Pharma Focus Asia

Connectivity Concepts in Neuronal Network Modeling

Johanna Senk, Birgit Kriener, Mikael Djurfeldt, Nicole Voges, Han-Jia Jiang, Lisa Schüttler, Gabriele Gramelsberger, Markus Diesmann, Hans E. Plesser, Sacha J. van Albada

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.

The connectivity structure of a neuronal network model is sometimes described with a statement such as “Ns source neurons and Nt target neurons are connected randomly with connection probability p”. One interpretation of this statement is an algorithm that considers each possible pair of source and target neurons exactly once and connects each such pair with probability p.

Materials and Methods:

Balanced random network
The balanced random network model used in Figs 1 and 9 is based on the model introduced by Brunel [1]. Our implementation extends the script which is part of the NEST source code ( by the option to switch between a “fixed in-degree” and a “fixed out-degree” version.

With the aim of supporting reproducibility in neuronal network modeling, we consider high-level connectivity in such models: connectivity that is described by rules applied to populations of nodes. As our main result, we propose a standardized nomenclature for often-used connectivity concepts and a graphical and symbolic notation for network diagrams.

The authors would like to thank Daniel Hjertholm for inspiring work on testing connectivity generation schemes, Sebastian Spreizer for immediately adopting the graphical notation in NEST Desktop, Espen Hagen for detailed comments on the manuscript, Hannah Bos for fruitful discussions, and our colleagues in the Simulation and Data Laboratory Neuroscience of the Jülich Supercomputing Centre for continuous collaboration. The authors gratefully acknowledge the computing time granted by the JARA Vergabegremium and provided on the JARA Partition part of the supercomputer JURECA at Forschungszentrum Jülich (computation grant JINB33).

Citation: Senk J, Kriener B, Djurfeldt M, Voges N, Jiang H-J, Schüttler L, et al. (2022) Connectivity concepts in neuronal network modeling. PLoS Comput Biol 18(9): e1010086.

Editor: Roberto Toro, Institut Pasteur, FRANCE

Received: October 7, 2021; Accepted: April 7, 2022; Published: September 8, 2022.

Copyright: © 2022 Senk et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: The code to reproduce all figures of this manuscript is publicly available at Zenodo:

Funding: This project has received funding from the European Union’s Horizon 2020 Framework Programme for Research and Innovation under Specific Grant Agreement 720270 (HBP SGA1) [to MDj, MDi, HEP], 785907 (HBP SGA2) [to JS, MDj, MDi, HEP, SvA], 945539 (HBP SGA3) [to JS, MDj, HJJ, MDi, HEP, SvA], and 754304 (DEEP-EST) [to HEP]; the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 368482240/GRK2416: ‘`RTG 2416 Multi-senses Multi-scales" [to MDi]; the Priority Program (SPP 2041 ‘`Computational Connectomics”) of the Deutsche Forschungsgemeinschaft [to SvA]; the Helmholtz Association Initiative and Networking Fund under project number SO-092 (Advanced Computing Architectures, ACA) [to JS, MDi]; the Excellence Initiative of the German federal and state governments (neuroIC001): ‘`ERS: disziplinärer Paketantrag NeuroIC: NeuroModelingTalk (NMT) Approaching the complexity barrier in neuroscientific modeling" [to JS, LS, GG, MDi]; and the Helmholtz Metadata Collaboration (HMC), an incubator platform of the Helmholtz Association within the framework of the Information and Data Science strategic initiative, under the funding ZT-I-PF-3-026 [to JS]. Open access publication funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 491111487. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

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