Connectivity structure induced dynamics and correlations in spiking neural networks

The cerebral cortex exhibits distinct connectivity patterns on different length scales. Long range connections between cortical areas are mostly excitatory, while connectivity within the areas is excitatory and inhibitory. Additionally, cortical areas exhibit a layered structure across depth. This laminar structure is accompanied by specific connectivity patterns between populations of neurons located in the layers. Experimental studies link the laminar structure to dynamical phenomena, like specific oscillations, which are more prominent in some layers than in others. In this thesis, I present several studies that relate the laminar connectivity as well as the connectivity on the single neuron level to the structure of correlation in the network activity. This question has so far been approached by theoretical studies using either phenomenological population models or simplified connectivity structure. First, I present a theoretical framework that describes the dynamics of randomly connected spiking neurons by their population dynamics. This dimensionality reduction facilitates the analysis of phenomena that arise from the laminar structure. Next, I derive a sensitivity measure which identifies dynamically relevant connectivity motifs within the network. Applying these theoretical tools to a model that describes a microcircuit in area V1, I predict population rate spectra, identify the sub-circuits that generate the observed oscillations and link the results to experimental findings. Extending the theoretical framework and the model by slow synaptic currents sheds light on their role in both, synchronizing and desynchronizing population activity. Inspired by experimental studies, which probe circuits by oscillatory stimuli, I analyze how these stimuli are processed by neuronal networks and how the network response is shaped by the connectivity structure. The effect of the connectivity within the populations on the stationary correlation structure is studied by means of a binary network. This sheds light on features that are neglected when summarizing neuronal activity in populations, like heterogeneities of neuronal activities and correlations between neurons. This study illustrates how network activity is decorrelated in the input to each neuron and how the connectivity structure on the single cell level shapes the decay time of stimuli induced network responses. Throughout this work, I employ simulations of neuronal networks to support approximations made in the derivation of theoretical framework and furthermore to model interactions which are not analytically tractable. I therefore document how I unified the connection routines in the neural simulator NEST and implemented the new connection framework which allows for the creation of connectivity structures with randomized connections as well as randomized synaptic parameters. In summary, this thesis relates laminar connectivity patterns to experimentally observed dynamical phenomena. The methodology introduced here facilitates the understanding of how connectivity structure of neuronal networks, on the population level as well as on the single cell level, shapes the dynamics emerging from the network