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Subthreshold Amplitude and Phase Resonance in Single Cells

Encyclopedia of Computational Neuroscience

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Synonyms

Membrane potential resonance; Membrane potential or subthreshold preferred frequency responses to oscillatory inputs

Definition

Subthreshold (or membrane potential) resonance refers to the ability of neurons to exhibit a peak in their voltage amplitude response to oscillatory input currents at a preferred (resonant) frequency.

Subthreshold (or membrane potential) phase-resonance refers to the ability of neurons to exhibit a zero-phase (or zero-phase-shift) response to oscillatory input currents at a nonzero (phase-resonant) frequency.

Linear subthreshold resonance refers to the subthreshold resonant properties (amplitude and phase) in linear models. In this entry we focus on 2D and 3D linear and linearized conductance-based models.

Detailed Description

Introduction

Subthreshold resonance has been observed in various neuron types in the hippocampus and the entorhinal cortex (Hutcheon and Yarom 2000; Pike et al. 2000; Schreiber et al. 2004; Zemankovics et al. 2010; Hu et al. 2002...

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References

  • Alexander JC, Doedel EJ, Othmer HG (1990) On the resonance structure in a forced excitable system. SIAM J Appl Math 50:1373–1418

    Article  Google Scholar 

  • Art JJ, Crawford AC, Fettiplace R (1986) Electrical resonance and membrane currents in turtle cochlear hair cells. Hear Res 22:31–36

    Article  CAS  PubMed  Google Scholar 

  • Castro-Alamancos MA, Rigas P, Tawara-Hirata Y (2007) Resonance (approximately 10 Hz) of excitatory networks in motor cortex: effects of voltage-dependent ion channel blockers. J Physiol 578:173–191

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Engel TA, Schimansky-Geier L, Herz AV, Schreiber S, Erchova I (2008) Subthreshold membrane-potential resonances shape spike-train patterns in the entorhinal cortex. J Neurophysiol 100:1576–1588

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Erchova I, Kreck G, Heinemann U, Herz AVM (2004) Dynamics of rat entorhinal cortex layer II and III cells: characteristics of membrane potential resonance at rest predict oscillation properties near threshold. J Physiol 560:89–110

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Gastrein P, Campanac E, Gasselin C, Cudmore RH, Bialowas A, Carlier E, Fronzaroli-Molinieres L, Ankri N, Debanne D (2011) The role of hyperpolarization-activated cationic current in spike-time precision and intrinsic resonance in cortical neurons in vitro. J Physiol 589:3753–3773

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Gutfreund Y, Yarom Y, Segev I (1995) Subthreshold oscillations and resonant frequency in guinea pig cortical neurons: physiology and modeling. J Physiol 483:621–640

    CAS  PubMed Central  PubMed  Google Scholar 

  • Haas JS, White JA (2002) Frequency selectivity of layer II stellate cells in the medial entorhinal cortex. J Neurophysiol 88:2422–2429

    Article  PubMed  Google Scholar 

  • Heys JG, Giacomo LM, Hasselmo ME (2010) Cholinergic modulation of the resonance properties of stellate cells in layer II of the medial entorhinal. J Neurophysiol 104:258–270

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conductance and excitation in nerve. J Physiol 117:500–544

    CAS  PubMed Central  PubMed  Google Scholar 

  • Hu H, Vervaeke K, Graham JFL, Storm J (2009) Complementary theta resonance filtering by two spatially segregated mechanisms in CA1 hippocampal pyramidal neurons. J Neurosci 29:14472–14483

    Article  CAS  PubMed  Google Scholar 

  • Hu H, Vervaeke K, Storm JF (2002) Two forms of electrical resonance at theta frequencies generated by M-current, h-current and persistent Na+ current in rat hippocampal pyramidal cells. J Physiol 545(3):783–805

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Hutcheon B, Miura RM, Puil E (1996a) Models of subthreshold membrane resonance in neocortical neurons. J Neurophysiol 76:698–714

    CAS  PubMed  Google Scholar 

  • Hutcheon B, Miura RM, Puil E (1996b) Subthreshold membrane resonance in neocortical neurons. J Neurophysiol 76:683–697

    CAS  PubMed  Google Scholar 

  • Hutcheon B, Miura RM, Yarom Y, Puil E (1994) Low threshold calcium current and resonance in thalamic neurons: a model of frequency preference. J Neurophysiol 71:583–594

    CAS  PubMed  Google Scholar 

  • Hutcheon B, Yarom Y (2000) Resonance oscillations and the intrinsic frequency preferences in neurons. Trends Neurosci 23:216–222

    Article  CAS  PubMed  Google Scholar 

  • Izhikevich E (2006) Dynamical systems in neuroscience: the geometry of excitability and bursting. MIT Press, Cambridge, MA

    Google Scholar 

  • Izhikevich EM (2001) Resonate-and-fire neurons. Neural Netw 14:883–894

    Article  CAS  PubMed  Google Scholar 

  • Izhikevich EM (2002) Resonance and selective communication via bursts in neurons having subthreshold oscillations. Biosystems 67:95–102

    Article  PubMed  Google Scholar 

  • Kopell N, Howard LN (1973) Plane wave solutions to reaction diffusion systems. Stud Appl Math 42:291–328

    Google Scholar 

  • Leung LS, Yu HW (1998) Theta-frequency resonance in hippocampal CA1 neurons in vitro demonstrated by sinusoidal current injection. J Neurophysiol 79:1592–1596

    CAS  PubMed  Google Scholar 

  • Pike FG, Goddard RS, Suckling JM, Ganter P, Kasthuri N, Paulsen O (2000) Distinct frequency preferences of different types of rat hippocampal neurons in response to oscillatory input currents. J Physiol 529:205–213

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Puil E, Gimbarzevsky B, Miura RM (1986) Quantification of membrane properties of trigeminal root ganglions in guinea pigs. J Neurophysiol 55:995–1016

    CAS  PubMed  Google Scholar 

  • Reinker S, Puil E, Miura RM (2004) Membrane resonance and stochastic resonance modulate firing patterns of thalamocortical neurons. J Comput Neurosci 16:15–25

    Article  PubMed  Google Scholar 

  • Richardson MJE, Brunel N, Hakim V (2003) From subthreshold to firing-rate resonance. J Neurophysiol 89:2538–2554

    Article  PubMed  Google Scholar 

  • Rotstein HG (2013) Frequency preference response to oscillatory inputs in two-dimensional neural models: a geometric approach to subthreshold amplitude and phase resonance. J Math Neurosci (In press)

    Google Scholar 

  • Rotstein HG, Nadim F (2013) Interaction between resonant and amplifying currents in two-dimensional neural models of frequency preference response to oscillatory input currents. J Comp Neurosci

    Google Scholar 

  • Rotstein HG, Oppermann T, White JA, Kopell N (2006) A reduced model for medial entorhinal cortex stellate cells: subthreshold oscillations, spiking and synchronization. J Comput Neurosci 21:271–292

    Article  PubMed  Google Scholar 

  • Schreiber S, Erchova I, Heinemann U, Herz AV (2004) Subthreshold resonance explains the frequency-dependent integration of periodic as well as random stimuli in the entorhinal cortex. J Neurophysiol 92:408–415

    Article  PubMed  Google Scholar 

  • Sciamanna G, J WC (2011) The ionic mechanism of gamma resonance in rat striatal fast-spiking neurons. J Neurophysiol 106:2936–2949

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Skinner FK (2006) Conductance-based models. Scholarpedia 1:1408

    Article  Google Scholar 

  • Tohidi V, Nadim F (2009) Membrane resonance in bursting pacemaker neurons of an oscillatory network is correlated with network frequency. J Neurosci 6427:6435

    Google Scholar 

  • Tseng H, Nadim F (2010) The membrane potential waveform on bursting pacemaker neurons is a predictor of their preferred frequency and the network cycle frequency. J Neurosci 30:10809–10819

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Wang WT, Wan YH, Zhu JL, Lei GS, Wang YY, Zhang P, Hu SJ (2006) Theta-frequency membrane resonance and its ionic mechanisms in rat subicular pyramidal neurons. Neuroscience 140:45–55

    Article  CAS  PubMed  Google Scholar 

  • Wu N, Hsiao CF, Chandler SH (2001) Membrane resonance and subthreshold membrane oscillations in mesencephalic v neurons: participants in burst generation. J Neurosci 21:3729–3739

    CAS  PubMed  Google Scholar 

  • Zemankovics R, Kali S, Páulsen O, Freund TF, Hájos N (2010) Differences in subthreshold resonance of hippocampal pyramidal cells and interneurons: the role of h-current and passive membrane characteristics. J Physiol 588:2109–2132

    Article  CAS  PubMed Central  PubMed  Google Scholar 

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Acknowledgments

The author wishes to thank Farzan Nadim and Frances Skinner for useful comments. This work was supported by NSF grant DMS-1313861 (HGR).

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    Horacio G. Rotstein

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  1. Horacio G. Rotstein
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Correspondence to Horacio G. Rotstein .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

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Rotstein, H.G. (2013). Subthreshold Amplitude and Phase Resonance in Single Cells. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_598-1

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  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_598-1

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  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7320-6

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Chapter history

  1. Latest

    Subthreshold Resonance and Phasonance in Single Neurons: 2D Models
    Published:
    13 November 2017

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_598-2

  2. Original

    Subthreshold Amplitude and Phase Resonance in Single Cells
    Published:
    08 February 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_598-1

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