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

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Abstract

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

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References

  • Baranauskas, G., Tkatch, T., & Surmeier, D. J. (1999). Delayed rectifier current in rat globus pallidus neurons are attributable to Kv2.1 and Kv3.1/3.2 K+ channels. Journal of Neuroscience, 19, 6394–6404.

    PubMed  CAS  Google Scholar 

  • Baufreton, J., Kirkham, E., Atherton, J. F., Menard, A., Magill, P. J., Bolam, J. P., et al. (2009). Sparse but selective and potent synaptic transmission from the globus pallidus to subthalamic nucleus. Journal of Neurophysiology, 102, 532–545.

    Article  PubMed  CAS  Google Scholar 

  • Bevan, M. D., Wilson, C. J., Bolam, J. P., & Magill, P. J. (2000). Equilibrium potential of GABAA current and implications for rebound burst firing in rat subthalamic neurons in vitro. Journal of Neurophysiology, 83, 3169–3172.

    PubMed  CAS  Google Scholar 

  • Bevan, M. D., Atherton, J. F., & Baufreton, J. (2006). Cellular principles underlying normal and pathological activity in the subthalamic nucleus. Current Opinion in Neurobiology, 16, 621–628.

    Article  PubMed  CAS  Google Scholar 

  • Bolam, J. P., Hanley, J. J., Booth, P. A. C., & Bevan, M. D. (2000). Synaptic organisation of the basal ganglia. Journal of Anatomy, 196, 527–542.

    Article  PubMed  CAS  Google Scholar 

  • Brown, P., Oliviero, A., Mazzone, P., Insola, A., Tonali, P., & Di Lazzaro, V. (2001). Dopamine dependency of oscillations between subthalamic nucleus and pallidum in Parkinson's disease. Journal of Neuroscience, 21, 1033–1038.

    PubMed  CAS  Google Scholar 

  • Car, D. B., Day, M., Cantrell, A. R., Held, J., Scheuer, T., Catterall, W. A., et al. (2003). Transmitter modulation of slow, activity-dependent alterations in sodium channel availability endows neurons with a novel form of cellular plasticity. Neuron, 39, 793–806.

    Article  Google Scholar 

  • Cooper, A. J., & Stanford, I. M. (2000). Electrophysiological and morphological characteristics of three subtypes of rat globus pallidus neurone in vitro. Journal de Physiologie, 527, 291–304.

    Article  CAS  Google Scholar 

  • DeLong, M. R., Crutcher, M. D., & Georgopoulos, A. P. (1985). Primate globus pallidus and subthalamic nucleus: functional organization. Journal of Neurophysiology, 53, 530–543.

    PubMed  CAS  Google Scholar 

  • Destexhe, A., Mainen, Z. F., & Sejnowski, T. J. (1998). Kinetic models of synaptic transmission. In C. Koch & I. Segev (Eds.), Methods in neural modeling (pp. 1–25). Cambridge: MIT.

    Google Scholar 

  • Ermentrout, B. (1996). Type I membranes, phase resetting curves, and synchrony. Neural Computation, 8, 979–1001.

    Article  PubMed  CAS  Google Scholar 

  • Ermentrout, G. B., & Kopell, N. (1984). Frequency plateaus in a chain of weakly coupled oscillators, I. SIAM Journal on Mathematical Analysis, 15, 215–237.

    Article  Google Scholar 

  • Günay, C., Edgerton, J. R., & Jaeger, D. (2008). Channel density distributions explain spiking variability in the globus pallidus: a combined physiology and computer simulation database approach. Journal of Neuroscience, 28, 7476–7491.

    Article  PubMed  Google Scholar 

  • Hallworth, N. E., & Bevan, M. D. (2005). Globus pallidus neurons dynamically regulate the activity pattern of subthalamic nucleus neurons through the frequency-dependent activation of postsynaptic GABAA and GABAB receptors. Journal of Neuroscience, 25, 6304–6315.

    Article  PubMed  CAS  Google Scholar 

  • Hoppensteadt, F. C., & Izhikevich, E. M. (1997). Weakly connected neural networks. New York: Springer.

    Book  Google Scholar 

  • Kita, H., & Kitai, S. T. (1994). The morphology of globus pallidus projection neurons in the rat: an intracellular staining study. Brain Research, 636, 308–319.

    Article  PubMed  CAS  Google Scholar 

  • Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence. Berlin: Springer.

    Book  Google Scholar 

  • Ljungstrom, T., Grunnet, M., Jensen, B. S., & Olesen, S. P. (2003). Functional coupling between hetrologously expressed dopemine D(2) receptors and KCNQ channels. Pflügers Archiv, 446, 684–694.

    Article  PubMed  CAS  Google Scholar 

  • Magill, P. J., Bolam, J. P., & Bevan, M. D. (2000). Relationship of activity in the subthalamic nucleus-globus pallidus network to cortical electroencephalogram. Journal of Neuroscience, 20, 820–833.

    PubMed  CAS  Google Scholar 

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

    PubMed  CAS  Google Scholar 

  • Nomura, M., Fukai, T., & Aoyagi, T. (2003). Synchrony of fast-spiking interneurons interconnected by GABAergic and electrical synapses. Neural Computation, 15, 2179–2198.

    Article  PubMed  Google Scholar 

  • Pfeuty, B., Mato, G., Golomb, D., & Hansel, D. (2003). Electrical synapses and synchrony: the role of intrinsic currents. Journal of Neuroscience, 23, 6280–6294.

    PubMed  CAS  Google Scholar 

  • Plenz, D., & Kitai, S. T. (1999). A basal ganglia pacemaker formed by the subthalamic nucleus and external globus pallidus. Nature, 400, 677–682.

    Article  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 tremulous 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine vervet model of parkinsonism. Journal of Neuroscience, 20, 8559–8571.

    PubMed  CAS  Google Scholar 

  • Rivlin-Etzion, M., Marmor, O., Heimer, G., Raz, A., Nini, A., & Bergman, H. (2006). Basal ganglia oscillations and pathophysiology of movement disorders. Current Opinion in Neurobiology, 16, 629–637.

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • Schultheiss, N. W., Edgerton, J. R., & Jaeger, D. (2010). Phase response curve analysis of a full morphological globus pallidus neuron model reveals distinct perisomatic and dendritic modes of synaptic integration. Journal of Neuroscience, 30, 2767–2782.

    Article  PubMed  CAS  Google Scholar 

  • Stanford, I. M. (2003). Independent neuronal oscillators of the rat globus pallidus. Journal of Neurophysiology, 89, 1713–1717.

    Article  PubMed  CAS  Google Scholar 

  • Stiefel, K. M., Gutkin, B. S., & Sejnowski, T. J. (2008). Cholinergic neuromodulation changes phase response curve shape and type in cortical pyramidal neurons. PLoS One, 3, e3947.

    Article  PubMed  Google Scholar 

  • Surmeier, D. J., Eberwine, J., Wilson, C. J., Cao, Y., Stefani, A., & Kitai, S. T. (1992). Dopamine receptor subtypes colocalize in rat striatonigral neurons. Proc Natl Acad Sci USA, 89, 10178–10182.

    Article  PubMed  CAS  Google Scholar 

  • Surmeier, D. J., Ding, J., Day, M., Wang, Z., & Shen, W. (2007). D1 and D2 dopamine-receptor modulation of striatal glutamatergic signaling in striatal medium spiny neurons. Trends in Neurosciences, 30, 228–235.

    Article  PubMed  CAS  Google Scholar 

  • Takekawa, T., Aoyagi, T., & Fukai, T. (2007). Synchronous and asynchronous bursting states: role of intrinsic neural dynamics. Journal of Computational Neuroscience, 23, 189–200.

    Article  PubMed  Google Scholar 

  • Terman, D., Rubin, J. E., Yew, A. C., & Wilson, C. J. (2002). Activity patterns in a model for the subthalamopallidal network of the basal ganglia. Journal of Neuroscience, 22, 2963–2976.

    PubMed  CAS  Google Scholar 

  • Wang, X. J., & Buzsáki, G. (1996). Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. Journal of Neuroscience, 16, 6402–6413.

    PubMed  CAS  Google Scholar 

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Acknowledgments

We thank Takeshi Takekawa for helpful comments on the numerical calculation of phase response curves.

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Authors and Affiliations

  1. Graduate School of Science and Engineering, Ritsumeikan University, Kusatsu, Shiga, 525-8577, Japan

    Tomohiro Fujita

  2. Laboratory for Neural Circuit Theory, RIKEN Brain Science Institute, Wako, Saitama, 351-0198, Japan

    Tomoki Fukai

  3. Department of Human and Computer Intelligence, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga, 525-8577, Japan

    Katsunori Kitano

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  1. Tomohiro Fujita
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  2. Tomoki Fukai
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  3. Katsunori Kitano
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Correspondence to Katsunori Kitano.

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Fujita, T., Fukai, T. & Kitano, K. Influences of membrane properties on phase response curve and synchronization stability in a model globus pallidus neuron. J Comput Neurosci 32, 539–553 (2012). https://doi.org/10.1007/s10827-011-0368-2

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  • DOI: https://doi.org/10.1007/s10827-011-0368-2

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