Dynamical and statistical structure of spatially organized neuronal networks

  • Dynamische und statistische Eigenschaften räumlich organisierter neuronaler Netzwerke

Layer, Moritz; Helias, Moritz (Thesis advisor); Kampa, Björn M. (Thesis advisor)

Jülich : Forschungszentrum Jülich GmbH, Zentralbibliothek, Verlag (2022)
Book, Dissertation / PhD Thesis

In: Schriften des Forschungszentrums Jülich. Reihe Information = Information 85
Page(s)/Article-Nr.: 1 Online-Ressource (xiii, 165 Seiten) : Illustrationen, Diagramme

Dissertation, RWTH Aachen University, 2022


The cerebral cortex, the outer layer of mammalian brains, comprises a vast number of neurons arranged and connected in a highly organized fashion. The likelihood of neurons to be connected and how fast they may exchange signals depends, among other properties, on their spatial distance. Cortical networks may be well described as completely random networks on microscopic scales because cortical neurons have essentially uniform connection probabilities within a few tens of micrometers. However, the distance-dependence of neuronal connections certainly is important on mesoscopic scales spanning several millimeters, where many neurons are most likely unconnected. While the theory of random networks is already well-established, how such a spatial organization affects a network's activity is not yet fully understood. The objective of this thesis is to provide an overview of the current analytical understanding of spatially organized networks on a mesoscopic scale, as well as to advance this understanding with three studies covering complementary aspects of spatially organized network theory.A variety of experimental recordings in cortex reveals that neuronal activity is coordinated across several millimeters: Multi-electrode-arrays covering a few square millimeters, for example, provide access to the local field potential, a measure of population activity, as well as single neuron spiking activity. While spiking activity exhibits distance-dependent correlation characteristics, population activity shows spatio-temporally coherent activity, like periodic patterns, waves, or bumps. In this thesis we employ a combination of network models, analytical tools, and simulations to gain an understanding of such findings. We particularly make use of mean-field theory, which is a viable tool for investigating statistical properties of populations made up of thousands of neurons, and it therefore may be utilized to gain a coarse-grained description of network activity at large scales. In the first main part, we present a Python package we developed to make previously developed analytical results from neuronal network mean-field theory applicable to concrete network models, giving access to estimates of model properties such as firing rates and power spectra, as well as more elaborate tools that can support network modeling. In the second study, we investigate how neurons may coordinate their activity dynamically across large distances, without the need for highly correlated input or long-range connections. In the third study, we explore how a temporal delay may affect pattern formation in planar networks. As we demonstrate, spatial organization is a critical network feature that does not merely lead to obvious phenomena like spatially structured activity. On the contrary, as we show in this thesis, spatial organization leads to a variety of interesting, non-trivial effects, that on first sight might even seem counterintuitive, and this topic certainly provides a multitude of intriguing research questions for the near future.


  • Department of Physics [130000]
  • [136930]
  • Department of Biology [160000]
  • Theoretical Systems Neurobiology Teaching and Research Area (cooperation with FZ Jülich) [163110]