Sustainable research on computational models of neuronal networks requires published models to be understandable, reproducible, and extendable. Missing details or ambiguities about mathematical concepts and assumptions, algorithmic implementations, or parameterizations hinder progress. Such flaws are unfortunately frequent and one reason is a lack of readily applicable standards and tools for model description. Our work aims to advance complete and concise descriptions of network connectivity but also to guide the implementation of connection routines in simulation software and neuromorphic hardware systems. We first review models made available by the computational neuroscience community in the repositories ModelDB and Open Source Brain, and investigate the corresponding connectivity structures and their descriptions in both manuscript and code. The review comprises the connectivity of networks with diverse levels of neuroanatomical detail and exposes how connectivity is abstracted in existing description languages and simulator interfaces. We find that a substantial proportion of the published descriptions of connectivity is ambiguous. Based on this review, we derive a set of connectivity concepts for deterministically and probabilistically connected networks and also address networks embedded in metric space. Beside these mathematical and textual guidelines, we propose a unified graphical notation for network diagrams to facilitate an intuitive understanding of network properties. Examples of representative network models demonstrate the practical use of the ideas. We hope that the proposed standardizations will contribute to unambiguous descriptions and reproducible implementations of neuronal network connectivity in computational neuroscience.

Full scale simulations of neuronal network models of the brain are challenging due to the high density of connections between neurons. This contribution reports run times shorter than the simulated span of biological time for a full scale model of the local cortical microcircuit with explicit representation of synapses on a recent conventional compute node. Realtime performance is relevant for robotics and closed-loop applications while sub-realtime is desirable for the study of learning and development in the brain, processes extending over hours and days of biological time.

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 linear 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.

Simulation software for spiking neuronal network models matured in the past decades regarding performance and flexibility. But the entry barrier remains high for students and early career scientists in computational neuroscience since these simulators typically require programming skills and a complex installation. Here, we describe an installation-free Graphical User Interface (GUI) running in the web browser, which is distinct from the simulation engine running anywhere, on the student’s laptop or on a supercomputer. This architecture provides robustness against technological changes in the software stack and simplifies deployment for self-education and for teachers. Our new open-source tool, NEST Desktop, comprises graphical elements for creating and configuring network models, running simulations, and visualizing and analyzing the results. NEST Desktop allows students to explore important concepts in computational neuroscience without the need to learn a simulator control language before. Our experiences so far highlight that NEST Desktop helps advancing both quality and intensity of teaching in computational neuroscience in regular university courses. We view the availability of the tool on public resources like the European ICT infrastructure for neuroscience EBRAINS as a contribution to equal opportunities.

Simulation speed matters for neuroscientific research: this includes not only how quickly the simulated model time of a large-scale spiking neuronal network progresses but also how long it takes to instantiate the network model in computer memory. On the hardware side, acceleration via highly parallel GPUs is being increasingly utilized. On the software side, code generation approaches ensure highly optimized code at the expense of repeated code regeneration and recompilation after modifications to the network model. Aiming for a greater flexibility with respect to iterative model changes, here we propose a new method for creating network connections interactively, dynamically, and directly in GPU memory through a set of commonly used high-level connection rules. We validate the simulation performance with both consumer and data center GPUs on two neuroscientifically relevant models: a cortical microcircuit of about 77,000 leaky-integrate-and-fire neuron models and 300 million static synapses, and a two-population network recurrently connected using a variety of connection rules. With our proposed ad hoc network instantiation, both network construction and simulation times are comparable or shorter than those obtained with other state-of-the-art simulation technologies while still meeting the flexibility demands of explorative network modeling.

Multi-electrode arrays covering several square millimeters of neural tissue provide simultaneous access to population signals such as extracellular potentials and spiking activity of one hundred or more individual neurons. The interpretation of the recorded data calls for multiscale computational models with corresponding spatial dimensions and signal predictions. Multi-layer spiking neuron network models of local cortical circuits covering about $1\,{\text{mm}^{2}}$ have been developed, integrating experimentally obtained neuron-type-specific connectivity data and reproducing features of observed in-vivo spiking statistics. Local field potentials can be computed from the simulated spiking activity. We here extend a local network and local field potential model to an area of $4\times 4\,{\text{mm}^{2}}$, preserving the neuron density and introducing distance-dependent connection probabilities and conduction delays. 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 in agreement with experimental recordings from sensory cortex. Also compatible with experimental observations, the correlation of local field potential signals is strong and decays over a distance of several hundred micrometers. Enhanced spatial coherence in the low-gamma band around $50\,\text{Hz}$ may explain the recent report of an apparent band-pass filter effect in the spatial reach of the local field potential.