Encyclopedia of Computational Neuroscience

Living Edition
| Editors: Dieter Jaeger, Ranu Jung

Basal Ganglia: Globus Pallidus Cellular Models

  • Dieter JaegerEmail author
Living reference work entry

Latest version View entry history

DOI: https://doi.org/10.1007/978-1-4614-7320-6_87-2
  • 22 Downloads

Definition

The globus pallidus is a part of the basal ganglia in the vertebrate brain. Cellular models of the globus pallidus are computer representations of the specific dynamics of globus pallidus neurons.

Detailed Description

Goals of Globus Pallidus Cellular Models

Detailed cellular models of globus pallidus (GP) neurons are typically constructed to better understand how they integrate synaptic input and how their intrinsic properties contribute to the input-output function of the GP. The exploration of GP function in larger network models is typically carried out using less detailed cell models. The level of complexity and biological realism best used for a GP neuron model depends on the questions one wants to address (Herz et al. 2006) and ranges from simple integrate-and-fire models to complex full morphological reconstructions with a full complement of ion channel types found in these neurons.

Models that Capture the Detailed Dynamic Properties of Globus Pallidus Neurons

The GP is divided into an external (GPe) and internal (GPi) segment. All detailed models to date have focused on GPe properties. The GPe is primarily made of large GABAergic inhibitory projection neurons with very few interneurons. Anatomically GPe neurons can be subdivided into arkypallidal neurons projecting almost exclusively to the striatum and prototypic neurons, which project to multiple downstream targets like the GPi and STN (Mallet et al. 2012). The electrical properties of GPe neurons are overlapping (Deister et al. 2013) and can be simulated by a variable density of the different ion channel types in the membrane (Gunay et al. 2008). Biophysically detailed GPe neuron modeling has revealed a complex dependency of cellular dynamics on the interactions between multiple voltage-gated channel types. The hallmark of these neurons is a fast spontaneous regular spiking activity that depends on steady depolarization through a persistent sodium channel (Mercer et al. 2007), though arkypallidal neurons have less persistent sodium current and slower spontaneous spike rates (Abdi et al. 2015). Each spike causes a calcium inflow through voltage-gated calcium channels and subsequent activation of calcium-dependent small conductance (SK) potassium channels that results in a spike – afterhyperpolarization that regularizes spiking (Deister et al. 2009). A biophysically detailed modeling study showed that dendritic integration of synaptic input in GPe neurons may depend on dendritic fast sodium channels that can lead to synaptically evoked dendritic spike initiation (Edgerton et al. 2010). Further, the phase response curve (i.e., the spike time delay or advance resulting from synaptic input) was shown to be principally different for distal dendritic input (Schultheiss et al. 2010), where excitatory input at the beginning of a spike cycle can lead to a delay in subsequent spiking (type II phase response curve). Overall, it is the detailed examination of local dendritic processing that provides the most compelling rationale for detailed morphological neuron models, and the GPe neuron models are no exception in revealing potentially significant aspects of such dendritic processing. Biophysically detailed GPe models are available for download in the Yale ModelDB archive at http://senselab.med.yale.edu/modeldb/ModelList.asp?id=88217.

Models that Capture the Interaction Between GP and Subthalamic Nucleus (STN)

A special GPe neuron modeling interest in the first decade of the twenty-first century has been concerned with the interactions between STN and GPe in the generation of pathological rhythmic bursting activity that is observed in Parkinson’s disease. The feedback pathway consisting of STN excitation of GPe and GPe inhibition of STN has been suspected to be the cause of such pathological oscillations based on earlier experimental results in slice cultures (Plenz and Kitai 1999) and was first modeled with a set of connected STN and GPe single-compartment neurons by the group of David Terman at Ohio State University (Terman et al. 2002). This model set off a host of subsequent modeling studies confirming the possibility of triggering oscillations in this network, notably in the beta band, with synaptic changes and disrupted striatal input patterns to GPe expected in parkinsonism (Holgado et al. 2010; Park and Rubchinsky 2012). These models typically employ dynamical systems analysis to examine the parameter range and stability required to exhibit different activity patterns. Nevertheless, to date the question of where beta activity originates in Parkinson’s disease is not solved, and cortical and striatal mechanisms are also thought to be important contributors (McCarthy et al. 2011; Kerr et al. 2013) and may interact with GP-STN oscillations (Nevado-Holgado et al. 2013; Ahn et al. 2016). Several models of GP-STN interactions are available for download in the Yale ModelDB archive.

Integration of GP Neuron Models in Large-Scale Network Simulations of Action Selection

The ultimate question of GP neuron modeling of course concerns the computational function of GP in basal ganglia information processing. Notably, GP neurons are included in basal ganglia network models that perform an action selection function (Gurney et al. 2001a, b; Humphries et al. 2006; Bogacz and Gurney 2007; Bogacz et al. 2016). This network simulation paradigm gives GPi a function as the key output of the selection pathway where selected actions are represented by decreased activity. In contrast GPe is part of a control pathway that allows setting selection thresholds via global modulation of GPi output rates. Networks are typically modeled with populations of leaky integrate-and-fire neurons with synaptic time constants matched to experimental data. In this type of model, simulated GP spike trains can replicate key features of rodent recordings (Magill et al. 2001). The Humphries et al. (2006) spiking network model is available on the Yale ModelDB archive.

Modeling the Effects of Deep Brain Stimulation in Parkinson’s Disease

Deep brain stimulation (DBS) in STN or GP has proven to be an effective treatment for Parkinson’s disease in many patients (Dostrovsky et al. 2002; Vitek et al. 2012). The mechanisms underlying these beneficial effects have been examined with simulations including GP neuron models at all levels of abstraction ranging from detailed biophysical dendritic models to network function. Detailed dendritic GP neuron models have been used to establish how pallidal deep brain stimulation results in changes of local neuron depolarization and firing (Johnson and McIntyre 2008). The effect of DBS to suppress pathological rhythmic synchronization has been the subject of numerous simulation studies and is typically carried out in networks of single-compartment neurons including GP as one structure (Rubin and Terman 2004; Cleary et al. 2013; Kang and Lowery 2013). Network modeling has also addressed the question of how stimulation of fibers and neurons in DBS differentially contributes to information flow in cortico-thalamic loops of information processing (So et al).

Cross-References

References

  1. Abdi A, Mallet N, Mohamed FY, Sharott A, Dodson PD, Nakamura KC, Suri S, Avery SV, Larvin JT, Garas FN, Garas SN, Vinciati F, Morin S, Bezard E, Baufreton J, Magill PJ (2015) Prototypic and arkypallidal neurons in the dopamine-intact external globus pallidus. J Neurosci 35:6667–6688CrossRefGoogle Scholar
  2. Ahn S, Zauber SE, Worth RM, Rubchinsky LL (2016) Synchronized Beta-band oscillations in a model of the Globus pallidus-subthalamic nucleus network under external input. Front Comput Neurosci 10:134CrossRefGoogle Scholar
  3. Bogacz R, Gurney K (2007) The basal ganglia and cortex implement optimal decision making between alternative actions. Neural Comput 19:442–477CrossRefGoogle Scholar
  4. Bogacz R, Martin Moraud E, Abdi A, Magill PJ, Baufreton J (2016) Properties of neurons in external Globus pallidus can support optimal action selection. PLoS Comp Biol 12:e1005004CrossRefGoogle Scholar
  5. Cleary DR, Raslan AM, Rubin JE, Bahgat D, Viswanathan A, Heinricher MM, Burchiel KJ (2013) Deep brain stimulation entrains local neuronal firing in human globus pallidus internus. J Neurophysiol 109:978–987CrossRefGoogle Scholar
  6. Deister CA, Chan CS, Surmeier DJ, Wilson CJ (2009) Calcium-activated SK channels influence voltage-gated ion channels to determine the precision of firing in Globus pallidus neurons. J Neurosci 29:8452–8461CrossRefGoogle Scholar
  7. Deister CA, Dodla R, Barraza D, Kita H, Wilson CJ (2013) Firing rate and pattern heterogeneity in the globus pallidus arise from a single neuronal population. J Neurophysiol 109:497–506CrossRefGoogle Scholar
  8. Dostrovsky JO, Hutchison WD, Lozano AM (2002) The globus pallidus, deep brain stimulation, and Parkinson's disease. Neuroscientist 8:284–290PubMedGoogle Scholar
  9. Edgerton JR, Hanson JE, Gunay C, Jaeger D (2010) Dendritic sodium channels regulate network integration in Globus pallidus neurons: a modeling study. J Neurosci 30:15146–15159CrossRefGoogle Scholar
  10. Gunay C, Edgerton JR, Jaeger D (2008) Channel density distributions explain spiking variability in the Globus pallidus: a combined physiology and computer simulation database approach. J Neurosci 28:7476–7491CrossRefGoogle Scholar
  11. Gurney K, Prescott TJ, Redgrave P (2001a) A computational model of action selection in the basal ganglia. II. Analysis and simulation of behaviour. BiolCybern 84:411–423Google Scholar
  12. Gurney K, Prescott TJ, Redgrave P (2001b) A computational model of action selection in the basal ganglia. I. A new functional anatomy. BiolCybern 84:401–410Google Scholar
  13. Herz AVM, Gollisch T, Machens CK, Jaeger D (2006) Modeling single-neuron dynamics and computations: a balance of detail and abstraction. Science 314:80–85CrossRefGoogle Scholar
  14. Holgado AJN, Terry JR, Bogacz R (2010) Conditions for the generation of Beta oscillations in the subthalamic nucleus-Globus pallidus network. J Neurosci 30:12340–12352CrossRefGoogle Scholar
  15. Humphries MD, Stewart RD, Gurney KN (2006) A physiologically plausible model of action selection and oscillatory activity in the basal ganglia. J Neurosci 26:12921–12942CrossRefGoogle Scholar
  16. Johnson MD, McIntyre CC (2008) Quantifying the neural elements activated and inhibited by globus pallidus deep brain stimulation. J Neurophysiol 100:2549–2563CrossRefGoogle Scholar
  17. Kang G, Lowery MM (2013) Interaction of oscillations, and their suppression via deep brain stimulation, in a model of the Cortico-basal ganglia network. IEEE Trans Neural Syst Rehab Eng 21:244–253CrossRefGoogle Scholar
  18. Kerr CC, Van Albada SJ, Neymotin SA, Chadderdon GL, Robinson PA, Lytton WW (2013) Cortical information flow in Parkinson’s disease: a composite network/field model. Front Comput Neurosci 7.  https://doi.org/10.3389/fncom.2013.00039
  19. Magill PJ, Bolam JP, Bevan MD (2001) Dopamine regulates the impact of the cerebral cortex on the subthalamic nucleus-globus pallidus network. Neuroscience 106:313–330CrossRefGoogle Scholar
  20. Mallet N, Micklem Benjamin R, Henny P, Brown Matthew T, Williams C, Bolam JP, Nakamura Kouichi C, Magill Peter J (2012) Dichotomous Organization of the External Globus Pallidus. Neuron 74:1075–1086CrossRefGoogle Scholar
  21. McCarthy MM, Moore-Kochlacs C, Gu X, Boyden ES, Han X, Kopell N (2011) Striatal origin of the pathologic beta oscillations in Parkinson's disease. Proc Natl Acad Sci 108:11620–11625CrossRefGoogle Scholar
  22. Mercer JN, Chan CS, Tkatch T, Held J, Surmeier DJ (2007) Nav1.6 sodium channels are critical to pacemaking and fast spiking in globus pallidus neurons. J Neurosci 27:13552–13566CrossRefGoogle Scholar
  23. Nevado-Holgado AJ, Mallet N, Magill PJ, Bogacz R (2013) Effective connectivity of the subthalamic nucleus – globus pallidus network during parkinsonian oscillations. J Physiol 592:1429–1455CrossRefGoogle Scholar
  24. Park C, Rubchinsky LL (2012) Potential mechanisms for imperfect synchronization in parkinsonian basal ganglia. PLoS One 7:e51530CrossRefGoogle Scholar
  25. Plenz D, Kitai ST (1999) A basal ganglia pacemaker formed by the subthalamic nucleus and external globus pallidus. Nature 400:677–682CrossRefGoogle Scholar
  26. Rubin JE, Terman D (2004) High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model. J Comput Neurosci 16:211–235CrossRefGoogle Scholar
  27. Schultheiss NW, Edgerton JR, Jaeger D (2010) Phase response curve analysis of a full morphological globus pallidus neuron model reveals distinct Perisomatic and dendritic modes of synaptic integration. J Neurosci 30:2767–2782CrossRefGoogle Scholar
  28. So RQ, Kent AR, Grill WM (2012) Relative contributions of local cell and passing fiber activation and silencing to changes in thalamic fidelity during deep brain stimulation and lesioning: a computational modeling study. J Comput Neurosci 32:499–519CrossRefGoogle Scholar
  29. Terman D, Rubin JE, Yew AC, Wilson CJ (2002) Activity patterns in a model for the Subthalamopallidal network of the basal ganglia. J Neurosci 22:2963–2976CrossRefGoogle Scholar
  30. Vitek JL, Zhang J, Hashimoto T, Russo GS, Baker KB (2012) External pallidal stimulation improves parkinsonian motor signs and modulates neuronal activity throughout the basal ganglia thalamic network. Exp Neurol 233:581–586CrossRefGoogle Scholar

Further Reading

  1. Kita H (2010) Chapter 13. Organization of the globus pallidus. In: Steiner H, Tseng KY (eds) Handbook of basal ganglia structure and function, vol 233–247. Elsevier Academic Press, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of BiologyEmory UniversityAtlantaUSA

Section editors and affiliations

  • Jonathan E. Rubin
    • 1
  1. 1.Department of MathematicsUniversity of PittsburghPittsburghUSA