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Subthreshold Resonance and Phasonance in Single Neurons: 2D Models

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Encyclopedia of Computational Neuroscience

Synonyms

Subthreshold resonance: Membrane potential (amplitude) resonance

Subthreshold phasonance: Membrane potential phasonance, subthreshold or membrane potential phase resonance

Definitions

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) phasonance refers to the ability of neurons to exhibit a zero-phase (or zero-phase-shift) response to oscillatory inputs currents at a nonzero (phasonant) frequency separating between advanced and delayed responses for frequencies smaller and larger than the phasonant frequency, respectively.

Linear subthreshold resonance and phasonance refers to the occurrence of these phenomena in linear systems.

Nonlinear subthreshold resonance and phasonancerefers to the occurrence of these phenomena in nonlinear systems where at least one of the linearity principles is not...

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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 

  • Boyce WE, DiPrima RC (2009) Elementary differential equations and boundary value problems. Wiley, Hoboken

    Google Scholar 

  • Canavier C (2014) Phase response curves: an overview. In: Jaeger D, Jung R (ed) Encyclopedia of computational neuroscience. Springer, New York, pp 80–82. SpringerReference (www.springerreference.com)

  • 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  Google Scholar 

  • D’angelo E, Nieus T, Maffei A, Armano S, Rossi P, Taglietti V, Fontana A, Naldi G (2001) Theta-frequency bursting and resonance in cerebellar granule cells: experimental evidence and modeling of a slow K+ - dependent mechanism. J Neurosci 21:759–770

    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  PubMed Central  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  PubMed Central  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  PubMed Central  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

    Article  CAS  PubMed  PubMed Central  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  PubMed Central  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

    Article  CAS  PubMed  PubMed Central  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  PubMed Central  Google Scholar 

  • Hu H, Vervaeke K, Graham JF, Storm LJ (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 

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

    Article  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, Miura RM, Puil E (1996a) Subthreshold membrane resonance in neocortical neurons. J Neurophysiol 76:683–697

    CAS  PubMed  Google Scholar 

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

    CAS  PubMed  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 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Book  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 

  • Mikiel-Hunter J, Kotak V, Rinzel J (2016) High-frequency resonance in the gerbil medial superior olive. PLoS Comput Biol 12:1005166

    Article  Google Scholar 

  • Moca VV, Nicolic D, Singer W, Muresan R (2014) Membrane resonance enables stable robust gamma oscillations. Cereb Cortex 24:119–142

    Article  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  PubMed Central  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 

  • Remme MWH, Lengyel M, and Gutkin BS (2012) A theoretical framework for the dynamics of multiple intrinsic oscillators in single neurons. In: Schultheiss NW, Prinz AA, Butera RA (eds) Phase response curves in neuroscience: theory, experiments and analysis. Spring Series in Computational Neuroscience, Springer, pp 53–72

    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 (2014) Frequency preference response to oscillatory inputs in two-dimensional neural models: a geometric approach to subthreshold amplitude and phase resonance. J Math Neurosci 4:11

    Article  PubMed  PubMed Central  Google Scholar 

  • Rotstein HG (2015) Subthreshold amplitude and phase resonance in models of quadratic type: nonlinear effects generated by the interplay of resonant and amplifying currents. J Comput Neurosci 38:325–354

    Article  PubMed  Google Scholar 

  • Rotstein HG (2017a) Subthreshold antiresonance and antiphasonance in single cells: 3D models. In: Jaeger D, Jung R (ed) Encyclopedia of computational neuroscience. Springer, New York. SpringerReference (www.springerreference.com)

  • Rotstein HG (2017b) The shaping of intrinsic membrane potential oscillations: positive/negative feedback, ionic resonance/amplification, nonlinearities and time scales. J Comput Neurosci 42:133–166

    Article  PubMed  Google Scholar 

  • Rotstein HG (2017c) Spiking resonances in models with the same slow resonant and fast amplifying currents but different subthreshold dynamic properties. J Comp Neurosci 43:243–271

    Google Scholar 

  • Rotstein HG (2017d) Resonance modulation, annihilation and generation of antiresonance and antiphasonance in 3D neuronal systems: interplay of resonant and amplifying currents with slow dynamics. J Comput Neurosci 43:35–63

    Article  PubMed  Google Scholar 

  • Rotstein HG, Nadim F (2014) Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents. J Comput Neurosci 37:9–28

    Article  PubMed  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, Wilson CJ (2011) The ionic mechanism of gamma resonance in rat striatal fast-spiking neurons. J. Neurophysiol 106:2936–2949

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  Google Scholar 

  • Stark E, Eichler R, Roux L, Fujisawa S, Rotstein HG, Buzsáki G (2013) Inhibition-induced theta resonance in cortical circuits. Neuron 80:1263–1276

    Article  CAS  PubMed  Google Scholar 

  • Tchumatchenko T, Clopath C (2014) Oscillations emerging from noise-driven steady state in networks with electrical synapses and subthreshold resonance. Nature Comm 5:5512

    Article  Google Scholar 

  • Tikidji-Hamburyan RA, Mart’ınez JJ, White JA, Canavier C (2015) Resonant interneurons can increase robustness of gamma oscillations. J. Neurosci 35:15682–15695

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Tohidi V, Nadim F (2009) Membrane resonance in bursting pacemaker neurons of an oscillatory network is correlated with network frequency. J Neurosci 29:6427–6435

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Touboul J (2008) Bifurcation analysis of a general class of nonlinear integrate-and-fire neurons. SIAM J Appl Math 68:1045–1079

    Article  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  PubMed Central  Google Scholar 

  • Ulrich D (2002) Dendritic resonance in rat neocortical pyramidal cells. J Neurophysiol 87:2753–2759

    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 

  • White JA, Budde T, Kay AR (1995) A bifurcation analysis of neuronal subthreshold oscillations. Biophys J 69:1203–1217

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Winfree AT (2001) The geometry of biological time, 2nd edn. Springer, New York

    Book  Google Scholar 

  • Wu N, Hsiao C-F, 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, Káli S, Paulsen O, Freund TF, Hájos N (2010) Differences in subthershold resonance of hippocampal pyramidal cells and interneurons: the role of h-current and passive membrane characteristics. J Physiol 588:2109–2132

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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Acknowledgments

The author wishes to thank Farzan Nadim, Frances Skinner and Eran Stark for useful comments. This work was supported by NSF grant DMS-1313861 (HGR) and DMS-1608077 (HGR). The author is grateful to the Courant Institute of Mathematical Sciences at New York University. The author is grateful to the Courant Institute of Mathematical Sciences at New York University.

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Correspondence to Horacio G. Rotstein .

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Rotstein, H.G. (2018). Subthreshold Resonance and Phasonance in Single Neurons: 2D Models. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_598-2

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

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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