{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T19:01:32Z","timestamp":1790017292570,"version":"4.0.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1014763","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T00:00:00Z","timestamp":1789948800000}}],"reference-count":49,"publisher":"Public Library of Science (PLoS)","issue":"9","license":[{"start":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T00:00:00Z","timestamp":1789430400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Extracting circuit mechanisms from neuronal population activity is challenging due to the heterogeneous neuronal properties and diverse strengths in synaptic connections. Standard inference methods, such as Generalized Linear Models (GLMs), typically regress for parameters on all neuronal activity at once. Such a global fitting approach can face identifiability difficulties\u2014for example, where the statistical estimation of strong, opposing weights becomes ill-conditioned in excitatory-inhibitory balanced networks. Here, we introduce FLux-based Effective Coupling (FLEC), a framework that maps spike trains directly to probability fluxes on network state space. Instead of enforcing a single global fit, FLEC infers connectivity and response heterogeneity by quantifying transition rates for each network configuration independently. We demonstrate that FLEC outperforms GLMs and Granger Causality in strongly coupled networks while matching GLM\u2019s performance in standard regimes. Additionally, when combined with Maximum Caliber to construct a minimal dynamical model, the framework better captures temporal statistics\u2014such as inter-spike intervals\u2014than Maximum Entropy models. Robust to parameter variations and unobserved hidden units, and applied to multi-electrode recordings from the salamander retina, FLEC offers a systematic, counting-based tool for inference in nonlinear neuronal circuits.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1014763","type":"journal-article","created":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T18:16:47Z","timestamp":1789496207000},"page":"e1014763","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Inferring effective neuronal circuits via network flux counting"],"prefix":"10.1371","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8792-4625","authenticated-orcid":true,"given":"Kevin S.","family":"Chen","sequence":"first","affiliation":[{"name":"Quantitative Biology Institute, Yale University","place":["New Haven, Connecticut, United States of America"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2559-2773","authenticated-orcid":true,"given":"Ying-Jen","family":"Yang","sequence":"additional","affiliation":[{"name":"Laufer Center of Physical and Quantitative Biology, Stony Brook University","place":["Stony Brook, New York, United States of America"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,9,15]]},"reference":[{"issue":"16","key":"pcbi.1014763.ref001","doi-asserted-by":"crossref","DOI":"10.1016\/j.cell.2025.05.007","article-title":"Infrequent strong connections constrain connectomic predictions of neuronal function","volume":"188","author":"TA Currier","year":"2025","journal-title":"Cell"},{"issue":"7","key":"pcbi.1014763.ref002","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1003138","article-title":"Successful reconstruction of a physiological circuit with known connectivity from spiking activity alone","volume":"9","author":"F Gerhard","year":"2013","journal-title":"PLoS Comput Biol"},{"issue":"3","key":"pcbi.1014763.ref003","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1152\/physrev.1996.76.3.687","article-title":"Principles of rhythmic motor pattern generation","volume":"76","author":"E Marder","year":"1996","journal-title":"Physiol Rev"},{"issue":"5544","key":"pcbi.1014763.ref004","doi-asserted-by":"crossref","first-page":"1030","DOI":"10.1126\/science.1067020","article-title":"The molecular biology of memory storage: a dialogue between genes and synapses","volume":"294","author":"ER Kandel","year":"2001","journal-title":"Science"},{"issue":"23","key":"pcbi.1014763.ref005","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.2417850122","article-title":"Symmetries and synchronization from whole-neural activity in the Caenorhabditis elegans connectome: Integration of functional and structural networks","volume":"122","author":"B Avila","year":"2025","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"7207","key":"pcbi.1014763.ref006","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1038\/nature07140","article-title":"Spatio-temporal correlations and visual signalling in a complete neuronal population","volume":"454","author":"JW Pillow","year":"2008","journal-title":"Nature"},{"key":"pcbi.1014763.ref007","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.03892","article-title":"Cross-synaptic synchrony and transmission of signal and noise across the mouse retina","volume":"3","author":"WN Grimes","year":"2014","journal-title":"Elife"},{"key":"pcbi.1014763.ref008","unstructured":"Rieke F, Warland D, Van Steveninck R d R, Bialek W. 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