Cited by 1Neural dynamics and brain functionstochastic dynamics and bifurcationIon channel regulation and function

Fast reconstruction of degenerate populations of conductance-based neuron models from spike times

Open access
Brandoit, Julien, Ernst, Damien, Drion, Guillaume, Fyon, Arthur·2026·PLOS Computational Biology

Abstract

Inferring the biophysical parameters of conductance-based models (CBMs) from experimentally accessible recordings remains a central challenge in computational neuroscience. Spike times are the most widely available data, yet they reveal little about which combinations of ion channel conductances generate the observed activity. This inverse problem is further complicated by neuronal degeneracy, where multiple distinct conductance sets yield similar spiking patterns. We introduce a method that addresses this challenge by combining deep learning with Dynamic Input Conductances (DICs), a theoretical framework that reduces complex CBMs to three interpretable feedback components governing excitability and firing patterns. Our approach first maps spike times directly to DIC densities at threshold using a lightweight neural network that learns a low-dimensional representation of neuronal activity. The predicted DIC values are then used to generate degenerate CBM populations via an iterative compensation algorithm, ensuring compatibility with the intermediate target DICs, and thereby reproducing the corresponding firing patterns, even in high-dimensional models. Applied to two neuronal models, this algorithmic pipeline reconstructs spiking, bursting, and irregular regimes with high accuracy and robustness to variability, including spike trains generated under noisy current injection mimicking physiological stochasticity. It produces diverse degenerate populations within milliseconds on standard hardware, enabling scalable and efficient inference from spike recordings alone. Beyond methodological advances, we provide an open-source software package with a graphical interface that allows experimentalists to generate and explore CBM populations directly from spike trains without requiring programming expertise. Together, this work positions DICs as a practical and interpretable link between experimentally observed activity and mechanistic models. By enabling fast and scalable reconstruction of degenerate populations directly from spike times, our approach provides a powerful way to investigate how neurons exploit conductance variability to achieve reliable computation and provides the foundation for experimental applications that span from neuromodulation studies to real-time model-guided interventions.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1371/journal.pcbi.1014337

Cites

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • 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].”

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

No references could be resolved yet.

Research works printed but not linked: 57

  1. [1]Tiesinga P, Fellous J-M, Sejnowski TJ. Regulation of spike timing in visual cortical circuits. Nat Rev Neurosci. 2008; 9(2): 97– 107. doi: 10.1038/nrn2315 18200026 PMC2868969 · DOI
  2. [2]Mainen ZF, Sejnowski TJ. Reliability of spike timing in neocortical neurons. Science. 1995; 268(5216): 1503– 6. doi: 10.1126/science.7770778 7770778 · DOI · Paper page
  3. [3]Williams AH, Poole B, Maheswaranathan N, Dhawale AK, Fisher T, Wilson CD, et al. Discovering Precise Temporal Patterns in Large-Scale Neural Recordings through Robust and Interpretable Time Warping. Neuron. 2020; 105(2):246-259.e8. doi: 10.1016/j.neuron.2019.10.020 31786013 PMC7336835 · DOI · Paper page
  4. [4]Marder E. Neuromodulation of neuronal circuits: back to the future. Neuron. 2012; 76(1): 1– 11. doi: 10.1016/j.neuron.2012.09.010 23040802 PMC3482119 · DOI · Paper page
  5. [5]Bargmann CI, Marder E. From the connectome to brain function. Nat Methods. 2013; 10(6): 483– 90. doi: 10.1038/nmeth.2451 23866325 · DOI · Paper page
  6. [6]McCormick DA, Nestvogel DB, He BJ. Neuromodulation of Brain State and Behavior. Annu Rev Neurosci. 2020; 43: 391– 415. doi: 10.1146/annurev-neuro-100219-105424 32250724 PMC12237593 · DOI · Paper page
  7. [7]Goaillard J-M, Marder E. Ion Channel Degeneracy, Variability, and Covariation in Neuron and Circuit Resilience. Annu Rev Neurosci. 2021; 44: 335– 57. doi: 10.1146/annurev-neuro-092920-121538 33770451 · DOI
  8. [8]Goldman MS, Golowasch J, Marder E, Abbott LF. Global structure, robustness, and modulation of neuronal models. J Neurosci. 2001; 21(14): 5229– 38. doi: 10.1523/JNEUROSCI.21-14-05229.2001 11438598 PMC6762863 · DOI · Paper page
  9. [9]Liu Z, Golowasch J, Marder E, Abbott LF. A model neuron with activity-dependent conductances regulated by multiple calcium sensors. J Neurosci. 1998; 18(7): 2309– 20. doi: 10.1523/JNEUROSCI.18-07-02309.1998 9502792 PMC6793093 · DOI
  10. [10]Golowasch J, Abbott LF, Marder E. Activity-dependent regulation of potassium currents in an identified neuron of the stomatogastric ganglion of the crab Cancer borealis. J Neurosci. 1999; 19(20):RC33. doi: 10.1523/JNEUROSCI.19-20-j0004.1999 10516335 PMC6782763 · DOI
  11. [11]Taylor AL, Goaillard J-M, Marder E. How multiple conductances determine electrophysiological properties in a multicompartment model. J Neurosci. 2009; 29(17): 5573– 86. doi: 10.1523/JNEUROSCI.4438-08.2009 19403824 PMC2821064 · DOI · Paper page
  12. [12]Yu N, Canavier CC. A Mathematical Model of a Midbrain Dopamine Neuron Identifies Two Slow Variables Likely Responsible for Bursts Evoked by SK Channel Antagonists and Terminated by Depolarization Block. J Math Neurosci. 2015; 5: 5. doi: 10.1186/s13408-015-0017-6 25852980 PMC4385104 · DOI
  13. [13]Fyon A, Pavlova O, Schaar N, Mesirca P, Ligot A, Gaillardon M. A new perspective on slow pacemaking in brain and heart. bioRxiv. 2026. doi: 10.1101/2025.10.30.685563 · DOI
  14. [14]Druckmann S, Banitt Y, Gidon A, Schürmann F, Markram H, Segev I. A novel multiple objective optimization framework for constraining conductance-based neuron models by experimental data. Front Neurosci. 2007; 1(1): 7– 18. doi: 10.3389/neuro.01.1.1.001.2007 18982116 PMC2570085 · DOI
  15. [15]Prinz AA, Billimoria CP, Marder E. Alternative to hand-tuning conductance-based models: construction and analysis of databases of model neurons. J Neurophysiol. 2003; 90(6): 3998– 4015. doi: 10.1152/jn.00641.2003 12944532 · DOI
  16. [16]Shepardson D. Algorithms for inverting Hodgkin-Huxley type neuron models. Georgia Institute of Technology. 2009. http://hdl.handle.net/1853/31686
  17. [17]Huys QJM, Ahrens MB, Paninski L. Efficient estimation of detailed single-neuron models. J Neurophysiol. 2006; 96(2): 872– 90. doi: 10.1152/jn.00079.2006 16624998 · DOI
  18. [18]Burghi TB, Schoukens M, Sepulchre R. Feedback identification of conductance-based models. Automatica. 2021; 123: 109297. doi: 10.1016/j.automatica.2020.109297 · DOI
  19. [19]Burghi TB, O’Leary T, Sepulchre R. Distributed online estimation of biophysical neural networks. In: 2022 IEEE 61st Conference on Decision and Control (CDC), 2022. 628– 34. 10.1109/cdc51059.2022.9993018 · DOI
  20. [20]Meng L, Kramer MA, Eden UT. A sequential Monte Carlo approach to estimate biophysical neural models from spikes. J Neural Eng. 2011; 8(6): 065006. doi: 10.1088/1741-2560/8/6/065006 22058277 PMC3529721 · DOI
  21. [21]Meng L, Kramer MA, Middleton SJ, Whittington MA, Eden UT. A unified approach to linking experimental, statistical and computational analysis of spike train data. PLoS One. 2014; 9(1):e85269. doi: 10.1371/journal.pone.0085269 24465520 PMC3894976 · DOI
  22. [22]Ditlevsen S, Samson A. Estimation in the partially observed stochastic Morris–Lecar neuronal model with particle filter and stochastic approximation methods. Ann Appl Stat. 2014; 8(2): 674– 702. doi: 10.1214/14-AOAS729 · DOI
  23. [23]Gonçalves PJ, Lueckmann JM, Deistler M, Nonnenmacher M, Öcal K, Bassetto G. Training deep neural density estimators to identify mechanistic models of neural dynamics. eLife. 2020; 9:e56261. doi: 10.7554/eLife.56261 PMC7581433 32940606 · DOI
  24. [24]Cranmer K, Brehmer J, Louppe G. The frontier of simulation-based inference. Proc Natl Acad Sci U S A. 2020; 117(48): 30055– 62. doi: 10.1073/pnas.1912789117 32471948 PMC7720103 · DOI · Paper page
  25. [25]Lueckmann JM, Goncalves PJ, Bassetto G, Öcal K, Nonnenmacher M, Macke JH. Flexible statistical inference for mechanistic models of neural dynamics. In: Advances in Neural Information Processing Systems, 2017. 10.1101/838383 · DOI
  26. [26]Vetter J, Moss G, Schröder C, Gao R, Macke JH. Sourcerer: sample-based maximum entropy source distribution estimation; 2024. https://arxiv.org/abs/2402.07808 · arXiv
  27. [27]Burghi TB, Ivanova M, Morozova E, Wang H, Marder E, O’Leary T. Rapid, interpretable data-driven models of neural dynamics using recurrent mechanistic models. Proc Natl Acad Sci U S A. 2025; 122(32):e2426916122. doi: 10.1073/pnas.2426916122 40758876 PMC12358897 · DOI · Paper page
  28. [28]Burghi TB, Schapiro K, Ivanova M, Wang H, Marder E, O’Leary T. Quantitative prediction of intracellular dynamics and synaptic currents in a small neural circuit. Front Comput Neurosci. 2025; 19: 1515194. doi: 10.3389/fncom.2025.1515194 40989108 PMC12451236 · DOI · Paper page
  29. [29]Abarbanel HDI, Creveling DR, Farsian R, Kostuk M. Dynamical State and Parameter Estimation. SIAM J Appl Dyn Syst. 2009; 8(4): 1341– 81. doi: 10.1137/090749761 · DOI
  30. [30]Meliza CD, Kostuk M, Huang H, Nogaret A, Margoliash D, Abarbanel HDI. Estimating parameters and predicting membrane voltages with conductance-based neuron models. Biol Cybern. 2014; 108(4): 495– 516. doi: 10.1007/s00422-014-0615-5 24962080 · DOI
  31. [31]Nogaret A, Meliza CD, Margoliash D, Abarbanel HDI. Automatic Construction of Predictive Neuron Models through Large Scale Assimilation of Electrophysiological Data. Sci Rep. 2016; 6: 32749. doi: 10.1038/srep32749 27605157 PMC5015021 · DOI
  32. [32]Drion G, Franci A, Dethier J, Sepulchre R. Dynamic Input Conductances Shape Neuronal Spiking. eNeuro. 2015; 2(1):ENEURO.0031-14.2015. doi: 10.1523/ENEURO.0031-14.2015 26464969 PMC4586923 · DOI
  33. [33]Fyon A, Franci A, Sacré P, Drion G. Dimensionality reduction of neuronal degeneracy reveals two interfering physiological mechanisms. PNAS Nexus. 2024; 3(10):pgae415. doi: 10.1093/pnasnexus/pgae415 39359396 PMC11443964 · DOI
  34. [35]Marder E, Taylor AL. Multiple models to capture the variability in biological neurons and networks. Nat Neurosci. 2011; 14(2): 133– 8. doi: 10.1038/nn.2735 21270780 PMC3686573 · DOI · Paper page
  35. [36]Golowasch J, Goldman MS, Abbott LF, Marder E. Failure of averaging in the construction of a conductance-based neuron model. J Neurophysiol. 2002; 87(2): 1129– 31. doi: 10.1152/jn.00412.2001 11826077 · DOI · Paper page
  36. [37]Fyon A, Sacré P, Franci A, Drion G. Reliable neuromodulation from adaptive control of ion channel expression. IFAC-PapersOnLine. 2023; 56(2): 458– 63. doi: 10.1016/j.ifacol.2023.10.1610 · DOI
  37. [38]Fyon A, Drion G. Neuromodulation and homeostasis: complementary mechanisms for robust neural function. 2024. doi: 10.48550/arXiv.2412.04172 · DOI
  38. [39]Brandoit J, Ernst D, Drion G, Fyon A. Spike-train datasets from conductance-based neuron models. Zenodo. 2025. 10.5281/zenodo.16912160 PMC13241015 42166500 · DOI
  39. [40]Hermans J, Delaunoy A, Rozet F, Wehenkel A, Begy V, Louppe G. A trust crisis in simulation-based inference? Your posterior approximations can be unfaithful. 2022. doi: 10.48550/arXiv.2110.06581 · DOI
  40. [41]Hu EJ, Shen Y, Wallis P, Allen-Zhu Z, Li Y, Wang S. LoRA: low-rank adaptation of large language models. 2021. doi: 10.48550/arXiv.2106.09685 · DOI · Paper page
  41. [42]Mendolia L, Wen C, Chicca E, Indiveri G, Sepulchre R, Redouté JM. A neuromodulable current-mode silicon neuron for robust and adaptive neuromorphic systems. In: 2025. 10.48550/arXiv.2512.01133 · DOI
  42. [43]Gutenkunst RN, Waterfall JJ, Casey FP, Brown KS, Myers CR, Sethna JP. Universally sloppy parameter sensitivities in systems biology models. PLoS Comput Biol. 2007; 3(10): 1871– 8. doi: 10.1371/journal.pcbi.0030189 17922568 PMC2000971 · DOI · Paper page
  43. [44]Transtrum MK, Machta BB, Brown KS, Daniels BC, Myers CR, Sethna JP. Perspective: Sloppiness and emergent theories in physics, biology, and beyond. J Chem Phys. 2015; 143(1): 010901. doi: 10.1063/1.4923066 26156455 · DOI
  44. [45]Schulz DJ, Goaillard J-M, Marder E. Variable channel expression in identified single and electrically coupled neurons in different animals. Nat Neurosci. 2006; 9(3): 356– 62. doi: 10.1038/nn1639 16444270 · DOI · Paper page
  45. [46]Marder E. Variability, compensation, and modulation in neurons and circuits. Proc Natl Acad Sci U S A. 2011; 108(supplement_3): 15542– 8. doi: 10.1073/pnas.1010674108 21383190 PMC3176600 · DOI
  46. [47]Marder E, O’Leary T, Shruti S. Neuromodulation of circuits with variable parameters: single neurons and small circuits reveal principles of state-dependent and robust neuromodulation. Annu Rev Neurosci. 2014; 37: 329– 46. doi: 10.1146/annurev-neuro-071013-013958 25032499 · DOI · Paper page
  47. [48]Prinz AA, Bucher D, Marder E. Similar network activity from disparate circuit parameters. Nat Neurosci. 2004; 7(12): 1345– 52. doi: 10.1038/nn1352 15558066 · DOI · Paper page
  48. [49]Qian K, Yu N, Tucker KR, Levitan ES, Canavier CC. Mathematical analysis of depolarization block mediated by slow inactivation of fast sodium channels in midbrain dopamine neurons. J Neurophysiol. 2014; 112(11): 2779– 90. doi: 10.1152/jn.00578.2014 25185810 PMC4254877 · DOI
  49. [50]Izhikevich EM. Dynamical systems in neuroscience. MIT Press. 2007. 10.7551/mitpress/2526.001.0001 · DOI
  50. [51]Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN. Attention is all you need. In: Proceedings of the 31st International Conference on Neural Information Processing Systems, 2017. 6000– 10. 10.48550/arXiv.1706.03762 · DOI · Paper page
  51. [52]Dinh L, Sohl-Dickstein J, Bengio S. Density estimation using Real NVP. In: 2017. 10.48550/arXiv.1605.08803 · DOI · Paper page
  52. [53]Bergstra J, Bengio Y. Random search for hyper-parameter optimization. J Mach Learn Res. 2012; 13: 281– 305.
  53. [54]Loshchilov I, Hutter F. Decoupled weight decay regularization. In: 2019. 10.48550/arXiv.1711.05101 · DOI · Paper page
  54. [55]Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. Bayesian data analysis. 3rd ed. Boca Raton, FL: CRC Press. 2013. 10.1201/9780429258411 · DOI · Paper page
  55. [56]Lemos P, Coogan A, Hezaveh Y, Perreault-Levasseur L. Sampling-based accuracy testing of posteriors in general-purpose inference engines. In: Proceedings of the 40th International Conference on Machine Learning, 2023.
  56. [57]Talts S, Betancourt M, Simpson D, Vehtari A, Gelman A. Validating Bayesian inference algorithms with simulation-based calibration. In: 2018. 10.48550/arXiv.1804.06788 · DOI
  57. [58]Cook SR, Gelman A, Rubin DB. Validation of software for Bayesian models using posterior quantiles. J Comput Graph Stat. 2006; 15(3): 675– 92. doi: 10.1198/106186006X136976 · DOI

Cited by

Sorted by citations

Authors
Brandoit, J., Ernst, D., Drion, G., & Fyon, A.
Affiliations
  • University of Liège (BE)
  • Télécom Paris (FR)
Corresponding author
Fyon, Arthur
Venue
PLOS Computational Biology
Published
2026-05-21
Volume
22
Issue
5
Pages
e1014337
ISSN
  • 1553-734X (ISSN-L)
  • 1553-7358
OpenAlex
W4415316636
Cited by
1
References
0
Citations by year
2026: 1
FWCI
3.05
Type
journal article
Language
en
Open access
Locations
  • PLoS Computational Biology (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion, cc-by-nc-sa)
  • ORBi (University of Liège) (submittedVersion, cc-by-sa)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University)
Funders
  • Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA40038025)
  • Fonds De La Recherche Scientifique - FNRS (ASP-REN40024838)
  • Belgian Federal Science Policy Office (NEMODEI2)
Topics
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Ion channel regulation and function
Keywords
conductance-based neuron model, inverse problems, deep learning, burst firing, spiking patterns, neuromodulation
MeSH terms
Deep Learning, Action Potentials, Algorithms, Animals, Computer Simulation, Humans, Ion Channels, Models, Neurological, Neurons, Neural Networks, Computer, Computational Biology

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review