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Neuronal networks quantified as vector fields

Szeier, Szilvia LU and Jörntell, Henrik LU (2025) In PLOS ONE 2(5 May).
Abstract

The function of the brain is defined by the interactions between its neurons. But these neurons exist in tremendous numbers, are continuously active, and densely interconnected. Thereby, they form one of the most complex dynamical systems known and there is a lack of approaches to characterize the functional properties of such biological neuronal networks without resorting to dimensionality reduction methods. Here, we introduce an approach to describe these functional properties by using its activity-defining constituents, the weights of the synaptic connections and the current activity of its neurons. We show how a high-dimensional vector field, which describes how the activity distribution across the neuron population is impacted at... (More)

The function of the brain is defined by the interactions between its neurons. But these neurons exist in tremendous numbers, are continuously active, and densely interconnected. Thereby, they form one of the most complex dynamical systems known and there is a lack of approaches to characterize the functional properties of such biological neuronal networks without resorting to dimensionality reduction methods. Here, we introduce an approach to describe these functional properties by using its activity-defining constituents, the weights of the synaptic connections and the current activity of its neurons. We show how a high-dimensional vector field, which describes how the activity distribution across the neuron population is impacted at each instant of time, naturally emerges from these constituents. We show why a mixture of excitatory and inhibitory neurons and a diversity of synaptic weights are critical to obtain a network vector field with a structural richness. We argue that this structural richness can be the foundation of achieving the diverse, dynamic activity patterns across the neuron population observed in recordings in vivo and thereby an underpinning of the behavioral flexibility and adaptability that characterizes biological creatures.

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author
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publishing date
type
Contribution to journal
publication status
published
subject
in
PLOS ONE
volume
2
issue
5 May
article number
e0000047
publisher
Public Library of Science (PLoS)
external identifiers
  • scopus:105028154491
ISSN
1932-6203
DOI
10.1371/journal.pcsy.0000047
language
English
LU publication?
yes
id
9c3638c0-8861-41fe-afa0-0705a7307be6
date added to LUP
2026-02-26 12:42:42
date last changed
2026-02-26 12:42:53
@article{9c3638c0-8861-41fe-afa0-0705a7307be6,
  abstract     = {{<p>The function of the brain is defined by the interactions between its neurons. But these neurons exist in tremendous numbers, are continuously active, and densely interconnected. Thereby, they form one of the most complex dynamical systems known and there is a lack of approaches to characterize the functional properties of such biological neuronal networks without resorting to dimensionality reduction methods. Here, we introduce an approach to describe these functional properties by using its activity-defining constituents, the weights of the synaptic connections and the current activity of its neurons. We show how a high-dimensional vector field, which describes how the activity distribution across the neuron population is impacted at each instant of time, naturally emerges from these constituents. We show why a mixture of excitatory and inhibitory neurons and a diversity of synaptic weights are critical to obtain a network vector field with a structural richness. We argue that this structural richness can be the foundation of achieving the diverse, dynamic activity patterns across the neuron population observed in recordings in vivo and thereby an underpinning of the behavioral flexibility and adaptability that characterizes biological creatures.</p>}},
  author       = {{Szeier, Szilvia and Jörntell, Henrik}},
  issn         = {{1932-6203}},
  language     = {{eng}},
  number       = {{5 May}},
  publisher    = {{Public Library of Science (PLoS)}},
  series       = {{PLOS ONE}},
  title        = {{Neuronal networks quantified as vector fields}},
  url          = {{http://dx.doi.org/10.1371/journal.pcsy.0000047}},
  doi          = {{10.1371/journal.pcsy.0000047}},
  volume       = {{2}},
  year         = {{2025}},
}