{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T22:24:19Z","timestamp":1792189459416,"version":"4.4.0"},"reference-count":52,"publisher":"National Academy of Sciences","issue":"32","license":[{"start":{"date-parts":[[2025,8,4]],"date-time":"2025-08-04T00:00:00Z","timestamp":1754265600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000065","name":"HHS | NIH | National Institute of Neurological Disorders and Stroke","doi-asserted-by":"publisher","award":["R35 NS 097343"],"award-info":[{"award-number":["R35 NS 097343"]}],"id":[{"id":"10.13039\/100000065","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100001201","name":"Kavli Foundation","doi-asserted-by":"publisher","award":["G118028"],"award-info":[{"award-number":["G118028"]}],"id":[{"id":"10.13039\/100001201","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2025,8,12]]},"abstract":"<jats:p>Obtaining predictive models of a neural system is notoriously challenging. Detailed models suffer from excess model complexity and are difficult to fit efficiently. Simplified models must negotiate a tradeoff between tractability, predictive power, and ease of interpretation. We present a modeling paradigm for estimating predictive, mechanistic models of neurons and small circuits that navigates these issues using methods from systems theory. The key insight is that membrane currents can be modeled using two scalable system components optimized for learning: linear state space models, and nonlinear artificial neural networks. Combining these components, we construct two types of membrane currents: lumped currents, which are flexible, and data-driven conductance-based currents, which are interpretable. The resulting class of models\u2014which we call recurrent mechanistic models (RMMs)\u2014can be trained in a matter of seconds to minutes on intracellular recordings during an electrophysiology experiment, representing a step change in performance over previous approaches. As a proof-of-principle, we use RMMs to learn the dynamics of two groups of neurons, and their synaptic connections, in the Stomatogastric Ganglion, a well-known central pattern generator. Due to their reliability, efficiency, and interpretability, RMMs enable qualitatively new kinds of experiments using predictive models in closed-loop neurophysiology and online estimation of neural properties in living preparations.<\/jats:p>","DOI":"10.1073\/pnas.2426916122","type":"journal-article","created":{"date-parts":[[2025,8,4]],"date-time":"2025-08-04T19:05:07Z","timestamp":1754334307000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":6,"title":["Rapid, interpretable data-driven models of neural dynamics using recurrent mechanistic models"],"prefix":"10.1073","volume":"122","author":[{"given":"Thiago B.","family":"Burghi","sequence":"first","affiliation":[{"name":"Department of Engineering","place":["Cambridge, United Kingdom"]},{"name":"University of Cambridge","place":["Cambridge, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maria","family":"Ivanova","sequence":"additional","affiliation":[{"name":"Department of Biology","place":["Waltham"]},{"name":"Brandeis University","place":["Waltham"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ekaterina","family":"Morozova","sequence":"additional","affiliation":[{"name":"Department of Biology","place":["Waltham"]},{"name":"Brandeis University","place":["Waltham"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huaxinyu","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Engineering","place":["Cambridge, United Kingdom"]},{"name":"University of Cambridge","place":["Cambridge, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9632-5448","authenticated-orcid":false,"given":"Eve","family":"Marder","sequence":"additional","affiliation":[{"name":"Department of Biology","place":["Waltham"]},{"name":"Brandeis University","place":["Waltham"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1029-0158","authenticated-orcid":false,"given":"Timothy","family":"O\u2019Leary","sequence":"additional","affiliation":[{"name":"Department of Engineering","place":["Cambridge, United Kingdom"]},{"name":"University of Cambridge","place":["Cambridge, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2025,8,4]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2004.10.032"},{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/090749761"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00422-014-0615-5"},{"key":"e_1_3_4_4_2","unstructured":"J. M. Lueckmann \u201cFlexible statistical inference for mechanistic models of neural dynamics\u201d in 31st Conference on Neural Information Processing Systems (NIPS 2017) I. Guyon Eds. (Long Beach CA USA 2017) pp. 1289\u20131299."},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-019-13177-3"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.42722"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1008053"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.56261"},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2023.3344723"},{"key":"e_1_3_4_10_2","doi-asserted-by":"publisher","DOI":"10.1103\/PRXLife.2.023007"},{"key":"e_1_3_4_11_2","doi-asserted-by":"crossref","unstructured":"J. Pillow M. Park \u201cAdaptive Bayesian methods for closed-loop neurophysiology\u201d in Closed Loop Neuroscience A. El Hady Ed. (Academic Press Cambridge MA 2016) pp. 3\u201318.","DOI":"10.1016\/B978-0-12-802452-2.00001-9"},{"key":"e_1_3_4_12_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107447615"},{"key":"e_1_3_4_13_2","doi-asserted-by":"crossref","unstructured":"T. B. Burghi M. Schoukens R. Sepulchre \u201cSystem identification of biophysical neuronal models\u201d in 59th IEEE Conference on Decision and Control R. Braatz C. C. Chung Eds. (Jeju Island South Korea 2020) pp. 6180\u20136185.","DOI":"10.1109\/CDC42340.2020.9304363"},{"key":"e_1_3_4_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuron.2021.07.002"},{"key":"e_1_3_4_15_2","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.47012"},{"key":"e_1_3_4_16_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41583-023-00740-7"},{"key":"e_1_3_4_17_2","unstructured":"M. Aguiar A. Das K. H. Johansson \u201cLearning flow functions of spiking systems\u201d in Proceedings of the 6th Annual Learning for Dynamics & Control Conference A. Abate M. Cannon K. Margellos A. Papachristodoulou Eds. (PMLR 2024) pp. 591\u2013602."},{"key":"e_1_3_4_18_2","unstructured":"M. Brenner \u201cTractable dendritic RNNs for reconstructing nonlinear dynamical systems\u201d in Proceedings of the 39th International Conference on Machine Learning K. Chaudhuri Eds. (PMLR 2022) pp. 2292\u20132320."},{"key":"e_1_3_4_19_2","doi-asserted-by":"publisher","DOI":"10.1152\/jn.00079.2006"},{"key":"e_1_3_4_20_2","doi-asserted-by":"publisher","DOI":"10.1038\/nn1352"},{"key":"e_1_3_4_21_2","doi-asserted-by":"publisher","DOI":"10.1113\/jphysiol.1952.sp004764"},{"key":"e_1_3_4_22_2","unstructured":"A. Gu \u201cCombining recurrent convolutional and continuous-time models with linear state-space layers\u201d in 35th Conference on Neural Information Processing Systems (NeurIPS) M. Ranzato A. Beygelzimer Y. Dauphin P. S. Liang J. Wortman Vaughan Eds. (Long Beach CA USA 2021) pp. 572\u2013585."},{"key":"e_1_3_4_23_2","unstructured":"A. Gu K. Goel C. R\u00e9 Efficiently modeling long sequences with structured state spaces. arXiv [Preprint] (2022). 10.48550\/arXiv.2111.00396 (Accessed 20 February 2025)."},{"key":"e_1_3_4_24_2","doi-asserted-by":"crossref","unstructured":"K. Doya \u201cBifurcations in the learning of recurrent neural networks\u201d in Proceedings 1992 IEEE International Symposium on Circuits and Systems S. A. White Ed. (IEEE 1992) vol. 6 pp. 2777\u20132780.","DOI":"10.1109\/ISCAS.1992.230622"},{"key":"e_1_3_4_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2020.109158"},{"key":"e_1_3_4_26_2","doi-asserted-by":"crossref","unstructured":"J. Keener J. Sneyd Mathematical Physiology (Springer New York NY ed. 2 2009) vol. 8\/1.","DOI":"10.1007\/978-0-387-75847-3_1"},{"key":"e_1_3_4_27_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1985.1085649"},{"key":"e_1_3_4_28_2","doi-asserted-by":"publisher","DOI":"10.1109\/9.241560"},{"key":"e_1_3_4_29_2","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.4438-08.2009"},{"key":"e_1_3_4_30_2","doi-asserted-by":"publisher","DOI":"10.1152\/jn.1992.67.2.318"},{"key":"e_1_3_4_31_2","volume-title":"Dynamical Systems in Neuroscience","author":"Izhikevich E. M.","year":"2007","unstructured":"E. M. Izhikevich, Dynamical Systems in Neuroscience (MIT Press, Cambridge, MA, 2007)."},{"key":"e_1_3_4_32_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-87708-2"},{"key":"e_1_3_4_33_2","doi-asserted-by":"publisher","DOI":"10.1523\/ENEURO.0031-14.2015"},{"key":"e_1_3_4_34_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00422-008-0257-6"},{"key":"e_1_3_4_35_2","doi-asserted-by":"publisher","DOI":"10.1152\/jn.00360.2016"},{"key":"e_1_3_4_36_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature05523"},{"key":"e_1_3_4_37_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.physiol.69.031905.161516"},{"key":"e_1_3_4_38_2","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.3011-08.2008"},{"key":"e_1_3_4_39_2","doi-asserted-by":"publisher","DOI":"10.1002\/dneu.22410"},{"key":"e_1_3_4_40_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00215119"},{"key":"e_1_3_4_41_2","doi-asserted-by":"publisher","DOI":"10.21105\/joss.00602"},{"key":"e_1_3_4_42_2","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.18-07-02309.1998"},{"key":"e_1_3_4_43_2","volume-title":"Feedback Systems: An Introduction for Scientists and Engineers","author":"Astr\u00f6m K. J.","year":"2008","unstructured":"K. J. Astr\u00f6m, R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers (Princeton University Press, Princeton, 2008)."},{"key":"e_1_3_4_44_2","doi-asserted-by":"publisher","DOI":"10.1007\/1-84628-178-4"},{"key":"e_1_3_4_45_2","doi-asserted-by":"crossref","unstructured":"D. Nguyen B. Widrow \u201cImproving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights\u201d in 1990 IJCNN International Joint Conference on Neural Networks M. Caudill Ed. (IEEE 1990) pp. 21\u201326.","DOI":"10.1109\/IJCNN.1990.137819"},{"key":"e_1_3_4_46_2","doi-asserted-by":"publisher","DOI":"10.1002\/9781118033029"},{"key":"e_1_3_4_47_2","unstructured":"R. Pascanu T. Mikolov Y. Bengio \u201cOn the difficulty of training recurrent neural networks\u201d in Proceedings of the 30th International Conference on Machine Learning ICML\u201913 S. Dasgupta D. McAllester Eds. (Atlanta GA USA 2013) vol. 28 pp. 1310\u20131318."},{"key":"e_1_3_4_48_2","unstructured":"A. H. Ribeiro K. Tiels L. A. Aguirre T. Sch\u00f6n \u201cBeyond exploding and vanishing gradients: Analysing RNN training using attractors and smoothness\u201d in Proceedings of the 23rd International Conference on AI and Statistics S. Chiappa R. Calandra Eds. (PMLR 2020) pp. 2370\u20132380."},{"key":"e_1_3_4_49_2","unstructured":"D. P. Kingma J. Ba Adam: A Method for Stochastic Optimization. arXiv [Preprint] (2017). 10.48550\/arXiv.1412.6980 (Accessed 1 December 2024)."},{"key":"e_1_3_4_50_2","first-page":"25","article-title":"Cancer borealis stomatogastric nervous system dissection","volume":"1207","author":"Gutierrez G. J.","year":"2009","unstructured":"G. J. Gutierrez, R. G. Grashow, Cancer borealis stomatogastric nervous system dissection. J. Vis. Exp. 1207, 25 (2009).","journal-title":"J. Vis. Exp."},{"key":"e_1_3_4_51_2","doi-asserted-by":"crossref","unstructured":"T. B. Burghi Research data supporting \u201cRapid interpretable data-driven models of neural dynamics using Recurrent Mechanistic Models\u201d. Apollo - University of Cambridge Repository. https:\/\/doi.org\/10.17863\/CAM.115630. Deposited 29 January 2025.","DOI":"10.1101\/2024.10.10.617633"},{"key":"e_1_3_4_52_2","doi-asserted-by":"crossref","unstructured":"T. B. Burghi. Computer code supporting \u201cRapid interpretable data-driven models of neural dynamics using Recurrent Mechanistic Models.\u201d GitHub. https:\/\/github.com\/thiagoburghi\/RMM. Deposited 5 January 2025.","DOI":"10.1101\/2024.10.10.617633"}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.2426916122","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,4]],"date-time":"2025-08-04T19:05:30Z","timestamp":1754334330000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/10.1073\/pnas.2426916122"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,4]]},"references-count":52,"journal-issue":{"issue":"32","published-print":{"date-parts":[[2025,8,12]]}},"alternative-id":["10.1073\/pnas.2426916122"],"URL":"https:\/\/doi.org\/10.1073\/pnas.2426916122","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,4]]},"assertion":[{"value":"2024-12-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-06-26","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-08-04","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e2426916122"}}