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Correlations and Population Dynamics in Cortical Networks

kriener{at}biologie.uni-freiburg.de Bernstein Center for Computational Neuroscience, and Neurobiology and Biophysics, Faculty of Biology, Albert-Ludwigs-University, D-79104 Freiburg, Germany

Tom Tetzlaff

tom.tetzlaff{at}umb.no Bernstein Center for Computational Neuroscience, Albert-Ludwigs-University, D-79104 Freiburg, Germany, and Institute of Mathematical Sciences and Technology, Norwegian University of Life Sciences, N-1432 Ås, Norway

Ad Aertsen

aertsen{at}biologie.uni-freiburg.de Bernstein Center for Computational Neuroscience, and Neurobiology and Biophysics, Faculty of Biology, Albert-Ludwigs-University, D-79104 Freiburg, Germany

Markus Diesmann

diesmann{at}brain.riken.jp Bernstein Center for Computational Neuroscience, Albert-Ludwigs-University, D-79104 Freiburg, Germany, and Brain Science Institute, RIKEN, Wako City, Saitama 351-0198, Japan

Stefan Rotter

stefan.rotter{at}biologie.uni-freiburg.de Bernstein Center for Computational Neuroscience, Albert-Ludwigs-University, D-79104 Freiburg, Germany, and Theory andData Analysis, Institute for Frontier Areas of Psychology and Mental Health, D-79098 Freiburg, Germany

The function of cortical networks depends on the collective interplay between neuronsand neuronal populations, which is reflected in the correlation of signals that can be recorded at different levels. To correctly interpret these observations it is important to understand the origin of neuronal correlations. Here we study how cells in large recurrent networks of excitatory and inhibitory neurons interact and how the associated correlations affect stationary states of idle network activity. We demonstrate that the structure of the connectivity matrix of such networks induces considerable correlations between synaptic currents as well as between subthreshold membrane potentials, provided Dale's principle is respected. If, in contrast, synaptic weights are randomly distributed, input correlations can vanish, even for densely connected networks. Although correlations are strongly attenuated when proceeding from membrane potentials to action potentials (spikes), the resulting weak correlations in the spike output can cause substantial fluctuations in the population activity, even in highly diluted networks. We show that simple mean-field models that take the structure of the coupling matrix into account can adequately describe the power spectra of the population activity. The consequences of Dale's principle on correlations and rate fluctuations are discussed in the light of recent experimental findings.

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