The role of inhibition in generating and controlling Parkinson's disease oscillations in the Basal Ganglia

Computational models advance deep brain stimulation for Parkinson's disease

Deep brain stimulation(DBS) has become an effective intervention for advanced Parkinson's disease(PD), but the exact mechanism of DBS is still unclear. In this review, we discuss the history of DBS, the anatomy and internal architecture of the basal ganglia (BG), the abnormal pathological changes of the BG in PD, and how computational models can help understand and advance DBS. We also describe two types of models: mathematical theoretical models and clinical predictive models. Mathematical theoretical models simulate neurons or neural networks of BG to shed light on the mechanistic principle underlying DBS, while clinical predictive models focus more on patients' outcomes, helping to adapt treatment plans for each patient and advance novel electrode designs. Finally, we provide insights and an outlook on future technologies.

Estimation of the transmission delays in the basal ganglia of the macaque monkey and subsequent predictions about oscillatory activity under dopamine depletion

The timescales of the dynamics of a system depend on the combination of the timescales of its components and of its transmission delays between components. Here, we combine experimental stimulation data from 10 studies in macaque monkeys that reveal the timing of excitatory and inhibitory events in the basal ganglia circuit, to estimate its set of transmission delays. In doing so, we reveal possible inconsistencies in the existing data, calling for replications, and we propose two possible sets of transmission delays. We then integrate these delays in a model of the primate basal ganglia that does not rely on direct and indirect pathways' segregation and show that extrastriatal dopaminergic depletion in the external part of the globus pallidus and in the subthalamic nucleus is sufficient to generate β-band oscillations (in the high part, 20-35 Hz, of the band). More specifically, we show that D2 and D5 dopamine receptors in these nuclei play opposing roles in the emergence of these oscillations, thereby explaining how completely deactivating D5 receptors in the subthalamic nucleus can, paradoxically, cancel oscillations.

Structural constraints on the emergence of oscillations in multi-population neural networks

Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world networks (in particular in biological networks) it is usually not possible to know the exact connection weights. Therefore, it is important to determine the structural properties of a network necessary to generate oscillations. Here, we provide a proof that uses dynamical system theory to prove that an odd number of inhibitory nodes and strong enough connections are necessary to generate oscillations in a single cycle threshold-linear network. We illustrate these analytical results in a biologically plausible network with either firing-rate based or spiking neurons. Our work provides structural properties necessary to generate oscillations in a network. We use this knowledge to reconcile recent experimental findings about oscillations in basal ganglia with classical findings.

Transient oscillations as computations for cognition: Analysis, modeling and function

Our view of neural oscillations is currently changing. The dominant picture of sustained oscillations is now often replaced by transient oscillations occurring in bursts. This phenomenon seems to be quite comprehensive, as it has been reported for different oscillation frequencies, including the theta, beta, and gamma bands, as well as cortical and subcortical regions in a variety of cognitive tasks and species. Here we review recent developments in their analysis, computational modeling, and functional roles. For the analysis of transient oscillations methods using lagged coherence and Hidden Markov Models have been developed and applied in recent studies to ascertain their transient nature and study their contribution to cognitive functions. Furthermore, computational models have been developed that account for their stochastic nature, which poses interesting functional constraints. Finally, as transient oscillations have been observed across many species, they are likely of functional significance and we consider challenges in characterizing their function.

Corticostriatal beta oscillation changes associated with cognitive function in Parkinson's disease

Cognitive impairment is the most frequent non-motor symptom in Parkinson's disease and is associated with deficits in a number of cognitive functions including working memory. However, the pathophysiology of Parkinson's disease cognitive impairment is poorly understood. Beta oscillations have previously been shown to play an important role in cognitive functions including working memory encoding. Decreased dopamine in motor cortico-striato-thalamo-cortical (CSTC) circuits increases the spectral power of beta oscillations and results in Parkinson's disease motor symptoms. Analogous changes in parallel cognitive CSTC circuits involving the caudate and dorsolateral prefrontal cortex (DLPFC) may contribute to Parkinson's disease cognitive impairment. The objective of our study is to evaluate whether changes in beta oscillations in the caudate and DLPFC contribute to cognitive impairment in Parkinson's disease patients. To investigate this, we used local field potential recordings during deep brain stimulation surgery in 15 patients with Parkinson's disease. Local field potentials were recorded from DLPFC and caudate at rest and during a working memory task. We examined changes in beta oscillatory power during the working memory task as well as the relationship of beta oscillatory activity to preoperative cognitive status, as determined from neuropsychological testing results. We additionally conducted exploratory analyses on the relationship between cognitive impairment and task-based changes in spectral power in additional frequency bands. Spectral power of beta oscillations decreased in both DLPFC and caudate during working memory encoding and increased in these structures during feedback. Subjects with cognitive impairment had smaller decreases in caudate and DLPFC beta oscillatory power during encoding. In our exploratory analysis, we found that similar differences occurred in alpha frequencies in caudate and theta and alpha in DLPFC. Our findings suggest that oscillatory power changes in cognitive CSTC circuits may contribute to cognitive symptoms in patients with Parkinson's disease. These findings may inform the future development of novel neuromodulatory treatments for cognitive impairment in Parkinson's disease.

Cortex-wide topography of 1/f-exponent in Parkinson's disease

Parkinson's disease (PD) is a progressive and debilitating brain disorder. Besides the characteristic movement-related symptoms, the disease also causes decline in sensory and cognitive processing. The extent of symptoms and brain-wide projections of neuromodulators such as dopamine suggest that many brain regions are simultaneously affected in PD. To characterise brain-wide disease-related changes in neuronal function, we analysed resting state magnetoencephalogram (MEG) from two groups: PD patients and healthy controls. Besides standard spectral analysis, we quantified the aperiodic components (κ, λ) of the neural activity by fitting a power law κ/f^λ - f is the frequency, κ and λ are the fitting parameters-to the MEG power spectrum and studied its relationship with age and Unified Parkinson's Disease Rating Scale (UPDRS). Consistent with previous results, the most significant spectral changes were observed in the high theta/low-alpha band (7-10 Hz) in all brain regions. Furthermore, analysis of the aperiodic part of the spectrum showed that in all but frontal regions λ was significantly larger in PD patients than in control subjects. Our results indicate that PD is associated with significant changes in aperiodic activity across the whole neocortex. Surprisingly, even early sensory areas showed a significantly larger λ in patients than in healthy controls. Moreover, λ was not affected by the Levodopa medication. Finally, λ was positively correlated with patient age but not with UPDRS-III. Because λ is closely associated with excitation-inhibition balance, our results propose new hypotheses about neural correlates of PD in cortical networks.

A model description of beta oscillations in the external globus pallidus

The external globus pallidus (GPe), a subcortical nucleus located in the indirect pathway of the basal ganglia, is widely considered to have tight associations with abnormal beta oscillations (13-30 Hz) observed in Parkinson's disease (PD). Despite that many mechanisms have been put forward to explain the emergence of these beta oscillations, however, it is still unclear the functional contributions of the GPe, especially, whether the GPe itself can generate beta oscillations. To investigate the role played by the GPe in producing beta oscillations, we employ a well described firing rate model of the GPe neural population. Through extensive simulations, we find that the transmission delay within the GPe-GPe pathway contributes significantly to inducing beta oscillations, and the impacts of the time constant and connection strength of the GPe-GPe pathway on generating beta oscillations are non-negligible. Moreover, the GPe firing patterns can be significantly modulated by the time constant and connection strength of the GPe-GPe pathway, as well as the transmission delay within the GPe-GPe pathway. Interestingly, both increasing and decreasing the transmission delay can push the GPe firing pattern from beta oscillations to other firing patterns, including oscillation and non-oscillation firing patterns. These findings suggest that if the transmission delays within the GPe are at least 9.8 ms, beta oscillations can be produced originally in the GPe neural population, which also may be the origin of PD-related beta oscillations and should be regarded as a promising target for treatments for PD.

Neuroprosthetics: from sensorimotor to cognitive disorders

Neuroprosthetics is a multidisciplinary field at the interface between neurosciences and biomedical engineering, which aims at replacing or modulating parts of the nervous system that get disrupted in neurological disorders or after injury. Although neuroprostheses have steadily evolved over the past 60 years in the field of sensory and motor disorders, their application to higher-order cognitive functions is still at a relatively preliminary stage. Nevertheless, a recent series of proof-of-concept studies suggest that electrical neuromodulation strategies might also be useful in alleviating some cognitive and memory deficits, in particular in the context of dementia. Here, we review the evolution of neuroprosthetics from sensorimotor to cognitive disorders, highlighting important common principles such as the need for neuroprosthetic systems that enable multisite bidirectional interactions with the nervous system.

Identifying control ensembles for information processing within the cortico-basal ganglia-thalamic circuit

In situations featuring uncertainty about action-reward contingencies, mammals can flexibly adopt strategies for decision-making that are tuned in response to environmental changes. Although the cortico-basal ganglia thalamic (CBGT) network has been identified as contributing to the decision-making process, it features a complex synaptic architecture, comprised of multiple feed-forward, reciprocal, and feedback pathways, that complicate efforts to elucidate the roles of specific CBGT populations in the process by which evidence is accumulated and influences behavior. In this paper we apply a strategic sampling approach, based on Latin hypercube sampling, to explore how variations in CBGT network properties, including subpopulation firing rates and synaptic weights, map to variability of parameters in a normative drift diffusion model (DDM), representing algorithmic aspects of information processing during decision-making. Through the application of canonical correlation analysis, we find that this relationship can be characterized in terms of three low-dimensional control ensembles within the CBGT network that impact specific qualities of the emergent decision policy: responsiveness (a measure of how quickly evidence evaluation gets underway, associated with overall activity in corticothalamic and direct pathways), pliancy (a measure of the standard of evidence needed to commit to a decision, associated largely with overall activity in components of the indirect pathway of the basal ganglia), and choice (a measure of commitment toward one available option, associated with differences in direct and indirect pathways across action channels). These analyses provide mechanistic predictions about the roles of specific CBGT network elements in tuning the way that information is accumulated and translated into decision-related behavior.

Excitatory deep brain stimulation quenches beta oscillations arising in a computational model of the subthalamo-pallidal loop

Parkinson’s disease (PD) is associated with abnormal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β band oscillations (13–30 Hz) in the cortico-basal ganglia circuits. Abnormally increased striato-pallidal inhibition and strengthening the synaptic coupling between subthalamic nucleus (STN) and globus pallidus externa (GPe), due to the loss of dopamine, are considered as the potential sources of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β oscillations in the basal ganglia. Deep brain stimulation (DBS) of the basal ganglia subregions is known as a way to reduce the pathological \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β oscillations and motor deficits related to PD. Despite the success of the DBS, its underlying mechanism is poorly understood and, there is controversy about the inhibitory or excitatory role of the DBS in the literature. Here, we utilized a computational network model of basal ganglia which consists of STN, GPe, globus pallidus interna, and thalamic neuronal population. This model can reproduce healthy and pathological \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β oscillations similar to what has been observed in experimental studies. Using this model, we investigated the effect of DBS to understand whether its effect is excitatory or inhibitory. Our results show that the excitatory DBS is able to quench the pathological synchrony and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β oscillations, while, applying inhibitory DBS failed to quench the PD signs. In light of simulation results, we conclude that the effect of the DBS on its target is excitatory.

Transient Response of Basal Ganglia Network in Healthy and Low-Dopamine State

The basal ganglia (BG) are crucial for a variety of motor and cognitive functions. Changes induced by persistent low-dopamine (e.g., in Parkinson’s disease; PD) result in aberrant changes in steady-state population activity (β band oscillations) and the transient response of the BG. Typically, a brief cortical stimulation results in a triphasic response in the substantia nigra pars reticulata (SNr; an output of the BG). The properties of the triphasic responses are shaped by dopamine levels. While mechanisms underlying aberrant steady state activity are well studied, it is still unclear which BG interactions are crucial for the aberrant transient responses in the BG. Moreover, it is also unclear whether mechanisms underlying the aberrant changes in steady-state activity and transient response are the same. Here, we used numerical simulations of a network model of BG to identify the key factors that determine the shape of the transient responses. We show that an aberrant transient response of the SNr in the low-dopamine state involves changes in the direct pathway and the recurrent interactions within the globus pallidus externa (GPe) and between GPe and subthalamic nucleus (STN). However, the connections from D2-type spiny projection neurons (D2-SPN) to GPe are most crucial in shaping the transient response and by restoring them to their healthy level, we could restore the shape of transient response even in low-dopamine state. Finally, we show that the changes in BG that result in aberrant transient response are also sufficient to generate pathologic oscillatory activity in the steady state.

Deep brain stimulation for parkinson's disease induces spontaneous cortical hypersynchrony in extended motor and cognitive networks

The mechanism of action of deep brain stimulation (DBS) to the basal ganglia for Parkinson's disease remains unclear. Studies have shown that DBS decreases pathological beta hypersynchrony between the basal ganglia and motor cortex. However, little is known about DBS's effects on long range corticocortical synchronization. Here, we use machine learning combined with graph theory to compare resting-state cortical connectivity between the off and on-stimulation states and to healthy controls. We found that turning DBS on increased high beta and gamma band synchrony (26 to 50 Hz) in a cortical circuit spanning the motor, occipitoparietal, middle temporal, and prefrontal cortices. The synchrony in this network was greater in DBS on relative to both DBS off and controls, with no significant difference between DBS off and controls. Turning DBS on also increased network efficiency and strength and subnetwork modularity relative to both DBS off and controls in the beta and gamma band. Thus, unlike DBS's subcortical normalization of pathological basal ganglia activity, it introduces greater synchrony relative to healthy controls in cortical circuitry that includes both motor and non-motor systems. This increased high beta/gamma synchronization may reflect compensatory mechanisms related to DBS's clinical benefits, as well as undesirable non-motor side effects.

A bidirectional Hopf bifurcation analysis of Parkinson's oscillation in a simplified basal ganglia model

In this paper, we study the parkinson oscillation mechanism in a computational model by bifurcation analysis and numerical simulation. Oscillatory activities can be induced by abnormal coupling weights and delays. The bidirectional Hopf bifurcation phenomena are found in simulations, which can uniformly explain the oscillation mechanism in this model. The Hopf1 represents the transition between the low firing rate stable state (SS) and oscillation state (OS), the Hopf2 represents the transition between the high firing rate stable state (HSS) and the OS, the mechanisms of them are different. The Hopf1 and Hopf2 bifurcations both show that when the state transfers from the stable region to the oscillation region, oscillatory activities always originate from the beta frequency band, and then gradually evolve into the alpha frequency band, the theta frequency band and delta frequency band in this model. We find that the changing trends of the DF and oscillation amplitude (OSAM) are contrary, oscillation activities in lower frequency band are more stable than that in higher frequency band. The effect of the delay in inhibitory pathways is greater than that of in excitatory pathways, and appropriate delays improve the discharge activation level (DAL) of the system. In all, we infer that oscillations can be induced by the follow factors: 1. Improvement of the DAL of the globus pallidus externa (GPe); 2. Reduce the DAL of the GPe from the HSS or the discharge saturation state; 3. The GPe can also resonate with the subthalamic nucleus (STN).

Basal ganglia and cortical control of thalamic rebound spikes

Movement-related decreases in firing rate have been observed in basal ganglia output neurons. They may transmit motor signals to the thalamus, but the effect of these firing rate decreases on downstream neurons in the motor thalamus is not known. One possibility is that they lead to thalamic post-inhibitory rebound spikes. However, it has also been argued that the physiological conditions permitting rebound spiking are pathological, and primarily present in Parkinson's disease. As in Parkinson's disease neural activity becomes pathologically correlated, we investigated the impact of correlations in basal ganglia output on the transmission of motor signals using a Hodgkin-Huxley model of thalamocortical neurons. We found that such correlations disrupt the transmission of motor signals via rebound spikes by decreasing the signal-to-noise ratio and increasing the trial-to-trial variability. We further examined the role of sensory responses in basal ganglia output neurons and the effect of cortical excitation of motor thalamus in modulating rebound spiking. Interestingly, both could either promote or suppress the generation of rebound spikes depending on their timing relative to the motor signal. Finally, we determined parameter regimes, such as levels of excitation, under which rebound spiking is feasible in the model, and confirmed that the conditions for rebound spiking are primarily given in pathological regimes. However, we also identified specific conditions in the model that would allow rebound spiking to occur in healthy animals in a small subset of thalamic neurons. Overall, our model provides novel insights into differences between normal and pathological transmission of motor signals.

Interaction of Indirect and Hyperdirect Pathways on Synchrony and Tremor-Related Oscillation in the Basal Ganglia

Low-frequency oscillatory activity (3-9 Hz) and increased synchrony in the basal ganglia (BG) are recognized to be crucial for Parkinsonian tremor. However, the dynamical mechanism underlying the tremor-related oscillations still remains unknown. In this paper, the roles of the indirect and hyperdirect pathways on synchronization and tremor-related oscillations are considered based on a modified Hodgkin-Huxley model. Firstly, the effects of indirect and hyperdirect pathways are analysed individually, which show that increased striatal activity to the globus pallidus external (GPe) or strong cortical gamma input to the subthalamic nucleus (STN) is sufficient to promote synchrony and tremor-related oscillations in the BG network. Then, the mutual effects of both pathways are analysed by adjusting the related currents simultaneously. Our results suggest that synchrony and tremor-related oscillations would be strengthened if the current of these two paths are in relative imbalance. And the network tends to be less synchronized and less tremulous when the frequency of cortical input is in the theta band. These findings may provide novel treatments in the cortex and striatum to alleviate symptoms of tremor in Parkinson's disease.

Connectivity and Functionality of the Globus Pallidus Externa Under Normal Conditions and Parkinson's Disease

The globus pallidus externa (GPe) functions as a central hub in the basal ganglia for processing motor and non-motor information through the creation of complex connections with the other basal ganglia nuclei and brain regions. Recently, with the adoption of sophisticated genetic tools, substantial advances have been made in understanding the distinct molecular, anatomical, electrophysiological, and functional properties of GPe neurons and non-neuronal cells. Impairments in dopamine transmission in the basal ganglia contribute to Parkinson's disease (PD), the most common movement disorder that severely affects the patients' life quality. Altered GPe neuron activity and synaptic connections have also been found in both PD patients and pre-clinical models. In this review, we will summarize the main findings on the composition, connectivity and functionality of different GPe cell populations and the potential GPe-related mechanisms of PD symptoms to better understand the cell type and circuit-specific roles of GPe in both normal and PD conditions.

The theoretical mechanism of Parkinson's oscillation frequency bands: a computational model study

Excessive synchronous oscillation activities appear in the brain is a key pathological feature of Parkinson's disease, the mechanism of which is still unclear. Although some previous studies indicated that β oscillation (13-30 Hz) may directly originate in the network composed of the subthalamic nucleus (STN) and external globus pallidus (GPe) neurons, specific onset mechanisms of which are unclear, especially theoretical evidences in numerical simulation are still little. In this paper, we employ a STN-GPe mean-field model to explore the onset mechanism of Parkinson's oscillation. In addition to β oscillation, we find that some other common oscillation frequency bands can appear in this network, such as the α oscillation band (8-12 Hz), the θ oscillation band (4-7 Hz) and δ oscillation band (1-3 Hz). In addition to the coupling weight between the STN and GPe, the delay is also a critical factor to affect oscillatory activities, which can not be neglected compared to other parameters. Through simulation and analysis, we propose two possible theories may induce the system to transfer from the stable state to the oscillatory state in this model: (1). The oscillation activity can be induced when the firing activation level of the population increases to large enough; (2). In some special cases, the population may stay in the high firing rate stable state and the mean discharge rate of which is too large to induce oscillations, then oscillation activities may be induced as the MD decreases to moderate value. In most situations, the change trends of the MD and oscillation dominant frequency are contrary, which may be an important physiological phenomenon shown in this model. The delays and firing rates were obtained by simulating, which may be verified in the experiment in the future.

FPGA-Based Real-Time Simulation Platform for Large-Scale STN-GPe Network

The real-time simulation of large-scale subthalamic nucleus (STN)-external globus pallidus (GPe) network model is of great significance for the mechanism analysis and performance improvement of deep brain stimulation (DBS) for Parkinson's states. This paper implements the real-time simulation of a large-scale STN-GPe network containing 512 single-compartment Hodgkin-Huxley type neurons on the Altera Stratix IV field programmable gate array (FPGA) hardware platform. At the single neuron level, some resource optimization schemes such as multiplier substitution, fixed-point operation, nonlinear function approximation and function recombination are adopted, which consists the foundation of the large-scale network realization. At the network level, the simulation scale of network is expanded using module reuse method at the cost of simulation time. The correlation coefficient between the neuron firing waveform of the FPGA platform and the MATLAB software simulation waveform is 0.9756. Under the same physiological time, the simulation speed of FPGA platform is 75 times faster than the Intel Core i7-8700K 3.70 GHz CPU 32GB RAM computer simulation speed. In addition, the established platform is used to analyze the effects of temporal pattern DBS on network firing activities. The proposed large-scale STN-GPe network meets the need of real time simulation, which would be rather helpful in designing closed-loop DBS improvement strategies.

Functional segregation and integration within the human subthalamic nucleus from a micro- and meso-level perspective

The subthalamic nucleus (STN) is a core basal ganglia structure involved in the control of motor, cognitive, motivational and affective functions. The (challenged) tripartite subdivision hypothesis places these functions into distinct sensorimotor, cognitive/associative, and limbic subregions based on the topography of cortical projections. To a large extent, this hypothesis is used to motivate the choice of target coordinates for implantation of deep brain stimulation electrodes for treatment of neurological and psychiatric disorders. Yet, the parallel organization of basal ganglia circuits has been known to allow considerable cross-talk, which might contribute to the occurrence of neuropsychiatric side effects when stimulating the dorsolateral, putative sensorimotor, part of the STN for treatment of Parkinson's disease. Any functional segregation within the STN is expected to be reflected both at micro-level microscopy and meso-level neural population activity. As such, we review the current empirical evidence from anterograde tracing and immunocytochemistry studies and from local field potential recordings for delineating the STN into distinct subregions. The spatial distribution of immunoreactivity presents as a combination of gradients, and although neural activity in distinct frequency bands appears spatially clustered, there is substantial overlap in peak locations. We argue that regional specialization without sharply defined borders is likely most representative of the STN's functional organization.

Uncoupling the roles of firing rates and spike bursts in shaping the STN-GPe beta band oscillations

The excess of 15-30 Hz (β-band) oscillations in the basal ganglia is one of the key signatures of Parkinson's disease (PD). The STN-GPe network is integral to generation and modulation of β band oscillations in basal ganglia. However, the role of changes in the firing rates and spike bursting of STN and GPe neurons in shaping these oscillations has remained unclear. In order to uncouple their effects, we studied the dynamics of STN-GPe network using numerical simulations. In particular, we used a neuron model, in which firing rates and spike bursting can be independently controlled. Using this model, we found that while STN firing rate is predictive of oscillations, GPe firing rate is not. The effect of spike bursting in STN and GPe neurons was state-dependent. That is, only when the network was operating in a state close to the border of oscillatory and non-oscillatory regimes, spike bursting had a qualitative effect on the β band oscillations. In these network states, an increase in GPe bursting enhanced the oscillations whereas an equivalent proportion of spike bursting in STN suppressed the oscillations. These results provide new insights into the mechanisms underlying the transient β bursts and how duration and power of β band oscillations may be controlled by an interplay of GPe and STN firing rates and spike bursts.

The globus pallidus orchestrates abnormal network dynamics in a model of Parkinsonism

The dynamical properties of cortico-basal ganglia (CBG) circuits are dramatically altered following the loss of dopamine in Parkinson’s disease (PD). The neural circuit dysfunctions associated with PD include spike-rate alteration concomitant with excessive oscillatory spike-synchronization in the beta frequency range (12–30 Hz). Which neuronal circuits orchestrate and propagate these abnormal neural dynamics in CBG remains unknown. In this work, we combine in vivo electrophysiological recordings with advanced optogenetic manipulations in normal and 6-OHDA rats to shed light on the mechanistic principle underlying circuit dysfunction in PD. Our results show that abnormal neural dynamics present in a rat model of PD do not rely on cortical or subthalamic nucleus activity but critically dependent on globus pallidus (GP) integrity. Our findings highlight the pivotal role played by the GP which operates as a hub nucleus capable of orchestrating firing rate and synchronization changes across CBG circuits both in normal and pathological conditions.

Oscillatory changes between basal ganglia nuclei occur in Parkinson’s disease. Here the authors determine that the globus pallidus is the source of beta oscillation generation in a rodent model of the disease.

Beta-Band Resonance and Intrinsic Oscillations in a Biophysically Detailed Model of the Subthalamic Nucleus-Globus Pallidus Network

Increased beta-band oscillatory activity in the basal ganglia network is associated with Parkinsonian motor symptoms and is suppressed with medication and deep brain stimulation (DBS). The origins of the beta-band oscillations, however, remains unclear with both intrinsic oscillations arising within the subthalamic nucleus (STN)-external globus pallidus (GPe) network and exogenous beta-activity, originating outside the network, proposed as potential sources of the pathological activity. The aim of this study was to explore the relative contribution of autonomous oscillations and exogenous oscillatory inputs in the generation of pathological oscillatory activity in a biophysically detailed model of the parkinsonian STN-GPe network. The network model accounts for the integration of synaptic currents and their interaction with intrinsic membrane currents in dendritic structures within the STN and GPe. The model was used to investigate the development of beta-band synchrony and bursting within the STN-GPe network by changing the balance of excitation and inhibition in both nuclei, and by adding exogenous oscillatory inputs with varying phase relationships through the hyperdirect cortico-subthalamic and indirect striato-pallidal pathways. The model showed an intrinsic susceptibility to beta-band oscillations that was manifest in weak autonomously generated oscillations within the STN-GPe network and in selective amplification of exogenous beta-band synaptic inputs near the network's endogenous oscillation frequency. The frequency at which this resonance peak occurred was determined by the net level of excitatory drive to the network. Intrinsic or endogenously generated oscillations were too weak to support a pacemaker role for the STN-GPe network, however, they were considerably amplified by sparse cortical beta inputs and were further amplified by striatal beta inputs that promoted anti-phase firing of the cortex and GPe, resulting in maximum transient inhibition of STN neurons. The model elucidates a mechanism of cortical patterning of the STN-GPe network through feedback inhibition whereby intrinsic susceptibility to beta-band oscillations can lead to phase locked spiking under parkinsonian conditions. These results point to resonance of endogenous oscillations with exogenous patterning of the STN-GPe network as a mechanism of pathological synchronization, and a role for the pallido-striatal feedback loop in amplifying beta oscillations.

Beta Oscillations in Working Memory, Executive Control of Movement and Thought, and Sensorimotor Function

Beta oscillations (∼13 to 30 Hz) have been observed during many perceptual, cognitive, and motor processes in a plethora of brain recording studies. Although the function of beta oscillations (hereafter "beta" for short) is unlikely to be explained by any single monolithic description, we here discuss several convergent findings. In prefrontal cortex (PFC), increased beta appears at the end of a trial when working memory information needs to be erased. A similar "clear-out" function might apply during the stopping of action and the stopping of long-term memory retrieval (stopping thoughts), where increased prefrontal beta is also observed. A different apparent role for beta in PFC occurs during the delay period of working memory tasks: it might serve to maintain the current contents and/or to prevent interference from distraction. We confront the challenge of relating these observations to the large literature on beta recorded from sensorimotor cortex. Potentially, the clear-out of working memory in PFC has its counterpart in the postmovement clear-out of the motor plan in sensorimotor cortex. However, recent studies support alternative interpretations. In addition, we flag emerging research on different frequencies of beta and the relationship between beta and single-neuron spiking. We also discuss where beta might be generated: basal ganglia, cortex, or both. We end by considering the clinical implications for adaptive deep-brain stimulation.

Bifurcation analysis of the dynamics of interacting subnetworks of a spiking network

We analyze the collective dynamics of hierarchically structured networks of densely connected spiking neurons. These networks of sub-networks may represent interactions between cell assemblies or different nuclei in the brain. The dynamical activity pattern that results from these interactions depends on the strength of synaptic coupling between them. Importantly, the overall dynamics of a brain region in the absence of external input, so called ongoing brain activity, has been attributed to the dynamics of such interactions. In our study, two different network scenarios are considered: a system with one inhibitory and two excitatory subnetworks, and a network representation with three inhibitory subnetworks. To study the effect of synaptic strength on the global dynamics of the network, two parameters for relative couplings between these subnetworks are considered. For each case, a bifurcation analysis is performed and the results have been compared to large-scale network simulations. Our analysis shows that Generalized Lotka-Volterra (GLV) equations, well-known in predator-prey studies, yield a meaningful population-level description for the collective behavior of spiking neuronal interaction, which have a hierarchical structure. In particular, we observed a striking equivalence between the bifurcation diagrams of spiking neuronal networks and their corresponding GLV equations. This study gives new insight on the behavior of neuronal assemblies, and can potentially suggest new mechanisms for altering the dynamical patterns of spiking networks based on changing the synaptic strength between some groups of neurons.

Different Dopaminergic Dysfunctions Underlying Parkinsonian Akinesia and Tremor

Although the occurrence of Parkinsonian akinesia and tremor is traditionally associated to dopaminergic degeneration, the multifaceted neural processes that cause these impairments are not fully understood. As a consequence, current dopamine medications cannot be tailored to the specific dysfunctions of patients with the result that generic drug therapies produce different effects on akinesia and tremor. This article proposes a computational model focusing on the role of dopamine impairments in the occurrence of akinesia and resting tremor. The model has three key features, to date never integrated in a single computational system: (a) an architecture constrained on the basis of the relevant known system-level anatomy of the basal ganglia-thalamo-cortical loops; (b) spiking neurons with physiologically-constrained parameters; (c) a detailed simulation of the effects of both phasic and tonic dopamine release. The model exhibits a neural dynamics compatible with that recorded in the brain of primates and humans. Moreover, it suggests that akinesia might involve both tonic and phasic dopamine dysregulations whereas resting tremor might be primarily caused by impairments involving tonic dopamine release and the responsiveness of dopamine receptors. These results could lead to develop new therapies based on a system-level view of the Parkinson's disease and targeting phasic and tonic dopamine in differential ways.

The beta oscillation conditions in a simplified basal ganglia network

Parkinson's disease is a type of motor dysfunction disease that is induced mainly by abnormal interactions between the subthalamic nucleus (STN) and globus pallidus (GP) neurons. Periodic oscillatory activities with frequencies of 13-30 Hz are the main physiological characteristics of Parkinson's disease. In this paper, we built a class of STN-GP networks to explore beta oscillation conditions. A theoretical formula was obtained for generating oscillations without internal GP connections. Based on this formula, we studied the effects of cortex inputs, striatum inputs, coupling weights and delays on oscillation conditions, and the theoretical results are in good agreement with the numerical results. The onset mechanism can be explained by the model, and the internal GP connection has little effect on oscillations. Finally, we compared oscillation conditions with those in previous studies and found that the delays and coupling weights required for generating oscillations may decrease as the number of nuclei increases. We hope that the results obtained will inspire future theoretical and experimental studies.

Generic dynamic causal modelling: An illustrative application to Parkinson's disease

We present a technical development in the dynamic causal modelling of electrophysiological responses that combines qualitatively different neural mass models within a single network. This affords the option to couple various cortical and subcortical nodes that differ in their form and dynamics. Moreover, it enables users to implement new neural mass models in a straightforward and standardized way. This generic framework hence supports flexibility and facilitates the exploration of increasingly plausible models. We illustrate this by coupling a basal ganglia-thalamus model to a (previously validated) cortical model developed specifically for motor cortex. The ensuing DCM is used to infer pathways that contribute to the suppression of beta oscillations induced by dopaminergic medication in patients with Parkinson's disease. Experimental recordings were obtained from deep brain stimulation electrodes (implanted in the subthalamic nucleus) and simultaneous magnetoencephalography. In line with previous studies, our results indicate a reduction of synaptic efficacy within the circuit between the subthalamic nucleus and external pallidum, as well as reduced efficacy in connections of the hyperdirect and indirect pathway leading to this circuit. This work forms the foundation for a range of modelling studies of the synaptic mechanisms (and pathophysiology) underlying event-related potentials and cross-spectral densities.

Model and Analysis for the Onset of Parkinsonian Firing Patterns in a Simplified Basal Ganglia

Parkinson's disease (PD) is a degenerative neurological disease that disrupts the movement cycle in the basal ganglia. As the disease progresses, dopamine depletion leads to changes to how the basal ganglia functions as well as the appearance of abnormal beta oscillations. There is much debate on just exactly how these connection strengths change and just how the oscillations emerge. One leading hypothesis claims that the oscillations develop in the globus pallidus external, subthalamic nucleus, and globus pallidus internal loop. We introduce a mathematical model that calculates the average firing rates of this loop while still accounting for the larger closed loop of the entire basal ganglia system. This model is constructed such that physiologically realistic results can be obtained while not sacrificing the use of analytic methods. Because of this, it is possible to determine how the change in the connection strengths can drive the necessary changes in firing rates seen in recordings and account for the generation of trademark beta oscillations of PD without relying on highly specific time delays, stochastic approaches, or numerical approximations. Additionally, we find that the entire cortico-basal ganglia-thalamo-cortical loop is essential for abnormal oscillations to originate.

The oscillatory boundary conditions of different frequency bands in Parkinson's disease

Parkinson's disease (PD) is a neurodegenerative disease that is common in the elderly population. The most important pathological change in PD is the degeneration and death of dopaminergic neurons in the substantia nigra of the midbrain, which results in a decrease in the dopamine (DA) content of the striatum. The exact cause of this pathological change is still unknown. Numerous studies have shown that the evolution of PD is associated with abnormal oscillatory activities in the basal ganglia, with different oscillation frequency ranges, such as the typical beta band (13-30 Hz), the alpha band (8-12 Hz), the theta band (4-7 Hz) and the delta band (1-3 Hz). Although some studies have implied that abnormal interactions between the subthalamic nucleus (STN) and globus pallidus (GP) neurons may be a key factor required to induce these oscillations, the relative mechanism is still unclear. The effects of other nerve nuclei in the basal ganglia, such as the striatum, on these oscillations are still unknown. The thalamus and cortex both have close input and output relationships with the basal ganglia, and many previous studies have indicated that they may also exert effects on Parkinson's disease oscillation, but the mechanisms involved are unclear. In this paper, we built a corticothalamic-basal ganglia (CTBG) mean firing-rate model to explore the onset mechanisms of these different oscillation phenomena. We found that, in addition to the STN-GP network, Parkinson's disease oscillations may also be induced by changing the coupling strength and delays in other pathways. Different frequency bands appear in the oscillating region, and various boundary conditions are depicted in parameter diagrams. The onset mechanism is well explained both by the model and by the numerical simulation results. Therefore, this model provides a unifying framework for studying the mechanism of Parkinson's disease oscillations, and we hope that the results obtained in this work can inspire future experimental studies.

Striatal cholinergic receptor activation causes a rapid, selective and state-dependent rise in cortico-striatal β activity

Cortico-basal ganglia-thalamic (CBT) β oscillations (15-30 Hz) are elevated in Parkinson's disease and correlated with movement disability. To date, no experimental paradigm outside of loss of dopamine has been able to specifically elevate β oscillations in the CBT loop. Here, we show that activation of striatal cholinergic receptors selectively increased β oscillations in mouse striatum and motor cortex. In individuals showing simultaneous β increases in both striatum and M1, β partial directed coherence (PDC) increased from striatum to M1 (but not in the reverse direction). In individuals that did not show simultaneous β increases, β PDC increased from M1 to striatum (but not in the reverse direction), and M1 was characterized by persistent β-high frequency oscillation phase-amplitude coupling. Finally, the direction of β PDC distinguished between β sub-bands. This suggests that (1) striatal cholinergic tone exerts state-dependent and frequency-selective control over CBT β power and coordination; (2) ongoing rhythmic dynamics can determine whether elevated β oscillations are expressed in striatum and M1; and (3) altered striatal cholinergic tone differentially modulates distinct β sub-bands.

Basal Ganglia Neuromodulation Over Multiple Temporal and Structural Scales-Simulations of Direct Pathway MSNs Investigate the Fast Onset of Dopaminergic Effects and Predict the Role of Kv4.2

The basal ganglia are involved in the motivational and habitual control of motor and cognitive behaviors. Striatum, the largest basal ganglia input stage, integrates cortical and thalamic inputs in functionally segregated cortico-basal ganglia-thalamic loops, and in addition the basal ganglia output nuclei control targets in the brainstem. Striatal function depends on the balance between the direct pathway medium spiny neurons (D1-MSNs) that express D1 dopamine receptors and the indirect pathway MSNs that express D2 dopamine receptors. The striatal microstructure is also divided into striosomes and matrix compartments, based on the differential expression of several proteins. Dopaminergic afferents from the midbrain and local cholinergic interneurons play crucial roles for basal ganglia function, and striatal signaling via the striosomes in turn regulates the midbrain dopaminergic system directly and via the lateral habenula. Consequently, abnormal functions of the basal ganglia neuromodulatory system underlie many neurological and psychiatric disorders. Neuromodulation acts on multiple structural levels, ranging from the subcellular level to behavior, both in health and disease. For example, neuromodulation affects membrane excitability and controls synaptic plasticity and thus learning in the basal ganglia. However, it is not clear on what time scales these different effects are implemented. Phosphorylation of ion channels and the resulting membrane effects are typically studied over minutes while it has been shown that neuromodulation can affect behavior within a few hundred milliseconds. So how do these seemingly contradictory effects fit together? Here we first briefly review neuromodulation of the basal ganglia, with a focus on dopamine. We furthermore use biophysically detailed multi-compartmental models to integrate experimental data regarding dopaminergic effects on individual membrane conductances with the aim to explain the resulting cellular level dopaminergic effects. In particular we predict dopaminergic effects on Kv4.2 in D1-MSNs. Finally, we also explore dynamical aspects of the onset of neuromodulation effects in multi-scale computational models combining biochemical signaling cascades and multi-compartmental neuron models.

Propagation of beta/gamma rhythms in the cortico-basal ganglia circuits of the parkinsonian rat

Much of the motor impairment associated with Parkinson’s disease is thought to arise from pathological activity in the networks formed by the basal ganglia (BG) and motor cortex. To evaluate several hypotheses proposed to explain the emergence of pathological oscillations in parkinsonism, we investigated changes to the directed connectivity in BG networks following dopamine depletion. We recorded local field potentials (LFPs) in the cortex and basal ganglia of rats rendered parkinsonian by injection of 6-hydroxydopamine (6-OHDA) and in dopamine-intact controls. We performed systematic analyses of the networks using a novel tool for estimation of directed interactions (nonparametric directionality, NPD). We used a “conditioned” version of the NPD analysis that reveals the dependence of the correlation between two signals on a third reference signal. We find evidence of the dopamine dependency of both low-beta (14–20 Hz) and high-beta/low-gamma (20–40 Hz) directed network interactions. Notably, 6-OHDA lesions were associated with enhancement of the cortical “hyperdirect” connection to the subthalamic nucleus (STN) and its feedback to the cortex and striatum. We find that pathological beta synchronization resulting from 6-OHDA lesioning is widely distributed across the network and cannot be located to any individual structure. Furthermore, we provide evidence that high-beta/gamma oscillations propagate through the striatum in a pathway that is independent of STN. Rhythms at high beta/gamma show susceptibility to conditioning that indicates a hierarchical organization compared with those at low beta. These results further inform our understanding of the substrates for pathological rhythms in salient brain networks in parkinsonism.

NEW & NOTEWORTHY We present a novel analysis of electrophysiological recordings in the cortico-basal ganglia network with the aim of evaluating several hypotheses concerning the origins of abnormal brain rhythms associated with Parkinson’s disease. We present evidence for changes in the directed connections within the network following chronic dopamine depletion in rodents. These findings speak to the plausibility of a “short-circuiting” of the network that gives rise to the conditions from which pathological synchronization may arise.

Evidence for a task-dependent switch in subthalamo-nigral basal ganglia signaling

Basal ganglia (BG) can either facilitate or inhibit movement through excitatory and inhibitory pathways; however whether these opposing signals are dynamically regulated during healthy behavior is not known. Here, we present compelling neurophysiological evidence from three complimentary experiments in non-human primates, indicating task-specific changes in tonic BG pathway weightings during saccade behavior with different cognitive demands. First, simultaneous local field potential recording in the subthalamic nucleus (STN; BG input) and substantia nigra pars reticulata (SNr; BG output) reveals task-dependent shifts in subthalamo-nigral signals. Second, unilateral electrical stimulation of the STN, SNr, and caudate nucleus results in strikingly different saccade directionality and latency biases across the BG. Third, a simple artificial neural network representing canonical BG signaling pathways suggests that pathway weightings can be altered by cortico-BG input activation. Overall, inhibitory pathways (striato-pallidal-subthalamo-nigral) dominate during goal-driven behavior with instructed rewards, while facilitatory pathways (striato-nigral and subthalamo-pallidal-nigral) dominate during unconstrained (free reward) conditions.

Basal ganglia can both facilitate or inhibit movement through excitatory and inhibitory pathways; however whether these opposing signals are dynamically regulated during behavior is not known. Here the authors use multinucleus LFP recordings and electrical microstimulation in monkeys performing saccade based tasks to show task specific changes in the tonic weighting of these pathways.

Sensorimotor Processing in the Basal Ganglia Leads to Transient Beta Oscillations during Behavior

Brief epochs of beta oscillations have been implicated in sensorimotor control in the basal ganglia of task-performing healthy animals. However, which neural processes underlie their generation and how they are affected by sensorimotor processing remains unclear. To determine the mechanisms underlying transient beta oscillations in the LFP, we combined computational modeling of the subthalamo-pallidal network for the generation of beta oscillations with realistic stimulation patterns derived from single-unit data recorded from different basal ganglia subregions in rats performing a cued choice task. In the recordings, we found distinct firing patterns in the striatum, globus pallidus, and subthalamic nucleus related to sensory and motor events during the behavioral task. Using these firing patterns to generate realistic inputs to our network model led to transient beta oscillations with the same time course as the rat LFP data. In addition, our model can account for further nonintuitive aspects of beta modulation, including beta phase resets after sensory cues and correlations with reaction time. Overall, our model can explain how the combination of temporally regulated sensory responses of the subthalamic nucleus, ramping activity of the subthalamic nucleus, and movement-related activity of the globus pallidus leads to transient beta oscillations during behavior.SIGNIFICANCE STATEMENT Transient beta oscillations emerge in the normal functioning cortico-basal ganglia loop during behavior. Here, we used a unique approach connecting a computational model closely with experimental data. In this way, we achieved a simulation environment for our model that mimics natural input patterns in awake, behaving animals. We demonstrate that a computational model for beta oscillations in Parkinson's disease (PD) can also account for complex patterns of transient beta oscillations in healthy animals. Therefore, we propose that transient beta oscillations in healthy animals share the same mechanism with pathological beta oscillations in PD. This important result connects functional and pathological roles of beta oscillations in the basal ganglia.

A Population of Indirect Pathway Striatal Projection Neurons Is Selectively Entrained to Parkinsonian Beta Oscillations

Classical schemes of basal ganglia organization posit that parkinsonian movement difficulties presenting after striatal dopamine depletion stem from the disproportionate firing rates of spiny projection neurons (SPNs) therein. There remains, however, a pressing need to elucidate striatal SPN firing in the context of the synchronized network oscillations that are abnormally exaggerated in cortical-basal ganglia circuits in parkinsonism. To address this, we recorded unit activities in the dorsal striatum of dopamine-intact and dopamine-depleted rats during two brain states, respectively defined by cortical slow-wave activity (SWA) and activation. Dopamine depletion escalated striatal net output but had contrasting effects on "direct pathway" SPNs (dSPNs) and "indirect pathway" SPNs (iSPNs); their firing rates became imbalanced, and they disparately engaged in network oscillations. Disturbed striatal activity dynamics relating to the slow (∼1 Hz) oscillations prevalent during SWA partly generalized to the exaggerated beta-frequency (15-30 Hz) oscillations arising during cortical activation. In both cases, SPNs exhibited higher incidences of phase-locked firing to ongoing cortical oscillations, and SPN ensembles showed higher levels of rhythmic correlated firing, after dopamine depletion. Importantly, in dopamine-depleted striatum, a widespread population of iSPNs, which often displayed excessive firing rates and aberrant phase-locked firing to cortical beta oscillations, preferentially and excessively synchronized their firing at beta frequencies. Conversely, dSPNs were neither hyperactive nor synchronized to a large extent during cortical activation. These data collectively demonstrate a cell type-selective entrainment of SPN firing to parkinsonian beta oscillations. We conclude that a population of overactive, excessively synchronized iSPNs could orchestrate these pathological rhythms in basal ganglia circuits.SIGNIFICANCE STATEMENT Chronic depletion of dopamine from the striatum, a part of the basal ganglia, causes some symptoms of Parkinson's disease. Here, we elucidate how dopamine depletion alters striatal neuron firing in vivo, with an emphasis on defining whether and how spiny projection neurons (SPNs) engage in the synchronized beta-frequency (15-30 Hz) oscillations that become pathologically exaggerated throughout basal ganglia circuits in parkinsonism. We discovered that a select population of so-called "indirect pathway" SPNs not only fire at abnormally high rates, but are also particularly prone to being recruited to exaggerated beta oscillations. Our results provide an important link between two complementary theories that explain the presentation of disease symptoms on the basis of changes in firing rate or firing synchronization/rhythmicity.

Computational models of basal ganglia dysfunction: the dynamics is in the details

The development, simulation, and analysis of mathematical models offer helpful tools for integrating experimental findings and exploring or suggesting possible explanatory mechanisms. As models relating to basal ganglia dysfunction have proliferated, however, there has not always been consistency among their findings. This work points out several ways in which biological details, relating to ionic currents and synaptic pathways, can influence the dynamics of models of the basal ganglia under parkinsonian conditions and hence may be important for inclusion in models. It also suggests some additional useful directions for future modeling studies relating to basal ganglia dysfunction.

Homologous Basal Ganglia Network Models in Physiological and Parkinsonian Conditions

The classical model of basal ganglia has been refined in recent years with discoveries of subpopulations within a nucleus and previously unknown projections. One such discovery is the presence of subpopulations of arkypallidal and prototypical neurons in external globus pallidus, which was previously considered to be a primarily homogeneous nucleus. Developing a computational model of these multiple interconnected nuclei is challenging, because the strengths of the connections are largely unknown. We therefore use a genetic algorithm to search for the unknown connectivity parameters in a firing rate model. We apply a binary cost function derived from empirical firing rate and phase relationship data for the physiological and Parkinsonian conditions. Our approach generates ensembles of over 1,000 configurations, or homologies, for each condition, with broad distributions for many of the parameter values and overlap between the two conditions. However, the resulting effective weights of connections from or to prototypical and arkypallidal neurons are consistent with the experimental data. We investigate the significance of the weight variability by manipulating the parameters individually and cumulatively, and conclude that the correlation observed between the parameters is necessary for generating the dynamics of the two conditions. We then investigate the response of the networks to a transient cortical stimulus, and demonstrate that networks classified as physiological effectively suppress activity in the internal globus pallidus, and are not susceptible to oscillations, whereas parkinsonian networks show the opposite tendency. Thus, we conclude that the rates and phase relationships observed in the globus pallidus are predictive of experimentally observed higher level dynamical features of the physiological and parkinsonian basal ganglia, and that the multiplicity of solutions generated by our method may well be indicative of a natural diversity in basal ganglia networks. We propose that our approach of generating and analyzing an ensemble of multiple solutions to an underdetermined network model provides greater confidence in its predictions than those derived from a unique solution, and that projecting such homologous networks on a lower dimensional space of sensibly chosen dynamical features gives a better chance than a purely structural analysis at understanding complex pathologies such as Parkinson's disease.

Pallidostriatal Projections Promote β Oscillations in a Dopamine-Depleted Biophysical Network Model

In the basal ganglia, focused rhythmicity is an important feature of network activity at certain stages of motor processing. In disease, however, the basal ganglia develop amplified rhythmicity. Here, we demonstrate how the cellular architecture and network dynamics of an inhibitory loop in the basal ganglia yield exaggerated synchrony and locking to β oscillations, specifically in the dopamine-depleted state. A key component of this loop is the pallidostriatal pathway, a well-characterized anatomical projection whose function has long remained obscure. We present a synaptic characterization of this pathway in mice and incorporate these data into a computational model that we use to investigate its influence over striatal activity under simulated healthy and dopamine-depleted conditions. Our model predicts that the pallidostriatal pathway influences striatal output preferentially during periods of synchronized activity within GPe. We show that, under dopamine-depleted conditions, this effect becomes a key component of a positive feedback loop between the GPe and striatum that promotes synchronization and rhythmicity. Our results generate novel predictions about the role of the pallidostriatal pathway in shaping basal ganglia activity in health and disease.

SIGNIFICANCE STATEMENT

This work demonstrates that functional connections from the globus pallidus externa (GPe) to striatum are substantially stronger onto fast-spiking interneurons (FSIs) than onto medium spiny neurons. Our circuit model suggests that when GPe spikes are synchronous, this pallidostriatal pathway causes synchronous FSI activity pauses, which allow a transient window of disinhibition for medium spiny neurons. In simulated dopamine-depletion, this GPe-FSI activity is necessary for the emergence of strong synchronization and the amplification and propagation of β oscillations, which are a hallmark of parkinsonian circuit dysfunction. These results suggest that GPe may play a central role in propagating abnormal circuit activity to striatum, which in turn projects to downstream basal ganglia structures. These findings warrant further exploration of GPe as a target for interventions for Parkinson's disease.

Interplay between periodic stimulation and GABAergic inhibition in striatal network oscillations

Network oscillations are ubiquitous across many brain regions. In the basal ganglia, oscillations are also present at many levels and a wide range of characteristic frequencies have been reported to occur during both health and disease. The striatum, the main input nucleus of the basal ganglia, receives massive glutamatergic inputs from the cortex and is highly susceptible to external oscillations. However, there is limited knowledge about the exact nature of this routing process and therefore, it is of key importance to understand how time-dependent, external stimuli propagate through the striatal circuitry. Using a network model of the striatum and corticostriatal projections, we try to elucidate the importance of specific GABAergic neurons and their interactions in shaping striatal oscillatory activity. Here, we propose that fast-spiking interneurons can perform an important role in transferring cortical oscillations to the striatum especially to those medium spiny neurons that are not directly driven by the cortical oscillations. We show how the activity levels of different populations, the strengths of different inhibitory synapses, degree of outgoing projections of striatal cells, ongoing activity and synchronicity of inputs can influence network activity. These results suggest that the propagation of oscillatory inputs into the medium spiny neuron population is most efficient, if conveyed via the fast-spiking interneurons. Therefore, pharmaceuticals that target fast-spiking interneurons may provide a novel treatment for regaining the spectral characteristics of striatal activity that correspond to the healthy state.

Quantification of motor network dynamics in Parkinson's disease by means of landscape and flux theory

The basal ganglia neural circuit plays an important role in motor control. Despite the significant efforts, the understanding of the principles and underlying mechanisms of this modulatory circuit and the emergence of abnormal synchronized oscillations in movement disorders is still challenging. Dopamine loss has been proved to be responsible for Parkinson's disease. We quantitatively described the dynamics of the basal ganglia-thalamo-cortical circuit in Parkinson's disease in terms of the emergence of both abnormal firing rates and firing patterns in the circuit. We developed a potential landscape and flux framework for exploring the modulatory circuit. The driving force of the circuit can be decomposed into a gradient of the potential, which is associated with the steady-state probability distributions, and the curl probability flux term. We uncovered the underlying potential landscape as a Mexican hat-shape closed ring valley where abnormal oscillations emerge due to dopamine depletion. We quantified the global stability of the network through the topography of the landscape in terms of the barrier height, which is defined as the potential difference between the maximum potential inside the ring and the minimum potential along the ring. Both a higher barrier and a larger flux originated from detailed balance breaking result in more stable oscillations. Meanwhile, more energy is consumed to support the increasing flux. Global sensitivity analysis on the landscape topography and flux indicates how changes in underlying neural network regulatory wirings and external inputs influence the dynamics of the system. We validated two of the main hypotheses(direct inhibition hypothesis and output activation hypothesis) on the therapeutic mechanism of deep brain stimulation (DBS). We found GPe appears to be another effective stimulated target for DBS besides GPi and STN. Our approach provides a general way to quantitatively explore neural networks and may help for uncovering more efficacious therapies for movement disorders.

Computational Model of Recurrent Subthalamo-Pallidal Circuit for Generation of Parkinsonian Oscillations

Parkinson's disease is a movement disorder caused by dopamine depletion in the basal ganglia. Abnormally synchronized neuronal oscillations between 8 and 15 Hz in the basal ganglia are implicated in motor symptoms of Parkinson's disease. However, how these abnormal oscillations are generated and maintained in the dopamine-depleted state is unknown. Based on neural recordings in a primate model of Parkinson's disease and other experimental and computational evidence, we hypothesized that the recurrent circuit between the subthalamic nucleus (STN) and the external segment of the globus pallidus (GPe) generates and maintains parkinsonian oscillations, and that the cortical excitatory input to the STN amplifies them. To investigate this hypothesis through computer simulations, we developed a spiking neuron model of the STN-GPe circuit by incorporating electrophysiological properties of neurons and synapses. A systematic parameter search by computer simulation identified regions in the space of the intrinsic excitability of GPe neurons and synaptic strength from the GPe to the STN that reproduce normal and parkinsonian states. In the parkinsonian state, reduced firing of GPe neurons and increased GPe-STN inhibition trigger burst activities of STN neurons with strong post-inhibitory rebound excitation, which is usually subject to short-term depression. STN neuronal bursts are shaped into the 8–15 Hz, synchronous oscillations via recurrent interactions of STN and GPe neurons. Furthermore, we show that cortical excitatory input to the STN can amplify or suppress pathological STN oscillations depending on their phase and strength, predicting conditions of cortical inputs to the STN for suppressing oscillations.

Analysis and application of neuronal network controllability and observability

Controllability and observability analyses are important prerequisite for designing suitable neural control strategy, which can help lower the efforts required to control and observe the system dynamics. First, 3-neuron motifs including the excitatory motif, the inhibitory motif, and the mixed motif are constructed to investigate the effects of single neuron and synaptic dynamics on network controllability (observability). Simulation results demonstrate that for networks with the same topological structure, the controllability (observability) of the node always changes if the properties of neurons and synaptic coupling strengths vary. Besides, the inhibitory networks are more controllable (observable) than the excitatory networks when the coupling strengths are the same. Then, the numerically determined controllability results of 3-neuron excitatory motifs are generalized to the desynchronization control of the modular motif network. The control energy and neuronal synchrony measure indexes are used to quantify the controllability of each node in the modular network. The best driver node obtained in this way is the same as the deduced one from motif analysis.

Neural mass models describing possible origin of the excessive beta oscillations correlated with Parkinsonian state

In Parkinson's disease, the enhanced beta rhythm is closely associated with akinesia/bradykinesia and rigidity. An increase in beta oscillations (12-35 Hz) within the basal ganglia (BG) nuclei does not proliferate throughout the cortico-basal ganglia loop in uniform fashion; rather it can be subdivided into two distinct frequency bands, i.e. the lower beta (12-20 Hz) and upper beta (21-35 Hz). A computational model of the excitatory and inhibitory neural network that focuses on the population properties is proposed to explore the mechanism underlying the pathological beta oscillations. Simulation results show several findings. The upper beta frequency in the BG originates from a high frequency cortical beta, while the emergence of exaggerated lower beta frequency in the BG depends greatly on the enhanced excitation of a reciprocal network consisting of the globus pallidus externus (GPe) and the subthalamic nucleus (STN). There is also a transition mechanism between the upper and lower beta oscillatory activities, and we explore the impact of self-inhibition within the GPe on the relationship between the upper beta and lower beta oscillations. It is shown that increased self-inhibition within the GPe contributes to increased upper beta oscillations driven by the cortical rhythm, while decrease in the self-inhibition within the GPe facilitates an enhancement of the lower beta oscillations induced by the increased excitability of the BG. This work provides an analysis for understanding the mechanism underlying pathological synchronization in neurological diseases.

Untangling Basal Ganglia Network Dynamics and Function: Role of Dopamine Depletion and Inhibition Investigated in a Spiking Network Model

The basal ganglia are a crucial brain system for behavioral selection, and their function is disturbed in Parkinson's disease (PD), where neurons exhibit inappropriate synchronization and oscillations. We present a spiking neural model of basal ganglia including plausible details on synaptic dynamics, connectivity patterns, neuron behavior, and dopamine effects. Recordings of neuronal activity in the subthalamic nucleus and Type A (TA; arkypallidal) and Type I (TI; prototypical) neurons in globus pallidus externa were used to validate the model. Simulation experiments predict that both local inhibition in striatum and the existence of an indirect pathway are important for basal ganglia to function properly over a large range of cortical drives. The dopamine depletion-induced increase of AMPA efficacy in corticostriatal synapses to medium spiny neurons (MSNs) with dopamine receptor D2 synapses (CTX-MSN D2) and the reduction of MSN lateral connectivity (MSN-MSN) were found to contribute significantly to the enhanced synchrony and oscillations seen in PD. Additionally, reversing the dopamine depletion-induced changes to CTX-MSN D1, CTX-MSN D2, TA-MSN, and MSN-MSN couplings could improve or restore basal ganglia action selection ability. In summary, we found multiple changes of parameters for synaptic efficacy and neural excitability that could improve action selection ability and at the same time reduce oscillations. Identification of such targets could potentially generate ideas for treatments of PD and increase our understanding of the relation between network dynamics and network function.

Propagation of Collective Temporal Regularity in Noisy Hierarchical Networks

Neuronal communication between different brain areas is achieved in terms of spikes. Consequently, spike-time regularity is closely related to many cognitive tasks and timing precision of neural information processing. A recent experiment on primate parietal cortex reports that spike-time regularity increases consistently from primary sensory to higher cortical regions. This observation conflicts with the influential view that spikes in the neocortex are fundamentally irregular. To uncover the underlying network mechanism, we construct a multilayered feedforward neural information transmission pathway and investigate how spike-time regularity evolves across subsequent layers. Numerical results reveal that despite the obviously irregular spiking patterns in previous several layers, neurons in downstream layers can generate rather regular spikes, which depends on the network topology. In particular, we find that collective temporal regularity in deeper layers exhibits resonance-like behavior with respect to both synaptic connection probability and synaptic weight, i.e., the optimal topology parameter maximizes the spike-timing regularity. Furthermore, it is demonstrated that synaptic properties, including inhibition, synaptic transient dynamics, and plasticity, have significant impacts on spike-timing regularity propagation. The emergence of the increasingly regular spiking (RS) patterns in higher parietal regions can, thus, be viewed as a natural consequence of spiking activity propagation between different brain areas. Finally, we validate an important function served by increased RS: promoting reliable propagation of spike-rate signals across downstream layers.

A neural mass model of basal ganglia nuclei simulates pathological beta rhythm in Parkinson's disease

An increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with movement disorder, such as Parkinson's disease. The motor cortex and an excitatory-inhibitory neuronal network composed of the subthalamic nucleus (STN) and the external globus pallidus (GPe) are thought to play an important role in the generation of these oscillations. In this paper, we propose a neuron mass model of the basal ganglia on the population level that reproduces the Parkinsonian oscillations in a reciprocal excitatory-inhibitory network. Moreover, it is shown that the generation and frequency of these pathological beta oscillations are varied by the coupling strength and the intrinsic characteristics of the basal ganglia. Simulation results reveal that increase of the coupling strength induces the generation of the beta oscillation, as well as enhances the oscillation frequency. However, for the intrinsic properties of each nucleus in the excitatory-inhibitory network, the STN primarily influences the generation of the beta oscillation while the GPe mainly determines its frequency. Interestingly, describing function analysis applied on this model theoretically explains the mechanism of pathological beta oscillations.