---
title: "Dale’s law, stability and nonlinearity enable transient and self‑sustained neural dynamics"
id: "biorxiv-18-dale-s-law-stability-and-nonlinearity-are-sufficient-constraints-to-ignite"
canonical_url: "https://medichelpline.com/clinical-feed/biorxiv-18-dale-s-law-stability-and-nonlinearity-are-sufficient-constraints-to-ignite"
content_type: "clinical_feed_article"
specialty: "Neurology"
source_name: "bioRxiv (Biomedical Preprints)"
source_url: "https://www.biorxiv.org/content/10.64898/2026.09.14.751508v1?rss=1"
published_at: "2026-09-21T12:00:00.000Z"
evidence_level: "Verified Feed"
license: "CC-BY-NC-4.0 / Informational Use"
---
# Dale’s law, stability and nonlinearity enable transient and self‑sustained neural dynamics
## Provenance & Clinical Metadata
- **Canonical URL:** https://medichelpline.com/clinical-feed/biorxiv-18-dale-s-law-stability-and-nonlinearity-are-sufficient-constraints-to-ignite
- **Specialty:** [Neurology](https://medichelpline.com/clinical-feed/neurology.md)
- **Primary Source:** bioRxiv (Biomedical Preprints)
- **Source URL:** [Original Journal Publication](https://www.biorxiv.org/content/10.64898/2026.09.14.751508v1?rss=1)
- **Published At:** 2026-09-21T12:00:00.000Z
- **Evidence Rating:** Verified Feed
## Executive GIST (TL;DR)
- The authors present a computational framework showing that three simple constraints—**Dale’s law**, network stability, and neuronal **nonlinearity**—are sufficient to produce a broad repertoire of network dynamics observed in motor cortex. - Using these constraints, they reverse-engineer families of connectivity matrices that generate **transient**, steady-state, and self-sustained periodic activity without weight learning or hand tuning. - A single dynamical mechanism underpins the repertoire: the interaction of **non-normal amplification**, inherent to Dalean networks, with neuronal nonlinearity, which can ignite and maintain multi-stable and controllable dynamics. - The approach produces networks that, without fitting to experimental data, reproduce population-level signatures characteristic of motor cortex activity. - The results imply that the richness of cortical dynamics may arise from basic biological ingredients rather than requiring extensive synaptic learning to sculpt dynamics. - The study emphasizes that Dalean connectivity (separate excitatory and inhibitory outputs), an imposed stability constraint, and nonlinear response functions together suffice to generate transient and self-sustained neural phenomena relevant to rhythmic and goal-directed movements. - The article is a preprint and has not been certified by peer review; details such as model specifics, parameter values, and validation procedures are provided in the full text and supplementary material but are not detailed in the abstract.
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Nicoleta Condruz Institute of Science and Technology Austria (ISTA) * [Find this author on Google Scholar](https://www.biorxiv.org/lookup/google-scholar?link_type=googlescholar&gs_type=author&author%5B0%5D=Nicoleta%2BCondruz%2B "Open in new tab") * [Find this author on PubMed](https://www.biorxiv.org/lookup/external-ref?access_num=Condruz%20N&link_type=AUTHORSEARCH "Open in new tab") * [Search for this author on this site](https://www.biorxiv.org/search/author1%3ANicoleta%2BCondruz%2B) * For correspondence: nicoleta.condruz@ist.ac.at Ivan Bulygin Institute of Science and Technology Austria (ISTA) * [Find this author on Google Scholar](https://www.biorxiv.org/lookup/google-scholar?link_type=googlescholar&gs_type=author&author%5B0%5D=Ivan%2BBulygin%2B "Open in new tab") * [Find this author on PubMed](https://www.biorxiv.org/lookup/external-ref?access_num=Bulygin%20I&link_type=AUTHORSEARCH "Open in new tab") * [Search for this author on this site](https://www.biorxiv.org/search/author1%3AIvan%2BBulygin%2B) Chaitanya Chintaluri Institute of Science and Technology Austria (ISTA) * [Find this author on Google Scholar](https://www.biorxiv.org/lookup/google-scholar?link_type=googlescholar&gs_type=author&author%5B0%5D=Chaitanya%2BChintaluri%2B "Open in new tab") * [Find this author on PubMed](https://www.biorxiv.org/lookup/external-ref?access_num=Chintaluri%20C&link_type=AUTHORSEARCH "Open in new tab") * [Search for this author on this site](https://www.biorxiv.org/search/author1%3AChaitanya%2BChintaluri%2B) Tim P Vogels Institute of Science and Technology Austria (ISTA) * [Find this author on Google Scholar](https://www.biorxiv.org/lookup/google-scholar?link_type=googlescholar&gs_type=author&author%5B0%5D=Tim%2BP%2BVogels%2B "Open in new tab") * [Find this author on PubMed](https://www.biorxiv.org/lookup/external-ref?access_num=Vogels%20TP&link_type=AUTHORSEARCH "Open in new tab") * [Search for this author on this site](https://www.biorxiv.org/search/author1%3ATim%2BP%2BVogels%2B) * [ORCID record for Tim P Vogels](http://orcid.org/0000-0003-3295-6181 "Open in new tab") * [Abstract](https://www.biorxiv.org/content/10.64898/2026.09.14.751508v1)[](https://www.biorxiv.org/panels_ajax_tab/biorxiv_tab_art/node:5798334/1) * [Info/History](https://www.biorxiv.org/content/10.64898/2026.09.14.751508v1.article-info)[](https://www.biorxiv.org/panels_ajax_tab/biorxiv_tab_info/node:5798334/1) * [Metrics](https://www.biorxiv.org/content/10.64898/2026.09.14.751508v1.article-metrics)[](https://www.biorxiv.org/panels_ajax_tab/article_tab_metrics/node:5798334/1) * [Supplementary material](https://www.biorxiv.org/content/10.64898/2026.09.14.751508v1.supplementary-material)[](https://www.biorxiv.org/panels_ajax_tab/biorxiv_tab_data/node:5798334/1) * [ Preview PDF](https://www.biorxiv.org/content/10.64898/2026.09.14.751508v1.full.pdf+html)[](https://www.biorxiv.org/panels_ajax_tab/biorxiv_tab_pdf/node:5798334/1) ![Loading](https://www.biorxiv.org/sites/all/modules/contrib/panels_ajax_tab/images/loading.gif) ## Abstract The motor cortex orchestrates a rich and flexible repertoire of network dynamics for rhythmic and goal-directed movements. Computational studies have begun to illuminate the mechanistic origins of this repertoire, but a comprehensive model that can explain the emergence of both transient and self-sustained dynamics is still missing. Here, we show that three simple ingredients: Dalean connectivity, stability, and nonlinear neural responses, suffice to reverse-engineer networks that produce transient, steady-state, and self-sustained periodic activity. A single dynamical principle underlies this repertoire: the interaction of non-normal amplification, inherent to Dalean networks, with neuronal nonlinearity, so to ignite and sustain multi-stable, controllable dynamics. Our approach yields entire families of connectivity matrices that require no hand-tuning or learning of weights. Without fitting them to data, these networks reproduce the population-level signatures of motor cortex, implying that the richness of cortical dynamics need not be sculpted by learning, but may emerge from simple biological ingredients. ### Competing Interest Statement The authors have declared no competing interest. Copyright The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a [CC-BY-NC 4.0 International license](http://creativecommons.org/licenses/by-nc/4.0/). bioRxiv and medRxiv thank the following for their generous financial support: > The Chan Zuckerberg Initiative, Cold Spring Harbor Laboratory, the Sergey Brin Family Foundation, California Institute of Technology, Centre National de la Recherche Scientifique, Fred Hutchinson Cancer Center, Imperial College London, Massachusetts Institute of Technology, Stanford University, The University of Edinburgh, University of Washington, and Vrije Universiteit Amsterdam. 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