Elsevier

Neurocomputing

Volumes 58–60, June 2004, Pages 117-121
Neurocomputing

Consequences of realistic network size on the stability of embedded synfire chains

https://doi.org/10.1016/j.neucom.2004.01.031Get rights and content

Abstract

Cortical activity in vivo is characterized by asynchronous irregular spiking. Additionally, precise spike synchronization is observed with respect to the experimental protocol. Attempting to model this behavior, theoretical studies have focused on two extreme cases: random and feed-forward networks (synfire chains). Here, we combine both descriptions by successively converting an isolated synfire chain into a completely embedded one. This method systematically reveals the effects of different aspects of the embedding scheme on the stability of the system. At realistic network sizes common-input correlations play a major role. Surprisingly, their impact is reduced by the dynamics of the embedding recurrent network.

Introduction

In the absence of specific stimuli, cortical activity in vivo is characterized by asynchronous irregular firing of the neurons at a low rate. However, the same system exhibits precise spatio-temporal spike patterns with respect to the experimental protocol (e.g. [9], [10]). During the past decade several theoretical studies (e.g. [3]) explored the existence and stability of asynchronous irregular activity states in random networks of integrate-and-fire neurons. The mechanism of spike synchronization and the generation of spatio-temporal spike patterns in divergent-convergent feed-forward networks (“synfire chains”, [1]) is also well understood (e.g. [5]).

Recent simulation studies pointed out the destabilizing effect of introducing non-random elements into balanced random networks. The embedding of feed-forward subnetworks increases the tendency of the whole network to start oscillating in a synchronous manner [2], [7]. This finding is challenging for a concept of the cortical network in which synfire chains serve as the building blocks or substrate for processing. So far, theoretical descriptions of destabilizing mechanisms in synfire chains have been documented only for the simple case, in which the “embedding” is modeled by providing the neurons in an isolated chain with independent Poissonian background inputs [2], [11]. Both studies derive an upper bound wcrit on the number w of neurons in each synfire layer, above which the asynchronous ground state is unstable. This upper bound on group size is well above the minimal w required for a stable propagation of synchronous spike volleys [4]. Thus, there is a range of w where a stable asynchronous ground state and a stable synchronous mode coexist. The question arises whether this state space structure required for functionally relevant synfire chains is also exhibited by more realistic network architectures.

In the present study, we systematically investigate how the interactions between a feed-forward and a random architecture affect the stability of the asynchronous state. For this purpose we focus on three aspects which were not taken into account in the case of an isolated synfire chain with uncorrelated Poissonian background:

  • (i)

    Cortical neurons receive a large amount of their synaptic inputs from the local area (≈1mm3, [6]). Consequently, it is reasonable to assume that neurons of the same layer in a synfire chain share not only the inputs of their preceding group but also a certain amount of inputs from the background. Hence, the total background inputs of different neurons in a synfire group are correlated, even if the individual inputs are described by Poisson processes.

  • (ii)

    Due to finite size effects, the asynchronous irregular states in unstructured random networks exhibit some small degree of global oscillations [3], even for network sizes of the order of 105. Therefore, the assumption that the neurons in the chain are driven by stationary Poisson inputs may have to be abandoned.

  • (iii)

    A major postulate of the isolated chain theories is that the activity in the chain does not affect the embedding network. It remains to be seen whether the neglect of these feedback connections can be justified.

Section snippets

Model

The behavior of an embedded synfire chain is studied with the help of computer simulations [8]. The nodes of the considered network architectures are modeled as single compartment leaky integrate-and-fire (I & F) neurons (membrane time constant τm=10ms, membrane capacity 250pF, resting potential 0mV, spike threshold ϑ=20mV, refractory period 0.5ms). Interactions between neurons are described by δ-function shaped synaptic currents resulting in exponential postsynaptic membrane potential

Results

To quantify the network dynamics under the four different conditions (independent Poisson case included), we record the spikes of the neurons in the 16th layer for 1s, compute the population activity histogram (bin size 10ms) and determine the ratio F between its variance and mean (Fano factor).

Fig. 1 shows the measured Fano factors as a function of the group size w for three different embedding scenarios. In all cases we observe a transition from low Fano factors at small w to high values at

Discussion

In the present work we demonstrated that the finite size of the local cortical network seriously challenges the functional relevance of feed-forward subnetworks. Due to correlations caused by common input, a clear separation between an excited synchronous state and a quiescent ground state can only be achieved with difficulty. The dynamics of the embedding recurrent network seems to compensate for the effects of the common input. The underlying mechanism still needs to be uncovered.

Clearly, it

Acknowledgements

We acknowledge stimulating discussions with Yuval Aviel and Moshe Abeles. Part of the work was carried out when M. Diesmann enjoyed an ICNC-NEURALCOMP fellowship in October 2002.

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