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Frequency-dependent coupling in response to oscillatory inputs in minimal networks of electrically coupled nodes: Gap junction networks and spatially extended neurons.

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Title: Frequency-dependent coupling in response to oscillatory inputs in minimal networks of electrically coupled nodes: Gap junction networks and spatially extended neurons.
Authors: Bel A; Departamento de Matemática, Universidad Nacional del Sur (UNS) and CONICET, Bahía Blanca, Argentina.; ETSI de Minas y Energía, Departamento de Ingeniería Geológica y Minera, Universidad Politécnica de Madrid, Madrid, España., Chialva U; Departamento de Matemática, Universidad Nacional del Sur (UNS) and CONICET, Bahía Blanca, Argentina., Rotstein HG; Federated Department of Biological Sciences, New Jersey Institute of Technology and Rutgers University, Newark, NJ, USA. horacio@njit.edu.
Source: Biological cybernetics [Biol Cybern] 2026 Jul 23; Vol. 120 (3-4). Date of Electronic Publication: 2026 Jul 23.
Publication Type: Journal Article
Language: English
Journal Info: Publisher: Springer Verlag Country of Publication: Germany NLM ID: 7502533 Publication Model: Electronic Cited Medium: Internet ISSN: 1432-0770 (Electronic) Linking ISSN: 03401200 NLM ISO Abbreviation: Biol Cybern Subsets: MEDLINE
Imprint Name(s): Publication: Berlin : Springer Verlag
Original Publication: Berlin, New York, Springer-Verlag.
MeSH Terms: Neurons*/physiology , Nerve Net*/physiology , Gap Junctions*/physiology , Biological Clocks*/physiology , Models, Neurological*, Action Potentials/physiology ; Animals ; Computer Simulation
Abstract: In electrically coupled networks, the coupling coefficient (CC) quantifies the strength of the connectivity between pairs of nodes. The CC is typically measured by computing the relative stationary responses to constant inputs of the indirectly activated (post-J) and the directly activated (pre-J) nodes. The natural extension of the CC to time-dependent inputs is frequency-dependent and has two components reflecting the contributions of the amplitude and phase frequency-dependent profiles (curves of these quantities as a function of the frequency INLINEMATH ) of the participating nodes: the quotient of amplitudes INLINEMATH and the phase-difference INLINEMATH profiles. The properties and mechanisms of generation of these frequency-dependent CCs (FD-CCs) are largely unknown beyond electrically coupled passive cells and their electrical linear circuit equivalents. For passive cells, INLINEMATH is monotonically decreasing (low-pass filter) and INLINEMATH is monotonically increasing and positive. Moreover, for linear systems, the FD-CCs depend on the properties of the post-J cell and the connectivity and are independent of the properties of the pre-J cell and the input amplitude. It remains largely unclear how the FD-CCs are shaped by the presence of (i) intrinsic cellular positive and negative feedback currents (resonance and amplification), and (ii) cellular nonlinearities that incorporates the dependence of the FD-CC on the post-J node in addition to the pre-J one. In this paper we address these issues by using biophysically plausible (conductance-based) mathematical modeling, numerical simulations, analytical calculations and dynamical systems tools. We conduct a systematic analysis of the properties of the FD-CC profiles in networks of two electrically connected nodes receiving oscillatory inputs, which is the minimal network architecture that allows for a systematic study of the biophysical and dynamic mechanisms that shape the FD-CC profiles. The participating neurons are either passive cells (low-pass filters) or resonators (band-pass filter) and exhibit lagging or mixed leading-lagging phase responses as the input frequency increases. The formalism and tools we develop and use in this paper are amenable to be extended to larger networks with an arbitrary number of nodes, to spatially extended multicompartment neuronal models, and to neurons having a variety of ionic currents.
(© 2026. The Author(s).)
Competing Interests: Declarations. Competing interests: The authors declare no competing interests.
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Grant Information: PGI 24/L13 Universidad Nacional del Sur, Argentina; IOS-2002863 National Science Foundation
Entry Date(s): Date Created: 20260723 Date Completed: 20260723 Latest Revision: 20260726
Update Code: 20260726
PubMed Central ID: PMC13395867
DOI: 10.1007/s00422-026-01047-3
PMID: 42489927
Database: MEDLINE
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ISSN:1432-0770
DOI:10.1007/s00422-026-01047-3