Academic Journal
View in EDS

Effects of spatial constraints of inhibitory connectivity on the dynamical development of criticality in spiking networks.

Bibliographic Details
Title: Effects of spatial constraints of inhibitory connectivity on the dynamical development of criticality in spiking networks.
Authors: Kern FB; International Research Center for Neurointelligence (WPI-IRCN), UTIAS, The University of Tokyo, Tokyo, Japan., Date T; Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo, Japan., Chao ZC; International Research Center for Neurointelligence (WPI-IRCN), UTIAS, The University of Tokyo, Tokyo, Japan.
Source: PLoS computational biology [PLoS Comput Biol] 2026 Oct 01; Vol. 22 (10), pp. e1014798. Date of Electronic Publication: 2026 Oct 01 (Print Publication: 2026).
Publication Type: Journal Article
Language: English
Journal Info: Publisher: Public Library of Science Country of Publication: United States NLM ID: 101238922 Publication Model: eCollection Cited Medium: Internet ISSN: 1553-7358 (Electronic) Linking ISSN: 1553734X NLM ISO Abbreviation: PLoS Comput Biol Subsets: MEDLINE
Imprint Name(s): Original Publication: San Francisco, CA : Public Library of Science, [2005]-
MeSH Terms: Action Potentials*/physiology , Nerve Net*/physiology , Models, Neurological*, Synapses/physiology ; Neuronal Plasticity/physiology ; Neurons/physiology ; Neural Inhibition/physiology ; Synaptic Transmission/physiology ; Animals ; Computational Biology ; Computer Simulation ; Humans
Abstract: Neural systems are hypothesized to operate near criticality, enhancing their capacity for optimal information processing, transmission and storage capabilities. Criticality has typically been studied in spiking neural networks and related systems organized in random or full connectivity, with the balance of excitation and inhibition being a key determinant of the critical point of the system. However, given that neurons in the brain are spatially distributed, with their distances significantly influencing connectivity and signal timing, it is unclear how the spatial organization of excitatory and inhibitory connectivity influences the network's development towards criticality. Here, we systematically constrain the distance and density of inhibitory connectivity in two-dimensional spiking networks and allow synaptic weights to develop with activity-dependent excitatory and inhibitory plasticity in the presence of a low level of stochastic intrinsic activity. We then investigate the relationship between inhibitory connectivity, synaptic weights, and the resulting network activity during and after development. We find that networks with longer-range inhibitory synapses tend towards more supercritical behavior compared to networks with a similar number of shorter-range inhibitory synapses. We show that this distance dependence is a consequence of weaker long-range synapses after development due to the presence of synaptic delays, which shift most spike pairs outside of the potentiation window of the inhibitory learning rule.
(Copyright: © 2026 Kern 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.)
Competing Interests: The authors have declared that no competing interests exist.
References: Phys Rev E. 2017 Jan;95(1-1):012413. (PMID: 28208383)
Front Cell Neurosci. 2020 Jul 17;14:213. (PMID: 32765222)
Neuron. 2015 Aug 19;87(4):684-98. (PMID: 26291155)
Mol Psychiatry. 2019 Sep;24(9):1248-1257. (PMID: 31089192)
PLoS Comput Biol. 2015 Jan 15;11(1):e1004043. (PMID: 25590427)
Nat Commun. 2020 Jun 5;11(1):2853. (PMID: 32503982)
J Neurosci. 2011 Jan 5;31(1):55-63. (PMID: 21209189)
Neuroscientist. 2013 Jun;19(3):228-37. (PMID: 22922685)
J Neurosci. 2012 Jul 18;32(29):9817-23. (PMID: 22815496)
Neural Netw. 2007 Apr;20(3):323-34. (PMID: 17517489)
J Neurosci. 2003 Dec 3;23(35):11167-77. (PMID: 14657176)
PLoS Comput Biol. 2010 Dec 02;6(12):e1001013. (PMID: 21152008)
J Neurosci. 2023 Apr 5;43(14):2515-2526. (PMID: 36868860)
PLoS Comput Biol. 2010 Jul 08;6(7):e1000846. (PMID: 20628615)
J Neurosci. 2009 Dec 9;29(49):15595-600. (PMID: 20007483)
Trends Neurosci. 2004 Apr;27(4):186-93. (PMID: 15046877)
Phys Rev Lett. 2005 Feb 11;94(5):058101. (PMID: 15783702)
Nat Rev Neurosci. 2006 Sep;7(9):687-96. (PMID: 16883309)
J Neurophysiol. 1997 Sep;78(3):1199-211. (PMID: 9310412)
Neuron. 2018 Dec 19;100(6):1446-1459.e6. (PMID: 30449656)
Neural Comput. 2004 Jul;16(7):1413-36. (PMID: 15165396)
Neuron. 2015 Apr 22;86(2):514-28. (PMID: 25843405)
Sci Rep. 2024 Aug 20;14(1):19329. (PMID: 39164334)
Front Physiol. 2012 Jun 07;3:163. (PMID: 22701101)
Chaos. 2011 Jun;21(2):025117. (PMID: 21721795)
Neuron. 2018 Oct 24;100(2):294-313. (PMID: 30359598)
PLoS Comput Biol. 2011 Jun;7(6):e1002038. (PMID: 21673863)
Proc Natl Acad Sci U S A. 1997 Jan 21;94(2):719-23. (PMID: 9012851)
PLoS One. 2007 May 09;2(5):e439. (PMID: 17502919)
Science. 2011 Dec 16;334(6062):1569-73. (PMID: 22075724)
J Neurosci. 2004 Jun 2;24(22):5216-29. (PMID: 15175392)
Philos Trans A Math Phys Eng Sci. 2008 Feb 13;366(1864):329-43. (PMID: 17673410)
Phys Rev Lett. 2019 May 24;122(20):208101. (PMID: 31172737)
Front Syst Neurosci. 2014 Sep 23;8:166. (PMID: 25294989)
Nat Neurosci. 2000 Sep;3(9):919-26. (PMID: 10966623)
PLoS Comput Biol. 2014 Apr 03;10(4):e1003557. (PMID: 24699277)
Genes Brain Behav. 2003 Oct;2(5):255-67. (PMID: 14606691)
PLoS One. 2017 May 26;12(5):e0178683. (PMID: 28552964)
Entry Date(s): Date Created: 20261001 Date Completed: 20261007 Latest Revision: 20261009
Update Code: 20261009
PubMed Central ID: PMC13645236
DOI: 10.1371/journal.pcbi.1014798
PMID: 42821632
Database: MEDLINE
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:cmedm&genre=article&issn=15537358&ISBN=&volume=22&issue=10&date=20261001&spage=e1014798&pages=e1014798&title=PLoS computational biology&atitle=Effects%20of%20spatial%20constraints%20of%20inhibitory%20connectivity%20on%20the%20dynamical%20development%20of%20criticality%20in%20spiking%20networks.&aulast=Kern%20FB&id=DOI:10.1371/journal.pcbi.1014798
    Name: Full Text Finder (for New FTF UI) (ns324271)
    Category: fullText
    Text: Full Text Finder
    MouseOverText: Full Text Finder
Header DbId: cmedm
DbLabel: MEDLINE
An: 42821632
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Effects of spatial constraints of inhibitory connectivity on the dynamical development of criticality in spiking networks.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AU" term="%22Kern+FB%22">Kern FB</searchLink>; International Research Center for Neurointelligence (WPI-IRCN), UTIAS, The University of Tokyo, Tokyo, Japan.<br /><searchLink fieldCode="AU" term="%22Date+T%22">Date T</searchLink>; Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo, Japan.<br /><searchLink fieldCode="AU" term="%22Chao+ZC%22">Chao ZC</searchLink>; International Research Center for Neurointelligence (WPI-IRCN), UTIAS, The University of Tokyo, Tokyo, Japan.
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22101238922%22">PLoS computational biology</searchLink> [PLoS Comput Biol] 2026 Oct 01; Vol. 22 (10), pp. e1014798. <i>Date of Electronic Publication: </i>2026 Oct 01 (<i>Print Publication: </i>2026).
– Name: TypePub
  Label: Publication Type
  Group: TypPub
  Data: Journal Article
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: TitleSource
  Label: Journal Info
  Group: Src
  Data: <i>Publisher: </i><searchLink fieldCode="PB" term="%22Public+Library+of+Science%22">Public Library of Science </searchLink><i>Country of Publication: </i>United States <i>NLM ID: </i>101238922 <i>Publication Model: </i>eCollection <i>Cited Medium: </i>Internet <i>ISSN: </i>1553-7358 (Electronic) <i>Linking ISSN: </i><searchLink fieldCode="IS" term="%221553734X%22">1553734X </searchLink><i>NLM ISO Abbreviation: </i>PLoS Comput Biol <i>Subsets: </i>MEDLINE
– Name: PublisherInfo
  Label: Imprint Name(s)
  Group: PubInfo
  Data: <i>Original Publication</i>: San Francisco, CA : Public Library of Science, [2005]-
– Name: SubjectMESH
  Label: MeSH Terms
  Group: Su
  Data: <searchLink fieldCode="MM" term="%22Action+Potentials%22">Action Potentials*</searchLink>/<searchLink fieldCode="MM" term="%22Action+Potentials+physiology%22">physiology</searchLink> <br /><searchLink fieldCode="MM" term="%22Nerve+Net%22">Nerve Net*</searchLink>/<searchLink fieldCode="MM" term="%22Nerve+Net+physiology%22">physiology</searchLink> <br /><searchLink fieldCode="MM" term="%22Models%2C+Neurological%22">Models, Neurological*</searchLink><br /><searchLink fieldCode="MH" term="%22Synapses%22">Synapses</searchLink>/<searchLink fieldCode="MH" term="%22Synapses+physiology%22">physiology</searchLink> ; <searchLink fieldCode="MH" term="%22Neuronal+Plasticity%22">Neuronal Plasticity</searchLink>/<searchLink fieldCode="MH" term="%22Neuronal+Plasticity+physiology%22">physiology</searchLink> ; <searchLink fieldCode="MH" term="%22Neurons%22">Neurons</searchLink>/<searchLink fieldCode="MH" term="%22Neurons+physiology%22">physiology</searchLink> ; <searchLink fieldCode="MH" term="%22Neural+Inhibition%22">Neural Inhibition</searchLink>/<searchLink fieldCode="MH" term="%22Neural+Inhibition+physiology%22">physiology</searchLink> ; <searchLink fieldCode="MH" term="%22Synaptic+Transmission%22">Synaptic Transmission</searchLink>/<searchLink fieldCode="MH" term="%22Synaptic+Transmission+physiology%22">physiology</searchLink> ; <searchLink fieldCode="MH" term="%22Animals%22">Animals</searchLink> ; <searchLink fieldCode="MH" term="%22Computational+Biology%22">Computational Biology</searchLink> ; <searchLink fieldCode="MH" term="%22Computer+Simulation%22">Computer Simulation</searchLink> ; <searchLink fieldCode="MH" term="%22Humans%22">Humans</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Neural systems are hypothesized to operate near criticality, enhancing their capacity for optimal information processing, transmission and storage capabilities. Criticality has typically been studied in spiking neural networks and related systems organized in random or full connectivity, with the balance of excitation and inhibition being a key determinant of the critical point of the system. However, given that neurons in the brain are spatially distributed, with their distances significantly influencing connectivity and signal timing, it is unclear how the spatial organization of excitatory and inhibitory connectivity influences the network's development towards criticality. Here, we systematically constrain the distance and density of inhibitory connectivity in two-dimensional spiking networks and allow synaptic weights to develop with activity-dependent excitatory and inhibitory plasticity in the presence of a low level of stochastic intrinsic activity. We then investigate the relationship between inhibitory connectivity, synaptic weights, and the resulting network activity during and after development. We find that networks with longer-range inhibitory synapses tend towards more supercritical behavior compared to networks with a similar number of shorter-range inhibitory synapses. We show that this distance dependence is a consequence of weaker long-range synapses after development due to the presence of synaptic delays, which shift most spike pairs outside of the potentiation window of the inhibitory learning rule.<br /> (Copyright: © 2026 Kern 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.)
– Name: Abstract
  Label: Competing Interests
  Group: Ab
  Data: The authors have declared that no competing interests exist.
– Name: Ref
  Label: References
  Group: RefInfo
  Data: Phys Rev E. 2017 Jan;95(1-1):012413. (PMID: <searchLink fieldCode="PM" term="%2228208383%22">28208383)</searchLink><br />Front Cell Neurosci. 2020 Jul 17;14:213. (PMID: <searchLink fieldCode="PM" term="%2232765222%22">32765222)</searchLink><br />Neuron. 2015 Aug 19;87(4):684-98. (PMID: <searchLink fieldCode="PM" term="%2226291155%22">26291155)</searchLink><br />Mol Psychiatry. 2019 Sep;24(9):1248-1257. (PMID: <searchLink fieldCode="PM" term="%2231089192%22">31089192)</searchLink><br />PLoS Comput Biol. 2015 Jan 15;11(1):e1004043. (PMID: <searchLink fieldCode="PM" term="%2225590427%22">25590427)</searchLink><br />Nat Commun. 2020 Jun 5;11(1):2853. (PMID: <searchLink fieldCode="PM" term="%2232503982%22">32503982)</searchLink><br />J Neurosci. 2011 Jan 5;31(1):55-63. (PMID: <searchLink fieldCode="PM" term="%2221209189%22">21209189)</searchLink><br />Neuroscientist. 2013 Jun;19(3):228-37. (PMID: <searchLink fieldCode="PM" term="%2222922685%22">22922685)</searchLink><br />J Neurosci. 2012 Jul 18;32(29):9817-23. (PMID: <searchLink fieldCode="PM" term="%2222815496%22">22815496)</searchLink><br />Neural Netw. 2007 Apr;20(3):323-34. (PMID: <searchLink fieldCode="PM" term="%2217517489%22">17517489)</searchLink><br />J Neurosci. 2003 Dec 3;23(35):11167-77. (PMID: <searchLink fieldCode="PM" term="%2214657176%22">14657176)</searchLink><br />PLoS Comput Biol. 2010 Dec 02;6(12):e1001013. (PMID: <searchLink fieldCode="PM" term="%2221152008%22">21152008)</searchLink><br />J Neurosci. 2023 Apr 5;43(14):2515-2526. (PMID: <searchLink fieldCode="PM" term="%2236868860%22">36868860)</searchLink><br />PLoS Comput Biol. 2010 Jul 08;6(7):e1000846. (PMID: <searchLink fieldCode="PM" term="%2220628615%22">20628615)</searchLink><br />J Neurosci. 2009 Dec 9;29(49):15595-600. (PMID: <searchLink fieldCode="PM" term="%2220007483%22">20007483)</searchLink><br />Trends Neurosci. 2004 Apr;27(4):186-93. (PMID: <searchLink fieldCode="PM" term="%2215046877%22">15046877)</searchLink><br />Phys Rev Lett. 2005 Feb 11;94(5):058101. (PMID: <searchLink fieldCode="PM" term="%2215783702%22">15783702)</searchLink><br />Nat Rev Neurosci. 2006 Sep;7(9):687-96. (PMID: <searchLink fieldCode="PM" term="%2216883309%22">16883309)</searchLink><br />J Neurophysiol. 1997 Sep;78(3):1199-211. (PMID: <searchLink fieldCode="PM" term="%229310412%22">9310412)</searchLink><br />Neuron. 2018 Dec 19;100(6):1446-1459.e6. (PMID: <searchLink fieldCode="PM" term="%2230449656%22">30449656)</searchLink><br />Neural Comput. 2004 Jul;16(7):1413-36. (PMID: <searchLink fieldCode="PM" term="%2215165396%22">15165396)</searchLink><br />Neuron. 2015 Apr 22;86(2):514-28. (PMID: <searchLink fieldCode="PM" term="%2225843405%22">25843405)</searchLink><br />Sci Rep. 2024 Aug 20;14(1):19329. (PMID: <searchLink fieldCode="PM" term="%2239164334%22">39164334)</searchLink><br />Front Physiol. 2012 Jun 07;3:163. (PMID: <searchLink fieldCode="PM" term="%2222701101%22">22701101)</searchLink><br />Chaos. 2011 Jun;21(2):025117. (PMID: <searchLink fieldCode="PM" term="%2221721795%22">21721795)</searchLink><br />Neuron. 2018 Oct 24;100(2):294-313. (PMID: <searchLink fieldCode="PM" term="%2230359598%22">30359598)</searchLink><br />PLoS Comput Biol. 2011 Jun;7(6):e1002038. (PMID: <searchLink fieldCode="PM" term="%2221673863%22">21673863)</searchLink><br />Proc Natl Acad Sci U S A. 1997 Jan 21;94(2):719-23. (PMID: <searchLink fieldCode="PM" term="%229012851%22">9012851)</searchLink><br />PLoS One. 2007 May 09;2(5):e439. (PMID: <searchLink fieldCode="PM" term="%2217502919%22">17502919)</searchLink><br />Science. 2011 Dec 16;334(6062):1569-73. (PMID: <searchLink fieldCode="PM" term="%2222075724%22">22075724)</searchLink><br />J Neurosci. 2004 Jun 2;24(22):5216-29. (PMID: <searchLink fieldCode="PM" term="%2215175392%22">15175392)</searchLink><br />Philos Trans A Math Phys Eng Sci. 2008 Feb 13;366(1864):329-43. (PMID: <searchLink fieldCode="PM" term="%2217673410%22">17673410)</searchLink><br />Phys Rev Lett. 2019 May 24;122(20):208101. (PMID: <searchLink fieldCode="PM" term="%2231172737%22">31172737)</searchLink><br />Front Syst Neurosci. 2014 Sep 23;8:166. (PMID: <searchLink fieldCode="PM" term="%2225294989%22">25294989)</searchLink><br />Nat Neurosci. 2000 Sep;3(9):919-26. (PMID: <searchLink fieldCode="PM" term="%2210966623%22">10966623)</searchLink><br />PLoS Comput Biol. 2014 Apr 03;10(4):e1003557. (PMID: <searchLink fieldCode="PM" term="%2224699277%22">24699277)</searchLink><br />Genes Brain Behav. 2003 Oct;2(5):255-67. (PMID: <searchLink fieldCode="PM" term="%2214606691%22">14606691)</searchLink><br />PLoS One. 2017 May 26;12(5):e0178683. (PMID: <searchLink fieldCode="PM" term="%2228552964%22">28552964)</searchLink>
– Name: DateEntry
  Label: Entry Date(s)
  Group: Date
  Data: <i>Date Created: </i>20261001 <i>Date Completed: </i>20261007 <i>Latest Revision: </i>20261009
– Name: DateUpdate
  Label: Update Code
  Group: Date
  Data: 20261009
– Name: PubmedCentralID
  Label: PubMed Central ID
  Group: ID
  Data: PMC13645236
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1371/journal.pcbi.1014798
– Name: AN
  Label: PMID
  Group: ID
  Data: 42821632
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=cmedm&AN=42821632
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1371/journal.pcbi.1014798
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        StartPage: e1014798
    Subjects:
      – SubjectFull: Synapses physiology
        Type: general
      – SubjectFull: Neuronal Plasticity physiology
        Type: general
      – SubjectFull: Neurons physiology
        Type: general
      – SubjectFull: Neural Inhibition physiology
        Type: general
      – SubjectFull: Synaptic Transmission physiology
        Type: general
      – SubjectFull: Animals
        Type: general
      – SubjectFull: Computational Biology
        Type: general
      – SubjectFull: Computer Simulation
        Type: general
      – SubjectFull: Humans
        Type: general
      – SubjectFull: Action Potentials physiology
        Type: general
      – SubjectFull: Nerve Net physiology
        Type: general
      – SubjectFull: Models, Neurological
        Type: general
    Titles:
      – TitleFull: Effects of spatial constraints of inhibitory connectivity on the dynamical development of criticality in spiking networks.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Kern FB
      – PersonEntity:
          Name:
            NameFull: Date T
      – PersonEntity:
          Name:
            NameFull: Chao ZC
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 10
              Text: 2026 Oct 01
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-electronic
              Value: 1553-7358
          Numbering:
            – Type: volume
              Value: 22
            – Type: issue
              Value: 10
          Titles:
            – TitleFull: PLoS computational biology
              Type: main
ResultId 1