Properties of Neurons in External Globus Pallidus Can Support Optimal Action Selection

The external globus pallidus (GPe) is a key nucleus within basal ganglia circuits that are thought to be involved in action selection. A class of computational models assumes that, during action selection, the basal ganglia compute for all actions available in a given context the probabilities that they should be selected. These models suggest that a network of GPe and subthalamic nucleus (STN) neurons computes the normalization term in Bayes’ equation. In order to perform such computation, the GPe needs to send feedback to the STN equal to a particular function of the activity of STN neurons. However, the complex form of this function makes it unlikely that individual GPe neurons, or even a single GPe cell type, could compute it. Here, we demonstrate how this function could be computed within a network containing two types of GABAergic GPe projection neuron, so-called ‘prototypic’ and ‘arkypallidal’ neurons, that have different response properties in vivo and distinct connections. We compare our model predictions with the experimentally-reported connectivity and input-output functions (f-I curves) of the two populations of GPe neurons. We show that, together, these dichotomous cell types fulfil the requirements necessary to compute the function needed for optimal action selection. We conclude that, by virtue of their distinct response properties and connectivities, a network of arkypallidal and prototypic GPe neurons comprises a neural substrate capable of supporting the computation of the posterior probabilities of actions.     

Mean-field modeling of the basal ganglia-thalamocortical system. II: Dynamics of parkinsonian oscillations

Neuronal correlates of Parkinson's disease (PD) include a shift to lower frequencies in the electroencephalogram (EEG) and enhanced synchronized oscillations at 3-7 and 7-30 Hz in the basal ganglia, thalamus, and cortex. This study describes the dynamics of a recent physiologically based mean-field model of the basal ganglia-thalamocortical system, and shows how it accounts for many key electrophysiological correlates of PD. Its detailed functional connectivity comprises partially segregated direct and indirect pathways through two populations of striatal neurons, a hyperdirect pathway involving a corticosubthalamic projection, thalamostriatal feedback, and local inhibition in striatum and external pallidum (GPe). In a companion paper, realistic steady-state firing rates were obtained for the healthy state, and after dopamine loss modeled by weaker direct and stronger indirect pathways, reduced intrapallidal inhibition, lower firing thresholds of the GPe and subthalamic nucleus (STN), a stronger projection from striatum to GPe, and weaker cortical interactions. Here it is shown that oscillations around 5 and 20 Hz can arise with a strong indirect pathway, which also causes increased synchronization throughout the basal ganglia. Furthermore, increased theta power with progressive nigrostriatal degeneration is correlated with reduced alpha power and peak frequency, in agreement with empirical results. Unlike the hyperdirect pathway, the indirect pathway sustains oscillations with phase relationships that coincide with those found experimentally. Alterations in the responses of basal ganglia to transient stimuli accord with experimental observations. Reduced cortical gains due to both nigrostriatal and mesocortical dopamine loss lead to slower changes in cortical activity and may be related to bradykinesia. Finally, increased EEG power found in some studies may be partly explained by a lower effective GPe firing threshold, reduced GPe-GPe inhibition, and/or weaker intracortical connections in parkinsonian patients. Strict separation of the direct and indirect pathways is not necessary to obtain these results.     

Globus Pallidus Externus Neurons Expressing parvalbumin Interconnect the Subthalamic Nucleus and Striatal Interneurons

The globus pallidus externus (GP) is a nucleus of the basal ganglia (BG), containing GABAergic projection neurons that arborize widely throughout the BG, thalamus and cortex. Ongoing work seeks to map axonal projection patterns from GP cell types, as defined by their electrophysiological and molecular properties. Here we use transgenic mice and recombinant viruses to characterize parvalbumin expressing (PV⁺) GP neurons within the BG circuit. We confirm that PV⁺ neurons 1) make up ~40% of the GP neurons 2) exhibit fast-firing spontaneous activity and 3) provide the major axonal arborization to the STN and substantia nigra reticulata/compacta (SNr/c). PV⁺ neurons also innervate the striatum. Retrograde labeling identifies ~17% of pallidostriatal neurons as PV⁺, at least a subset of which also innervate the STN and SNr. Optogenetic experiments in acute brain slices demonstrate that the PV⁺ pallidostriatal axons make potent inhibitory synapses on low threshold spiking (LTS) and fast-spiking interneurons (FS) in the striatum, but rarely on spiny projection neurons (SPNs). Thus PV⁺ GP neurons are synaptically positioned to directly coordinate activity between BG input nuclei, the striatum and STN, and thalamic-output from the SNr.     

Mean-field modeling of the basal ganglia-thalamocortical system. I: Firing rates in healthy and parkinsonian states

Parkinsonism leads to various electrophysiological changes in the basal ganglia-thalamocortical system (BGTCS), often including elevated discharge rates of the subthalamic nucleus (STN) and the output nuclei, and reduced activity of the globus pallidus external (GPe) segment. These rate changes have been explained qualitatively in terms of the direct/indirect pathway model, involving projections of distinct striatal populations to the output nuclei and GPe. Although these populations partly overlap, evidence suggests dopamine depletion differentially affects cortico-striato-pallidal connection strengths to the two pallidal segments. Dopamine loss may also decrease the striatal signal-to-noise ratio, reducing both corticostriatal coupling and striatal firing thresholds. Additionally, nigrostriatal degeneration may cause secondary changes including weakened lateral inhibition in the GPe, and mesocortical dopamine loss may decrease intracortical excitation and especially inhibition. Here a mean-field model of the BGTCS is presented with structure and parameter estimates closely based on physiology and anatomy. Changes in model rates due to the possible effects of dopamine loss listed above are compared with experiment. Our results suggest that a stronger indirect pathway, possibly combined with a weakened direct pathway, is compatible with empirical evidence. However, altered corticostriatal connection strengths are probably not solely responsible for substantially increased STN activity often found. A lower STN firing threshold, weaker intracortical inhibition, and stronger striato-GPe inhibition help explain the relatively large increase in STN rate. Reduced GPe-GPe inhibition and a lower GPe firing threshold can account for the comparatively small decrease in GPe rate frequently observed. Changes in cortex, GPe, and STN help normalize the cortical rate, also in accord with experiments. The model integrates the basal ganglia into a unified framework along with an existing thalamocortical model that already accounts for a wide range of electrophysiological phenomena. A companion paper discusses the dynamics and oscillations of this combined system.     

Computational modeling of epileptiform activities in medial temporal lobe epilepsy combined with <Emphasis Type="Italic">in vitro</Emphasis> experiments

Electrical stimulation of sub-cortical brain regions (the basal ganglia), known as deep brain stimulation (DBS), is an effective treatment for Parkinson’s disease (PD). Chronic high frequency (HF) DBS in the subthalamic nucleus (STN) or globus pallidus interna (GPi) reduces motor symptoms including bradykinesia and tremor in patients with PD, but the therapeutic mechanisms of DBS are not fully understood. We developed a biophysical network model comprising of the closed loop cortical-basal ganglia-thalamus circuit representing the healthy and parkinsonian rat brain. The network properties of the model were validated by comparing responses evoked in basal ganglia (BG) nuclei by cortical (CTX) stimulation to published experimental results. A key emergent property of the model was generation of low-frequency network oscillations. Consistent with their putative pathological role, low-frequency oscillations in model BG neurons were exaggerated in the parkinsonian state compared to the healthy condition. We used the model to quantify the effectiveness of STN DBS at different frequencies in suppressing low-frequency oscillatory activity in GPi. Frequencies less than 40 Hz were ineffective, low-frequency oscillatory power decreased gradually for frequencies between 50 Hz and 130 Hz, and saturated at frequencies higher than 150 Hz. HF STN DBS suppressed pathological oscillations in GPe/GPi both by exciting and inhibiting the firing in GPe/GPi neurons, and the number of GPe/GPi neurons influenced was greater for HF stimulation than low-frequency stimulation. Similar to the frequency dependent suppression of pathological oscillations, STN DBS also normalized the abnormal GPi spiking activity evoked by CTX stimulation in a frequency dependent fashion with HF being the most effective. Therefore, therapeutic HF STN DBS effectively suppresses pathological activity by influencing the activity of a greater proportion of neurons in the output nucleus of the BG.     

Possible mechanisms of involvement of the subthalamic nucleus and structures interconnected with this nucleus in movement disorders evoked by dopamine depletion

A possible mechanism of involvement of the subthalamic nucleus (STN) in movement disorders evoked by dopamine deficit is suggested. Multifunctional role of the STN is based on following reasons. Various STN cells participate in the cortico-basal ganglia-thalamocortical loop and in the basal ganglia-pedunculopontine-basal ganglia loop. Complexity of neural circuits is determined by functional heterogeneity of neurons in the nuclei, reciprocally connected with the STN, as well as by opposite modulation of activity of these neurons by dopamine due to activation of different types of pre- and postsynaptic receptors. Dopamine influences activity of STN neurons directly, through pre- and postsynaptic receptors. It is assumed that high-frequency stimulation of the STN can reduce or eliminate Parkinsonian symptoms not only owing to inhibition of activity of GABAergic neurons in the output basal ganglia nuclei, projected into the thalamus or pedunculopontine nucleus, but also due to excitation of glutamatergic or cholinergic neurons in the output nuclei, and due to potentiation of excitatory inputs to preserved dopaminergic neurons and subsequent rise in dopamine concentration.     

Influences of membrane properties on phase response curve and synchronization stability in a model globus pallidus neuron

The activity patterns of the globus pallidus (GPe) and subthalamic nucleus (STN) are closely associated with motor function and dysfunction in the basal ganglia. In the pathological state caused by dopamine depletion, the STN–GPe network exhibits rhythmic synchronous activity accompanied by rebound bursts in the STN. Therefore, the mechanism of activity transition is a key to understand basal ganglia functions. As synchronization in GPe neurons could induce pathological STN rebound bursts, it is important to study how synchrony is generated in the GPe. To clarify this issue, we applied the phase-reduction technique to a conductance-based GPe neuronal model in order to derive the phase response curve (PRC) and interaction function between coupled GPe neurons. Using the PRC and interaction function, we studied how the steady-state activity of the GPe network depends on intrinsic membrane properties, varying ionic conductances on the membrane. We noted that a change in persistent sodium current, fast delayed rectifier Kv3 potassium current, M-type potassium current and small conductance calcium-dependent potassium current influenced the PRC shape and the steady state. The effect of those currents on the PRC shape could be attributed to extension of the firing period and reduction of the phase response immediately after an action potential. In particular, the slow potassium current arising from the M-type potassium and the SK current was responsible for the reduction of the phase response. These results suggest that the membrane property modulation controls synchronization/asynchronization in the GPe and the pathological pattern of STN–GPe activity.     

Rapid target-specific remodeling of fast-spiking inhibitory circuits after loss of dopamine

In Parkinson's disease (PD), dopamine depletion alters neuronal activity in the direct and indirect pathways and leads to increased synchrony in the basal ganglia network. However, the origins of these?changes remain elusive. Because GABAergic interneurons regulate activity of projection neurons and?promote neuronal synchrony, we recorded from pairs of striatal fast-spiking (FS) interneurons and direct- or indirect-pathway MSNs after dopamine depletion with 6-OHDA. Synaptic properties of?FS-MSN connections remained similar, yet within 3?days of dopamine depletion, individual FS cells doubled their connectivity to indirect-pathway MSNs, whereas connections to direct-pathway MSNs remained unchanged. A model of the striatal microcircuit revealed that such increases in FS innervation were effective at enhancing synchrony within targeted cell populations. These data suggest that after dopamine depletion, rapid target-specific microcircuit organization in the striatum may lead to increased synchrony of indirect-pathway MSNs that contributes to pathological network oscillations and motor symptoms of PD.     

Potential Mechanisms for Imperfect Synchronization in Parkinsonian Basal Ganglia

Neural activity in the brain of parkinsonian patients is characterized by the intermittently synchronized oscillatory dynamics. This imperfect synchronization, observed in the beta frequency band, is believed to be related to the hypokinetic motor symptoms of the disorder. Our study explores potential mechanisms behind this intermittent synchrony. We study the response of a bursting pallidal neuron to different patterns of synaptic input from subthalamic nucleus (STN) neuron. We show how external globus pallidus (GPe) neuron is sensitive to the phase of the input from the STN cell and can exhibit intermittent phase-locking with the input in the beta band. The temporal properties of this intermittent phase-locking show similarities to the intermittent synchronization observed in experiments. We also study the synchronization of GPe cells to synaptic input from the STN cell with dependence on the dopamine-modulated parameters. Earlier studies showed how the strengthening of dopamine-modulated coupling may lead to transitions from non-synchronized to partially synchronized dynamics, typical in Parkinson''s disease. However, dopamine also affects the cellular properties of neurons. We show how the changes in firing patterns of STN neuron due to the lack of dopamine may lead to transition from a lower to a higher coherent state, roughly matching the synchrony levels observed in basal ganglia in normal and parkinsonian states. The intermittent nature of the neural beta band synchrony in Parkinson''s disease is achieved in the model due to the interplay of the timing of STN input to pallidum and pallidal neuronal dynamics, resulting in sensitivity of pallidal output to the phase of the arriving STN input. Thus the mechanism considered here (the change in firing pattern of subthalamic neurons through the dopamine-induced change of membrane properties) may be one of the potential mechanisms responsible for the generation of the intermittent synchronization observed in Parkinson''s disease.     

A biologically constrained model of the whole basal ganglia addressing the paradoxes of connections and selection

The basal ganglia nuclei form a complex network of nuclei often assumed to perform selection, yet their individual roles and how they influence each other is still largely unclear. In particular, the ties between the external and internal parts of the globus pallidus are paradoxical, as anatomical data suggest a potent inhibitory projection between them while electrophysiological recordings indicate that they have similar activities. Here we introduce a theoretical study that reconciles both views on the intra-pallidal projection, by providing a plausible characterization of the relationship between the external and internal globus pallidus. Specifically, we developed a mean-field model of the whole basal ganglia, whose parameterization is optimized to respect best a collection of numerous anatomical and electrophysiological data. We first obtained models respecting all our constraints, hence anatomical and electrophysiological data on the intrapallidal projection are globally consistent. This model furthermore predicts that both aforementioned views about the intra-pallidal projection may be reconciled when this projection is weakly inhibitory, thus making it possible to support similar neural activity in both nuclei and for the entire basal ganglia to select between actions. Second, we predicts that afferent projections are substantially unbalanced towards the external segment, as it receives the strongest excitation from STN and the weakest inhibition from the striatum. Finally, our study strongly suggests that the intrapallidal connection pattern is not focused but diffuse, as this latter pattern is more efficient for the overall selection performed in the basal ganglia.     

Metabolic changes in the basal ganglia of patients with Huntington's disease: an in situ hybridization study of cytochrome oxidase subunit I mRNA

On the basis of the functional model of the basal ganglia developed in the 1980s and the neuropathological findings in Huntington's disease (HD), changes in the neuronal activity of the basal ganglia have previously been proposed to explain the abnormal movements observed in this pathology. In particular, it has been stated that the neurodegenerative process affecting the basal ganglia in the disease should provoke a hypoactivity in the internal segment of the pallidum (GPi) that could explain choreic movements observed in the disease. To test this functional hypothesis, we performed an in situ hybridization study on control and HD brains postmortem, taking cytochrome oxidase subunit I (COI) mRNAs expression as index of neuronal activity. As most of the HD patients studied were under chronic neuroleptic (NL) treatment, we also studied the brains of non-HD patients under chronic NL treatment. Our results show that in HD brain the number of neurons expressing COI mRNA tends to be lower in the striatum, GPe and GPi, suggesting a severe involvement of these structures during the neurodegenerative process. Moreover, COI mRNA level of expression was markedly reduced within neurons of the putamen and GPe. Surprisingly, COI mRNA expression was not modified in the GPi in HD brains compared with controls. This paradoxical result in the GPi may be explained by the antagonistic effect of GPe hypoactivity and the degenerative process involving neurons of GPi. Our results indicate that the functional modifications, and consequently the pathophysiology of abnormal movements, observed in HD basal ganglia are more complex than expected from the currently accepted model of the basal ganglia organization.     

Oscillatory entrainment of striatal neurons in freely moving rats

Oscillations and synchrony in basal ganglia circuits may play a key role in the organization of voluntary actions and habits. We recorded single units and local field potentials from multiple striatal and cortical locations simultaneously, over a range of behavioral states. We observed opposite gradients of oscillatory entrainment, with dorsal/lateral striatal neurons entrained to high-voltage spindle oscillations ("spike wave discharges") and ventral/medial striatal neurons entrained to the hippocampal theta rhythm. While the majority of units were likely medium-spiny projection neurons, a second neuronal population showed characteristic features of fast-spiking GABAergic interneurons, including tonic activity, brief waveforms, and high-frequency bursts. These fired at an earlier spindle phase than the main neuronal population, and their density within striatum corresponded closely to the intensity of spindle oscillations. The orchestration of oscillatory activity by networks of striatal interneurons may be an important mechanism in the pathophysiology of neurological disorders such as Parkinson's disease.     

Transmission of the Subthalamic Nucleus Oscillatory Activity to the Cortex: A Computational Approach

Parkinsonian tremor is most likely due to oscillatory neuronal activities of central oscillators such as the subthalamic nucleus (STN)-external segment of the globus pallidus (GPe) pacemaker within the basal ganglia (BG). Activity from the central oscillator is proposed to be transmitted via transcortical pathways to the periphery. A computational model of the BG is proposed for simulating the transmission of the STN oscillatory activity to the cortex, based closely on known anatomy and physiology of the BG. According to the results of the simulation, for transmission of the STN oscillatory activity to the cortex, the STN oscillatory activity has to be transmitted simultaneously to the thalamus via STN-internal segment of the globus pallidus (GPi)-thalamus and STN-GPe-GPi-thalamus pathways. This transmission is controlled by the various factors such as the phase between the STN and GPe oscillatory activities, the STN oscillatory activity frequency, the low-threshold calcium spike bursts of the thalamus and the GPi spontaneous activity.     

A computational modelling approach to investigate different targets in deep brain stimulation for Parkinson’s disease

We investigated by a computational model of the basal ganglia the different network effects of deep brain stimulation (DBS) for Parkinson’s disease (PD) in different target sites in the subthalamic nucleus (STN), the globus pallidus pars interna (GPi), and the globus pallidus pars externa (GPe). A cellular-based model of the basal ganglia system (BGS), based on the model proposed by Rubin and Terman (J Comput Neurosci 16:211–235, 2004), was developed. The original Rubin and Terman model was able to reproduce both the physiological and pathological activities of STN, GPi, GPe and thalamo-cortical (TC) relay cells. In the present study, we introduced a representation of the direct pathway of the BGS, allowing a more complete framework to simulate DBS and to interpret its network effects in the BGS. Our results suggest that DBS in the STN could functionally restore the TC relay activity, while DBS in the GPe and in the GPi could functionally over-activate and inhibit it, respectively. Our results are consistent with the experimental and the clinical evidences on the network effects of DBS.     

New aspects of physiological and pathophysiological functions of adenosine A2A receptor in basal ganglia

There is now growing interest in the functional role of adenosine A2A receptors. Their distribution within the brain is restricted in the basal ganglia, particularly abundant in the striatum, which are thought to play a crucial role in the control of motor behavior. Indeed, newly developed A2A receptor selective antagonists have a profound influence on motor functions, with anti-Parkinsonian activities in several animal models. Striatal spiny neurons serve as a major anatomical locus for the relay of cortical information flow through the basal ganglia. The GABA releasing projection neurons represent the A2A receptor-mediated main target of adenosine. The GABAergic synaptic neurotransmission is regulated by adenosine via A2A receptors on the presynaptic terminals. Blockade of this modulatory function by A2A antagonists could repair striatopallidal abnormal neuronal activities provoked by striatal dopamine depletion in the Parkinsonian state. A2A receptor antagonists provide a novel therapeutic potential for the treatment of Parkinson's disease.     

Retinoic acid functions as a key GABAergic differentiation signal in the basal ganglia

Although retinoic acid (RA) has been implicated as an extrinsic signal regulating forebrain neurogenesis, the processes regulated by RA signaling remain unclear. Here, analysis of retinaldehyde dehydrogenase mutant mouse embryos lacking RA synthesis demonstrates that RA generated by Raldh3 in the subventricular zone of the basal ganglia is required for GABAergic differentiation, whereas RA generated by Raldh2 in the meninges is unnecessary for development of the adjacent cortex. Neurospheres generated from the lateral ganglionic eminence (LGE), where Raldh3 is highly expressed, produce endogenous RA, which is required for differentiation to GABAergic neurons. In Raldh3?/? embryos, LGE progenitors fail to differentiate into either GABAergic striatal projection neurons or GABAergic interneurons migrating to the olfactory bulb and cortex. We describe conditions for RA treatment of human embryonic stem cells that result in efficient differentiation to a heterogeneous population of GABAergic interneurons without the appearance of GABAergic striatal projection neurons, thus providing an in vitro method for generation of GABAergic interneurons for further study. Our observation that endogenous RA is required for generation of LGE-derived GABAergic neurons in the basal ganglia establishes a key role for RA signaling in development of the forebrain.     

Cellular principles underlying normal and pathological activity in the subthalamic nucleus

The motor symptoms of Parkinson's disease are associated with abnormal, correlated, low frequency, rhythmic burst activity in the subthalamic nucleus and connected nuclei. Research into the mechanisms controlling the pattern of subthalamic activity has intensified because therapies that manipulate the pattern of subthalamic activity, such as deep brain stimulation and levodopa administration, improve motor function in Parkinson's disease. Recent findings suggest that dopamine denervation of the striatum and extrastriatal basal ganglia profoundly alters the transmission and integration of glutamatergic cortical and GABAergic pallidal inputs to subthalamic neurons, leading to pathological activity that resonates throughout the basal ganglia and wider motor system.     

Existence and Control of Go/No-Go Decision Transition Threshold in the Striatum

A typical Go/No-Go decision is suggested to be implemented in the brain via the activation of the direct or indirect pathway in the basal ganglia. Medium spiny neurons (MSNs) in the striatum, receiving input from cortex and projecting to the direct and indirect pathways express D1 and D2 type dopamine receptors, respectively. Recently, it has become clear that the two types of MSNs markedly differ in their mutual and recurrent connectivities as well as feedforward inhibition from FSIs. Therefore, to understand striatal function in action selection, it is of key importance to identify the role of the distinct connectivities within and between the two types of MSNs on the balance of their activity. Here, we used both a reduced firing rate model and numerical simulations of a spiking network model of the striatum to analyze the dynamic balance of spiking activities in D1 and D2 MSNs. We show that the asymmetric connectivity of the two types of MSNs renders the striatum into a threshold device, indicating the state of cortical input rates and correlations by the relative activity rates of D1 and D2 MSNs. Next, we describe how this striatal threshold can be effectively modulated by the activity of fast spiking interneurons, by the dopamine level, and by the activity of the GPe via pallidostriatal backprojections. We show that multiple mechanisms exist in the basal ganglia for biasing striatal output in favour of either the `Go'' or the `No-Go'' pathway. This new understanding of striatal network dynamics provides novel insights into the putative role of the striatum in various behavioral deficits in patients with Parkinson''s disease, including increased reaction times, L-Dopa-induced dyskinesia, and deep brain stimulation-induced impulsivity.     

Effects of the Activity of the Internal Globus Pallidus-Pedunculopontine Loop on the Transmission of the Subthalamic Nucleus-External Globus Pallidus-Pacemaker Oscillatory Activities to the Cortex

Resting tremor is the most specific sign for idiopathic Parkinson' disease. It has been proposed that parkinsonian tremor results from the activity of the central oscillators. One of the hypotheses, which have been proposed about the possible principles underlying such central oscillations, is the subthalamic nucleus (STN)-external globus pallidus (GPe)-pacemaker hypothesis. Activity from the central oscillator is proposed to be transmitted via trans-cortical pathways to the periphery. A computational model of the basal ganglia (BG) is proposed for simulating the effects of the internal globus pallidus (GPi)-pedunculopontine (PPN) loop activity on the transmission of the STN-GPe-pacemaker oscillatory activities to the cortex, based on known anatomy and physiology of the BG. According to the result of the simulation, the GPi-PPN loop activity can suppress the transmission of the STN-GPe-pacemaker oscillatory activities to the cortex. This suppressive effect is controlled by various factors such as the strength of the synaptic connection from the PPN to the GPi, the strength of the synaptic connection from the GPi to the PPN, the spontaneous tonic activities of the GPi and PPN, the direct excitatory projections from the STN to the PPN, the frequency of the STN oscillatory burst activity, the duration of the STN burst, and the maximum T-type calcium channel conductance in the type-I PPN neurons.     

Transitions between irregular and rhythmic firing patterns in excitatory-inhibitory neuronal networks

Changes in firing patterns are an important hallmark of the functional status of neuronal networks. We apply dynamical systems methods to understand transitions between irregular and rhythmic firing in an excitatory-inhibitory neuronal network model. Using the geometric theory of singular perturbations, we systematically reduce the full model to a simpler set of equations, one that can be studied analytically. The analytic tools are used to understand how an excitatory-inhibitory network with a fixed architecture can generate both activity patterns for possibly different values of the intrinsic and synaptic parameters. These results are applied to a recently developed model for the subthalamopallidal network of the basal ganglia. The results suggest that an increase in correlated activity, corresponding to a pathological state, may be due to an increased level of inhibition from the striatum to the inhibitory GPe cells along with an increased ability of the excitatory STN neurons to generate rebound bursts. Action Editor: Carson Chow