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Astrocytes,the most abundant glial type in the cortex, interact with neighboring synapses,neurons and glia through complex cellular machinery (Bazargani et al., 2016).Astrocytes form mostly nonoverlapping microdomains, and a single suchmicrodomain can be reached by several hundreds of neurons and as many as~100,000 synapses (Zisis et al., 2021). Experimental studies have demonstratedcoordinated neuronal and astrocytic activity invivo (Lines et al., 2020). Computational methods can help to integratethe data on cellular mechanisms and structural organization of the corticaltissue, and to explore how neuron-astrocyte interactions modulatepopulation-level activity. In the past two decades, the number of publishedcomputational models that include some form of neuron-astrocyte interaction hasbeen steadily increasing (Manninen et al., 2018; Manninen, Aćimović etal., 2018). The majority of the published models was implemented in custom madecode that is often not publicly available. Implementing these models in wellestablished open source simulation tools improves reproducibility of theresults and sharing of the models (Manninen et al., 2018; Manninen, Acimovic etal., 2018). Two earlier efforts to develop open source tools for simulation ofneuronal and glial networks include Arachne (Aleksin et al., 2017), and animplementation in the Brian simulator (Stimberg et al., 2019). We developed a new solution for efficient simulationof large heterogeneous populations of neurons and astrocytes implemented as a module in theNEST simulator (https://www.nest-simulator.org/). We first extended theconcept of a synapse in NEST to include interaction between three compartments,pre- and postsynaptic neurons and the neighboring astrocytic compartment. Next,we developed new method to establish efficiently interactions within a largeheterogeneous cellular population of neurons and astrocytes. Finally, we testedthe new tool by analyzing spontaneous activity regimes in medium-size networkscomposed of several hundreds of cells. In summary, we present a new module for NEST simulator that supports reproducible, open access and efficient development of computational models for large heterogeneous populations of neurons and astrocytes.

Dissertation, RWTH Aachen University, 2022; Aachen : RWTH Aachen University 1 Online-Ressource : Illustrationen, Diagramme (2022). = Dissertation, RWTH Aachen University, 2022, The human brain, as an example of a complex nervous system, is made up of approximately 8.6*10^11 neurons that communicate with one another via short electrical pulses. There are numerous models that, based on experimental results, describe neuronal activity at the level of individual neurons and synapses or neuronal populations. At the same time, extensive knowledge about the brain's macroscopic properties is available. This includes, for example, functional aspects like decision making or learning and multielectrode-array recordings of patterns of neural activity like spatiotemporal oscillations or neural avalanches. In the spirit of the quote attributed to Richard Feynman: "What I cannot create, I do not understand", with this work we would like to make a small contribution to understanding how the interaction of the many individual parts gives rise to the behavior observed on larger spatial and temporal scales. At the population level, the Wilson-Cowan equations constitute a well-established model of neuronal activity. In this thesis, we use stochastic variants of this model to show how the multiscale problem can be addressed by adapting field theoretical methods from statistical physics. In this context, our work focuses on developing a description of the interplay between nonlinearities and stochasticity that goes beyond the mean-field approximation. The first of the approaches presented, the loop expansion of the effective action, provides a formulation of the statistical moments that is self-consistent with respect to the mean activity. By means of the functional renormalization group self-consistency can in principle be achieved for all orders of the statistical moments. For this second approach, we develop an approximation which renders the numerical computation of the flow of momentum-dependent vertex functions much more efficient. We then consider networks connected in a distance-dependent manner to investigate activity beyond completely homogeneous populations of neurons. Using the Wilson renormalization group, we demonstrate that a spatially structured, stochastic version of the Wilson-Cowan model exhibits Gell-Mann-Low type critical behavior at the point of balance between excitation and inhibition. In this particular type of criticality, interactions that extend to macroscopic length scales enable nonlinear, collective information processing while maintaining near-optimal memory for external stimuli. Neural information processing is adaptable as reflected by the brain's ability to learn and alter its behavior. Synaptic plasticity is regarded as a crucial mechanism that, driven by correlated neuronal activity, implements the necessary changes at the microscopic level. Voltage-based plasticity rules extend the ordinary spike-timing-dependent plasticity by incorporating the membrane potential of the postsynaptic neuron as a third factor. On the one hand, this additional component allows voltage-based rules to reproduce experimental results more accurately and to realize biologically plausible approximations of powerful algorithms from machine learning; on the other hand, it complicates their implementation in simulation software. We design an efficient event-driven algorithm suitable for large-scale simulations on distributed memory systems. In perspective, this enables the training of large biologically inspired neural networks and paves the way for studying their collective dynamics., Published by RWTH Aachen University, Aachen

Many phenomena observed in biological neural networks can only be explained by assuming nonlinearinteractions. Due to effects like synaptic failure and channel noise, neuronal dynamics is also inherentlystochastic. The investigation of the interaction of both of these properties is challenging because due to thenonlinearity, correlations of higher order influence those of lower order. Nonlinear, stochastic systems exhibita plethora of dynamical states. The cortex, especially, is often suggested to operate close to a critical pointat which linear response theory fails since the neural dynamics is dominated by large fluctuations on alllength scales [1].This is the realm of the Renormalization Group (RG), stemming from statistical and particle physics. Weuse this technique in the form introduced by Kenneth G. Wilson [2] to study a two-dimensional stochasticneural field model. Its connectivity is composed of two Gaussian kernels, one mimicking the excitatoryand the other the inhibitory input. Its dynamics is given by a nonlinear gain and intrinsic nonlinear neurondynamics. Gaussian white noise accounting for unspecified external input and intrinsic stochasticity drivesour system. In its long-distance approximation, this model is similar to that proposed by Kardar, Parisi, andZhang (KPZ) [3].Along the lines taken in their approach, we derive RG-flow equations describing the couplings in ourneural field model on different length scales. From this, one finds the upper critical dimension dc=2,which corresponds to the dimension of networks in cortex. Above dc , mean-field theory is exact as theGaussian fixed point is attractive for small interactions, whereas below dc , the interaction dominates thebehavior. For d=dc , however, we find that the Gaussian fixed point becomes unstable and the interactionparameter flows into a strong coupling regime – similar to the KPZ model. A strong coupling fixed pointmay be present, which would indicate self-similarity - the signature of a critical state. Our analysis thereforeimplies certain constrains on the architecture of the neural network (within our model) if it is supposed towork at a critical point. For example, we conclude that we get stable dynamics only if the excitatoryinputs extend wider than the inhibitory ones.AcknowledgementsPartly supported by seed funds MSCALE and CLS002 of the RWTH University; the JARA Center for Doctoral studies within the graduate School for Simulation and Data Science (SSD); the Helmholtz association: Young investigator's grant VH-NG-1028; EU-Grant 785907 (HBP).References[1] Beggs, J. M., Plenz, D. (2003), Neuronal avalanches in neocortical circuits, Journal of Neuroscience, 23, 35, 11167–11177., 10.1523/JNEUROSCI.23-35-11167.2003[2] Wilson, K. G., Kogut, J. (1974), The renormalization group and the ε expansion, Physics Reports, 12, 2 , 75 - 199.[3] Kardar, M., Parisi, G., Zhang, Y.(1986), Dynamic Scaling of Growing Interfaces, Phys. Rev. Lett. 56, 889–892., 10.1103/PhysRevLett.56.88

It is often suggested that the cortex operates close to a critical point at which linear response theory fails since the neural dynamics is dominated by large fluctuations on all length scales. The functional Renormalization Group (fRG) is not stained with this flaw because in principle it treats statistics of arbitrary order in an unbiased and self-consistent way. We apply fRG to a self-interacting, stochastic, quadratic rate neuron and show how this method incorporates corrections to the mean dynamics and time-dependent statistics due to fluctuations in the presence of nonlinear neuronal gain. To obtain a simplified treatment of the frequency-dependence of all observables, we adapt the Blaizot Méndez-Galain Wschebor (BMW) scheme to the vertex expansion, which yields good predictions.We expect that the insights into fRG-techniques gained within our study will help to tackle challenges occurring in the description of phenomena in spatially extended networks, notably the calculation of critical exponents and the coarse-graining of microscopic models.