A generic property of the communication between neurons is the exchange of pulses at discrete time points, the action potentials. However, the prevalent theory of spiking neuronal networks of integrate-and-fire model neurons relies on two assumptions: the superposition of many afferent synaptic impulses is approximated by Gaussian white noise, equivalent to a vanishing magnitude of the synaptic impulses, and the transfer of time varying signals by neurons is assessable by linearization. Going beyond both approximations, we find that in the presence of synaptic impulses the response to transient inputs differs qualitatively from previous predictions. It is instantaneous rather than exhibiting low-pass characteristics, depends non-linearly on the amplitude of the impulse, is asymmetric for excitation and inhibition and is promoted by a characteristic level of synaptic background noise. These findings resolve contradictions between the earlier theory and experimental observations. Here we review the recent theoretical progress that enabled these insights. We explain why the membrane potential near threshold is sensitive to properties of the afferent noise and show how this shapes the neural response. A further extension of the theory to time evolution in discrete steps quantifies simulation artifacts and yields improved methods to cross check results.
Keywords: leaky integrate-and-fire model, perfect integrator, diffusion approximation, non-linear response, shot noise
Citation: Helias M, Deger M, Rotter S and Diesmann M (2011) Finite post synaptic potentials cause a fast neuronal response. Front. Neurosci. 5:19. doi: 10.3389/fnins.2011.00019
Received: 23 October 2010;
Accepted: 07 February 2011;
Published online: 24 February 2011.
Edited by:Wulfram Gerstner, Ecole Polytechnique Fédérale de Lausanne, Switzerland
Reviewed by:Wulfram Gerstner, Ecole Polytechnique Fédérale de Lausanne, Switzerland
Copyright: © 2011 Helias, Deger, Rotter and Diesmann. This is an open-access article subject to an exclusive license agreement between the authors and Frontiers Media SA, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are credited.
*Correspondence: Moritz Helias is a research scientist whose main interests are the dynamics of recurrent spiking neural networks, in particular how correlations are shaped by dynamical properties of neurons and the mutual interplay with synaptic plasticity. Since his graduation in theoretical physics at the University of Hamburg, he works at the interface of numerical simulations and theoretical descriptions. During his PhD studies of neuroscience at the Bernstein Center Freiburg he became a developer of the neural simulation software NEST. Currently he is a postdoc at the RIKEN Brain Science Institute. firstname.lastname@example.org