Intrinsic dynamics in neuronal networks. I. Theory

Many networks in the mammalian nervous system remain active in the absence of stimuli. This activity falls into two main patterns: steady firing at lo w rates and rhythmic bursting. How are these firing patterns generated? Spe cifically, how do dynamic interactions between excitatory and inhibitory ne urons produce these firing patterns, and how do networks switch from one fi ring pattern to the other? We investigated these questions theoretically by examining the intrinsic dynamics of large networks of neurons. Using both a semianalytic model based on mean firing rate dynamics and simulations wit h large neuronal networks, we found that the dynamics, and thus the firing patterns, are controlled largely by one parameter, the fraction of endogeno usly active cells. When no endogenously active cells are present, networks are either silent or fire at a high rate; as the number of endogenously act ive cells increases, there is a transition to bursting; and, with a further increase, there is a second transition to steady firing at a low rate. A s econdary role is played by network connectivity, which determines whether a ctivity occurs at a constant mean firing rate or oscillates around that mea n. These conclusions require only conventional assumptions: excitatory inpu t to a neuron increases its firing rate, inhibitory input decreases it, and neurons exhibit spike-frequency adaptation. These conclusions also lead to two experimentally testable predictions: 1) isolated networks that fire at low rates must contain endogenously active cells and 2) a reduction in the fraction of endogenously active cells in such networks must lead to bursti ng.