Biological Cybernetics

, Volume 99, Issue 4–5, pp 303–318 | Cite as

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

  • Michele Giugliano
  • Giancarlo La Camera
  • Stefano Fusi
  • Walter Senn
Review

Abstract

The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane’s inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite–soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.

Keywords

Populations of spiking neurons Dynamics Integrate-and-fire model Patch clamp Calcium spikes 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Michele Giugliano
    • 1
    • 2
  • Giancarlo La Camera
    • 3
  • Stefano Fusi
    • 4
    • 5
  • Walter Senn
    • 6
  1. 1.Laboratory of Neural MicrocircuitryEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Theoretical NeurobiologyUniversity of AntwerpWilrijkBelgium
  3. 3.Laboratory of NeuropsychologyNational Institute of Mental Health, National Institutes of HealthBethesdaUSA
  4. 4.Center for Theoretical Neuroscience, College of Physicians and SurgeonsColumbia UniversityNew YorkUSA
  5. 5.Institute of NeuroinformaticsUniversity of Zurich-ETHZurichSwitzerland
  6. 6.Department of PhysiologyUniversity of BernBernSwitzerland

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