Spatiotemporal coordination of collective activity in neuronal ensembles

The brain is a complex multiscale dynamical system made of neurons, connected with each other by synapses. Neurons are multidimensional nonlinear systems able to exhibit dynamical activities at different temporal and spatial scales. The correct operation of the brain requires a carefully orchestrated activity across these scales, which includes the establishment of synchronized behavior within and among multiple neuronal populations. In this thesis we study different collective dynamical phenomena in brain networks that reveal exquisite coordination, by means of different models of cortical neuronal networks. First we study temporally coordinated patterns in the thalamus. During the sleep and awake states, this brain area is characterized by the presence of two dynamical regimes: in the sleep state the activity is dominated by spindle oscillations, weakly affected by external stimuli, while in the awake state the activity is primarily driven by external stimuli. We have developed a simple thalamic model that exhibits two dynamical regimes with different information-processing capabilities, and study the transition between them. Our results give a novel description of the role that thalamocortical and reticular thalamic cells, and their connectivity, play in the dynamical regimes observed in the thalamus, and in the transition between them. Secondly we study the synchronization of neuronal oscillations in the gamma range. Collective oscillations emerging from the synchronized activity of several neurons can increase the functional connectivity between neural assemblies by coherently coordinating their phases. This synchrony could involve distant regions in the brain. We study the dynamics of two delayed-coupled populations using spiking models, examining how different synaptic delays give rise to in-phase/anti-phase transitions at particular frequencies within the gamma range, how this behavior is related to the phase coherence between the two populations at different frequencies and how information is exchanged between the two networks. The results confirm that zero-lag synchronization maximizes information transmission, although out-of-phase synchronization allows for efficient communication under specific conditions. The brain self-organizes in different spatiotemporal organized patterns across temporal and spatial scales. We examine how these scales interact in the functioning brain, by considering the coupled behavior of two mesoscopic neural masses (NM) that communicate with each other through a microscopic neuronal network (NN). We use the synchronization between the two NM models as a tool to probe the interaction between the mesoscopic scales of those neural populations and the microscopic scale of the mediating NN. Our results show that the neuronal network, which operates at a fast temporal scale, is indeed sufficient to mediate coupling between the two mesoscopic oscillators, which evolve dynamically at a slower scale. We also establish how this synchronization depends on the topological properties of the microscopic NN. When synchronized neuronal oscillations exhibit a consistent phase pattern across recording sites, spatiotemporal phenomena arise in the form of brain waves. We study traveling waves emerging from a one-dimensional network of inhibitory neurons with asymmetric synaptic coupling. These networks exhibit anomalous dispersion with counter-intuitive backward propagating waves. When neurons at the head of the chain are periodically forced, waves emerge with wavefronts moving in a direction opposite to that of the synaptic connectivity. We investigate the generality of this phenomenon by studying an integrate-and-fire continuum model approximation, and derive a self-consistency condition for the existence of traveling waves which allows the calculation of the dispersion curve. Our results reveal how wave propagation depends on a variety of neuronal properties.