{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T18:51:38Z","timestamp":1791399098926,"version":"4.3.3"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1014798","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T00:00:00Z","timestamp":1791331200000}}],"reference-count":46,"publisher":"Public Library of Science (PLoS)","issue":"10","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"World Premier International Research Center Initiative (WPI), MEXT"},{"name":"Forefront Physics and Mathematics Program to Drive Transformation (FoPM), a World-leading Innovative Graduate Study (WINGS) Program"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>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\u2019s 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.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1014798","type":"journal-article","created":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T17:50:01Z","timestamp":1790877001000},"page":"e1014798","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Effects of spatial constraints of inhibitory connectivity on the dynamical development of criticality in spiking networks"],"prefix":"10.1371","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3420-4576","authenticated-orcid":true,"given":"Felix Benjamin","family":"Kern","sequence":"first","affiliation":[{"name":"International Research Center for Neurointelligence (WPI-IRCN), UTIAS, The University of Tokyo","place":["Tokyo, Japan"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Takahisa","family":"Date","sequence":"additional","affiliation":[{"name":"Graduate School of Science, The University of Tokyo","place":["Tokyo, Japan"],"department":["Department of Physics"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9402-0851","authenticated-orcid":true,"given":"Zenas C.","family":"Chao","sequence":"additional","affiliation":[{"name":"International Research Center for Neurointelligence (WPI-IRCN), UTIAS, The University of Tokyo","place":["Tokyo, Japan"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,10,1]]},"reference":[{"issue":"1864","key":"pcbi.1014798.ref001","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1098\/rsta.2007.2092","article-title":"The criticality hypothesis: How local cortical networks might optimize information processing","volume":"366","author":"JM Beggs","year":"2007","journal-title":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"key":"pcbi.1014798.ref002","doi-asserted-by":"crossref","first-page":"163","DOI":"10.3389\/fphys.2012.00163","article-title":"Being critical of criticality in the brain","volume":"3","author":"JM Beggs","year":"2012","journal-title":"Frontiers in Physiology"},{"issue":"3","key":"pcbi.1014798.ref003","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.neunet.2007.04.017","article-title":"Edge of chaos and prediction of computational performance for neural circuit models","volume":"20","author":"R Legenstein","year":"2007","journal-title":"Neural Netw"},{"issue":"7","key":"pcbi.1014798.ref004","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1162\/089976604323057443","article-title":"Real-time computation at the edge of chaos in recurrent neural networks","volume":"16","author":"N Bertschinger","year":"2004","journal-title":"Neural Comput"},{"issue":"35","key":"pcbi.1014798.ref005","doi-asserted-by":"crossref","first-page":"11167","DOI":"10.1523\/JNEUROSCI.23-35-11167.2003","article-title":"Neuronal avalanches in neocortical circuits","volume":"23","author":"JM Beggs","year":"2003","journal-title":"The Journal of Neuroscience: The Official Journal of the Society for Neuroscience"},{"issue":"1","key":"pcbi.1014798.ref006","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1523\/JNEUROSCI.4637-10.2011","article-title":"Information capacity and transmission are maximized in balanced cortical networks with neuronal avalanches","volume":"31","author":"WL Shew","year":"2011","journal-title":"J Neurosci"},{"issue":"5","key":"pcbi.1014798.ref007","doi-asserted-by":"crossref","first-page":"058101","DOI":"10.1103\/PhysRevLett.94.058101","article-title":"Critical branching captures activity in living neural networks and maximizes the number of metastable States","volume":"94","author":"C Haldeman","year":"2005","journal-title":"Phys Rev Lett"},{"issue":"22","key":"pcbi.1014798.ref008","doi-asserted-by":"crossref","first-page":"5216","DOI":"10.1523\/JNEUROSCI.0540-04.2004","article-title":"Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures","volume":"24","author":"JM Beggs","year":"2004","journal-title":"J Neurosci"},{"issue":"5","key":"pcbi.1014798.ref009","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1038\/nphys289","article-title":"Optimal dynamical range of excitable networks at criticality","volume":"2","author":"O Kinouchi","year":"2006","journal-title":"Nature Phys"},{"issue":"49","key":"pcbi.1014798.ref010","doi-asserted-by":"crossref","first-page":"15595","DOI":"10.1523\/JNEUROSCI.3864-09.2009","article-title":"Neuronal avalanches imply maximum dynamic range in cortical networks at criticality","volume":"29","author":"WL Shew","year":"2009","journal-title":"J Neurosci"},{"issue":"6","key":"pcbi.1014798.ref011","doi-asserted-by":"crossref","DOI":"10.1016\/j.neuron.2018.10.045","article-title":"Whole-Brain Neuronal Activity Displays Crackling Noise Dynamics","volume":"100","author":"A Ponce-Alvarez","year":"2018","journal-title":"Neuron"},{"issue":"12","key":"pcbi.1014798.ref012","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1001013","article-title":"Self-organized criticality in developing neuronal networks","volume":"6","author":"C Tetzlaff","year":"2010","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1014798.ref013","doi-asserted-by":"crossref","DOI":"10.3389\/fphy.2021.639389","article-title":"Self-Organized Criticality in the Brain","volume":"9","author":"D Plenz","year":"2021","journal-title":"Frontiers in Physics"},{"key":"pcbi.1014798.ref014","doi-asserted-by":"crossref","DOI":"10.3389\/fnsys.2014.00166","article-title":"Self-Organized Criticality as a Fundamental Property of Neural Systems","volume":"8","author":"J Hesse","year":"2014","journal-title":"Frontiers in Systems Neuroscience"},{"key":"pcbi.1014798.ref015","doi-asserted-by":"crossref","DOI":"10.3389\/fphy.2021.619661","article-title":"Self-organization toward criticality by synaptic plasticity","volume":"9","author":"R Zeraati","year":"2021","journal-title":"Frontiers in Physics"},{"issue":"1","key":"pcbi.1014798.ref016","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1004043","article-title":"Synaptic plasticity enables adaptive self-tuning critical networks","volume":"11","author":"N Stepp","year":"2015","journal-title":"PLoS Comput Biol"},{"issue":"5","key":"pcbi.1014798.ref017","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0178683","article-title":"Criticality meets learning: Criticality signatures in a self-organizing recurrent neural network","volume":"12","author":"B Del Papa","year":"2017","journal-title":"PLOS ONE"},{"issue":"6","key":"pcbi.1014798.ref018","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1002038","article-title":"Neurobiologically realistic determinants of self-organized criticality in networks of spiking neurons","volume":"7","author":"M Rubinov","year":"2011","journal-title":"PLoS Comput Biol"},{"issue":"12","key":"pcbi.1014798.ref019","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1038\/nphys758","article-title":"Dynamical synapses causing self-organized criticality in neural networks","volume":"3","author":"A Levina","year":"2007","journal-title":"Nature Phys"},{"issue":"29","key":"pcbi.1014798.ref020","doi-asserted-by":"crossref","first-page":"9817","DOI":"10.1523\/JNEUROSCI.5990-11.2012","article-title":"Critical-state dynamics of avalanches and oscillations jointly emerge from balanced excitation\/inhibition in neuronal networks","volume":"32","author":"S-S Poil","year":"2012","journal-title":"J Neurosci"},{"issue":"5","key":"pcbi.1014798.ref021","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0000439","article-title":"On the dynamics of the spontaneous activity in neuronal networks","volume":"2","author":"A Mazzoni","year":"2007","journal-title":"PLOS ONE"},{"issue":"7","key":"pcbi.1014798.ref022","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1000846","article-title":"Avalanches in a stochastic model of spiking neurons","volume":"6","author":"M Benayoun","year":"2010","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1014798.ref023","doi-asserted-by":"crossref","DOI":"10.1017\/nws.2021.3","article-title":"Logic and learning in network cascades","volume":"9","author":"GJ Wilkerson","year":"2021","journal-title":"Net Sci"},{"issue":"2","key":"pcbi.1014798.ref024","doi-asserted-by":"crossref","first-page":"025117","DOI":"10.1063\/1.3600760","article-title":"Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus","volume":"21","author":"DB Larremore","year":"2011","journal-title":"Chaos"},{"key":"pcbi.1014798.ref025","doi-asserted-by":"crossref","first-page":"129638","DOI":"10.1016\/j.physa.2024.129638","article-title":"\u201cAll-or-none\u201d dynamics and local-range dominated interaction leading to criticality in neural systems","volume":"638","author":"J Yang","year":"2024","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"issue":"2","key":"pcbi.1014798.ref026","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1073\/pnas.94.2.719","article-title":"The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability","volume":"94","author":"MV Tsodyks","year":"1997","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"9","key":"pcbi.1014798.ref027","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1038\/78829","article-title":"Competitive Hebbian learning through spike-timing-dependent synaptic plasticity","volume":"3","author":"S Song","year":"2000","journal-title":"Nat Neurosci"},{"issue":"2","key":"pcbi.1014798.ref028","doi-asserted-by":"crossref","DOI":"10.1063\/5.0152633","article-title":"Noise and spike-time-dependent plasticity drive self-organized criticality in spiking neural network: Toward neuromorphic computing","volume":"123","author":"N Ikeda","year":"2023","journal-title":"Applied Physics Letters"},{"issue":"6062","key":"pcbi.1014798.ref029","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1126\/science.1211095","article-title":"Inhibitory plasticity balances excitation and inhibition in sensory pathways and memory networks","volume":"334","author":"TP Vogels","year":"2011","journal-title":"Science"},{"issue":"2","key":"pcbi.1014798.ref030","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1016\/j.neuron.2015.03.014","article-title":"Inhibitory and excitatory spike-timing-dependent plasticity in the auditory cortex","volume":"86","author":"JA D\u2019amour","year":"2015","journal-title":"Neuron"},{"key":"pcbi.1014798.ref031","doi-asserted-by":"crossref","first-page":"213","DOI":"10.3389\/fncel.2020.00213","article-title":"Silent Synapse-Based Mechanisms of Critical Period Plasticity","volume":"14","author":"W Xu","year":"2020","journal-title":"Front Cell Neurosci"},{"issue":"1","key":"pcbi.1014798.ref032","doi-asserted-by":"crossref","first-page":"19329","DOI":"10.1038\/s41598-024-70014-4","article-title":"The recovery of parabolic avalanches in spatially subsampled neuronal networks at criticality","volume":"14","author":"K Srinivasan","year":"2024","journal-title":"Sci Rep"},{"key":"pcbi.1014798.ref033","doi-asserted-by":"crossref","first-page":"012413","DOI":"10.1103\/PhysRevE.95.012413","article-title":"Power-law statistics and universal scaling in the absence of criticality","volume":"95","author":"J Touboul","year":"2017","journal-title":"Phys Rev E"},{"issue":"20","key":"pcbi.1014798.ref034","doi-asserted-by":"crossref","first-page":"208101","DOI":"10.1103\/PhysRevLett.122.208101","article-title":"Criticality between Cortical States","volume":"122","author":"AJ Fontenele","year":"2019","journal-title":"Phys Rev Lett"},{"issue":"3","key":"pcbi.1014798.ref035","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1177\/1073858412456743","article-title":"The logic of inhibitory connectivity in the neocortex","volume":"19","author":"E Fino","year":"2013","journal-title":"Neuroscientist"},{"issue":"4","key":"pcbi.1014798.ref036","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1003557","article-title":"Influence of wiring cost on the large-scale architecture of human cortical connectivity","volume":"10","author":"D Samu","year":"2014","journal-title":"PLoS Comput Biol"},{"issue":"4","key":"pcbi.1014798.ref037","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.tins.2004.02.007","article-title":"Interneuron Diversity Series: Circuit Complexity and Axon Wiring Economy of Cortical Interneurons","volume":"27","author":"G Buzs\u00e1ki","year":"2004","journal-title":"Trends in Neurosciences"},{"issue":"9","key":"pcbi.1014798.ref038","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1038\/nrn1954","article-title":"The origin and specification of cortical interneurons","volume":"7","author":"CP Wonders","year":"2006","journal-title":"Nat Rev Neurosci"},{"issue":"2","key":"pcbi.1014798.ref039","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.neuron.2018.10.009","article-title":"Development and Functional Diversification of Cortical Interneurons","volume":"100","author":"L Lim","year":"2018","journal-title":"Neuron"},{"issue":"5","key":"pcbi.1014798.ref040","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1034\/j.1601-183X.2003.00037.x","article-title":"Model of autism: increased ratio of excitation\/inhibition in key neural systems","volume":"2","author":"JLR Rubenstein","year":"2003","journal-title":"Genes Brain Behav"},{"issue":"4","key":"pcbi.1014798.ref041","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1016\/j.neuron.2015.07.033","article-title":"Excitatory\/Inhibitory Balance and Circuit Homeostasis in Autism Spectrum Disorders","volume":"87","author":"SB Nelson","year":"2015","journal-title":"Neuron"},{"issue":"9","key":"pcbi.1014798.ref042","doi-asserted-by":"crossref","first-page":"1248","DOI":"10.1038\/s41380-019-0426-0","article-title":"Excitation-inhibition balance as a framework for investigating mechanisms in neuropsychiatric disorders","volume":"24","author":"VS Sohal","year":"2019","journal-title":"Mol Psychiatry"},{"issue":"2","key":"pcbi.1014798.ref043","doi-asserted-by":"crossref","first-page":"023005","DOI":"10.1088\/1367-2630\/14\/2\/023005","article-title":"Hierarchical modular structure enhances the robustness of self-organized criticality in neural networks","volume":"14","author":"S-J Wang","year":"2012","journal-title":"New J Phys"},{"issue":"14","key":"pcbi.1014798.ref044","doi-asserted-by":"crossref","first-page":"2515","DOI":"10.1523\/JNEUROSCI.1420-22.2023","article-title":"Structural Modularity Tunes Mesoscale Criticality in Biological Neuronal Networks","volume":"43","author":"S Okujeni","year":"2023","journal-title":"J Neurosci"},{"issue":"1","key":"pcbi.1014798.ref045","doi-asserted-by":"crossref","first-page":"2853","DOI":"10.1038\/s41467-020-16548-3","article-title":"Control of criticality and computation in spiking neuromorphic networks with plasticity","volume":"11","author":"B Cramer","year":"2020","journal-title":"Nat Commun"},{"issue":"3","key":"pcbi.1014798.ref046","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1152\/jn.1997.78.3.1199","article-title":"Propagating neuronal discharges in neocortical slices: computational and experimental study","volume":"78","author":"D Golomb","year":"1997","journal-title":"J Neurophysiol"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1014798","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T00:00:00Z","timestamp":1791331200000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1014798","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T18:03:25Z","timestamp":1791396205000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1014798"}},"subtitle":[],"editor":[{"given":"Prejaas","family":"Tewarie","sequence":"first","affiliation":[{"name":"University of Nottingham","place":["UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND"]}],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2026,10,1]]},"references-count":46,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2026,10,1]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1014798","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,1]]}}}