Skip to main content

Advertisement

SpringerLink
Log in

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

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

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

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Notes

  1. http://pages.isir.upmc.fr/EvoNeuro/

  2. http://senselab.med.yale.edu/modeldb/

References

  • Adler, A., Joshua, M., Rivlin-Etzion, M., Mitelman, R., Marmor, O., Prut, Y., Bergman, H. (2010). Neurons in both pallidal segments change their firing properties similarly prior to closure of the eyes. Journal of Neurophysiology, 103(1), 346–359.

    PubMed  Google Scholar 

  • Albin, R., Young, A., Penney, J. (1989). The functional anatomy of basal ganglia disorders. Trends in Neurosciences, 12(10), 366–375.

    PubMed  CAS  Google Scholar 

  • Aldriege, J., Gilman, S., Dauth, G. (1990). Spontaneous neuronal unit activity in the primate basal ganglia and the effects of precentral cerebral cortical ablations. Brain Research, 516(1), 46–56.

    Google Scholar 

  • Alexander, G., & Crutcher, M. (1990). Functional architecture of basal ganglia circuits: neural substrates of parallel processing. Trends in Neurosciences, 13(7), 266–271.

    PubMed  CAS  Google Scholar 

  • Alexander, G., DeLong, M., Strick, P. (1986). Parallel organization of functionally segregated circuits linking basal ganglia and cortex. Annual Review of Neuroscience, 9(1), 357–381.

    PubMed  CAS  Google Scholar 

  • Aubert, I., Ghorayeb, I., Normand, E., Bloch, B. (2000). Phenotypical characterization of the neurons expressing the d1 and d2 dopamine receptors in the monkey striatum. The Journal of Comparative Neurology, 418(1), 22–32.

    PubMed  CAS  Google Scholar 

  • Bauswein, E., Fromm, C., Preuss, A. (1989). Corticostriatal cells in comparison with pyramidal tract neurons: contrasting properties in the behaving monkey. Brain Research, 493(1), 198–203.

    PubMed  CAS  Google Scholar 

  • Beckstead, R. (1983). A pallidostriatal projection in the cat and monkey. Brain Research Bulletin, 11(6), 629–632.

    PubMed  CAS  Google Scholar 

  • Bergman, H., Wichmann, T., Karmon, B., DeLong, M. (1994). The primate subthalamic nucleus. ii. neuronal activity in the mptp model of parkinsonism. Journal of Neurophysiology, 72(2), 507–520.

    PubMed  CAS  Google Scholar 

  • Berke, J. (2011). Functional properties of striatal fast-spiking interneurons. Frontiers in systems neuroscience, 5, 1–7.

    Google Scholar 

  • Berke, J., Okatan, M., Skurski, J., Eichenbaum, H. (2004). Oscillatory entrainment of striatal neurons in freely moving rats. Neuron, 43(6), 883–896.

    PubMed  CAS  Google Scholar 

  • Berns, G., & Sejnowski, T. (1994). A model of basal ganglia function unifying reinforcement learning and action selection. In Joint Symposium on Neural Computation (pp. 129–148).

  • Bevan, M., Booth, P., Eaton, S., Bolam, J. (1998). Selective innervation of neostriatal interneurons by a subclass of neuron in the globus pallidus of the rat. The Journal of Neuroscience, 18(22), 9438.

    PubMed  CAS  Google Scholar 

  • Bogacz, R., & Gurney, K. (2007). The basal ganglia and cortex implement optimal decision making between alternative actions. Neural Computation, 19(2), 442–477.

    PubMed  Google Scholar 

  • Carter, A., Soler-Llavina, G., Sabatini, B. (2007). Timing and location of synaptic inputs determine modes of subthreshold integration in striatal medium spiny neurons. The Journal of Neuroscience, 27(33), 8967–8977.

    PubMed  CAS  Google Scholar 

  • Cooper, A., & Stanford, I. (2000). Electrophysiological and morphological characteristics of three subtypes of rat globus pallidus neurone in vitro. The Journal of Physiology, 527(Pt 2), 291.

    PubMed Central  PubMed  CAS  Google Scholar 

  • Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.A.M.T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. Evolutionary Computation, IEEE Transactions on, 6(2), 182–197.

    Google Scholar 

  • Deco, G., Jirsa, V., Robinson, P., Breakspear, M., Friston, K. (2008). The dynamic brain: from spiking neurons to neural masses and cortical fields. PLoS Computational Biology, 4(8), e1000092.

    PubMed Central  PubMed  Google Scholar 

  • Destexhe, A., Mainen, Z., Sejnowski, T. (1998). Kinetic models of synaptic transmission. Methods in Neuronal Modeling, 2, 1–25.

    Google Scholar 

  • Elias, S., Ritov, Y., Bergman, H. (2008). Balance of increases and decreases in firing rate of the spontaneous activity of basal ganglia high-frequency discharge neurons. Journal of Neurophysiology, 100(6), 3086–3104.

    PubMed  Google Scholar 

  • Filion, M., Tremblay, L., et al. (1991). Abnormal spontaneous activity of globus pallidus neurons in monkeys with mptp-induced parkinsonism. Brain Research, 547(1), 140–144.

    Google Scholar 

  • Frank, M. (2006). Hold your horses: a dynamic computational role for the subthalamic nucleus in decision making. Neural Networks, 19(8), 1120–1136.

    PubMed  Google Scholar 

  • Georgopoulos, A., DeLong, M., Crutcher, M. (1983). Relations between parameters of step-tracking movements and single cell discharge in the globus pallidus and subthalamic nucleus of the behaving monkey. The Journal of Neuroscience, 3(8), 1586–1598.

    PubMed  CAS  Google Scholar 

  • Georgopoulos, A., Kalaska, J., Caminiti, R., Massey, J. (1982). On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex. The Journal of Neuroscience, 2(11), 1527–1537.

    PubMed  CAS  Google Scholar 

  • Geyer, M., & Markou, A. (1995). Animal models of psychiatric disorders. Psychopharmacology: The Fourth Generation of Progress (pp. 787–798).

  • Gillies, A., & Willshaw, D. (2004). Models of the subthalamic nucleus: the importance of intranuclear connectivity. Medical Engineering & Physics, 26(9), 723–732.

    CAS  Google Scholar 

  • Girard, B., Tabareau, N., Pham, Q., Berthoz, A., Slotine, J. (2008). Where neuroscience and dynamic system theory meet autonomous robotics: a contracting basal ganglia model for action selection. Neural Networks, 21(4), 628–641.

    PubMed  CAS  Google Scholar 

  • Gittis, A., Nelson, A., Thwin, M., Palop, J., Kreitzer, A. (2010). Distinct roles of gabaergic interneurons in the regulation of striatal output pathways. The Journal of Neuroscience, 30(6), 2223–2234.

    PubMed Central  PubMed  CAS  Google Scholar 

  • Goldberg, J., Boraud, T., Maraton, S., Haber, S., Vaadia, E., Bergman, H. (2002). Enhanced synchrony among primary motor cortex neurons in the 1-methyl-4-phenyl-1, 2, 3, 6-tetrahydropyridine primate model of parkinson’s disease. The Journal of Neuroscience, 22(11), 4639–4653.

    PubMed  CAS  Google Scholar 

  • Gurney, K., Prescott, T., Redgrave, P. (2001). A computational model of action selection in the basal ganglia. I. A new functional anatomy. Biological Cybernetics, 84(6), 401–410.

    PubMed  CAS  Google Scholar 

  • Hardman, C., Henderson, J., Finkelstein, D., Horne, M., Paxinos, G., Halliday, G. (2002). Comparison of the basal ganglia in rats, marmosets, macaques, baboons, and humans: volume and neuronal number for the output, internal relay, and striatal modulating nuclei. The Journal of Comparative Neurology, 445(3), 238–255.

    PubMed  Google Scholar 

  • Holgado, A., Terry, J., Bogacz, R. (2010). Conditions for the generation of beta oscillations in the subthalamic nucleus–globus pallidus network. The Journal of Neuroscience, 30(37), 12340–12352.

    PubMed  CAS  Google Scholar 

  • Hori, Y., Minamimoto, T., Kimura, M. (2009). Neuronal encoding of reward value and direction of actions in the primate putamen. Journal of Neurophysiology, 102(6), 3530–3543.

    PubMed  Google Scholar 

  • Humphries, M., Stewart, R., Gurney, K. (2006). A physiologically plausible model of action selection and oscillatory activity in the basal ganglia. The Journal of Neuroscience, 26(50), 12921.

    PubMed  CAS  Google Scholar 

  • Humphries, M., Wood, R., Gurney, K. (2009). Dopamine-modulated dynamic cell assemblies generated by the gabaergic striatal microcircuit. Neural Networks, 22(8), 1174–1188.

    PubMed  Google Scholar 

  • Hunt, C., Pang, D., Jones, E. (1991). Distribution and density of gaba cells in intralaminar and adjacent nuclei of monkey thalamus. Neuroscience, 43(1), 185–196.

    PubMed  CAS  Google Scholar 

  • Iwamuro, H., Tachibana, Y., Saito, N., Nambu, A. (2009). Organization of motor cortical inputs to the subthalamic nucleus in the monkey. The Basal Ganglia IX, 109–117.

  • Johnston, J., Gerfen, C., Haber, S., van der Kooy, D. (1990). Mechanisms of striatal pattern formation: conservation of mammalian compartmentalization. Developmental Brain Research, 57(1), 93–102.

    PubMed  CAS  Google Scholar 

  • Kalaska, J., Cohen, D., Hyde, M., Prud’Homme, M. (1989). A comparison of movement direction-related versus load direction-related activity in primate motor cortex, using a two-dimensional reaching task. The Journal of Neuroscience, 9(6), 2080–2102.

    PubMed  CAS  Google Scholar 

  • Kiritani, T., Wickersham, I., Seung, H., Shepherd, G. (2012). Hierarchical connectivity and connection-specific dynamics in the corticospinal–corticostriatal microcircuit in mouse motor cortex. The Journal of Neuroscience, 32(14), 4992–5001.

    PubMed Central  PubMed  CAS  Google Scholar 

  • Kita, H., & Kitai, S. (1991). Intracellular study of rat globus pallidus neurons: membrane properties and responses to neostriatal, subthalamic and nigral stimulation. Brain Research, 564(2), 296–305.

    PubMed  CAS  Google Scholar 

  • Kita, H., Nambu, A., Kaneda, K., Tachibana, Y., Takada, M. (2004). Role of ionotropic glutamatergic and gabaergic inputs on the firing activity of neurons in the external pallidum in awake monkeys. Journal of Neurophysiology, 92(5), 3069–3084.

    PubMed  CAS  Google Scholar 

  • Kita, H., Tachibana, Y., Nambu, A., Chiken, S. (2005). Balance of monosynaptic excitatory and disynaptic inhibitory responses of the globus pallidus induced after stimulation of the subthalamic nucleus in the monkey. The Journal of Neuroscience, 25(38), 8611–8619.

    PubMed  CAS  Google Scholar 

  • Kita, H., Tokuno, H., Nambu, A. (1999). Monkey globus pallidus external segment neurons projecting to the neostriatum. Neuroreport, 10(7), 1467.

    PubMed  CAS  Google Scholar 

  • Koch, C. (2005). Biophysics of computation: information processing in single neurons. USA: Oxford University Press.

    Google Scholar 

  • Koós, T., Tepper, J., et al. (1999). Inhibitory control of neostriatal projection neurons by gabaergic interneurons. Nature Neuroscience, 2, 467–472.

    PubMed  Google Scholar 

  • Kumar, A., Cardanobile, S., Rotter, S., Aertsen, A. (2011). The role of inhibition in generating and controlling parkinsons disease oscillations in the basal ganglia. Frontiers in Systems Neuroscience, 5, 1–14.

    CAS  Google Scholar 

  • Lapper, S., Smith, Y., Sadikot, A., Parent, A., Bolam, J. (1992). Cortical input to parvalbumin-immunoreactive neurones in the putamen of the squirrel monkey. Brain Research, 580(1), 215–224.

    PubMed  CAS  Google Scholar 

  • Leblois, A., Boraud, T., Meissner, W., Bergman, H., Hansel, D. (2006). Competition between feedback loops underlies normal and pathological dynamics in the basal ganglia. The Journal of Neuroscience, 26(13), 3567–3583.

    PubMed  CAS  Google Scholar 

  • Lévesque, J., & Parent, A. (2005a). Gabaergic interneurons in human subthalamic nucleus. Movement Disorders, 20(5), 574–584.

    Google Scholar 

  • Lévesque, M., & Parent, A. (2005b). The striatofugal fiber system in primates: a reevaluation of its organization based on single-axon tracing studies. Proceedings of the National Academy of Sciences, 102(33), 11888–11893.

    Google Scholar 

  • Liénard, J., Guillot, A., Girard, B. (2010). Multi-objective evolutionary algorithms to investigate neurocomputational issues: the case study of basal ganglia models. From Animals to Animats, 11, 597–606.

    Google Scholar 

  • Magdoom, K., Subramanian, D., Chakravarthy, V., Ravindran, B., Amari, S., Meenakshisundaram, N. (2011). Modeling basal ganglia for understanding parkinsonian reaching movements. Neural Computation, 23(2), 477–516.

    PubMed  CAS  Google Scholar 

  • Mallet, N., Micklem, B., Henny, P., Brown, M., Williams, C., Bolam, J., Nakamura, K., Magill, P. (2012). Dichotomous organization of the external globus pallidus. Neuron, 74(6), 1075–1086.

    PubMed Central  PubMed  CAS  Google Scholar 

  • Marani, E., Heida, T., Lakke, E., Usunoff, K. (2008). The subthalamic nucleus: cytology of the subthalamic nucleus. Springer Verlag.

  • Matsumoto, N., Minamimoto, T., Graybiel, A., Kimura, M. (2001). Neurons in the thalamic cm-pf complex supply striatal neurons with information about behaviorally significant sensory events. Journal of Neurophysiology, 85(2), 960–976.

    PubMed  CAS  Google Scholar 

  • Matsumura, M., Kojima, J., Gardiner, T., Hikosaka, O. (1992). Visual and oculomotor functions of monkey subthalamic nucleus. Journal of Neurophysiology, 67(6), 1615–1632.

    PubMed  CAS  Google Scholar 

  • Mink, J. (1996). The basal ganglia: focused selection and inhibition of competing motor programs. Progress in Neurobiology, 50(4), 381–425.

    PubMed  CAS  Google Scholar 

  • Mitchell, S., Richardson, R., Baker, F., DeLong, M. (1987). The primate globus pallidus: neuronal activity related to direction of movement. Experimental Brain Research, 68(3), 491–505.

    PubMed  CAS  Google Scholar 

  • Morishima, M., & Kawaguchi, Y. (2006). Recurrent connection patterns of corticostriatal pyramidal cells in frontal cortex. The Journal of Neuroscience, 26(16), 4394–4405.

    PubMed  CAS  Google Scholar 

  • Mouchet, P., & Yelnik, J. (2004). Basic electrotonic properties of primate pallidal neurons as inferred from a detailed analysis of their morphology: a modeling study. Synapse, 54(1), 11–23.

    PubMed  CAS  Google Scholar 

  • Nadjar, A., Brotchie, J., Guigoni, C., Li, Q., Zhou, S., Wang, G., Ravenscroft, P., Georges, F., Crossman, A., Bezard, E. (2006). Phenotype of striatofugal medium spiny neurons in parkinsonian and dyskinetic nonhuman primates: a call for a reappraisal of the functional organization of the basal ganglia. The Journal of Neuroscience, 26(34), 8653–8661.

    PubMed  CAS  Google Scholar 

  • Nakano, K., Hasegawa, Y., Tokushige, A., Nakagawa, S., Kayahara, T., Mizuno, N. (1990). Topographical projections from the thalamus, subthalamic nucleus and pedunculopontine tegmental nucleus to the striatum in the japanese monkey, macaca fuscata. Brain Research, 537(1–2), 54–68.

    PubMed  CAS  Google Scholar 

  • Nambu, A. (2008). Seven problems on the basal ganglia. Current Opinion in Neurobiology, 18(6), 595–604.

    PubMed  CAS  Google Scholar 

  • Nambu, A. (2011). Somatotopic organization of the primate basal ganglia. Frontiers in Neuroanatomy, 5, 1–9.

    Google Scholar 

  • Nambu, A., Hatanaka, N., Takara, S., Tachibana, Y., Takada, M. (2009). Information processing in the striatum of behaving monkeys. The Basal Ganglia IX, 41–48.

  • Nambu, A., & Llinas, R. (1994). Electrophysiology of globus pallidus neurons in vitro. Journal of Neurophysiology, 72(3), 1127–1139.

    PubMed  CAS  Google Scholar 

  • Nambu, A., Tokuno, H., Hamada, I., Kita, H., Imanishi, M., Akazawa, T., Ikeuchi, Y., Hasegawa, N. (2000). Excitatory cortical inputs to pallidal neurons via the subthalamic nucleus in the monkey. Journal of Neurophysiology, 84(1), 289–300.

    PubMed  CAS  Google Scholar 

  • Nauta, H., & Cole, M. (1978). Efferent projections of the subthalamic nucleus: an autoradiographic study in monkey and cat. The Journal of Comparative Neurology, 180(1), 1–16.

    PubMed  CAS  Google Scholar 

  • Nestler, E., & Hyman, S. (2010). Animal models of neuropsychiatric disorders. Nature Neuroscience, 13(10), 1161–1169.

    PubMed Central  PubMed  CAS  Google Scholar 

  • Parent, A., Charara, A., Pinault, D. (1995). Single striatofugal axons arborizing in both pallidal segments and in the substantia nigra in primates. Brain Research, 698(1–2), 280–284.

    PubMed  CAS  Google Scholar 

  • Parent, A., & Hazrati, L. (1995). Functional anatomy of the basal ganglia. ii. the place of subthalamic nucleus and external pallidium in basal ganglia circuitry. Brain Research Reviews, 20(1), 128–154.

    PubMed  CAS  Google Scholar 

  • Parent, A., & Smith, Y. (1987). Organization of efferent projections of the subthalamic nucleus in the squirrel monkey as revealed by retrograde labeling methods. Brain Research, 436(2), 296–310.

    PubMed  CAS  Google Scholar 

  • Parent, M., & Parent, A. (2005). Single-axon tracing and three-dimensional reconstruction of centre médian-parafascicular thalamic neurons in primates. The Journal of Comparative Neurology, 481(1), 127–144.

    PubMed  Google Scholar 

  • Parent, M., & Parent, A. (2006). Single-axon tracing study of corticostriatal projections arising from primary motor cortex in primates. The Journal of Comparative Neurology, 496(2), 202–213.

    PubMed  Google Scholar 

  • Parent, M., & Parent, A. (2007). The microcircuitry of primate subthalamic nucleus. Parkinsonism & Related Disorders, 13, S292—S295.

    Google Scholar 

  • Paxinos, G., Huang, X., Toga, A. (2000). The rhesus monkey brain in stereotaxic coordinates (Vol. 2). San Diego: Academic Press.

  • Plenz, D., & Kitai, S. (1998). Up and down states in striatal medium spiny neurons simultaneously recorded with spontaneous activity in fast-spiking interneurons studied in cortex–striatum–substantia nigra organotypic cultures. The Journal of Neuroscience, 18(1), 266–283.

    PubMed  CAS  Google Scholar 

  • Plotkin, J., Wu, N., Chesselet, M., Levine, M. (2005). Functional and molecular development of striatal fast-spiking gabaergic interneurons and their cortical inputs. European Journal of Neuroscience, 22(5), 1097–1108.

    PubMed  Google Scholar 

  • Rafols, J., & Fox, C. (1976). The neurons in the primate subthalamic nucleus: a golgi and electron microscopic study. The Journal of Comparative Neurology, 168(1), 75–111.

    PubMed  CAS  Google Scholar 

  • Rav-Acha, M., Sagiv, N., Segev, I., Bergman, H., Yarom, Y. (2005). Dynamic and spatial features of the inhibitory pallidal gabaergic synapses. Neuroscience, 135(3), 791–802.

    PubMed  CAS  Google Scholar 

  • Raz, A., Vaadia, E., Bergman, H. (2000). Firing patterns and correlations of spontaneous discharge of pallidal neurons in the normal and the tremulous 1-methyl-4-phenyl-1, 2, 3, 6-tetrahydropyridine vervet model of parkinsonism. The Journal of Neuroscience, 20(22), 8559–8571.

    PubMed  CAS  Google Scholar 

  • Redgrave, P., Prescott, T., Gurney, K. (1999). The basal ganglia: a vertebrate solution to the selection problem?Neuroscience, 89, 1009–1024.

    PubMed  CAS  Google Scholar 

  • Rodrigues, S., Chizhov, A., Marten, F., Terry, J. (2010). Mappings between a macroscopic neural-mass model and a reduced conductance-based model. Biological Cybernetics, 102(5), 361–371.

    PubMed  Google Scholar 

  • Rubin, J., & Terman, D. (2004). High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model. Journal of Computational Neuroscience, 16(3), 211–235.

    PubMed  Google Scholar 

  • Sadek, A., Magill, P., Bolam, J. (2007). A single-cell analysis of intrinsic connectivity in the rat globus pallidus. The Journal of Neuroscience, 27(24), 6352–6362.

    PubMed  CAS  Google Scholar 

  • Sadikot, A., Parent, A., Francois, C. (1992a). Efferent connections of the centromedian and parafascicular thalamic nuclei in the squirrel monkey: A pha-l study of subcortical projections. The Journal of Comparative Neurology, 315(2), 137–159.

    CAS  Google Scholar 

  • Sadikot, A., Parent, A., Francois, C. (1992b). Efferent connections of the centromedian and parafascicular thalamic nuclei in the squirrel monkey: A pha-l study of subcortical projections. The Journal of Comparative Neurology, 315(2), 137–159.

    CAS  Google Scholar 

  • Sato, F., Lavallee, P., Levesque, M., Parent, A. (2000a). Single-axon tracing study of neurons of the external segment of the globus pallidus in primate. Journal of Comparative Neurology, 417(1), 17–31.

    CAS  Google Scholar 

  • Sato, F., Parent, M., Levesque, M., Parent, A. (2000b). Axonal branching pattern of neurons of the subthalamic nucleus in primates. The Journal of Comparative Neurology, 424(1), 142–152.

    CAS  Google Scholar 

  • Shink, E., Bevan, M., Bolam, J., Smith, Y. (1996). The subthalamic nucleus and the external pallidum: two tightly interconnected structures that control the output of the basal ganglia in the monkey. Neuroscience, 73(2), 335–357.

    PubMed  CAS  Google Scholar 

  • Shink, E., & Smith, Y. (1995). Differential synaptic innervation of neurons in the internal and external segments of the globus pallidus by the GABA-and glutamate-containing terminals in the squirrel monkey. The Journal of Comparative Neurology, 358(1), 119–141.

    PubMed  CAS  Google Scholar 

  • Shouno, O., Takeuchi, J., Tsujino, H. (2009). A spiking neuron model of the basal ganglia circuitry that can generate behavioral variability. The Basal Ganglia IX, 191–200.

  • Sidibe, M., & Smith, Y. (1996). Differential synaptic innervation of striatofugal neurones projecting to the internal or external segments of the globus pallidus by thalamic afferents in the squirrel monkey. The Journal of Comparative Neurology, 365(3), 445–465.

    PubMed  CAS  Google Scholar 

  • Sidibe, M., & Smith, Y. (1999). Thalamic inputs to striatal interneurons in monkeys: synaptic organization and co-localization of calcium binding proteins. Neuroscience, 89(4), 1189–1208.

    PubMed  CAS  Google Scholar 

  • Smith, Y., Hazrati, L., Parent, A. (1990). Efferent projections of the subthalamic nucleus in the squirrel monkey as studied by the pha-l anterograde tracing method. The Journal of Comparative Neurology, 294(2), 306–323.

    PubMed  CAS  Google Scholar 

  • Spooren, W., Lynd-Balta, E., Mitchell, S., Haber, S. (1996). Ventral pallidostriatal pathway in the monkey: evidence for modulation of basal ganglia circuits. The Journal of Comparative Neurology, 370(3), 295–312.

    PubMed  CAS  Google Scholar 

  • Starr, P., Rau, G., Davis, V., Marks, W., Ostrem, J., Simmons, D., Lindsey, N., Turner, R. (2005). Spontaneous pallidal neuronal activity in human dystonia: comparison with parkinson’s disease and normal macaque. Journal of Neurophysiology, 93(6), 3165–3176.

    PubMed  Google Scholar 

  • Tachibana, Y., Kita, H., Chiken, S., Takada, M., Nambu, A. (2008). Motor cortical control of internal pallidal activity through glutamatergic and gabaergic inputs in awake monkeys. European Journal of Neuroscience, 27(1), 238–253.

    PubMed  Google Scholar 

  • Tandé, D., Féger, J., Hirsch, E., François, C. (2006). Parafascicular nucleus projection to the extrastriatal basal ganglia in monkeys. Neuroreport, 17(3), 277.

    PubMed  Google Scholar 

  • Tepper, J., Koós, T., Wilson, C. (2004). Gabaergic microcircuits in the neostriatum. Trends in Neurosciences, 27(11), 662–669.

    PubMed  CAS  Google Scholar 

  • Tepper, J., Wilson, C., Koós, T. (2008). Feedforward and feedback inhibition in neostriatal gabaergic spiny neurons. Brain Research Reviews, 58(2), 272.

    PubMed Central  PubMed  CAS  Google Scholar 

  • Tsirogiannis, G., Tagaris, G., Sakas, D., Nikita, K. (2010). A population level computational model of the basal ganglia that generates parkinsonian local field potential activity. Biological Cybernetics, 102(2), 155–176.

    PubMed  Google Scholar 

  • Turner, R., & Anderson, M. (1997). Pallidal discharge related to the kinematics of reaching movements in two dimensions. Journal of Neurophysiology, 77(3), 1051.

    PubMed  CAS  Google Scholar 

  • Turner, R., & DeLong, M. (2000). Corticostriatal activity in primary motor cortex of the macaque. The Journal of Neuroscience, 20(18), 7096–7108.

    PubMed  CAS  Google Scholar 

  • Van Albada, S., & Robinson, P. (2009). Mean-field modeling of the basal ganglia-thalamocortical system. I Firing rates in healthy and parkinsonian states. Journal of Theoretical Biology, 257(4), 642–663.

    PubMed  CAS  Google Scholar 

  • Wang, Y., Li, S., Chen, Q., Hu, W. (2007). Biology inspired robot behavior selection mechanism: using genetic algorithm. LNCS, 4688, 777.

  • Wichmann, T., Bergman, H., Starr, P., Subramanian, T., Watts, R., DeLong, M. (1999). Comparison of mptp-induced changes in spontaneous neuronal discharge in the internal pallidal segment and in the substantia nigra pars reticulata in primates. Experimental Brain Research, 125(4), 397–409.

    PubMed  CAS  Google Scholar 

  • Wichmann, T., & Soares, J. (2006). Neuronal firing before and after burst discharges in the monkey basal ganglia is predictably patterned in the normal state and altered in parkinsonism. Journal of Neurophysiology, 95(4), 2120–2133.

    PubMed  Google Scholar 

  • Wickens, J. (1997). Basal ganglia: Structure and computations. Network: Computation in Neural Systems, 8(4), R77–R109.

    Google Scholar 

  • Willner, P. (1984). The validity of animal models of depression. Psychopharmacology, 83(1), 1–16.

    PubMed  CAS  Google Scholar 

  • Wilson, C. (2007). Gabaergic inhibition in the neostriatum. Progress in Brain Research, 160, 91–110.

    PubMed  CAS  Google Scholar 

  • Yelnik, J., Francis, C., Percheron, G., Tandéa, D. (1991). Morphological taxonomy of the neurons of the primate striatum. The Journal of Comparative Neurology, 313(2), 273–294.

    PubMed  CAS  Google Scholar 

  • Yelnik, J., & Percheron, G. (1979). Subthalamic neurons in primates: a quantitative and comparative analysis. Neuroscience, 4(11), 1717–1743.

    PubMed  CAS  Google Scholar 

Download references

Acknowledgments

We warmly thank Dr. Martin Parent for interesting discussion on the single-axon tracing studies, and Dr. Ignasi Cos for helpful comments and suggestions on this work.

Conflict of interests

The authors display no conflict of interest.

Author information

Authors and Affiliations

  1. Institut des Systèmes Intelligents et de Robotique, Université Pierre & Marie Curie, CC173, 4 Place Jussieu, 75005, Paris, France

    Jean Liénard & Benoît Girard

  2. UMR7222, CNRS, 75005, Paris, France

    Jean Liénard & Benoît Girard

Authors
  1. Jean Liénard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Benoît Girard
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jean Liénard.

Additional information

Action Editor: David Terman

This research was funded by the ANR, project EvoNeuro ANR-09-EMER-005-01.

Appendix

Appendix

1.1 A.1 Mean firing rates at rest

The mean firing rates at rest estimations were derived from the figures in Table 8, under the simplifying assumption that each of the monkey recordings \(\mu \pm \sigma (n)\) constitute an independent sample of a normally distributed random variable. Using an arbitrary big number b, for each set of data we draw \(b*n\) random sample from the \(\mathcal {N(\mu ,\sqrt {\sigma })}\) distribution, and fit the sum of all the simulated data to a normal distribution using least squares.

Table 8 Firing rates at rest as reported for some twenty monkeys; the data are represented in the form “Mean ± SD (number of neurons)”
Full size table

1.2 A.2 Isoforces of other connections

As supplementary materials, we provide in Fig. 11 the found isoforces of the MSN and STN projections toward GPe and GPi/SNr, and of the GPe outgoing projections (without the GPe \(\rightarrow \) GPi/SNr projection which is already shown in Fig. 6).

Fig. 11
figure 11

Connection isoforces of other basal ganglia connections discussed in this paper. See the caption of Fig. 6 for more explanations

Full size image

1.3 A.3 Illustration of one solution and source code

In order to illustrate further the results of our optimization, in Table 9 are summarized the specific values of the parameters of one solution chosen at random in the pool of optimal solutions. High variations are exhibited in the values of the parameters throughout the set of solutions (as per Tables 6 and 7). The exhaustive parameter values of the solutions presented in this paper is available online along with the source code, in order to permit further studies, on the EvoNeuro project websiteFootnote 1 and on modeldb with the accession number 150206.Footnote 2

Table 9 Parameter values for one solution chosen at random among the 1151 different optimal solutions
Full size table

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liénard, J., Girard, B. A biologically constrained model of the whole basal ganglia addressing the paradoxes of connections and selection. J Comput Neurosci 36, 445–468 (2014). https://doi.org/10.1007/s10827-013-0476-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-013-0476-2

Keywords

Search

Navigation