Nicolas Brunel

Nicolas Brunel

Professor of Neurobiology

External Address: 
311 Research Drive, Durham, NC 27710


We use theoretical models of brain systems to investigate how they process and learn information from their inputs. Our current work focuses on the mechanisms of learning and memory, from the synapse to the network level, in collaboration with various experimental groups. Using methods from
statistical physics, we have shown recently that the synaptic
connectivity of a network that maximizes storage capacity reproduces
two key experimentally observed features: low connection probability
and strong overrepresentation of bidirectionnally connected pairs of
neurons. We have also inferred `synaptic plasticity rules' (a
mathematical description of how synaptic strength depends on the
activity of pre and post-synaptic neurons) from data, and shown that
networks endowed with a plasticity rule inferred from data have a
storage capacity that is close to the optimal bound.

Education & Training

  • Ph.D., Pierre and Marie Curie University (France) 1993

Selected Grants

Neurobiology Training Program awarded by National Institutes of Health (Mentor). 2019 to 2024

Canonical computations for motor learning by the cerebellar cortex micro-circuit awarded by National Institutes of Health (Co-Principal Investigator). 2019 to 2024

Striatal Microcircuit Drivers of Adaptive Learning in Habit Formation awarded by National Institutes of Health (Co Investigator). 2018 to 2023

Investigating ripple oscillations as a mechanism for human memory retrieval awarded by National Institutes of Health (Principal Investigator). 2019 to 2022

Medical Scientist Training Program awarded by National Institutes of Health (Mentor). 1997 to 2022

An Integrated Nonparametric Bayesian and Deep Neural Network Framework for Biologically-Inspired Lifelong Learning awarded by Defense Advanced Research Projects Agency (Co Investigator). 2018 to 2021

Circuitry underlying response summation in mouse and primate: theory and experiment awarded by Salk Institute Biotechnology/Industrial Associatio (Principal Investigator). 2018 to 2021

CRCNS: Multiscale dynamics of cortical circuits for visual recognition & memory awarded by University of Chicago (Principal Investigator). 2017 to 2021

Learning spatio-temporal statistics from the environment in recurrent networks awarded by Office of Naval Research (Principal Investigator). 2017 to 2020

Learning spatio-temporal statistics from the environment in recurrent networks awarded by University of Texas Health Science Center at Houston (Principal Investigator). 2017 to 2020


Brunel, Nicolas, and Vincent Hakim. “Population Density Models.Encyclopedia of Computational Neuroscience, edited by Dieter Jaeger and Ranu Jung, Springer, 2014.

Brunel, Nicolas, and Vincent Hakim. “Fokker-Planck Equation.Encyclopedia of Computational Neuroscience, edited by Dieter Jaeger and Ranu Jung, Springer, 2014.

Brunel, Nicolas. “Dynamics of neural networks.” Principles of Neural Coding, 2013, pp. 489–512. Manual, doi:10.1201/b14756. Full Text

Brunel, Nicolas, and Vincent Hakim. “Neuronal Dynamics.Encyclopedia of Complexity and Systems Science, edited by Robert A. Meyers, Springer, 2009, pp. 6099–116.

Inglebert, Yanis, et al. “Synaptic plasticity rules with physiological calcium levels.Proc Natl Acad Sci U S A, vol. 117, no. 52, Dec. 2020, pp. 33639–48. Pubmed, doi:10.1073/pnas.2013663117. Full Text

Gillett, Maxwell, et al. “Characteristics of sequential activity in networks with temporally asymmetric Hebbian learning.Proc Natl Acad Sci U S A, vol. 117, no. 47, Nov. 2020, pp. 29948–58. Pubmed, doi:10.1073/pnas.1918674117. Full Text

Sanzeni, Alessandro, et al. “Response nonlinearities in networks of spiking neurons.Plos Comput Biol, vol. 16, no. 9, Sept. 2020, p. e1008165. Pubmed, doi:10.1371/journal.pcbi.1008165. Full Text Open Access Copy

Sanzeni, Alessandro, et al. “Inhibition stabilization is a widespread property of cortical networks.Elife, vol. 9, June 2020. Epmc, doi:10.7554/elife.54875. Full Text

Fore, Taylor R., et al. “Acetylcholine Modulates Cerebellar Granule Cell Spiking by Regulating the Balance of Synaptic Excitation and Inhibition.J Neurosci, vol. 40, no. 14, Apr. 2020, pp. 2882–94. Pubmed, doi:10.1523/JNEUROSCI.2148-19.2020. Full Text

Vaz, Alex P., et al. “Coupled ripple oscillations between the medial temporal lobe and neocortex retrieve human memory.Science, vol. 363, no. 6430, Mar. 2019, pp. 975–78. Pubmed, doi:10.1126/science.aau8956. Full Text Open Access Copy

Pereira, Ulises, and Nicolas Brunel. “Unsupervised Learning of Persistent and Sequential Activity.Front Comput Neurosci, vol. 13, 2019, p. 97. Pubmed, doi:10.3389/fncom.2019.00097. Full Text

Bouvier, Guy, et al. “Cerebellar learning using perturbations.Elife, vol. 7, Nov. 2018. Pubmed, doi:10.7554/eLife.31599. Full Text

Pereira, Ulises, and Nicolas Brunel. “Attractor Dynamics in Networks with Learning Rules Inferred from In Vivo Data.Neuron, vol. 99, no. 1, July 2018, pp. 227-238.e4. Pubmed, doi:10.1016/j.neuron.2018.05.038. Full Text

Martí, Daniel, et al. “Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks.Phys Rev E, vol. 97, no. 6–1, June 2018, p. 062314. Pubmed, doi:10.1103/PhysRevE.97.062314. Full Text Open Access Copy


Roxin, A., et al. “Rate models with delays and the dynamics of large networks of spiking neurons.” Progress of Theoretical Physics Supplement, vol. 161, 2006, pp. 68–85. Scopus, doi:10.1143/PTPS.161.68. Full Text

Fourcaud-Trocmé, Nicolas, and Nicolas Brunel. “Dynamics of the instantaneous firing rate in response to changes in input statistics.J Comput Neurosci, vol. 18, no. 3, 2005, pp. 311–21. Pubmed, doi:10.1007/s10827-005-0337-8. Full Text

Brunel, N. “Dynamics of networks of randomly connected excitatory and inhibitory spiking neurons.J Physiol Paris, vol. 94, no. 5–6, 2000, pp. 445–63. Pubmed, doi:10.1016/s0928-4257(00)01084-6. Full Text

Brunel, N. “Phase diagrams of sparsely connected networks of excitatory and inhibitory spiking neurons.” Neurocomputing, vol. 32–33, 2000, pp. 307–12. Scopus, doi:10.1016/S0925-2312(00)00179-X. Full Text

Brunel, N., and X. J. Wang. “Fast network oscillations with intermittent principal cell firing in a model of a recurrent excitatory-inhibitory circuit.” European Journal of Neuroscience, vol. 12, BLACKWELL SCIENCE LTD, 2000, pp. 79–79.

Brunel, N., and J. P. Nadal. “Modeling memory: what do we learn from attractor neural networks?C R Acad Sci Iii, vol. 321, no. 2–3, 1998, pp. 249–52. Pubmed, doi:10.1016/s0764-4469(97)89830-7. Full Text

Brunel, N. “Cross-correlations in sparsely connected recurrent networks of spiking neurons.” Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1327, 1997, pp. 31–36. Scopus, doi:10.1007/bfb0020128. Full Text

Brunel, Nicolas, and Jean-Pierre Nadal. “Optimal tuning curves for neurons spiking as a Poisson process.Esann, edited by Michel Verleysen, D-Facto public, 1997.

Ninio, J., and N. Brunel. “Time to detect a single difference between two correlated images.” Perception, vol. 25, PION LTD, 1996, pp. 89–89.

Brunel, N., and D. J. Amit. “Learning internal representations in an analog attractor neural network.” International Journal of Neural Systems, Supplementary Issue, 1995, edited by D. J. Amit et al., WORLD SCIENTIFIC PUBL CO PTE LTD, 1995, pp. 19–23.