10% of the total 30,000 – 40,000, i.e. ⬃1000 –2000 synapses). Thus, even in an extreme divergent scenario a single pallidal neuron samples the activity of less than 1% of the STN neurons. The detailed synaptology of the GPe back projection to the striatum (Bevan et al., 1998; Kita and Kita, 2001; Kita et al., 1999; Spooren et al., 1996) is further complicated by the differential contact with the striatal fast spiking interneurons, and it is still under active study.

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CELLULAR PHYSIOLOGY OF PALLIDAL CELLS Intracellular electrophysiological studies of pallidal cells were initially carried out with sharp microelectrodes on anaesthetized animals (in-vivo). More recent studies have employed slice (in-vitro) preparations in whole-cell and perforated patch configurations. Several studies have been done in tissue culture or in acute dissociated cells. Most of these intracellular studies have been carried out in rodents; nevertheless as in other sections of this review we will use the primate terminology of GPe and GPi for their rodent homologues, the GP and the EP, respectively. Intracellular physiological studies have concluded that the GPe and GPi contain two to three electrophysiologically distinct types of neurons: quiescent cells that probably belong to the basal forebrain cholinergic group (Bengtson and Osborne, 2000), a group of rebound bursters, and a majority of tonic fast-firing neurons (Bugaysen et al., 2010; Cooper and Stanford, 2000; Kita and Kitai, 1991; Nakanishi et al., 1990; Nambu and Llina´s, 1994). Nevertheless, we cannot rule out the possibility that there is only a single population of pallidal cells which expresses different phenotypes under various recording conditions, especially whole-cell and sharp electrode recordings that disrupt the intracellular medium. This issue should be resolved by future studies (e.g. with perforated patch recordings). A comprehensive review of these intracellular studies is beyond the scope of this manuscript. We limit this review to pallidal neurons that probably correspond to in-vivo high-frequency discharge pallidal neurons (e.g. Type A of Cooper and Stanford, 2000; Type I of Nakanishi et al., 1990, 1991; Type II of Nambu and Llina´s, 1994). Physiological characteristics of the main pallidal neurons Most (⬎70%) GPe neurons that have been studied intracellularly in anesthetized rats exhibit repetitive firing of short-duration action potentials at a frequency of 2– 40 Hz (Kita and Kitai, 1991). These pallidal neurons are able to sustain repetitive firing at a frequency of about 100 Hz and generate short bursts of very high frequency firing (up to about 500 Hz). Nevertheless, spike frequency adaptation was observed in these neurons, that is, when the neurons were driven by depolarizing current pulses, the inter-spikeinterval (ISI) was shorter at the beginning of the pulse than at the end. The average firing frequency during the depolarizing pulse was proportional to the intensity of the current (Fig. 1B, Kita and Kitai, 1991). However, a sigmoidal I–f relation was seen when the firing frequency at the beginning of the current pulses (i.e. 1/ISI of the first two spikes) was plotted against the intensity of injected currents (Fig. 1E, Kita and Kitai, 1991). It is interesting that the same group reported that GPi neurons in-vitro demonstrated spontaneous repetitive firing of spikes with a frequency of 2–30 spikes/s. These neurons were capable of producing high frequency (up to 300 Hz) repetitive firing without strong spike adaptation in response to a strong

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depolarizing pulse. However, no I–f curves were reported in this study (Nakanishi et al., 1990). Nambu and Llina´s studied the guinea pig GPe neuron using a brain slice in-vitro preparation. Their type-II neurons resemble the type I reported by the Kita and Kitai group (Kita and Kitai, 1991; Nakanishi et al., 1991). These neurons fired spontaneously at the resting potential level. They exhibited linear I–f relations (Fig. 5G of Nambu and Llina´s, 1994) reaching a discharge rate of up to 200 spikes/s with only weak adaptation. Nambu and Llina´s were the first to report that sodium-dependent 20 –100 Hz subthreshold membrane oscillations are often elicited in these cells by membrane depolarization (Nambu and Llina´s, 1994, Fig. 10). Other intracellular studies are consistent with this description of pallidal cells. The Cooper and Stanford (2000) type A GPe cells exhibited regular activity up to a maximum firing frequency of 350 Hz following current injection with moderate spike frequency adaptation. Most of the pallidal cells recorded by Rav-Acha et al. (2005) exhibited spontaneous regular 2–20 Hz activity. The repetitive firing activated by positive current injection showed a linear I–f relationship (Rav-Acha et al., 2005, Fig. 1d). Finally, recent studies of the autonomous pacemaking of GPe neurons (Chan et al., 2011, 2004; Deister et al., 2009; Mercer et al., 2007) have confirmed that these fast spiking pacemakers are capable of a broad range of discharge rates, from an arbitrary slow rate up to 200 spikes/s for sustained periods. Ionic channels of the pallidal neurons As a whole, intracellular studies of pallidal neurons indicate the currents that underlie autonomous discharge (pacemaker currents) of these neurons and contribute to their regularity are voltage-activated sodium currents, hyperpolarization and cyclic nucleotide-gated (HCN) currents, Kv4 A-type currents, and small conductance calcium-activated potassium (SK) currents (Chan et al., 2004; Deister et al., 2009; Mercer et al., 2007). This issue is beyond the scope of this manuscript and well-reviewed elsewhere (Surmeier et al., 2005). Recent advanced compartmental modeling of pallidal neurons (Günay et al., 2008; Schultheiss et al., 2010) suggests that the soma and dendrites differ in their expression of ionic channels, which impacts the processing of synaptic inputs. This critical information should be incorporated in future models and thinking and will be further explored in section “Dynamical system characterization of basal ganglia neurons” of this review.

SPIKING ACTIVITY OF NEURONS IN THE PALLIDAL NETWORK The core elements of neural computation are the single spikes of single neurons. Today, the best method to study the spiking activity of neurons in a behaving animal is through metal extracellular electrodes (Lemon, 1984). This method, pioneered in the motor cortex by Evarts (1964, 1966) and in the basal ganglia by DeLong (1971, 1972) enables reliable recording of spikes of single or several

neurons for tens of minutes and during the performance of behavioral tasks, which remains unfeasible when using today’s intracellular and other (e.g. optogenetic) recording techniques. Thus, extracellular recording of the spiking activity of several neurons, and statistical analysis of their discharge rate, pattern and correlation of spontaneous and event related activity are in our view the most valuable tools for understanding the computational goals, algorithms, and physiological mechanisms of neural networks. Nevertheless, there are limits to the extracellular technique. First, both false positive and false negative errors can occur during the detection of spiking activity (Hill et al., 2011; Joshua et al., 2007). Although error-free experiments are in the realm of the impossible, the reliability of extracellular studies can be improved with one of the several newly published methods that provide objective qualification of isolation quality and detection errors (e.g. Joshua et al., 2007). The small size of the neurons and the metal tip of the electrode (⬍15 ␮M) may lead to situations where small shifts in the microelectrode tip cause the recording of a different neuron (or groups of neurons) which may go undetected in real-time and even by inspection of the spike shape. Tests of discharge rate stationarity can further help rule out such cases (Gourévitch and Eggermont, 2007). Finally, spike shadowing may occur when trying to record the activity of more than one neuron by the same electrode or attempting to sort their activity by the shape of their action potentials (Bar-Gad et al., 2001b). In the following subsections we summarize the main findings of extra-cellular recording of the spiking activity in pallidal networks. Although it may lean towards results by our own group, any lacunae do not reflect a lesser importance or reliability of the results of other groups, but rather the natural bias and lack of knowledge of the authors of this review. Discharge rate and the different classes of neurons in the pallidal network In-vivo pallidal neurons are very active cells. Most GPi and GPe cells spontaneously discharge at a relatively high frequency rate of 50 – 80 spikes/s during maintenance of a relaxed neutral posture, or during inter-trial-intervals while performing behavioral tasks (Fig. 2B, C). This discharge rate is much higher than the discharge rate of striatal MSNs, which is less than 1 spike/s (Fig. 2A), the mean discharge of 1–5 spikes/s in most cortical areas (Abeles, 1991; Cohen and Kohn, 2011), or the 20 –25 spikes/s of STN neurons (Wichmann et al., 1994a). GPi neurons discharge at approximately 60 – 80 spikes/s (DeLong, 1971; DeLong et al., 1985). This mean discharge rate represents the mean of a broad Gaussian distribution of discharge rates of single GPi neurons, and the discharge rate of GPi neurons range from 20 to 140 spikes/s (Bronfeld et al., 2010, Fig. 6a; Filion and Tremblay, 1991, Fig. 3; Miller and DeLong, 1987, Fig. 6a). GPe neurons can be divided into two populations based upon their discharge rate and patterns. Most (⬎85%) GPe neurons resemble GPi neurons and spontaneously discharge at relatively high frequencies (50 –70

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Fig. 2. Examples of two second analog traces of extracellular recording of the main projection neurons of the striatum, GPe and GPi. Typical example of extracellular recording filtered between 300 and 6000 Hz of the low frequency discharge of a striatal medium spiny neuron (A), as well as the discharge of GPe HFD-P— external segment of globus pallidus high-frequency discharge pauser (B) and GPi—internal segment of globus pallidus— high-frequency discharge neuron (C).

spikes/s). In most cases, this high-frequency discharge is randomly interrupted by long duration (0.3–2 s) pauses (DeLong, 1971; Elias et al., 2007, and see section “GPe pauses”). In contrast, the second population of GPe neu-

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rons discharges at lower frequencies (⬍15 spikes/s) with intermittent, short (10 –20 spikes) high-frequency bursts. Our unpublished observation (Finkes et al.) reveals a bimodal distribution of GPe discharge rates, and a combined in-vivo and in-vitro study (Bugaysen et al., 2010) indicates that the different discharge properties of GPe neurons reflects their intrinsic properties (but see Chan et al., 2004). Finally the third population of pallidal cells is known as the border cells. They are found in the borders of the two pallidal segments. They are characterized by spontaneous, periodic, 20 – 40 Hz broad action potentials, and are believed to represent an extension of the cholinergic neurons of the substantia innominate or nucleus basalis of Meynert (Bengtson and Osborne, 2000; DeLong, 1971, 1972; Mitchell et al., 1987a, b; Richardson and DeLong, 1986). In this manuscript, we limit ourselves to major populations of high-frequency discharge pallidal neurons and ignore the GPe low frequency discharge bursters, the border cells, and other minor groups of neurons in the pallidal network. Discharge patterns in the pallidal network The firing pattern of a neuron is usually classified as Poisson-like, periodic or bursty (Abeles, 1982a; Kaneoke and Vitek, 1996). In in-vitro and in pathological in-vivo conditions (e.g. dopamine depletion in the dorsal striatum, Parkinson’s disease) periodic bursts are often observed in the basal ganglia. Electro-physiologists usually characterize neuronal firing patterns by inspection of the distribution

Fig. 3. (A, B) I–f curves of class I and II excitability neurons. Schematic representation of the current injected into the soma as a function of time (upper row), the neural responses (middle row), and the resulting I (Current)–f (discharge rate) of class I excitability (left) and class II excitability (right) neurons.

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Fig. 4. Schematic representation of the superposition of the behavior of basal ganglia neurons on the I–f curve of class I and II neurons. (A) The working range of class I (mono-stable integrator) striatal and subthalamic (S) neurons. (B) Working ranges of class II (bi-stable resonators) GPe (E) and GPi (I) neurons.

(histogram) of the ISIs, the coefficient of variance (standard deviation/mean; CV) of the ISIs, and the auto-correlogram (auto-correlation function). The auto-correlogram reveals the discharge probability of a neuron as a function of time since a previous spike (time zero of the autocorrelogram). It is important to note that the auto-correlogram is not limited to first order ISI; rather all spikes emitted in the time lag since time zero are included. Other measures like the ISI return map and the Fano factor are less often used and will not be discussed here. The Poisson-like firing pattern is characterized by an exponential distribution of the ISIs, an ISI CV close to one and a flat auto-correlogram. In the canonical interpretation, the Poisson-like firing pattern describes neurons with a constant probability (over time) to emit a spike. The term “Poisson-like” is used to describe their discharge pattern because the refractory period does not allow very short ISIs. Thus, the auto-correlogram is not expected to be really flat, but rather to have an initial trough representing the absolute and the relative refractory period and then afterwards to stabilize at a constant level (the discharge rate of the neuron under study). The periodic firing pattern is characterized by a sharp ISI distribution histogram, an oscillatory auto-correlation function and ISI CV values close to zero. The bursty discharge pattern describes the tendency of a neuron to fire several action potentials in rapid succession. This pattern is characterized by an initial peak (following the trough of the refractory period) in the auto-correlogram and ISI CV values greater than one. The area of the peak in the auto-correlation function can be used to estimate the average burst size. The number of spikes within a burst is approximately twice the size of the auto-correlogram peak area (Abeles, 1982b). The typical report of peaks in the auto-correlograms of spike trains of pallidal cells (Bergman et al., 1998, Fig. 4A-diagonal; Raz et al., 2001, Fig. 1a, b 2ed column; Raz et al., 2000,Fig. 12a) indicates that pallidal cells fire in a bursty mode. Thus, auto-correlation analysis of the GPi discharge in the normal monkey has led to the conclusion that most (⬎75%) pallidal cells tend to emit short (150 –200 ms) bursts, with an average of close to one (above the average discharge rate) spike/burst (Bergman et al.,

1994). However, short peaks in the auto-correlation function may be the result of the refractory period of cells with a high firing rate and not reflect a bursty discharge pattern (Bar-Gad et al., 2001a). This is because at the end of the refractory period that follows the spike at time zero of the auto-correlogram, the cell has a probability P of firing. However, at long offsets the probability of firing is influenced by additional refractory periods (since as mentioned above, auto-correlograms are not limited to first order ISI). This causes the firing probability to decrease to the steady state value P/(1⫹P ⫻ Tr), where P is the discharge probability in a time unit and Tr is the duration of the absolute refractory period. The mathematics are somewhat more complicated for realistic cases with a relative refractory period following the absolute one (Bar-Gad et al., 2001a), but the phenomenon does not change. The artificial peak in the auto-correlogram is more pronounced in spike trains of high-frequency discharge cells with a long refractory period. This is probably why it tends to be neglected in spike train analyses of data collected in areas with low firing rates, such as the cerebral cortex. In these areas its magnitude is generally very small (Bar-Gad et al., 2001a, Table 1 and Fig. 3). However, in areas with a high firing rate, such as the GPe and the GPi, the effect is significant and obscures underlying firing patterns. The underlying firing pattern can be better assessed by the hazard function (Bar-Gad et al., 2001a), which reveals that following the refractory period, most pallidal cells tend to have a constant probability for spiking. We have not carried out a comprehensive study of the population of high-frequency discharge pallidal neurons, but we believe that aside from the pause phenomenon (see below) the high frequency spontaneous discharge pattern of most pallidal cells is governed by a constant discharge (Poisson-like) probability. GPe pauses In Mahlon DeLong’s pioneering study (1971) it was shown that the discharge of almost all GPe high-frequency neurons is interrupted by long intervals of total silence or pauses. A recent study by our group used mathematical

J. A. Goldberg and H. Bergman / Neuroscience 198 (2011) 171–192 Table 1. Increases vs. decreases in discharge rate in the responses of pallidal cells to behavioral events Source

Georgopoulos et al. (1983) Anderson and Horak (1985) Mitchell et al. (1987a) Mink and Thach (1991b) Brotchie et al. (1991a) Jaeger et al. (1995, Fig. 4) Turner and Anderson (1997) Boraud et al. (2000) Joshua et al. (2009b, Table 2)

Number of neurons

# Inc/Dec

81/19

4.2

64/36

1.8

GPe 148; GPi 89

1.9–3.6 71/29 91/19; 188/20

2.4 4.8–9.4 ⬃1.5

216

GPe 368 GPi 158

Ratio Inc/Dec

61/39

1.6

67/15

4.5 3.0–5.0

The changes in the discharge rate in the GPe and GPi are given as either the number of neurons with increase/decrease (Inc/Dec) in discharge rate (third column) or the ratio of increase to decreases in discharge rate (fourth column). For studies where values are given for GPe and GPi neurons and for different behavioral epochs, we provide a representative number in the table.

algorithms to explore the statistical properties of the extracellularly recorded spiking activity of well-isolated highfrequency discharge GPe and GPi/SNr neurons from five monkeys during different states of behavioral activity (Elias et al., 2007). Only a few of the GPi/SNr high-frequency discharge neurons were classified as pausers, in contrast to more than half of the GPe neurons. The GPe average pause duration was equal to 0.5– 0.7 s (in the different monkeys). The inter-pause intervals followed a Poisson distribution with a mean frequency of 10 –20 pauses/minute (i.e. on average, after 5 s of high-frequency discharge, the GPe neuron pause for slightly more than half a second). No linear relationship was found between the pause parameters (duration or frequency) and the firing rate of the GPe cells. Pauses behaved like an “all or none” phenomenon and were usually preceded and followed by the average high-frequency discharge rate. When changes in discharge rate were observed before or after the pauses, these changes were not dominated by a decrease in firing rate (Elias et al., 2007, Fig. 7a, b). The average amplitude and duration of the spike waveform was modulated only after the pause but not before it (Elias et al., 2007, Fig. 7c, d). Finally, the probability of GPe cells to pause spontaneously was extremely variable among monkeys (30 –90%) and inversely related to the degree of the monkey’s motor activity (Adler et al., 2010; Elias et al., 2007, Fig. 10). Local microinjections of the GABA(A) antagonist bicuculline to the primate GPe led to an increase in the firing rate and a change in the firing pattern of GPe neurons, along with the development of hyper-kinetic movements (chorea). GPe neurons close to the bicuculline microinjection site exhibited strong bi-phasic activity in which neurons transitioned between high-frequency discharge and

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pauses became longer and occurred more frequently than in the control state (Bronfeld et al., 2010, see Fig. 3; Matsumura et al., 1995). Similar responses of GPe neurons to bicuculline were observed in-vitro in the rat, suggesting a basic cellular mechanism underlying the bi-phasic firing pattern (Bronfeld et al., 2010). The presence of pauses has been considered to be a basic characteristic of the GPe and a signature of this nucleus in electrophysiological recordings (Arkadir et al., 2004; Galvan et al., 2005; Hamada et al., 1990). However, pauses have been found mainly in the GPe of normal awake primates. Pauses have not been described in intracellular studies of pallidal neurons in-vitro even when these neurons produce a spontaneous repetitive discharge (Cooper and Stanford, 2000; Deister et al., 2009; Nambu and Llina´s, 1994; Rav-Acha et al., 2008, 2005; Stanford, 2003). More recent studies have revealed that under specific conditions GPe neurons in slice preparations can support alternatively occurring long depolarization with a high-frequency spike discharge and hyperpolarized quiescent phases (Hashimoto and Kita, 2006, Figs. 3 and 5). Interestingly (see section “Dynamical system characterization of basal ganglia neurons”) these conditions are characterized by treatments that depolarize the GPe dendrites and, at the same time hyperpolarize the GPe somata with current injections (Hashimoto and Kita, 2006). Cross-correlation of spontaneous spiking activity in the pallidal network Cross-correlation functions (cross-correlograms) of the spike trains of simultaneously recorded pairs of neurons depict the probability of neurons to fire as a function of time that has elapsed since the discharge of a second (trigger) neuron. Cross-correlograms can thus reveal the functional connectivity between the neurons under study (e.g. direct excitatory, inhibitory synapses or common synaptic inputs). Flat cross-correlograms indicate that a functional connectivity between the neurons does not exist (independent activity), or that it is too weak to be detected by the finite duration recording of the spike trains (Abeles, 1982a; Perkel et al., 1967). Several multi-electrode studies by our group have used cross-correlation methods to assess the functional connectivity of pallidal neurons (Heimer et al., 2002a, 2006; Nini et al., 1995; Raz et al., 2000). These studies revealed a very low level (usually ⬍5% of the studied pairs) of correlated activity between the spike trains of pallidal neurons in the normal state. Most of the crosscorrelograms of simultaneously recorded pallidal cells were flat, even when calculated for periods when the monkeys were engaged in behavioral tasks. This is probably due to the high discharge rate of pallidal neurons (Nevet et al., 2007), which minimize the effects of overlap of the response of pallidal neurons. Moreover, the diversity of pallidal responses to behavioral events (Joshua et al., 2009b) and the symmetric distribution of their signal and response correlations (Joshua et al., 2009a, see below section—Similarity of encoding between pallidal neurons)

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further minimize the effects of common behavioral responses on the cross-correlograms. To further test the independence of pallidal activity, we studied the spiking activity of neighboring pairs recorded by the same electrodes. A narrow peak dominated the correlations of all pairs of pallidal neurons recorded on the same electrode. This type of peak is classically interpreted as a sign of non-independent activity due to strong common input (Abeles, 1982a; Perkel et al., 1967). However, mathematical analysis (Bar-Gad et al., 2001b) shows that such peaks may derive from a technical inability to detect overlapping spikes by spike-sorting techniques (the shadowing effect). A comparison of the expected shadowing effect with the actual pallidal correlations suggests that similar to remote pallidal pairs (recorded by two different microelectrodes), most (⬎90%) neighboring pallidal pairs do not exhibit real correlations of their spiking activity (Bar-Gad et al., 2003a). Average flat cross-correlograms could be due to symmetric modulations of correlations over time. This can be tested by the Joint-Peri-Stimulus-Histogram (JPSTH) method (Aertsen et al., 1989; Vaadia et al., 1995). When we first applied this method to the study of the temporal evolution of the pallidal correlation, we found a very strong modulation of the correlation triggered by reward predictions and delivery. However, careful examination of our data revealed that these results were due to a temporal correlation with another parameter (e.g. licking movement) and probably did not reflect a major modulation of pallidal functional connectivity (Arkadir et al., 2002; Ben-Shaul et al., 2001). As for spiking activity, pauses of pairs of GPe cells that were recorded simultaneously were not correlated (Elias et al., 2007, Fig. 8a, c). Likewise, we found no relationship between pause onset and offset and the spiking activity of simultaneously recorded GPe cells (Elias et al., 2007, Fig. 8a, b). Even after GPe bicuculline injections and the development of GPe strong bi-phasic activity, neuronal activity remained uncorrelated within and between the GPe and the GPi (Bronfeld et al., 2010). It is not easy to compare correlations studies of neurons in different areas of the brains and across different research groups. This is because correlation analysis is very sensitive to recording conditions as well as to the behavioral task and context (Bar-Gad et al., 2001b; Brody, 1999a, b; Ecker et al., 2010). Nevertheless, the lack of pallidal correlations seems to be in sharp contrast with the many reports of narrow and broad temporal synchronization found in cross-correlation histograms of pairs of cortical neurons (e.g. Abeles, 1982a; Eggermont, 1990; Engel et al., 1991; Gray et al., 1989; Kimura et al., 1976; Krüger and Aiple, 1988). Although a few recent studies have challenged the consensus of correlated (redundant) cortical activity (Ecker et al., 2010; Renart et al., 2010), a more recent review of the literature (Cohen and Kohn, 2011) summarized the recent reports of the average values of noise correlation (a count statistic of the co-variability of the neuronal responses of two neurons to the behavioral event that probably reflects the same phenomenon as the

spike-to-spike correlation histograms used in the classical correlation studies) in the primate cortex. Their Table 1 summarizes 26 studies and reveals that the range of average noise correlation in the cortex is between 0.01 and 0.26. The noise correlation values are affected by the distance between the neurons, the similarity of their tuning curves and the recording area (correlations in motor cortical areas are consistently lower than in sensory cortices) and even by the cortical layer, but still seems to be in the range of 0.1– 0.2 and significantly different from zero. Cohen and Kohn (2011) further show that correlation values are affected by the discharge rate (Cohen and Kohn, 2011, Fig. 2c, d) and attributed the finding of no correlation between cortical pairs (Ecker et al., 2010) to the low discharge rate of neurons in this study. The lack of correlation between the pallidal neurons with a high discharge rate is therefore even more striking given the monotonic relationships between discharge rate and correlation (Cohen and Kohn, 2011; de la Rocha et al., 2007). However, this relation reflects the physiological link between membrane subthreshold membrane fluctuations and the spikes, and might be different for pallidal vs. cortical neurons. Neuronal responses to behavioral events in the pallidal network GPe and GPi neurons change their firing in relationship to behavioral events and motor activity. In line with the classical roles assigned to the basal ganglia in the motor system, most early studies explored the relationship between pallidal discharge rate and movement parameters (Aldridge et al., 1980; Anderson, 1978; Anderson and DeVito, 1987; Anderson and Turner, 1991; DeLong, 1971, 1972; DeLong et al., 1985; DeLong and Strick, 1974; Georgopoulos et al., 1983; Hamada et al., 1990; Jaeger et al., 1993, 1995; Mushiake and Strick, 1995; Turner and Anderson, 1997, 2005). Nevertheless, many of these studies failed to find consistent relationships between movement parameters and pallidal discharge (Brotchie et al., 1991a; Gdowski et al., 2007; Mink and Thach, 1991a,b). Some of current models of the basal ganglia emphasize their role in action selection (Mink, 1996). If this is the case, one would expect that the basal ganglia (including pallidal) activity would precede action. It is therefore very instructive that most studies (Anderson and Horak, 1985; Brotchie et al., 1991a; Jaeger et al., 1995; Mink and Thach, 1991b) have reported that pallidal activity is modulated late in comparison to the onset of action or muscle activation. More recent studies, probably influenced by the third generation of basal ganglia models (section “Current models and the major anatomical constraints of the basal ganglia” above) that integrate limbic/cognitive and motor domains, have reported significant pallidal responses to nonmotor events such as the behavioral context, prediction of future reward and reward delivery (Arkadir et al., 2004; Bromberg-Martin et al., 2010; Brotchie et al., 1991b; Gdowski et al., 2001; Morris et al., 2005; Turner and Anderson, 2005). Between the lines, these studies hint that if you train a monkey to perform a movement for reward,

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basal ganglia activity will encode the action(s) that lead to reward. Thus, one should not expect to understand the role of neural network by simple observation of the behavioral events that the neurons in the network respond to. Given this tacit hypothesis, we focus below on the general features of pallidal responses to behavioral events (i.e. their duration, magnitude and polarity). The linear dis-inhibition action selection model predicts that most GPi responses to behavioral events should be decreases or pauses in their ongoing high-frequency discharge (Chevalier et al., 1985; Deniau and Chevalier, 1985; Mink, 1996). Similar predictions can also be made for GPe neurons, considering the predominant GABA innervation of the pallidal neurons by striatal afferents. In fact, initial studies of SNr neuron responses to memoryguided saccades concur with this prediction (Hikosaka and Wurtz, 1983). However, there is now a consensus in the basal ganglia research community that most pallidal responses to behavioral events take the form of increases in discharge rates (Table 1). Similar results have been reported by more recent studies for the SNr (Basso et al., 2005; Bayer et al., 2004; Handel and Glimcher, 1999, 2000; Nevet et al., 2007) in line with the proposed similarity of the functional connectivity between SNr and GPi. A possible explanation for the predominance of increases in discharge rates of pallidal neurons in response to behavioral events is that the focus of the inhibition induces lateral rebound excitation in the surrounding area. The finding that in GPi (but not GPe) neurons, decreases in discharge rate tended to begin earlier than increases in this experiment (Turner and Anderson, 1997, Figs. 3 and 4) fits with this explanation. However, this interesting observation should be re-tested and confirmed by future studies. Dis-inhibition models often depict the hypothetical response of pallidal cells as all or none, with complete cessation of discharge. However, although such extreme response amplitudes have been reported in the literature, the average modulation of pallidal discharge in response to behavioral events is in the range of 10 –20 spikes/s (Joshua et al., 2009b; Turner and Anderson, 1997). Thus, in the pallidum the average peak amplitude response represent much smaller fraction of the background activity (10 –30%) than that found in areas with low background discharge rate such as the cortex and the striatum (100 – 500%). No significant difference has been reported for the amplitude of increases vs. decreases of discharge. The average increase in discharge rate reported in population studies of pallidal activity therefore reflects the higher frequency of responses with an increase in discharge rate. Our recent study that looked for a balance between increases and decreases of the spontaneous discharge rate of pallidal neurons also found a symmetric distribution of the frequency and the amplitude of these bi-phasic changes in the pallidal spontaneous discharge rate (Elias et al., 2008). Finally, if the role of the basal ganglia is to select or to initiate action we should expect to find short and transient responses in the pallidal networks. Such responses are

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often shown in the figures of early studies that employed behavioral paradigms with over-trained ballistic movements. However, when monkeys are engaged in behavioral tasks with longer delays, we often observe persistent and long-lasting modulation of pallidal activity (Arkadir et al., 2004; Joshua et al., 2009b; Morris et al., 2005). In conclusion, the typical changes in pallidal discharge in response to behavioral events are either increases or decreases in their discharge rate. These response can be long (⬎1 s) and have moderate amplitude (⬃10 –30% of the ongoing discharge rate). Similarity of encoding between pallidal neurons (signal correlation) Early cross-correlations studies of neuronal activity (Abeles, 1982a; Kimura et al., 1976; Perkel et al., 1967) used the spike-to-spike correlation analysis described above (section “Cross-correlation of spontaneous spiking activity in the pallidal network”) and focused on detection and quantification of the functional connectivity between neurons (e.g. direct excitatory, inhibitory synapses or common synaptic inputs). Recent studies (e.g. Averbeck and Lee, 2004; Lee et al., 1998; Oram et al., 1998; Zohary et al., 1994) have used data from simultaneously recorded neurons to explore the similarities of their responses to behavioral events (signal correlation). We recently studied the functional interactions between simultaneously recorded pairs of neurons in the basal ganglia while monkeys performed a classical conditioning task that included rewarding, neutral, and aversive events. Neurons belonging to a single basal ganglia neuromodulator group (midbrain dopaminergic neurons, striatal cholinergic interneurons) exhibited similar responses to behavioral events, whereas GPe and GPi neurons responded in a highly diverse manner (Joshua et al., 2009a). The distribution of the signal correlations of the GPe and GPi pairs was symmetrically distributed with an average close to zero (Joshua et al., 2009a, Fig. S1A, C, D).

THE SPIKING ACTIVITY OF THE PALLIDAL NETWORKS FOLLOWING DOPAMINE DEPLETION (PARKINSON’S DISEASE) The search for a better understanding of the enigma of the basal ganglia has always been motivated by a drive to find a treatment for the highly prevalent human diseases associated with basal ganglia disorders. The most common of these is Parkinson’s disease, which is characterized by motor dysfunctions (akinesia, muscle rigidity, 4 –7 Hz rest tremor and postural instability) as well as emotional and cognitive deficits. However, many other human disorders are related to the basal ganglia, including Huntington’s disease, major depression, obsessive compulsive disorders and perhaps even schizophrenia. A major breakthrough in our ability to study the pathophysiology of Parkinson’s disease took place 25–30 years ago with the discovery of the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) neurotoxin (Ballard et al., 1985; Davis et al., 1979; Langston et al., 1983) and the MPTP primate mod-

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els of Parkinson’s disease (Burns et al., 1983; Langston et al., 1984). Discharge rate in the pallidal networks following dopamine depletion Early physiological studies of Parkinsonian MPTP-treated monkeys reported changes in the discharge rate within the GPe, GPi (Filion and Tremblay, 1991; Miller and DeLong, 1987) and the STN (Bergman et al., 1994). In accordance with the predictions of the D1/D2 direct/indirect model of the basal ganglia (Albin et al., 1989; Bergman et al., 1990) these studies found that following dopamine depletion there was a decrease in average GPe discharge rate and an increase in the GPi discharge rate. However, some more recent studies (e.g. Bergman et al., 1994; Raz et al., 2000) have failed to confirm the changes in discharge rate in the primate GPe and GPi, probably reflecting the technical problems associated with single unit recording, as well as the differences between the MPTP procedures and their clinical effects. Reverse trends of pallidal discharge rates in response to dopamine replacement therapy have been reported in both human patients (Hutchinson et al., 1997; Lee et al., 2007; Merello et al., 1999) and primates (Filion et al., 1991; Heimer et al., 2006; Papa et al., 1999). These changes, probably reflecting the effects of super-doses of dopamine following the sensitization of dopamine receptors, tend to be more robust than the changes in the spontaneous discharge rate of pallidal neurons following MPTP intoxication (e.g. Heimer et al., 2002b, Fig. 2; Papa et al., 1999). The critical role of these rate changes in the pathophysiology of Parkinson’s disease has been verified by subsequent findings showing that inactivation (and lesion) of the GPi (and the STN—the major source of glutamatergic input to the GPi) could improve the motor symptoms in Parkinsonian animals (Aziz et al., 1991; Bergman et al., 1990) and human patients (Alvarez et al., 2005, 2009; Coban et al., 2009; Kleiner-Fisman et al., 2010; Obeso et al., 2009; Strutt et al., 2009; York et al., 2007). Discharge patterns in the pallidal networks following dopamine depletion Physiological studies of pallidal activity suggest that changes in the discharge pattern can be found in the GPe and GPi of MPTP monkeys. A common finding is an increase in the fraction of basal ganglia neurons that discharge in bursts. These bursts are either irregular or periodic and have been found both in the GPe and the GPi (Bergman et al., 1994; Boraud et al., 2001; Filion and Tremblay, 1991; Miller and DeLong, 1987; Raz et al., 2000; Wichmann and Soares, 2006). In the MPTP primate, the pallidal cells present periodic bursts at the tremor frequency and at double tremor frequency (Bergman et al., 1994; Heimer et al., 2006; Raz et al., 2000). Both STN inactivation (Wichmann et al., 1994b) and dopamine replacement therapy (Heimer et al., 2006) significantly ameliorate the 4 –7 Hz tremor (of the MPTP-treated Vervet monkeys) and reduce the GPi 8 –20 Hz oscillations, underscoring the critical role of the double rather than the

tremor frequency oscillations in the generation of the Parkinsonian tremor and other motor symptoms. The Poissonian nature of pallidal discharge also breaks down in human patients with Parkinson’s disease, where oscillatory activity is observed at the local field potentials and the spike trains of GPi and STN neurons (Kühn et al., 2005; Levy et al., 2002a, b; Silberstein et al., 2003; Weinberger et al., 2006, 2009; Zaidel et al., 2010). In addition to the tremor (4 –7 Hz) frequency and doubletremor (10 Hz) frequency oscillations observed in the MPTP monkeys, beta (15–30 Hz) oscillations are frequently observed in these human recordings. Similar oscillations in the beta range are commonly found in the STN and the GPe of 6-OHDA rodent model (Mallet et al., 2008a, b; Sharott et al., 2005). The origin of this discrepancy between the primates that do not display beta oscillations vs. the human and the rodent 6-OHDA model is still a mystery. It may reflect bias of recording areas (human microelectrode recording are biased toward the STN whereas the rodent and primate studies are biased towards the GPe), the species difference, the disease model (idiopathic PD, MPTP, 6-OHDA; systemic vs. local injections; bilateral vs. unilateral clinical effects etc.). Synchronization of pallidal activity following striatal dopamine depletion Physiological studies of simultaneously recorded neurons in the GPe and the GPi (Heimer et al., 2002a, 2006; Nini et al., 1995; Raz et al., 2000) in MPTP-treated monkeys demonstrate that their pair-wise cross-correlograms become peaked and oscillatory. A similar synchronization was observed in the GPe of the 6-OHDA rodent model (Mallet et al., 2008a, Figs. 1, 6 and 7). In most cases, the maximal power of the synchronous oscillations in the primate pallidum was found to be at double the tremor frequency (Heimer et al., 2006; Raz et al., 1996, 2000, 2001). As with the human beta oscillations (Doyle et al., 2005) this abnormal pallidal synchronization decreases in response to dopamine replacement therapy (Heimer et al., 2006). Erez et al. (2011) analyzed the responses of simultaneously recorded pairs of pallidal neurons to periodic flexion-extension movements of the elbow in the MPTP Parkinsonian monkey. As in the normal pallidum (Joshua et al., 2009a) they found that movement-based signal correlation values were diverse and their mean was not significantly different from zero (i.e. the pallidal neurons were not activated synchronously in response to movement). However, the mean of the noise correlation, which measures the inter-trial correlations (like the spike to spike correlation described above), was significantly greater than zero, implying that the background spiking activity was synchronized. This contrasts with the symmetric (around zero) distribution of noise correlation values of GPe and GPi pairs (Joshua et al., 2009a, Suppl Fig. 2d) and the flat spike to spike correlograms (Heimer et al., 2002a, 2006; Nini et al., 1995; Raz et al., 2000) in normal monkeys. In the healthy primate, even neighboring pallidal neurons present a negligible level of synchrony, despite their

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higher probability to receive common inputs and to innervate each other via lateral connectivity (Bar-Gad et al., 2003a). We recently assessed the relation between distance and synchrony in the GPe and GPi of MPTP-treated monkeys (Mitelman et al., 2011). To do so, we compared the synchrony of discharge of close pairs of neurons, recorded by the same electrode (estimated distance less than 100 ␮m) with remote pairs, recorded by different electrodes (500 –2500 ␮m distance). However, spike trains of neighboring cells recorded by the same extracellular electrode exhibit the shadowing effect (lack of detection of spikes that occur within a few milliseconds of each other) that can both induce artificial correlations, as well as conceal existing correlations between oscillatory neurons. The previously discussed (section “Cross-correlation of spontaneous spiking activity in the pallidal network”) methods for estimation of the cross-correlogram of pair of neighboring neurons (with shadowing effect) assume that the autocorrelation functions are known (Bar-Gad et al., 2001b). However, in the Parkinsonian state, the auto-correlation functions might be severely affected by shadowing effects, and therefore the real (i.e. unshadowed) auto-correlation functions are unknown. We therefore introduced artificial shadowing in the remote pairs, similar to the effect we observed in the close ones. After the artificial shadowing, neighboring cells did not show a higher tendency to oscillate synchronously than remote ones. On the contrary, the average fraction of artificially shadowed remote pairs exhibiting synchronous oscillations was higher than that found for the close pairs. A similar trend was found when the unshadowed remote pairs were separated according to the estimated distance between electrode tips. We found that a similar fraction of close (less than 750 ␮m distance) and remote (more than 750 ␮m distance) pallidal pairs were significantly synchronized. Thus, in contrast to findings in the 6-OHDA rodent where the level of synchrony was found to moderately decrease with the distance (Mallet et al., 2008a, Fig. 5e, f), the synchronous oscillations in the GPe and the GPi of MPTP-treated primates were homogenously distributed (Mitelman et al., 2011). The causal relationship between chronic dopamine depletion, the emergence of synchronous oscillations in the pallidum and the main Parkinsonian motor symptoms has been called into question by recent rodent (Degos et al., 2009) and primate (Leblois et al., 2007) studies. The GPi neuronal activity of nonhuman primates was recorded during a progressive dopamine depletion process. Parkinsonian motor symptoms appeared progressively during the intoxication protocol. However, synchronous oscillations of the spontaneous neuronal activity remained unchanged during this period and appeared only after the major motor symptoms of Parkinsonism developed. The authors therefore suggested that the pathological disruption of movement-related activity, rather than the development of pallidal synchronous oscillations are causally related to Parkinsonian symptoms. However, the spike-to-spike correlation may be an insensitive estimator of neuronal synchronization. A combined experimental and theoretical study of the retina revealed that weak pairwise correlations

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can imply strongly correlated network states in a neural population (Ganmor et al., 2011; Schneidman et al., 2006). Thus, a weak synchronization state, as can be observed at the initial stages of Parkinson’s disease, might be undetected by pair-wise correlation analysis.

DYNAMICAL SYSTEM CHARACTERIZATION OF BASAL GANGLIA NEURONS The neuronal models used to study network dynamics are usually too simplified to describe the richness of firing patterns exhibited by neurons. On the other hand, fullblown multi-compartmental models are so high-dimensional that they undermine the generality of their predictions. A possible solution to this catch-22 comes from the field of non-linear dynamic analysis (Izhikevich, 2007), which provides theorems that help close this gap. Dynamical system analysis of neurons in a nutshell Non-linear dynamic analysis in neuroscience (Izhikevich, 2007) shows that high-dimensional dynamical systems generally exhibit interesting behavior that is captured by lower dimensional representations of these systems. The low dimension representation of neural activity renders excessively complex models unnecessary. In this framework, neurons can be classified by their bifurcation behavior into four classes and described as mono-stable/bistable integrator/resonators. The major claim here is that neurons in the input stages of the basal ganglia (striatal projection and STN neurons) behave like mono-stable integrators (as already suggested for the MSNs by Izhikevich, 2007; Ponzi and Wickens, 2010) and pallidal neurons like bi-stable integrators. Hodgkin (1948) was the first to point out the existence of two common patterns of neuronal responses (discharge rate) to current injection. Neurons with class I excitability behavior can discharge at arbitrary low frequencies and their discharge rate increases monotonically and continuously with the strength of the injected current (Fig. 3A). Neurons with class II excitability are quiescent at low levels of injected DC currents. However, at some intensity they start to discharge at a high discharge rate (e.g. 100 spikes/ s). They will usually exhibit subthreshold oscillations for currents that approach this threshold. The discharge rate is only slightly modulated by further increases in the intensity of the current injection (Fig. 3B). The maximal discharge rate of class II excitability neurons is often significantly higher than that of class I excitability neurons (e.g. 250 – 300 vs. 50 – 80 spikes/s). Experimentally identifying the correct category of a given neuron can be tricky, as it can depend on the stimuli used to drive the neuron, and neurons can in principle exhibit different behavior under slight changes in parameters (Izhikevich, 2007). Generally speaking, mono-stable integrators exhibit class I excitability, and the other three dynamical classes (bi-stable integrator and mono- and bi-stable resonators) exhibit class II excitability behavior.

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Dynamical system analysis of the neurons of the BG main axis Previous studies (Izhikevich, 2007, section 8.4.2; Ponzi and Wickens, 2010) proposed that striatal low-frequency discharge projection neurons correspond to mono-stable integrators (saddle node on invariant circle bifurcation dynamics) with class I excitability behavior (Fig. 4A). Here we further hypothesize that high-frequency discharge pallidal neurons (with and without pauses) display the behavior of bi-stable resonators (subcritical Andronov-Hopf bifurcation) with class II excitability in-vivo (Fig. 4B). We suggest classifying high-frequency discharge pallidal neurons as bi-stable resonators (class II excitability) despite the evidence that the behavior of these neurons in-vitro is class I excitability, that is, they exhibit arbitrarily low frequency firing in the I–f curves (Kita and Kitai, 1991; Nambu and Llina´s, 1994; Rav-Acha et al., 2005) and a gradual increase in discharge rate upon application of a ramp current (Mercer et al., 2007, Fig. 7F, G and see section “Physiological characteristics of the main pallidal neurons” above). A recent study showing that neurons can switch from integrators in-vitro to resonators under in-vivo conditions (Prescott et al., 2008) argues in favor of classifying pallidal neurons in-vivo as bi-stable resonators. During wakefulness, neurons in the intact brain are bombarded by synaptic input that causes tonic depolarization, increased membrane conductance, and noisy fluctuations in the membrane potential. On the other hand, neurons studied in-vitro in slices experience little background synaptic input. Such differences in operating conditions can compromise the extrapolation of in-vitro data to explain neuronal operation in-vivo. Prescott et al. (2008) used long depolarizing stimuli and a dynamic clamp to reproduce in-vivo like conditions in slice hippocampal experiments. They showed that hippocampal pyramidal cells can switch from integrators/class I excitability to resonators/class II excitability behaviors. In awake behaving animals the long and aspiny dendrites of pallidal cells are covered by 30,000 – 40,000 synapses (Percheron et al., 1994; Yelnik et al., 1996), and therefore even at the low discharge rate of their striatal afferent neurons, membrane conductance and fluctuations are likely to be much higher in the in-vivo than in the in-vitro state. Thus, the I–f properties may differ qualitatively between in-vitro and in-vivo conditions and we therefore suggest that the behavior of pallidal neurons in-vivo is indicative of bi-stable resonator (class II excitability). Many of the features of the behavior of pallidal neurons described above are in line with those of class II bi-stable resonators. The pausing phenomenon of the GPe cells characterized by a random (Poisson like) temporal distribution and sharp rather than ramp-like changes in discharge rate closely resembles the behavior expected from a neuron whose membrane potential is located in the bi-stable region near the unstable equilibrium point. Note that this equilibrium point is different from the bifurcation point, and represents the step in the I–f function of class II excitability neurons. Thus, the bifurcation point and the

bi-stable equilibrium points are not necessarily identical in the case of class II excitability. The different fraction of pausers out of the total GPe high-frequency neurons found in different studies and even between different monkeys within the same study suggest that the location of GPe neurons on the dynamical map represents some of the individual features of each neuron. Furthermore, as expected, when the arousal of the monkey decreases, and it is less engaged in a behavioral task, the discharge frequency of GPe neurons decreases and the frequency and the duration of GPe pauses increases (Adler et al., 2010; Elias et al., 2007). The high spontaneous discharge rate of pallidal neurons is of course in line with bi-stable resonator behavior. The predominance of inhibitory inputs to the pallidal cells should favor depression of the pallidal discharge rate in response to behavioral events. Therefore, it is even more striking that as expected from resonators (Izhikevich, 2007, Fig. 7.21), most pallidal responses to behavioral events in in-vivo studies (see section “Neuronal responses to behavioral events in the pallidal network”) are elevations of the discharge rate. As expected from resonators, the amplitude of the modulation of the responses is small compared to the average discharge rate. Electrophysiologists (including—mea culpa—H.B. one of the authors of this manuscript) tend to report the best “exceptional” responses in the figures of their manuscripts. It is not surprising that in many cases, the behavioral related pause response of pallidal cells is depicted to exhibit a drastic reduction in discharge rate from 50 –70 spikes/s to zero spikes/s. Nevertheless, the average amplitude of the responses of GPe and GPi neurons are 10 –20 spikes/second, that is, 10 –30% of their background discharge rate. This should be compared to the average modulation of 5–10 spikes/s for the responses of cortical and striatal neurons, which yields a change in 100 –500% of their background low discharge rate. The computational advantages of bi-stable resonators vs. mono-stable integrators have usually been discussed under the assumption that the responses of bi-stable resonators are due to transitions between the quiescent and the spike states (Izhikevich, 2007). Further studies and insights are needed to shed light on the conditions in the pallidal network where the neurons are in the spiking regimen most of the time. Our working hypothesis is that bi-stable resonator network enables the use of the inhibitory transmitter (GABA) as a carrier of information to the next station of the network. This means that the BG monolayer networks, where the local collaterals of the main projection neurons provide competitive mechanisms within the layer, have no need for intervening interneurons. Another possibility is that the responses of mono-stable integrators are typically short, due to adaption or fatigue. On the other hand, bi-stable resonators can easily modulate their discharge rate for prolonged periods, and therefore are more suitable for real-time continuous control of action. Finally, bi-stable resonators enable temporal rather than discharge rate encoding. Temporal coding (i.e. encoding information in the temporal structure of neuron spike

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trains) is more efficient than rate encoding and reduces the need for averaging the responses of a large population of neurons (Buonomano and Merzenich, 1999; Kumar et al., 2010). Pallidal neurons as autonomous and weakly coupled pacemakers The theory of phase-coupled oscillators provides a complementary approach to the dynamical system analysis of pallidal neurons. It posits that because the pallidal neurons are autonomous pacemakers (Chan et al., 2004) their synaptic input should not be classified as excitatory or inhibitory. Rather, synaptic inputs to pacemaking neurons are categorized as either advancing or delaying the time of the next action potential (Ermentrout and Kleinfeld, 2001). A recent analytical model further helps fuse the theory of weakly coupled oscillators with nonlinear cable theory (used to model dendrites) to study the effects of a long dendrite on the synchronization of a pacemaking neuron (Goldberg et al., 2007). The tendency of a neuron to synchronize depends on the location of the synapse along its dendrites, the firing rate of the pacemaking neuron, and the dendritic nonlinearities. In fact, a recent phase response curve analysis of a full morphological model of the pallidal neuron revealed distinct somatic and dendritic modes of synaptic integration (Schultheiss et al., 2010). Somatic excitatory inputs delivered throughout the inter spike interval advance the phase of the spontaneous spike cycle, yielding a type I phase response curve (only positive phase shift). In contrast, dendritic HCN currents cause distal excitatory inputs to either delay or advance the next spike depending on whether they occur early or late in the spike cycle, that is, a type II phasic response curve (both negative and positive phase shifts, leading to a stronger tendency toward synchronization by lateral coupling). Thus, these results lend weight to the hypothesis that the dendrites and the soma of pallidal neurons form two distinct dynamical subsystems. Why in-vivo pallidal neurons may express class II excitability behavior In summary, we have proposed two mechanisms by which pallidal neurons can express class II excitability or bistable resonator behavior, despite the in-vitro measurements that show that their response to somatic current injections resembles that of class I neurons. The first is that the barrage of synaptic input changes the class of the pallidal neurons in a way similar to that proposed by Prescott et al. (2008). The second is through a mechanism proposed by Goldberg et al. (2007) and later by Schultheiss et al. (2010) that dendritic HCN currents cause pallidal neurons to respond to synaptic input like class II resonators (type II phase response), despite the fact that the soma may actually exhibit class I excitability. Either way, exhibiting class II excitability behavior and type II phase response curves implies that these neurons will tend to synchronize to excitatory input (Ermentrout, 1996; Izhikevich, 1999; Lago-Fernández et al., 2001). This may explain why pallidal neurons tend to synchronize to

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subthalamic inputs rather than to striatal inputs (Goldberg et al., 2003). Several groups have reported robust resetting of GPe or GPi activity by striatal (Chan et al., 2004, Figs. 6 and 7; Rav-Acha et al., 2005, Fig. 8) and GPe (Kita, 2001, Fig. 5) IPSPs, respectively. Nevertheless, the dynamical behavior of pallidal neurons leads to higher sensitivity to STN excitatory inputs and strong STN-pallidal coupling.

COMPUTATIONAL PHYSIOLOGY OF THE BASAL GANGLIA AND THEIR DISORDERS A prominent feature of neural computation is redundancy expansion and reduction of the information processed by different neural networks. The redundancy reduction/expansion process is clearly observed in the relative number of afferent and efferent fibers to and from the CNS in comparison to the number of neurons in the CNS. In the human and non-human primates there are probably several million afferent fibers transferring information from the peripheral receptors to the CNS (e.g. about 1 million fibers in the optic nerve). Similarly, there are about an equal number of fibers leading commands from the CNS to the muscular apparatus (again, about 1 million fibers in the primate pyramidal cortico-spinal pathways). The total numbers of CNS neurons is probably several orders of magnitude larger and is roughly estimated at 1012–1014 neurons. It is therefore often claimed that cortical neurons mainly “speak” with their peers rather than receiving or transmitting information to the peripheral nervous system (Abeles, 1991; Braitenberg and Schuz, 1991). Redundancy expansion and reduction is not limited to the periphery-CNS transition. Rather, it is observed in many neural networks, including the basal ganglia and the cerebellum. The computational advantages of these processes is their ability to better extract the relevant information in different components of the network (e.g. the ⫻ and Y coordinates of visual perception can be expanded to X, Y, X2 and Y2 and then reduced to the angle in the orientation network and to distance in the reaching and grasp network; S. Druckmann, personal communication). Similarly, compression followed by reintroduction of error-correcting redundancy can yield optimal population coding in a network of noisy neurons (Tkacik et al., 2010). Our working hypothesis (Bar-Gad et al., 2003b) holds that the basal ganglia carry out efficient and flexible feature extraction (dimensionality reduction) of the cortical and thalamic activity representing the current state of the animal. This is supported by evidence for plasticity in the efficacy of the cortico-striatal synapse, which is mainly modulated by dopamine and other modulators that provide the pleasure/arousal prediction errors signal to the striatum. It is further supported by the lateral competitive dynamics (Földiák, 1989, 1990) in each of the three layers of the basal ganglia main axis (striatum/STN, GPe and GPi) and the significant reduction in the number of neurons along this axis. We further hypothesize that the different dynamical behavior of neurons in the three layers of the BG support our proposed scheme of information process-

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ing along the BG axis. The different computational capabilities of a network of linear elements (striatum) followed by the pallidal network of non-linear elements (probably with reduced functional lateral connectivity) could lead to a very efficient feature extraction processes. Linear feature extraction networks (e.g. networks that perform principal component analysis, PCA, Diamantaras and Kung, 1996) can only find linear interactions between the inputs. In cases of non-linear interactions between the input elements and the higher order statistics of interaction, a linear network cannot reduce the dimensionality of the input effectively. The addition of a non-linear layer makes possible the extraction of higher order statistics and the breakdown of the inputs into their independent features (Oja et al., 1991). The three-layer structure of the basal ganglia also enables a transformation of rate coding at the input stage of the basal ganglia (striatum and STN) to temporal or phase coding by the pallidal networks. Temporal coding (i.e. modulation of the discharge variability rather than the discharge rate) is in line with the relatively small amplitude of responses of pallidal neurons and with their long duration of their responses. Hence changes in the variability of discharge (Nawrot et al., 2008) should be much more pronounced in the pallidal network than the changes recently observed in the variability of cortical activity (Churchland et al., 2010, 2011). Finally, we suggest that the GPe may be the “noise generator” of the main axis of the basal ganglia. A critical tradeoff in behavior is represented by a balance between exploration and exploitation (Sutton and Barto, 1998). Exploration can be achieved by random manipulation of the behavioral policy (i.e. the state to action mapping) of the actor part of the learning agent. The random pauses of GPe neurons are ideal candidates for noise injections into the basal ganglia main axis or actor portion. As expected, the frequency of these pauses is dependent on the arousal level and peaks during periods of low arousal and decreases during periods when monkeys are engaged in over-trained behavioral tasks (Adler et al., 2010).

DISCUSSION We have focused on the pallidal complex as part of the main axis, or actor part, of the basal ganglia reinforcement learning network. We put forward the hypothesis that this axis achieves its computational goal of efficient feature extraction and redundancy reduction of thalamo-cortical information via its unique anatomical and physiological characteristics. This includes a striking decrease in the number of neurons along the axis of three layers, with mono-stable integrators followed by bi-stable resonators. The resonator properties enable the use of GABA (an inhibitory transmitter) as a carrier of information in the basal ganglia network. Moreover, these resonator properties resolve the paradox of more increases in the discharge rate of pallidal neurons in response to behavioral events despite the predominance of their GABAergic inputs. Thus, GABA can be efficiently used for lateral competitive dy-

namics and the transmission of information to the next layer, without the need for interleaving interneurons in the basal ganglia network. There are many issues that should be investigated and clarified in future studies. For example, our model correctly predicts that GPe bi-stability (or even instability) is augmented when the GPe discharge rate decreases, as has been observed following eye closure (Adler et al., 2010) and MPTP-induced dopamine depletion (Boraud et al., 2002; Raz et al., 2000). However, the frequency and the duration of GPe pauses increased even in situations where the GPe discharge rate increased (Bronfeld et al., 2010). At the level of single GPe cells, we failed to find correlations between the frequency and duration of the pauses and the cell discharge rate (Elias et al., 2007). Finally, after dopamine depletion and the induction of a Parkinsonian state in mice, there is a progressive decline in autonomous GPe pacemaking, due to down-regulation of the HCN channel. Viral delivery of HCN subunits and L-type calcium channel antagonists restore pacemaking but the Parkinsonian motor disability is not reversed (Chan et al., 2011). Thus, GPe bi-stability does not simply model the discharge rate of the GPe cells. It is likely that the dopaminergic (and other neuromodulators) innervation of the GPe should be taken into account (Charara and Parent, 1994; Cossette et al., 1999; Francois et al., 2000; Jan et al., 2000; Prensa et al., 2000). In this review we deliberately neglected the effects of micro/macro stimulation, local inactivation and high-frequency continuous stimulation (deep brain stimulation, DBS) of the pallidal complex. The interested reader can consult the recent reviews on these topics (Johnson and McIntyre, 2008; Nambu, 2007; Turner and Desmurget, 2010). Many other critical issues should be better clarified by future thinking, for example, the roles of the direct pathways, the limbic parts of the basal ganglia including the ventral striatum, ventral pallidum and the SNr. However, science is making progress by formulating hypotheses that can be experimentally tested. We hope that the hypotheses outlined in this manuscript will encourage such studies of the basal ganglia networks. Regardless of whether these future experimental studies confirm or disconfirm our hypotheses, they will advance our understanding of the computational physiology of the basal ganglia networks and their disorders. Acknowledgments—This study was supported in part by the FP7 select & act and the Vorst family foundation grants (to H.B.). During the preparation of this article JAG was supported by the IDP Foundation, Chicago, Illinois.

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(Accepted 30 August 2011) (Available online 10 September 2011)