Fundamental activity constraints lead to specific interpretations of the connectome

The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to experimental observations. Nevertheless, structurally realistic network models of spiking neurons are necessarily underconstrained even if experimental data on brain connectivity are incorporated to the best of our knowledge. Guided by physiological observations, any model must therefore explore the parameter ranges within the uncertainty of the data. Based on simulation results alone, however, the mechanisms underlying stable and physiologically realistic activity often remain obscure. We here employ a mean-field reduction of the dynamics, which allows us to include activity constraints into the process of model construction. We shape the phase space of a multi-scale network model of the vision-related areas of macaque cortex by systematically refining its connectivity. Fundamental constraints on the activity, i.e., prohibiting quiescence and requiring global stability, prove sufficient to obtain realistic layer- and area-specific activity. Only small adaptations of the structure are required, showing that the network operates close to an instability. The procedure identifies components of the network critical to its collective dynamics and creates hypotheses for structural data and future experiments. The method can be applied to networks involving any neuron model with a known gain function.Comment: J. Schuecker and M. Schmidt contributed equally to this wor

How pattern formation in ring networks of excitatory and inhibitory spiking neurons depends on the input current regime

Pattern formation, i.e., the generation of an inhomogeneous spatial activity distribution in a dynamical system with translation invariant structure, is a well-studied phenomenon in neuronal network dynamics, specifically in neural field models. These are population models to describe the spatio-temporal dynamics of large groups of neurons in terms of macroscopic variables such as population firing rates. Though neural field models are often deduced from and equipped with biophysically meaningful properties, a direct mapping to simulations of individual spiking neuron populations is rarely considered. Neurons have a distinct identity defined by their action on their postsynaptic targets. In its simplest form they act either excitatorily or inhibitorily. When the distribution of neuron identities is assumed to be periodic, pattern formation can be observed, given the coupling strength is supracritical, i.e., larger than a critical weight. We find that this critical weight is strongly dependent on the characteristics of the neuronal input, i.e., depends on whether neurons are mean- or fluctuation driven, and different limits in linearizing the full non-linear system apply in order to assess stability. In particular, if neurons are mean-driven, the linearization has a very simple form and becomes independent of both the fixed point firing rate and the variance of the input current, while in the very strongly fluctuation-driven regime the fixed point rate, as well as the input mean and variance are important parameters in the determination of the critical weight. We demonstrate that interestingly even in “intermediate” regimes, when the system is technically fluctuation-driven, the simple linearization neglecting the variance of the input can yield the better prediction of the critical coupling strength. We moreover analyze the effects of structural randomness by rewiring individual synapses or redistributing weights, as well as coarse-graining on the formation of inhomogeneous activity patterns

VIOLA - A multi-purpose and web-based visualization tool for neuronal-network simulation output

Neuronal network models and corresponding computer simulations are invaluable tools to aid the interpretation of the relationship between neuron properties, connectivity and measured activity in cortical tissue. Spatiotemporal patterns of activity propagating across the cortical surface as observed experimentally can for example be described by neuronal network models with layered geometry and distance-dependent connectivity. The interpretation of the resulting stream of multi-modal and multi-dimensional simulation data calls for integrating interactive visualization steps into existing simulation-analysis workflows. Here, we present a set of interactive visualization concepts called views for the visual analysis of activity data in topological network models, and a corresponding reference implementation VIOLA (VIsualization Of Layer Activity). The software is a lightweight, open-source, web-based and platform-independent application combining and adapting modern interactive visualization paradigms, such as coordinated multiple views, for massively parallel neurophysiological data. For a use-case demonstration we consider spiking activity data of a two-population, layered point-neuron network model subject to a spatially confined excitation originating from an external population. With the multiple coordinated views, an explorative and qualitative assessment of the spatiotemporal features of neuronal activity can be performed upfront of a detailed quantitative data analysis of specific aspects of the data. Furthermore, ongoing efforts including the European Human Brain Project aim at providing online user portals for integrated model development, simulation, analysis and provenance tracking, wherein interactive visual analysis tools are one component. Browser-compatible, web-technology based solutions are therefore required. Within this scope, with VIOLA we provide a first prototype.Comment: 38 pages, 10 figures, 3 table

Conditions for wave trains in spiking neural networks

Spatiotemporal patterns such as traveling waves are frequently observed in recordings of neural activity. The mechanisms underlying the generation of such patterns are largely unknown. Previous studies have investigated the existence and uniqueness of different types of waves or bumps of activity using neural-field models, phenomenological coarse-grained descriptions of neural-network dynamics. But it remains unclear how these insights can be transferred to more biologically realistic networks of spiking neurons, where individual neurons fire irregularly. Here, we employ mean-field theory to reduce a microscopic model of leaky integrate-and-fire (LIF) neurons with distance-dependent connectivity to an effective neural-field model. In contrast to existing phenomenological descriptions, the dynamics in this neural-field model depends on the mean and the variance in the synaptic input, both determining the amplitude and the temporal structure of the resulting effective coupling kernel. For the neural-field model we employ liner stability analysis to derive conditions for the existence of spatial and temporal oscillations and wave trains, that is, temporally and spatially periodic traveling waves. We first prove that wave trains cannot occur in a single homogeneous population of neurons, irrespective of the form of distance dependence of the connection probability. Compatible with the architecture of cortical neural networks, wave trains emerge in two-population networks of excitatory and inhibitory neurons as a combination of delay-induced temporal oscillations and spatial oscillations due to distance-dependent connectivity profiles. Finally, we demonstrate quantitative agreement between predictions of the analytically tractable neural-field model and numerical simulations of both networks of nonlinear rate-based units and networks of LIF neurons.Comment: 36 pages, 8 figures, 4 table

Dynamic Communications Between GABAA Switch, Local Connectivity, and Synapses During Cortical Development: A Computational Study

Several factors regulate cortical development, such as changes in local connectivity and the influences of dynamical synapses. In this study, we simulated various factors affecting the regulation of neural network activity during cortical development. Previous studies have shown that during early cortical development, the reversal potential of GABAA shifts from depolarizing to hyperpolarizing. Here we provide the first integrative computational model to simulate the combined effects of these factors in a unified framework (building on our prior work: Khalil et al., 2017a,b). In the current study, we extend our model to monitor firing activity in response to the excitatory action of GABAA. Precisely, we created a Spiking Neural Network model that included certain biophysical parameters for lateral connectivity (distance between adjacent neurons) and nearby local connectivity (complex connections involving those between neuronal groups). We simulated different network scenarios (for immature and mature conditions) based on these biophysical parameters. Then, we implemented two forms of Short-term synaptic plasticity (depression and facilitation). Each form has two distinct kinds according to its synaptic time constant value. Finally, in both sets of networks, we compared firing rate activity responses before and after simulating dynamical synapses. Based on simulation results, we found that the modulation effect of dynamical synapses for evaluating and shaping the firing activity of the neural network is strongly dependent on the physiological state of GABAA. Moreover, the STP mechanism acts differently in every network scenario, mirroring the crucial modulating roles of these critical parameters during cortical development. Clinical implications for pathological alterations of GABAergic signaling in neurological and psychiatric disorders are discussed

VIOLA—A Multi-Purpose and Web-Based Visualization Tool for Neuronal-Network Simulation Output

Neuronal network models and corresponding computer simulations are invaluable tools to aid the interpretation of the relationship between neuron properties, connectivity, and measured activity in cortical tissue. Spatiotemporal patterns of activity propagating across the cortical surface as observed experimentally can for example be described by neuronal network models with layered geometry and distance-dependent connectivity. In order to cover the surface area captured by today's experimental techniques and to achieve sufficient self-consistency, such models contain millions of nerve cells. The interpretation of the resulting stream of multi-modal and multi-dimensional simulation data calls for integrating interactive visualization steps into existing simulation-analysis workflows. Here, we present a set of interactive visualization concepts called views for the visual analysis of activity data in topological network models, and a corresponding reference implementation VIOLA (VIsualization Of Layer Activity). The software is a lightweight, open-source, web-based, and platform-independent application combining and adapting modern interactive visualization paradigms, such as coordinated multiple views, for massively parallel neurophysiological data. For a use-case demonstration we consider spiking activity data of a two-population, layered point-neuron network model incorporating distance-dependent connectivity subject to a spatially confined excitation originating from an external population. With the multiple coordinated views, an explorative and qualitative assessment of the spatiotemporal features of neuronal activity can be performed upfront of a detailed quantitative data analysis of specific aspects of the data. Interactive multi-view analysis therefore assists existing data analysis workflows. Furthermore, ongoing efforts including the European Human Brain Project aim at providing online user portals for integrated model development, simulation, analysis, and provenance tracking, wherein interactive visual analysis tools are one component. Browser-compatible, web-technology based solutions are therefore required. Within this scope, with VIOLA we provide a first prototype

Reconciliation of weak pairwise spike-train correlations and highly coherent local field potentials across space

Chronic and acute implants of multi-electrode arrays that cover several mm$^2$ of neural tissue provide simultaneous access to population signals like extracellular potentials and the spiking activity of 100 or more individual neurons. While the recorded data may uncover principles of brain function, its interpretation calls for multiscale computational models with corresponding spatial dimensions and signal predictions. Such models can facilitate the search of mechanisms underlying observed spatiotemporal activity patterns in cortex. Multi-layer spiking neuron network models of local cortical circuits covering ~1 mm$^2$ have been developed, integrating experimentally obtained neuron-type specific connectivity data and reproducing features of in-vivo spiking statistics. With forward models, local field potentials (LFPs) can be computed from the simulated spiking activity. To account for the spatial scale of common neural recordings, we extend a local network and LFP model to 4x4 mm$^2$. The upscaling preserves the neuron densities, and introduces distance-dependent connection probabilities and delays. As detailed experimental connectivity data is partially lacking, we address this uncertainty in model parameters by testing parameter combinations within biologically plausible bounds. Based on model predictions of spiking activity and LFPs, we find that the upscaling procedure preserves the overall spiking statistics of the original model and reproduces asynchronous irregular spiking across populations and weak pairwise spike-train correlations observed in sensory cortex. In contrast with the weak spike-train correlations, the correlation of LFP signals is strong and distance-dependent, compatible with experimental observations. Enhanced spatial coherence in the low-gamma band may explain the recent experimental report of an apparent band-pass filter effect in the spatial reach of the LFP.Comment: 44 pages, 9 figures, 5 table