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Cited by 5Neural dynamics and brain functionUndergraduate Neuroscience Education and ResearchNeural Networks and Applications

Rapid, interpretable data-driven models of neural dynamics using recurrent mechanistic models

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Burghi, Thiago B., Ivanova, Maria, Morozova, Ekaterina, Wang, Huaxinyu, Marder, Eve, O’Leary, Timothy·2025·Proceedings of the National Academy of Sciences
DOI 10.1073/pnas.2426916122PMC PMC12358897
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Abstract

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—which we call recurrent mechanistic models (RMMs)—can 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.

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  • There are attempts to develop new methods to characterize the parameters of biological neurons to estimate or evaluate their contributions to neuronal dynamics.

    “Therefore, there are attempts to develop new methods to characterize the parameters of biological neurons to estimate or evaluate their contributions to neuronal dynamics [48][49][50].”

    From A feature and not a bug: Replication failures can lead to new biology (2026) · cites this paper as [48]

  • The resulting class of models, recurrent mechanistic models (RMMs), can be trained during an electrophysiology experiment.

    “The resulting class of models, recurrent mechanistic models (RMMs)-can be trained during an electrophysiology experiment.”

    From A feature and not a bug: Replication failures can lead to new biology (2026) · cites this paper as [48]

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  1. [3]C. D. Meliza, Estimating parameters and predicting membrane voltages with conductance-based neuron models. Biol. Cybern. 108, 495– 516 (2014). 24962080
  2. [4]J. M. Lueckmann, “Flexible statistical inference for mechanistic models of neural dynamics” in 31st Conference on Neural Information Processing Systems (NIPS 2017), I. Guyon, Eds. (Long Beach, CA, USA, 2017), pp. 1289–1299.
  3. [5]K. Abu-Hassan, Optimal solid state neurons. Nat. Commun. 10, 5309 (2019). 31796727 PMC6890780
  4. [6]L. M. Alonso, E. Marder, Visualization of currents in neural models with similar behavior and different conductance densities. eLife 8, e42722 (2019). 30702427 PMC6395073
  5. [7]J. D. Taylor, S. Winnall, A. Nogaret, Estimation of neuron parameters from imperfect observations. PLoS Comput. Biol. 16, e1008053 (2020). 32673311 PMC7386621
  6. [8]P. J. Gonçalves, Training deep neural density estimators to identify mechanistic models of neural dynamics. eLife 9, e56261 (2020). 32940606 PMC7581433
  7. [9]T. B. Burghi, R. Sepulchre, Adaptive observers for biophysical neuronal circuits. IEEE Trans. Autom. Control. 69, 5020– 5033 (2024).
  8. [10]S. A. Wells, J. D. Taylor, P. G. Morris, A. Nogaret, Inferring the dynamics of ionic currents from recursive piecewise data assimilation of approximate neuron models. PRX Life 2, 023007 (2024).
  9. [11]J. Pillow, M. Park, “Adaptive Bayesian methods for closed-loop neurophysiology” in Closed Loop Neuroscience, A. El Hady, Ed. (Academic Press, Cambridge, MA, 2016), pp. 3–18.
  10. [12]W. Gerstner, W. M. Kistler, R. Naud, L. Paninski, Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition (Cambridge University Press, Cambridge, UK, 2014).
  11. [13]T. B. Burghi, M. Schoukens, R. Sepulchre, “System identification of biophysical neuronal models” in 59th IEEE Conference on Decision and Control, R. Braatz, C. C. Chung, Eds. (Jeju Island, South Korea, 2020), pp. 6180–6185.
  12. [15]K. W. Latimer, F. Rieke, J. W. Pillow, Inferring synaptic inputs from spikes with a conductance-based neural encoding model. eLife 8, e47012 (2019). 31850846 PMC6989090
  13. [16]D. Durstewitz, G. Koppe, M. I. Thurm, Reconstructing computational system dynamics from neural data with recurrent neural networks. Nat. Rev. Neurosci. 24, 693– 710 (2023). 37794121
  14. [17]M. Aguiar, A. Das, K. H. Johansson, “Learning flow functions of spiking systems” in Proceedings of the 6th Annual Learning for Dynamics & Control Conference, A. Abate, M. Cannon, K. Margellos, A. Papachristodoulou, Eds. (PMLR, 2024), pp. 591–602.
  15. [18]M. Brenner, “Tractable dendritic RNNs for reconstructing nonlinear dynamical systems” in Proceedings of the 39th International Conference on Machine Learning, K. Chaudhuri, Eds. (PMLR, 2022), pp. 2292–2320.
  16. [19]Q. J. M. Huys, M. B. Ahrens, L. Paninski, Efficient estimation of detailed single-neuron models. J. Neurophysiol. 96, 872– 890 (2006). 16624998
  17. [20]A. A. Prinz, D. Bucher, E. Marder, Similar network activity from disparate circuit parameters. Nat. Neurosci. 7, 1345– 1352 (2004). 15558066
  18. [21]A. L. Hodgkin, A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500– 544 (1952). 12991237 PMC1392413
  19. [22]A. Gu, “Combining recurrent, convolutional, and continuous-time models with linear state-space layers” 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. 572–585.
  20. [23]A. Gu, K. Goel, C. Ré, Efficiently modeling long sequences with structured state spaces. arXiv [Preprint] (2022). 10.48550/arXiv.2111.00396 (Accessed 20 February 2025). · DOI · Paper page
  21. [24]K. Doya, “Bifurcations in the learning of recurrent neural networks” in Proceedings 1992 IEEE International Symposium on Circuits and Systems, S. A. White, Ed. (IEEE, 1992), vol. 6, pp. 2777–2780.
  22. [25]A. H. Ribeiro, K. Tiels, J. Umenberger, T. B. Schön, L. A. Aguirre, On the smoothness of nonlinear system identification. Automatica 121, 109158 (2020).
  23. [26]J. Keener, J. Sneyd, Mathematical Physiology (Springer, New York, NY, ed. 2, 2009), vol. 8/1.
  24. [27]S. Boyd, L. Chua, Fading memory and the problem of approximating nonlinear operators with Volterra series. IEEE Trans. Circ. Syst. 32, 1150– 1161 (1985).
  25. [28]I. W. Sandberg, Uniform approximation and the circle criterion. IEEE Trans. Autom. Control. 38, 1450– 1458 (1993).
  26. [30]J. Golowasch, E. Marder, Ionic currents of the lateral pyloric neuron of the stomatogastric ganglion of the crab. J. Neurophysiol. 67, 318– 331 (1992). 1373762
  27. [31]E. M. Izhikevich, Dynamical Systems in Neuroscience (MIT Press, Cambridge, MA, 2007).
  28. [32]G. B. Ermentrout, D. H. Terman, Mathematical Foundations of Neuroscience (Springer, New York, 2010).
  29. [33]G. Drion, A. Franci, J. Dethier, R. Sepulchre, Dynamic input conductances shape neuronal spiking. Eneuro 2, ENEURO.0031-14.2015 (2015). PMC4586923 26464969
  30. [34]W. V. Geit, E. D. Schutter, P. Achard, Automated neuron model optimization techniques: A review. Biol. Cybern. 99, 241– 251 (2008). 19011918
  31. [35]M. Almog, A. Korngreen, Is realistic neuronal modeling realistic? J. Neurophysiol. 116, 2180– 2209 (2016). 27535372 PMC5102320
  32. [36]D. A. McCormick, Y. Shu, Y. Yu, Hodgkin and Huxley model – still standing? Nature 445, E1– E2 (2007). 17203021
  33. [37]E. Marder, D. Bucher, Understanding circuit dynamics using the stomatogastric nervous system of lobsters and crabs. Annu. Rev. Physiol. 69, 291– 316 (2007). 17009928
  34. [38]D. M. Blitz, M. P. Nusbaum, State-dependent presynaptic inhibition regulates central pattern generator feedback to descending inputs. J. Neurosci. 28, 9564– 9574 (2008). 18799688 PMC2610852
  35. [40]B. Johnson, J. Peck, R. Harris-Warrick, Differential modulation of chemical and electrical components of mixed synapses in the lobster stomatogastric ganglion. J. Comp. Physiol. A 175, 233– 249 (1994). 8071898
  36. [41]M. Innes, Flux: Elegant machine learning with Julia. J. Open Sour. Softw. 3, 602 (2018).
  37. [42]Z. Liu, J. Golowasch, E. Marder, L. F. Abbott, A model neuron with activity-dependent conductances regulated by multiple calcium sensors. J. Neurosci. 18, 2309– 2320 (1998). 9502792 PMC6793093
  38. [43]K. J. Aström, R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers (Princeton University Press, Princeton, 2008).
  39. [44]P. S. C. Heuberger, P. M. J. van den Hof, B. Wahlberg, Modelling and Identification with Rational Orthogonal Basis Functions (Springer, London, 2005).
  40. [45]D. Nguyen, B. Widrow, “Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights” in 1990 IJCNN International Joint Conference on Neural Networks, M. Caudill, Ed. (IEEE, 1990), pp. 21–26.
  41. [46]L. Farina, S. Rinaldi, Positive Linear Systems: Theory and Applications (John Wiley & Sons, 2000).
  42. [47]R. Pascanu, T. Mikolov, Y. Bengio, “On the difficulty of training recurrent neural networks” in Proceedings of the 30th International Conference on Machine Learning, ICML’13, S. Dasgupta, D. McAllester, Eds. (Atlanta, GA, USA, 2013), vol. 28, pp. 1310–1318.
  43. [48]A. H. Ribeiro, K. Tiels, L. A. Aguirre, T. Schön, “Beyond exploding and vanishing gradients: Analysing RNN training using attractors and smoothness” in Proceedings of the 23rd International Conference on AI and Statistics, S. Chiappa, R. Calandra, Eds. (PMLR, 2020), pp. 2370–2380.
  44. [49]D. P. Kingma, J. Ba, Adam: A Method for Stochastic Optimization. arXiv [Preprint] (2017). 10.48550/arXiv.1412.6980 (Accessed 1 December 2024). · DOI · Paper page
  45. [50]G. J. Gutierrez, R. G. Grashow, Cancer borealis stomatogastric nervous system dissection. J. Vis. Exp. 1207, 25 (2009). PMC2705892 19308017
  46. [51]T. B. Burghi, Research data supporting “Rapid, interpretable data-driven models of neural dynamics using Recurrent Mechanistic Models”. Apollo - University of Cambridge Repository. 10.17863/CAM.115630. Deposited 29 January 2025. PMC12358897 40758876 · DOI
  47. [52]T. B. Burghi. Computer code supporting “Rapid, interpretable data-driven models of neural dynamics using Recurrent Mechanistic Models.” GitHub. https://github.com/thiagoburghi/RMM. Deposited 5 January 2025. PMC12358897 40758876

Cited by

Sorted by citations

Authors
Burghi, T. B., Ivanova, M., Morozova, E., Wang, H., Marder, E., & O’Leary, T.
Affiliations
  • University of Cambridge (GB)
  • Brandeis University (US)
Corresponding author
  • Burghi, Thiago B.
  • Marder, Eve
ORCID
Venue
Proceedings of the National Academy of Sciences
Publisher
National Academy of Sciences
Published
2025-08-04
Volume
122
Issue
32
Pages
e2426916122-e2426916122
ISSN
  • 0027-8424 (ISSN-L)
  • 1091-6490
DOI
10.1073/pnas.2426916122
PMC
PMC12358897
OpenAlex
W4412934533
Cited by
5
References
3
Citations by year
2026: 4 · 2025: 1
FWCI
2.42
Type
journal article
Language
en
Open access
Licence
Locations
  • Proceedings of the National Academy of Sciences (publishedVersion, cc-by-nc-nd)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion)
  • PubMed Central (publishedVersion, cc-by-nc-nd)
  • PubMed (publishedVersion)
  • Apollo (University of Cambridge) (submittedVersion, cc-by-nc-nd)
Funders
  • HHS | NIH | National Institute of Neurological Disorders and Stroke (R35 NS 097343)
  • Kavli Foundation (G118028)
Topics
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Undergraduate Neuroscience Education and Research
  • Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
Keywords
neural dynamics, membrane currents, state-space model, artificial neural networks, interpretability, stomatogastric ganglion, central pattern generator, synaptic connectivity, intracellular recording
MeSH terms
Animals, Models, Neurological, Neurons, Neural Networks, Computer

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