Emergence of structures in neuronal network activities

Nonlinear responses of individual neurons are both experimentally established and considered fundamental for the functioning of neuronal circuitry. Consequently, one may envisage the collective dynamics of large networks of neurons exhibiting a large repertoire of nonlinear behaviors. However, an ongoing and central challenge in the modeling of neural dynamics involves the trade-off between tractability and biological realism. This is particularly important in exploring the range of possible dynamics of large networks. Our approach uses Gaussian white noise as a probe, thus capturing the full range of system responses and characteristics by using an approach inspired by the well-established Wiener - Volterra nonlinear system identification approach. We assess model behavior over a range of network architectures and noise stimulation rates and demonstrate non-monotonicity and nonlinearity as a system property. Perhaps surprisingly, our computational model suggests that recurrent systems of nonlinear neurons exhibit a range of complex behaviors that do not readily yield to linear modeling in every setting. Our results suggest that a linear interpretation of experimental data is likely to discount the critical importance of properties emerging from network architecture. The main contribution of this effort is to highlight the importance of the network's architecture operating on the nonlinear properties of individual neurons and the experimental probing approaches of the circuitry.