Email updates

Keep up to date with the latest news and content from BMC Neuroscience and BioMed Central.

This article is part of the supplement: Seventeenth Annual Computational Neuroscience Meeting: CNS*2008

Open Access Poster presentation

Theory of neuronal spike densities for synchronous activity in cortical feed-forward networks

Sven Goedeke1, Tilo Schwalger2 and Markus Diesmann12*

Author Affiliations

1 Bernstein Center for Computational Neuroscience, Albert-Ludwigs-University, 79104 Freiburg, Germany

2 Computational Neuroscience Group, RIKEN Brain Science Institute, Wako-shi, Saitama 351-0106, Japan

For all author emails, please log on.

BMC Neuroscience 2008, 9(Suppl 1):P143  doi:10.1186/1471-2202-9-S1-P143

The electronic version of this article is the complete one and can be found online at:

Published:11 July 2008

© 2008 Goedeke et al; licensee BioMed Central Ltd.

Poster presentation

Synchronization of spiking activity in neuronal networks of the cortex has been proposed as a mechanism underlying higher brain functions. This idea is challenged by ongoing cortical activity generating large fluctuations in synaptic input, causing the neurons to operate in a noisy environment. The propagation of synchronized spiking in feed-forward subnetworks ("synfire chains") has been studied to demonstrate the feasibility of precise spike timing [1]. However, the theoretical analysis of even this toy model is impeded by the intricacy of calculating the distribution of spike times in response to time-dependent inputs. Therefore, most quantitative results rely on simulations or semi-numerical methods, and insight into the structure of the dynamics is limited. Recently [2], we showed that for a biophysically plausible integrate-and-fire neuron model the probability of emitting a response spike is concentrated on the rising phase of the membrane potential transient caused by synchronous input and that during this time the instantaneous spiking rate is governed by the derivative of this transient. These observations were confirmed by an ad hoc calculation of the neuron's spike density. A corresponding instantaneous rate model enabled us to investigate the synchronization dynamics analytically. Inherent to the approach, the theory for the spike density breaks down at the peak of the membrane potential transient and during its descent. Meanwhile based on an exact series expression for the first passage time density of differentiable random processes (Wiener-Rice series) new successful approximations have been presented [3]. Here, we use the first term of the series to approximate the spike density of a stochastic integrate-and-fire neuron model receiving time-dependent input.

The figure displays the densities of response spikes for four characteristic input parameters describing synchronous activity in feed-forward subnetworks (vertical: number of input spikes; horizontal: temporal dispersion of the input). Extending [2], the results of the new approximation (blue curves) are valid during the rising and the descending phase of the membrane potential transient and are in excellent agreement with the simulation results (gray curves). While in the earlier theory the relationship between output and input dispersion is independent of the amplitude of the input, the new theory resolves this degeneracy; it also holds in the less synchronized and subthreshold regime. We finally have a theory at hand covering the full dynamical range of synchronized spiking in cortical feed-forward networks. The approximation is valid for a wide range of relative time constants. In conclusion, our work provides a more fundamental theory for the earlier findings. The method has the potential to be applied to other time-dependent problems in computational neuroscience.

thumbnailFigure 1. Comparison of theoretical (blue) and simulated (gray) spike density of a population of leaky integrate-and-fire neurons in response to transient excitatory synaptic input caused by synchronous activity of presynaptic neurons. In the four panels, the number of input spikes decreases from top (95) to bottom (50) and their temporal precision from left (1 ms) to right (5 ms). The vertical axes are individually scaled.


Partially funded by DIP F1.2, BMBF Grant 01GQ0420 to the Bernstein Center for Computational Neuroscience Freiburg, EU Grant 15879 (FACETS), and German National Academic Foundation.


  1. Diesmann M, Gewaltig MO, Aertsen A: Stable propagation of synchronous spiking in cortical neural networks.

    Nature 1999, 402(6761):529-533. PubMed Abstract | Publisher Full Text OpenURL

  2. Goedeke S, Diesmann M: The mechanism of synchronization in feed-forward neuronal networks.

    New J Phys 2008, 10:015007. Publisher Full Text OpenURL

  3. Verechtchaguina T, Sokolov IM, Schimansky-Geier L: First passage time densities in resonate-and-fire models.

    Phys Rev E 2006, 73:031108. Publisher Full Text OpenURL