CHAOTIC BALANCED STATE IN A MODEL OF CORTICAL CIRCUITS

The nature and origin of the temporal irregularity in the electrical a ctivity of cortical neurons in vivo are not well understood. We consid er the hypothesis that this irregularity is due to a balance of excita tory and inhibitory currents into the cortical cells. We study a netwo rk model with excitatory and inhibitory populations of simple binary u nits. The internal feedback is mediated by relatively large synaptic s trengths, so that the magnitude of the total excitatory and inhibitory feedback is much larger than the neuronal threshold. The connectivity is random and sparse. The mean number of connections per unit is larg e, though small compared to the total number of cells in the network. The network also receives a large, temporally regular input from exter nal sources. We present an analytical solution of the mean-field theor y of this model, which is exact in the limit of large network size. Th is theory reveals a new cooperative stationary state state of large ne tworks, which we term a balanced In this state, a balance between the excitatory and inhibitory inputs emerges dynamically for a wide range of parameters, resulting in a net input whose temporal fluctuations ar e of the same order as its mean. The internal synaptic inputs act as a strong negative feedback, which linearizes the population responses t o the external drive despite the strong nonlinearity of the individual cells. This feedback also greatly stabilizes the system's state and e nables it to track a time-dependent input on time scales much shorter than the time constant of a single cell. The spatiotemporal statistics of the balanced state are calculated. It is shown that the autocorrel ations decay on a short time scale, yielding an approximate Poissonian temporal statistics. The activity levels of single cells are broadly distributed, and their distribution exhibits a skewed shape with a lon g power-law tail. The chaotic nature of the balanced state is revealed by showing that the evolution of the microscopic state of the network is extremely sensitive to small deviations in its initial conditions. The balanced state generated by the sparse, strong connections is an asynchronous chaotic state. It is accompanied by weak spatial cross-co rrelations, the strength of which vanishes in the limit of large netwo rk size. This is in contrast to the synchronized chaotic states exhibi ted by more conventional network models with high connectivity of weak synapses.