Action Potential Onset Dynamics and the Response Speed of Neuronal Populations
 B. Naundorf,
 T. Geisel,
 F. Wolf
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The result of computational operations performed at the single cell level are coded into sequences of action potentials (APs). In the cerebral cortex, due to its columnar organization, large number of neurons are involved in any individual processing task. It is therefore important to understand how the properties of coding at the level of neuronal populations are determined by the dynamics of single neuron AP generation. Here, we analyze how the AP generating mechanism determines the speed with which an ensemble of neurons can represent transient stochastic input signals. We analyze a generalization of the θneuron, the normal form of the dynamics of TypeI excitable membranes. Using a novel sparse matrix representation of the FokkerPlanck equation, which describes the ensemble dynamics, we calculate the transmission functions for small modulations of the mean current and noise noise amplitude. In the highfrequency limit the transmission function decays as ω^{−γ}, where γ surprisingly depends on the phase θ_{ s } at which APs are emitted. If at θ_{ s } the dynamics is insensitive to external inputs, the transmission function decays as (i) ω^{−3} for the case of a modulation of a white noise input and as (ii) ω^{−2} for a modulation of the mean input current in the presence of a correlated and uncorrelated noise as well as (iii) in the case of a modulated amplitude of a correlated noise input. If the insensitivity condition is lifted, the transmission function always decays as ω^{−1}, as in conductance based neuron models. In a physiologically plausible regime up to 1 kHz the typical response speed is, however, independent of the highfrequency limit and is set by the rapidness of the AP onset, as revealed by the full transmission function. In this regime modulations of the noise amplitude can be transmitted faithfully up to much higher frequencies than modulations in the mean input current. We finally show that the linear response approach used is valid for a large regime of stimulus amplitudes.
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 Title
 Action Potential Onset Dynamics and the Response Speed of Neuronal Populations
 Journal

Journal of Computational Neuroscience
Volume 18, Issue 3 , pp 297309
 Cover Date
 20050601
 DOI
 10.1007/s1082700503298
 Print ISSN
 09295313
 Online ISSN
 15736873
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 population of spiking neurons
 spike luitiation
 dynamics integrateandfive model
 Industry Sectors
 Authors

 B. Naundorf ^{(1)}
 T. Geisel ^{(1)}
 F. Wolf ^{(1)}
 Author Affiliations

 1. MaxPlanckInstitut für Dynamik und Selbstorganisation and Fakultät für Physik, Universität Göttingen, 37073, Göttingen, Germany