Non-equilibrium encoding of time-dependent input signals by neurons with effective refractoriness

Abstract

Event Abstract Back to Event Non-equilibrium encoding of time-dependent input signals by neurons with effective refractoriness Moritz Deger1*, Moritz Helias2, Stefano Cardanobile1, Fatihcan M. Atay3 and Stefan Rotter1 1 Albert-Ludwig University, Bernstein Center Freiburg & Faculty of Biology, Germany 2 Brain Science Institute, RIKEN, Japan 3 Max Planck Institute for Mathematics in the Sciences, MPI, Germany Spike trains emitted by cortical neurons can be effectively described by stochastic point processes. The Poisson process with absolute refractoriness is a particularly simple point process, which admits the mathematical analysis of its dynamic properties. As we show, through the generalization to randomly distributed refractory times (Fig. A), this process can represent a large class of well-known renewal processes, including certain types of gamma- and log-normal processes. These are frequently used models for stationary neuronal spike trains. To study the non-equilibrium dynamics of ensembles of such processes we employ a description in terms of the occupation numbers of two states: Active and refractory. These occupation numbers follow a distributed delay differential equation. Based on this dynamics, the time-dependent spike rate of an ensemble of processes encoding an arbitrary input trajectory can be studied. In particular, we consider the case of a step change of the input rate, which induces a stochastic transient of the output spike rate (Fig. B). Moreover, for the periodic response to periodic input profiles, we obtain the mapping of the discrete spectra of input and output, by which all harmonics are coupled linearly, with coefficients depending on the refractoriness. For the special case of cosine input and a fixed refractory time, we find resonances, phase jumps and frequency doubling in the time-dependent ensemble spike rate. Since a large class of renewal processes can be represented as Poisson processes with random refractory time, our approach represents a widely applicable framework to define and analyze non-stationary point process models of neural activity. Figure 1: Ensemble of Poisson processes with random refractoriness, with different widths of the refractory time distribution. A: Probability density of refractory time (dotted lines) and normalized hazard function for constant input rate (solid lines). B: Transients of the ensemble rate upon step change of the input rate at t=0. Theoretical result (solid lines) and simulation of an ensemble of 106 processes averaged over 225 trials (crosses). Error bars denote the standard deviation over trials. Figure 1 Keywords: computational neuroscience Conference: Bernstein Conference on Computational Neuroscience, Berlin, Germany, 27 Sep - 1 Oct, 2010. Presentation Type: Presentation Topic: Bernstein Conference on Computational Neuroscience Citation: Deger M, Helias M, Cardanobile S, Atay FM and Rotter S (2010). Non-equilibrium encoding of time-dependent input signals by neurons with effective refractoriness. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference on Computational Neuroscience. doi: 10.3389/conf.fncom.2010.51.00024 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 20 Sep 2010; Published Online: 23 Sep 2010. * Correspondence: Dr. Moritz Deger, Albert-Ludwig University, Bernstein Center Freiburg & Faculty of Biology, Freiburg, Germany, md-web@gmx.org Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Moritz Deger Moritz Helias Stefano Cardanobile Fatihcan M Atay Stefan Rotter Google Moritz Deger Moritz Helias Stefano Cardanobile Fatihcan M Atay Stefan Rotter Google Scholar Moritz Deger Moritz Helias Stefano Cardanobile Fatihcan M Atay Stefan Rotter PubMed Moritz Deger Moritz Helias Stefano Cardanobile Fatihcan M Atay Stefan Rotter Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.