Phase transitions and nonlinear phenomena in neuronal network models

Communication and cooperation between billions of neurons underlie the power of the brain. How do complex functions of the brain arise from its cellular constituents? How do groups of neurons self-organize into patterns of activity? These are crucial questions in neuroscience. In order to answer them, it is necessary to have solid theoretical understanding of how single neurons communicate at the microscopic level, and how cooperative activity emerges. In this thesis we aim to understand how complex collective phenomena can arise in a simple model of neuronal networks. We use a model with balanced excitation and inhibition and complex network architecture, and we develop analytical and numerical methods for describing its neuronal dynamics. We study how interaction between neurons generates various collective phenomena, such as spontaneous appearance of network oscillations and seizures, and early warnings of these transitions in neuronal networks. Within our model, we show that phase transitions separate various dynamical regimes, and we investigate the corresponding bifurcations and critical phenomena. It permits us to suggest a qualitative explanation of the Berger effect, and to investigate phenomena such as avalanches, band-pass filter, and stochastic resonance. The role of modular structure in the detection of weak signals is also discussed. Moreover, we find nonlinear excitations that can describe paroxysmal spikes observed in electroencephalograms from epileptic brains. It allows us to propose a method to predict epileptic seizures. Memory and learning are key functions of the brain. There are evidences that these processes result from dynamical changes in the structure of the brain. At the microscopic level, synaptic connections are plastic and are modified according to the dynamics of neurons. Thus, we generalize our cortical model to take into account synaptic plasticity and we show that the repertoire of dynamical regimes becomes richer. In particular, we find mixed-mode oscillations and a chaotic regime in neuronal network dynamics.

Functional analysis of String/CDC25 phosphatase in post-mitotic neurons

Cell cycle and differentiation are two highly coordinated processes during organ development. Recent studies have demonstrated that core cell cycle regulators also play cell cycle-independent functions in post-mitotic neurons, and are essential for the maintenance of neuronal homeostasis. CDC25 phosphatases are well-established CDK activators and their activity is mainly associated to proliferating tissues. The expression and activity of mammalian CDC25s has been reported in adult brains. However, their physiological relevance and the potential substrates in a non-proliferative context have never been addressed. string (stg) encodes the Drosophila CDC25 homolog. Previous studies from our group showed that stg is expressed in photoreceptors (PRs) and in lamina neurons, which are two differentiated cell types that compose the fly visual system. The aims of this work are to uncover the function of stg and to identify its potential neuronal substrates, using the Drosophila visual system as a model. To gain insight into the function of stg in a non-dividing context we used the GAL4/UAS system to promote downregulation of stg in PR-neurons, through the use of an RNAi transgene. The defects caused by stg loss-of-function were evaluated in the developing eye imaginal disc by immunofluorescence, and during adult stages by scanning electron microscopy. This genetic approach was combined with a specific proteomic method, two-dimensional difference gel electrophoresis (2D-DIGE), to identify the potential substrates in PR-cells. Our results showed that stg downregulation in PRs affects the well-patterned retina organization, inducing the loss of apical maintenance of PR-nuclei on the eye disc, and ommatidia disorganization. We also detected an abnormal accumulation of cytoskeletal proteins and a disruption of the axon structure. As a consequence, the projection of PR-axons into the lamina and medulla neuropils of the optic lobe was impaired. Upon stg downregulation, we also detected that PR-cells accumulate Cyclin B. Although the rough eye phenotype observed upon stg downregulation suggests neurodegeneration, we did not detect neuronal death during larval stages, suggesting that it likely occurs during pupal stages or during adulthood. By 2D-DIGE, we identified seven proteins which were differentially expressed upon stg downregulation, and are potential neuronal substrates of Stg. Altogether, our observations suggest that Stg phosphatase plays an essential role in the Drosophila visual system neurons, regulating several cell components and processes in order to ensure their homeostasis.