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Neurochemical Oscillations in the Basal Ganglia

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Abstract

This work represents an attempt to elucidate the neurochemical processes in the basal ganglia by mathematical modelling. The correlation between neurochemistry and electrophysiology has been used to construct a dynamical system based on the basal ganglia’s network structure. Mathematical models were constructed for different physical scales to reformulate the neurochemical and electrophysiological behaviour from synapses up to multi-compartment systems. Transformation functions have been developed to transit between the different scales. We show through numerical simulations that this network produces oscillations in the electrical potentials as well as in neurotransmitter concentrations. In agreement with pharmacological experiments, a parameter sensitivity analysis reveals temporary changes in the neurochemical and electrophysiological systems after single exposure to antipsychotic drugs. This behaviour states the structural stability of the system. The correlation between the neurochemical dynamics and drug-induced behaviour provides the perspective for novel neurobiological hypotheses.

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References

  • Aharon, S., Parnas, H., Parnas, I., 1994. The magnitude and significance of Ca2+ domains for release of neurotransmitters. Bull. Math. Biol. 56(6), 1095–1119.

    MATH  Google Scholar 

  • Alexander, G.E., DeLong, M.R., Strick, P.L., 1986. Parallel organization of functionally segregated circuits linking basal ganglia and cortex. Annu. Rev. Neurosci. 9, 357–381.

    Article  Google Scholar 

  • Betarbet, R., Turner, R., Chockkan, V., DeLong, M.R., Allers, K.A., Walters, J., Levey, A.I., Greenamyre, J.T., 1997. Dopaminergic neurons intrinsic to the primate striatum. J. Neurosci. 17(17), 6761–6768.

    Google Scholar 

  • Bevan, M., Magill, P.J., Terman, D., Bolam, J.P., Wilson, C.J., 2002. Move to the rhythm: Oscillations in the subthalamic nucleus-external globus pallidus network. Trends Neurosci. 25, 523–531.

    Article  Google Scholar 

  • Boraud, T., Goldberg, P., Brown, J.A., Graybiel, A.M., Magill, P.J., 2005. Oscillations in the basal ganglia: The good, the bad, and the unexpected. The Basal Ganglia VIII, 3–25.

    Google Scholar 

  • Carlsson, A., 1988. The current statues of the dopamine hypothesis of schizophrenia. Neuropsychopharm 1, 179–186.

    Article  Google Scholar 

  • Carlsson, M., Carlsson, A., 1990. Interactions between glutamatergic and monoaminergic systems within the basal ganglia—implications for schizophrenia and Parkinson’s disease. TINS 13(7), 272–276.

    Google Scholar 

  • Carlsson, A., Waters, N., Carlsson, M.L., 1999. Neurotransmitter interactions in schizophrenia-Therapeutic implications. Biol. Psychiatry 46, 1388–1395.

    Article  Google Scholar 

  • Cassim, F., Labyt, E., Devos, D., Defebvre, L., Destexhe, A., Derambure, P., 2002. Relationship between oscillations in the basal ganglia and synchronisation of cortical activity. Epileptic Disord. 4, 31–45.

    Google Scholar 

  • Chesselet, M.F., 2002. Dopamine–GABA Interactions. Dopamine in the CNS 2, 1st edn., pp. 151–172. Springer, Berlin.

    Google Scholar 

  • Coyle, J.T., 2006. Glutamate and Schizophrenia: Beyond the Dopamine Hypothesis. Cell. Mol. Neurobiol. 26(4–6), 365–384.

    Google Scholar 

  • Destexhe, A., Mainen, Z.F., Sejnowski, T.J., 1994. Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. J. Comput. Neurosci. 1, 195–230.

    Article  Google Scholar 

  • Destexhe, A., Mainen, Z.F., Sejnowski, T.J., 1998. Kinetic models of synaptic transmission. In: Methods in Neuronal Modeling, 2nd edn. MIT Press, Cambridge.

    Google Scholar 

  • DiFiglia, M., 1987. Synaptic organization of cholinergic neurons in the monkey neostriatum. J. Comput. Neurol. 255(2), 245–258.

    Article  Google Scholar 

  • DiFiglia, M., Pasik, P., Pasik, T., 1976. A Golgi study of neuronal types in the neostriatum of monkeys. Brain Res. 114(2), 245–256.

    Article  Google Scholar 

  • E, W., Engquist, B., 2003. The heterogeneous multi-scale methods. Commun. Math. Sci. 1, 87–133.

    MATH  MathSciNet  Google Scholar 

  • Frank, M.J., (2004). Dynamic dopamine modulation of striato-cortical circuits in cognition: Converging neuropsychological, psychopharmacological and computational studies. PhD thesis.

  • Frankle, W.G., Lerma, J., Laruelle, M., 2003. The synaptic hypothesis of schizophrenia. Neuron 39(2), 205–216.

    Article  Google Scholar 

  • Fujimoto, K., Kita, H., 1993. Response characteristics of subthalamic neurons to the stimulation of the sensorimotor cortex in the rat. Brain Res. 609, 185–192.

    Article  Google Scholar 

  • Gerfen, C., Wilson, C., 1996. The basal ganglia. In: Swanson, L., Bjorklund, A., Hokfelt, T. (Eds.), Handbook of Chemical Neuroanatomy. Integrated Systems of the CNS, Pt III, vol. 12, pp. 371–468. Elsevier, Amsterdam.

    Google Scholar 

  • Globus, M.Y.T., Busto, R., Dietrich, W.D., Martinez, E., Valdes, I., Ginsberg, M.D., 1988. Effect of ischemia on the in vivo release of striatal dopamine, glutamate, and aminobutyric acid studied by intracerebral microdialysis. J. Neurochem. 51(5), 1455–1464.

    Article  Google Scholar 

  • Graveland, G.A., Williams, R.S., DiFiglia, M., 1985. A Golgi study of the human neostriatum: Neurons and afferent fibers. J. Comput. Neurol. 234(3), 317–333.

    Article  Google Scholar 

  • Graybiel, A.M., Ragsdale, C.W. Jr., 1978. Histochemically distinct compartments in the striatum of human, monkeys, and cat demonstrated by acetylthiocholinesterase staining. Proc. Natl. Acad. Sci. USA 75(11), 5723–5726.

    Article  Google Scholar 

  • Graybiel, A.M., Pickel, V.M., Joh, T.H., Reis, D.J., Ragsdale, C.W. Jr., 1981. Direct demonstration of a correspondence between the dopamine islands and acetylcholinesterase patches in the developing striatum. Proc. Natl. Acad. Sci. USA 78(9), 5871–5875.

    Article  Google Scholar 

  • Haken, H., 2004. Synergetics: Introduction and Advanced Topics (Physics and Astronomy Online Library). Springer, Berlin.

    Google Scholar 

  • Heine, M., Groc, L., Frischknecht, R., Béïque, J.C., Lounis, B., Rumbaugh, G., Huganir, R.L., Cognet, L., Choquet, D., 2008. Science 320(5873), 201–205.

    Article  Google Scholar 

  • Humphries, M.D., Stewart, R.D., Gurney, K.N., 2006. A physiologically plausible model of action selection and oscillatory activity in the basal ganglia. J. Neurosci. 26(50), 12921–12942.

    Article  Google Scholar 

  • Hutchinson, P.J., O’Connell, M.T., Al-Rawi, P.G., Maskell, L.B., Kett-White, R., Gupta, A.K., Kirkpatrick, P.J., Pickard, J.D., 2000. Clinical cerebral microdialysis: a methodological study. J. Neurosurg. 93, 37–43.

    Article  Google Scholar 

  • Hutchinson, P.J., O’Connell, M.T., Kirkpatrick, P.J., Pickard, J.D., 2002. How can we measure substrate, metabolite and neurotransmitter concentrations in the human brain? Physiol. Meas. 23, R75–R109.

    Article  Google Scholar 

  • Kanthan, R., Shuaib, A., Griebel, R., Miyashita, H., 1995. Intracerebral human microdialysis. In vivo study of an acute focal ischemic model of the human brain. Stroke 26, 870–873.

    Google Scholar 

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

    Article  Google Scholar 

  • Koch, C., 2004. Biophysics of Computation: Information Processing in Single Neurons (Computational Neuroscience). Oxford University Press, London.

    Google Scholar 

  • Konradi, C., Cepeda, C., Levine, M.S., 2002. Dopamine–glutamate interactions. In: Dopamine in the CNS 2, 1st edn., pp. 117–133. Springer, Berlin.

    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. J. Neurosci. 26(13), 3567–3583.

    Article  Google Scholar 

  • Lee, S.H., Wynn, J.K., Green, M.F., Kim, H., Lee, K.J., Nam, M., Park, J.K., Chung, Y.C., 2006. Quantitative EEG and low resolution electromagnetic tomography (LORETA) imaging of patients with persistent auditory hallucinations. Schizophr. Res. 83(2–3), 111–119.

    Article  Google Scholar 

  • Levin, S.A., Chao, D., 1999. Herding behaviour: The emergence of large-scale phenomena from local interactions. In: Differ. Equ. with Appl. Biol. Fields Institute Communications, pp. 81–96. AMS, Providence.

    Google Scholar 

  • Light, G.A., Hsu, J.L., Hsieh, M.H., Meyer-Gomes, K., Sprock, J., Swerdlow, N.R., Braff, D.L., 2006. Gamma band oscillations reveal neural network cortical coherence dysfunction in schizophrenia patients. Biol. Psychiatry 60(11), 1231–1240.

    Article  Google Scholar 

  • Magill, P.J., Sharott, A., Bolam, J.P., Brown, P., 2004. Brain state-dependency of coherent oscillatory activity in the cerebral cortex and basal ganglia of the rat. J. Neurophysiol. 92, 2122–2136.

    Article  Google Scholar 

  • Marin, O., Anderson, S.A., Rubenstein, J.L., 2000. Origin and molecular specification of striatal interneurons. J. Neurosci. 20(16), 6063–6076.

    Google Scholar 

  • Meyerson, B.A., Linderoth, B., Karlsson, H., Ungerstedt, U., 1990. Microdialysis in the human brain: extracellular measurements in the thalamus of Parkinsonian patients. Life Sci. 46, 301–308.

    Article  Google Scholar 

  • Moghaddam, B., 2003. Bringing order to the glutamate chaos in schizophrenia. Neuron 40, 881–884.

    Article  Google Scholar 

  • Moghaddam, B., Adams, B.W., 1998. Reversal of phencyclidine effects by a group II metabotropic glutamate receptor agonist in rats. Science 281, 1349–1352.

    Article  Google Scholar 

  • Moghaddam, B., Krystal, J.H., 2003. The neurochemistry of schizophrenia In: Schizophrenia, 2nd edn., pp. 349–364. Blackwell Science, Oxford.

    Google Scholar 

  • Nakanishi, H., Kita, H., Kitai, S.T., 1987. Intracellular study of rat substantia nigra pars reticulata neurons in an in vitro slice preparation: electrical membrane properties and response characteristics to subthalamic stimulation. Brain Res. 437, 45–55.

    Article  Google Scholar 

  • Noori, H.R., 2008. The predominance of electric transport in synaptic transmission. In: Nature Neuroscience Proceedings.

  • Noori, H.R., 2009. Averaging transformations of synaptic potentials on networks. Preprint.

  • Parnas, H., Hovav, G., Parnas, I., 1989. Effect of Ca2+ diffusion on the time course of neurotransmitter release. Biophys. J. 55, 859–874.

    Article  Google Scholar 

  • Parnas, H., Segel, L., Dudel, J., Parnas, I., 2000. Autoreceptors, membrane potential and the regulation of transmitter release. Trends Neurosci. 23, 60–68.

    Article  Google Scholar 

  • Pavliotis, G.A., Stuart, A.M., 2008. Multiscale Methods: Averaging and Homogenization. Springer, Berlin.

    MATH  Google Scholar 

  • Pediaditakis, N., 2006. Considering the major mental disorders as clinical expressions of periodic pathological oscillations of the overall operating mode of brain function. Med. Hypotheses 67(2), 395–400.

    Article  Google Scholar 

  • Ragsdale, C.W. Jr., Graybiel, A.M., 1990. A simple ordering of neocortical areas established by the compartmental organization of their striatal projections. Proc. Natl. Acad. Sci. USA 87(16), 6196–6199.

    Article  Google Scholar 

  • Ronne-Engstrom, E., Hillered, L., Flink, R., Spannare, B., Ungerstedt, U., Carlson, H., 1992. Intracerebral microdialysis of extracellular amino acids in the human epileptic focus. J. Cereb. Blood Flow Metab. 12, 873–876.

    Google Scholar 

  • Rubin, J., Terman, D., 2002. Geometric singular perturbation analysis of neuronal dynamics. In: Fiedler, B. (Ed.), Handbook of Dynamical Systems II: Toward Applications, pp. 93–146. Elsevier, Amsterdam.

    Chapter  Google Scholar 

  • Rubin, J., Terman, D., 2004. High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model. J. Comput. Neurosci. 16, 211–235.

    Article  Google Scholar 

  • Sela, R., Segel, L., Parnas, I., Parnas, H., 2005. Release of neurotransmitter induced by Ca2+-uncaging: Reexamination of the Ca-voltage hypothesis for release. J. Comput. Neurosci. 19, 5–20.

    Article  MathSciNet  Google Scholar 

  • Shenton, M.E., Dickey, C.C., Frumin, M., McCarley, R.W., 2001. A review of MRI findings in schizophrenia. Schizophr. Res. 49(1–2), 1–52.

    Article  Google Scholar 

  • Sunol, C., Tusell, J.M., Gelpi, E., Rodriguez-Farre, E., 1988. Convulsant effect of lindane and regional brain concentration of GABA and dopamine. Toxicology 49, 247–252.

    Article  Google Scholar 

  • Ungerstedt, U., 1984. Measurement of neurotransmitter release by intracranial dialysis. In: Measurement of Neurotransmitter Release in Vivo, pp. 81–105. Wiley, Chichester.

    Google Scholar 

  • Van der Stelt, O., Belger, A., Lieberman, J.A., 2004. Macroscopic fast neuronal oscillations and synchrony in schizophrenia. Proc. Natl. Acad. Sci. USA 101(51), 17567–17568.

    Article  Google Scholar 

  • Wassle, H., Chun, M.H., 1988. Dopaminergic and indoleamine-accumulating amacrine cell express GABA-like immunoreactivity in the cat retina. J. Neurosci. 8, 3383–3394.

    Google Scholar 

  • Winograd, M., Destexhe, A., Sanchez-Vives, M.V., 2008. Hyperpolarization-activated graded persistent activity in the prefrontal cortex. PNAS 105(20), 7298–7303.

    Article  Google Scholar 

  • Yelnik, J., Francois, C., Percheron, G., Tande, D., 1991. Morphological taxonomy of the neurons of the primate striatum. J. Comput. Neurol. 313(2), 273–294.

    Article  Google Scholar 

  • Yusim, K., Parnas, H., Segel, L., 1999. Theory of fast neurotransmitter release control based on voltage-dependent interaction between autoreceptors and proteins of the exocytotic machinery. Bull. Math. Biol. 61, 701–725.

    Article  Google Scholar 

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Authors and Affiliations

  1. Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany

    Hamid Reza Noori

  2. Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Willi Jäger

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  1. Hamid Reza Noori
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  2. Willi Jäger
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Correspondence to Hamid Reza Noori.

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Noori, H.R., Jäger, W. Neurochemical Oscillations in the Basal Ganglia. Bull. Math. Biol. 72, 133–147 (2010). https://doi.org/10.1007/s11538-009-9441-7

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