Variable responses of neuronal networks to repeated sensory or electrical stimuli reflect the interaction of the stimulus' response with ongoing activity in the brain and its modulation by adaptive mechanisms, such as cognitive context, network state, or cellular excitability and synaptic transmission capability. Here, we focus on reliability, length, delays, and variability of evoked responses with respect to their spatial distribution, interaction with spontaneous activity in the networks, and the contribution of GABAergic inhibition. We identified network-intrinsic principles that underlie the formation and modulation of spontaneous activity and stimulus-response relations with the use of state-dependent stimulation in generic neuronal networks in vitro. The duration of spontaneously recurring network-wide bursts of spikes was best predicted by the length of the preceding interval. Length, delay, and structure of responses to identical stimuli systematically depended on stimulus timing and distance to the stimulation site, which were described by a set of simple functions of spontaneous activity. Response length at proximal recording sites increased with the duration of prestimulus inactivity and was best described by a saturation function y(t) ϭ A(1 Ϫ e Ϫ␣t ). Concomitantly, the delays of polysynaptic late responses at distant sites followed an exponential decay y(t) ϭ Be Ϫ␤t ϩ C. In addition, the speed of propagation was determined by the overall state of the network at the moment of stimulation. Disinhibition increased the number of spikes/network burst and interburst interval length at unchanged gross firing rate, whereas the response modulation by the duration of prestimulus inactivity was preserved. Our data suggest a process of network depression during bursts and subsequent recovery that limit evoked responses following distinct rules. We discuss shortterm synaptic depression due to depletion of neurotransmitter vesicles as an underlying mechanism. The seemingly unreliable patterns of spontaneous activity and stimulus-response relations thus follow a predictable structure determined by the interdependencies of network structures and activity states.

Synchronization among neurons is critical for many processes in the nervous system, ranging from the processing of sensory information to the onset of pathological conditions such as epilepsy. Here, we study synchronization in an array of neurons, each modeled by a set of nonlinear ordinary differential equations. We find that an array of 20x20 coupled neurons undergoes a series of alternating low and high synchronization states, as measured by phase-locking and frequency entrainment, as the coupling constant is tuned. The role of long-range connections in inducing "small-world networks" has recently been of great interest in many physical and biological problems. Since long-range connections do exist in the brain, we investigated the role of such connections in our neural array. Introducing a biologically realistic percentage of long-range connections has no significant effect on synchronization. We find that it is rather the type of coupling and the total number of connections that determine the synchronization state of the array. We also show that some coupling conditions can lead to frustration in the system, resulting from an inability to simultaneously satisfy conflicting phase requirements. This frustration leads to a drift in the overall behavior of the network, which may offer an explanation for transitions between different types of neural oscillations observed experimentally.

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