Mesoscale Systems, Finite Size Effects, and Balanced Neural Networks

Cortical populations are typically in an asynchronous state, sporadically interrupted by brief epochs of coordinated population activity. Current cortical models are at a loss to explain this combination of states. At one extreme are network models where recurrent in- hibition dynamically stabilizes an asynchronous low activity state. While these networks are widely used they cannot produce the coherent population-wide activity that is reported in a variety of datasets. At the other extreme are models where short term synaptic depression between excitatory neurons can generate the epochs of population-wide activity. However, in these networks inhibition plays only a perfunctory role in network stability, which is at odds with many reports across cortex. In this study we analyze spontaneously active in vitro preparations of primary auditory cortex that show dynamics that are emblematic of this mix- ture of states. To capture this complex population activity we consider models where large excitation is balanced by recurrent inhibition yet we include short term synaptic depression dynamics of the excitatory connections. This model gives very rich nonlinear behavior that mimics the core features of the in vitro data, including the possibility of low frequency (2- 12 Hz) rhythmic dynamics within population events. Our study extends balanced network models to account for nonlinear, population-wide correlated activity, thereby providing a critical step in a mechanistic theory of realistic cortical activity. We further investigate an extension of this model that l exhibits clearly non-Arrhenius behavior, whereby lower noise systems may exhibit faster escape from a stable state. We show that this behavior is due to the system size dependent vector field, intrinsically linking noise and dynamics