Balanced networks of excitatory and inhibitory neurons are a popular paradigm to describe the ground state of cortical activity. Although such networks can assume a state of asynchronous and irregular activity with low firing rates and low pairwise correlations, recurrent connectivity inevitably induces correlations between spike trains . To elucidate the influence of network topology on correlations, we have recently employed the framework of linearly interacting point processes  as an analytically tractable model for network dynamics . A power series of the connectivity matrix can be used to disentangle the different contributions to pairwise correlations from direct and indirect interactions between neurons.
In the present study we show that this framework can be applied to approximate dynamics of networks of integrate-and-fire neurons, if the reset after each spike is formally described as self-inhibition. The reset then effectively decreases overall correlations. We study ring networks, where we are able to derive analytical expressions for the distance dependence of correlations and fluctuations in population activity. Rates and correlations in simulated networks are predicted accurately, provided that spike train correlations are reasonably small and the linear impulse response of single neurons is known.
We gratefully acknowledge support by the German Research Foundation (CRC 780, subproject C4) and by the German Federal Ministry of Education and Research (BMBF grant 01GQ0420 to BCCN Freiburg).
Neural Computation 2008, 20:2226-2185. Publisher Full Text
Front Comput Neurosci Conference Abstract: Bernstein Conference on Computational Neuroscience 2010.