Skip to main content
SpringerLink
Log in

Subthreshold Antiresonance and Antiphasonance in Single Neurons: 3D Models

  • Living reference work entry
  • First Online:
Encyclopedia of Computational Neuroscience

Synonyms

Subthreshold antiphasonance: Membrane potential antiphasonance; Subthreshold antiresonance: Membrane potential (amplitude) antiresonance; Subthreshold or membrane potential antiphase resonance

Definitions

Subthreshold (or membrane potential) antiresonance refers to the ability of neurons to exhibit a minimum in their voltage amplitude response to oscillatory input currents at a nonzero input (antiresonant) frequency.

Subthreshold (or membrane potential) antiphasonance refers to the ability of neurons to exhibit a zero-phase (or zero-phase-shift) response to oscillatory inputs currents at a nonzero (antiphasonant) frequency separating between delayed and advance responses for frequencies smaller and larger than the antiphasonant frequency, respectively.

Linear subthreshold antiresonance and antiphasonance refers to the occurrence of these phenomena in linear systems.

In this article, we focus on the description of antiresonance and antiphasonance in 3D linearized...

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

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

    Google Scholar 

  • Fox DM, Rotstein HG, Nadim F (2016) Neuromodulation produces complex changes in resonance profiles of neurons in an oscillatory network. Society for Neuroscience Abstracts, 811.08

    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 

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

    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 

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

    Article  PubMed  Google Scholar 

  • Rotstein HG (2017a) 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 (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, 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 

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

    Article  Google Scholar 

Download references

Acknowledgements

The author wishes to thank Farzan Nadim, David Fox and Eran Stark for useful comments.

This work was supported by NSF grants DMS-1313861 (HGR) and CRCNS-DMS-1608077 (HGR).

The author is grateful to the Courant Institute of Mathematical Sciences at New York University.

Author information

Authors and Affiliations

  1. Federated Department of Biological Sciences, Rutgers University and New Jersey Institute of Technology, Newark, NJ, 07102, USA

    Horacio G. Rotstein

  2. Institute for Brain and Neuroscience Research, New Jersey Institute of Technology and Rutgers University, Newark, NJ, 07102, USA

    Horacio G. Rotstein

Authors
  1. Horacio G. Rotstein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

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

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Science+Business Media LLC

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Rotstein, H.G. (2018). Subthreshold Antiresonance and Antiphasonance in Single Neurons: 3D 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_100659-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_100659-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-7320-6

  • Online ISBN: 978-1-4614-7320-6

  • eBook Packages: Springer Reference Biomedicine and Life SciencesReference Module Biomedical and Life Sciences

Publish with us

Policies and ethics

Search

Navigation