Modeling firing-rate dynamics: From spiking to firing-rate networks

Abstract

Event Abstract Back to Event Modeling firing-rate dynamics: From spiking to firing-rate networks Evan S. Schaffer1* and L. F. Abbott1 1 Columbia University, United States Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models have the obvious shortcoming of using a single time constant (typically a membrane or synaptic time constant) to describe all changes in rate, and they require neurons in a network to fire asynchronously. This is likely to be violated in many cases; in fact, transient synchronization of subgroups of neurons may be an important mechanism for generating rapid behavioral responses. To address this issue without losing the advantages associated with a simple firing-rate description, we have developed a form of firing-rate model based on an approximate Fokker-Planck analysis. A Fokker-Planck equation can be used to describe the distribution of membrane potentials for a population of neurons receiving noisy input. However, most methods for approximating solutions to this type of equation lead to considerably more complex equations than are practical for large networks. For example, there is no closed-form solution describing a population of Integrate-and-Fire (IAF) neurons receiving arbitrary time-varying input. A linear approximation to the response can be calculated, yielding impressively high accuracy, but it involves cumbersome equations (e.g. Brunel & Hakim, 1999; Mattia & Del Giudice, 2002; Ostojic et al., 2009). We show here that in a variant of this model, the Quadratic IAF, the fully nonlinear rate response can be approximated in a surprisingly simple form. Importantly, this approximate solution makes no assumptions about the shape, amplitude, or continuity of the input current. With an understanding of how dynamic external inputs drive firing rates for both asynchronous and synchronous populations of neurons, we study how units described in this way can be linked to describe the firing-rate dynamics of spiking networks with various patterns of synaptic connectivity. We find that the novel firing-rate model captures the time-varying firing-rates of the spiking network across a wide range of parameters. This holds equally well in parameter ranges where the asynchronous state is stable, and where highly synchronized firing occurs. Furthermore, the model also reproduces the dynamics of transient synchronization, which can be quite complicated. Finally, we show that the rich firing dynamics of a network of both excitatory and inhibitory neurons can be well approximated by a coupled E-I rate network. The simplicity of the model we have derived makes it highly amenable to use as the basis for network models. This will hopefully make tractable the study of the dynamics of large networks. Conference: Computational and Systems Neuroscience 2010, Salt Lake City, UT, United States, 25 Feb - 2 Mar, 2010. Presentation Type: Poster Presentation Topic: Poster session II Citation: Schaffer ES and Abbott LF (2010). Modeling firing-rate dynamics: From spiking to firing-rate networks. Front. Neurosci. Conference Abstract: Computational and Systems Neuroscience 2010. doi: 10.3389/conf.fnins.2010.03.00269 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: 05 Mar 2010; Published Online: 05 Mar 2010. * Correspondence: Evan S Schaffer, Columbia University, New York, United States, ess2129@columbia.edu 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 Evan S Schaffer L. F Abbott Google Evan S Schaffer L. F Abbott Google Scholar Evan S Schaffer L. F Abbott PubMed Evan S Schaffer L. F Abbott 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.