Effects of noise in a cortical neural model

Recently Phys. Rev. E 64, 011920 (2001)]; Phys. Rev. Lett. 88, 118102 (2002)]] made long-term observations of spontaneous activity of in-vitro cortical networks, which differ from predictions of current models in many features. In this paper we generalize the excitatory-inhibitory cortical model introduced in a previous paper [Neural Comput. 14, 2371 (2002)]], including intrinsic white noise and analyzing effects of noise on the spontaneous activity of the nonlinear system, in order to account for the experimental results of Segev et al. Analytically we can distinguish different regimes of activity, depending on the model parameters. Using analytical results as a guide line, we perform simulations of the nonlinear stochastic model in two different regimes, B and C. The power spectrum density (PSD) of the activity and the interevent-interval distributions are computed, and compared with experimental results. In regime B the network shows stochastic resonance phenomena and noise induces aperiodic collective synchronous oscillations that mimics experimental observations at 0.5 mM Ca concentration. In regime C the model shows spontaneous synchronous periodic activity that mimics activity observed at 1 mM Ca concentration and the PSD shows two peaks at the first and second harmonics in agreement with experiments at 1 mM Ca. Moreover (due to intrinsic noise and nonlinear activation function effects) the PSD shows a broad band peak at low frequency. This feature, observed experimentally, does not find explanation in the previous models. Besides we identify parametric changes (namely, increase of noise or decreasing of excitatory connections) that reproduces the fading of periodicity found experimentally at long times, and we identify a way to discriminate between those two possible effects measuring experimentally the low frequency PSD.