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Theory of neuronal spike densities for synchronous activity in cortical feed-forward networks
© Goedeke et al; licensee BioMed Central Ltd. 2008
Published: 11 July 2008
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 . 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 , 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 . 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.
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.
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