Firing patterns in the adaptive exponential integrate-and-fire model

Biological Cybernetics

Volumn 99, Issue 4-5, 2008, Pages 335-347

  Naud, Richard ^a   Marcille, Nicolas ^a   Clopath, Claudia ^a   Gerstner, Wulfram ^a  

^a EPFL   (Switzerland)

Author keywords

Chaos; Electrophysiological taxonomy; Firing patterns; Simplified single neuron models

Indexed keywords

INTEGRATION; LEARNING ALGORITHMS; NEURAL NETWORKS; PHASE DIAGRAMS; PHASE TRANSITIONS; TAXONOMIES;

CHAOS; CONSTANT CURRENTS; CORTICAL NEURONS; DETERMINISTIC MODELS; ELECTROPHYSIOLOGICAL TAXONOMY; EQUATION MODELS; FIRING PATTERNS; INTEGRATE AND FIRES; LARGE NETWORKS; MODELING FRAMEWORKS; PARAMETER VALUES; REAL EXPERIMENTS; SIMPLE MODELS; SIMPLIFIED SINGLE-NEURON MODELS; SINGLE NEURONS; SPIKING NEURON NETWORKS; TONIC SPIKING; TWO TYPES;

MILITARY OPERATIONS;

ACTION POTENTIAL; ANIMAL; ARTICLE; BIOLOGICAL MODEL; BRAIN CORTEX; HUMAN; NERVE CELL; PHYSIOLOGY;

ACTION POTENTIALS; ANIMALS; CEREBRAL CORTEX; HUMANS; MODELS, NEUROLOGICAL; NEURONS;

EID: 56449095252     PISSN: 03401200     EISSN: 14320770     Source Type: Journal    
DOI: 10.1007/s00422-008-0264-7     Document Type: Article

References (36)

1. Badel L, Lefort S, Brette R, Petersen C, Gerstner W, Richardson M (2007) Dynamic i - v curves are reliable predictors of naturalistic pyramidal-neuron voltage traces. J Neurophysiol. doi: 10.1152/jn.01107.2007
2. BP Bean 2007 The action potential in mammalian central neurons Nat Rev Neurosci 8 6 451 465 10.1038/nrn2148
3. M Beierlein JR Gibson BW Connors 2003 Two dynamically distinct inhibitory networks in layer 4 of the neocortex J Neurophysiol 90 5 2987 3000 10.1152/jn.00283.2003
4. J Benda AVM Herz 2003 A universal model for spike-frequency adaptation Neural Comput 15 11 2523 2564 10.1162/089976603322385063
5. R Brette W Gerstner 2005 Adaptive exponential integrate-and-fire model as an effective description of neuronal activity J Neurophysiol 94 5 3637 3642 10.1152/jn.00686.2005
6. JC Brumberg BS Gutkin 2007 Cortical pyramidal cells as non-linear oscillators: experiment and spike-generation theory Brain Res 1171 122 137 10.1016/j.brainres.2007.07.028
7. TR Chay J Rinzel 1985 Bursting, beating, and chaos in an excitable membrane model Biophys J 47 3 357 366
8. C Clopath R Jolivet A Rauch HR Luscher W Gerstner 2007 Predicting neuronal activity with simple models of the threshold type: Adaptive exponential integrate-and-fire model with two compartments Neurocomputing 70 10-12 1668 1673
9. BW Connors MJ Gutnick 1990 Intrinsic firing patterns of diverse neocortical neurons Trends Neurosci 13 3 99 104
10. Druckmann S, Bannitt Y, Gidon AA, Schuermann F, Segev I (2007) A novel multiple objective optimization framework for constraining conductance-based neuron models by experimental data. Front Neurosci 1(1)
11. Fourcaud-Trocme N, Hansel D, van Vreeswijk C, BrunelN (2003) How spike generation mechanisms determine the neuronal response to fluctuating inputs. J Neurosci 23(37):11,628-11,640
12. Gerstner W, Kistler WM (2002) Spiking neuron models : single neurons, populations, plasticity. Cambridge University Press, Cambridge, UK.URL http://www.loc.gov/catdir/samples/cam031/2002067657.html
13. S Hill G Tononi 2005 Modeling sleep and wakefulness in the thalamocortical system J Neurophysiol 93 3 1671 1698 10.1152/jn.00915.2004
14. Holden AV (1986) Chaos. Princeton University Press, Princeton, NJ
15. B Hutcheon Y Yarom 2000 Resonance, oscillation and the intrinsic frequency preferences of neurons Trends Neurosci 23 5 216 222
16. EM Izhikevich 2003 Simple model of spiking neurons IEEE Trans Neural Netw 14 6 1569 1572 10.1109/TNN.2003.820440
17. Izhikevich EM (2007) Dynamical systems in neuroscience : the geometry of excitability and bursting. MIT Press, Cambridge, MA
18. EM Izhikevich GM Edelman 2008 Large-scale model of mammalian thalamocortical systems Proc Natl Acad Sci USA 105 9 3593 3598 10.1073/pnas.0712231105
19. Jolivet R, Kobayashi R, Rauch A, Naud R, Shinomoto S, Gerstner W (2007) A benchmark test for a quantitative assessment of simple neuron models. J Neurosci Methods. doi: 10.1016/j.jneumeth.2007.11.006
20. Koch C (1999) Biophysics of computation : information processing in single neurons. Oxford University Press, New York. URL http://www.loc.gov/ catdir/enhancements/fy0605/97051390-d.html
21. H Korn P Faure 2003 Is there chaos in the brain? II. Experimental evidence and related models C R Biol 326 9 787 840
22. PE Latham BJ Richmond S Nirenberg PG Nelson 2000 Intrinsic dynamics in neuronal networks. II. Experiment J Neurophysiol 83 2 828 835
23. ZF Mainen TJ Sejnowski 1996 Influence of dendritic structure on firing pattern in model neocortical neurons Nature 382 6589 363 366 10.1038/382363a0
24. H Markram 2006 The blue brain project Nat Rev Neurosci 7 2 153 160 10.1038/nrn1848
25. H Markram M Toledo-Rodriguez Y Wang A Gupta G Silberberg C Wu 2004 Interneurons of the neocortical inhibitory system Nat Rev Neurosci 5 10 793 807 10.1038/nrn1519
26. A Mauro F Conti F Dodge R Schor 1970 Subthreshold behavior and phenomenological impedance of the squid giant axon J Gen Physiol 55 4 497 523
27. MJE Richardson N Brunel V Hakim 2003 From subthreshold to firing-rate resonance J Neurophysiol 89 5 2538 2554 10.1152/jn.00955.2002
28. Rinzel J, Ermentrout GB (1998) Analysis of neural excitability and oscillations. In: Koch C, Segev I (eds) Methods in neuronal modeling, 2nd edn. MIT Press, Cambridge, pp 251-291
29. NH Sabah KN Leibovic 1969 Subthreshold oscillatory responses of the Hodgkin-Huxley cable model for the squid giant axon Biophys J 9 10 1206 1222
30. Strogatz SH (1994) Nonlinear dynamics and Chaos: with applications to physics, biology, chemistry, and engineering. Addison-Wesley Pub., Reading, MA. URL http://www.loc.gov/catdir/enhancements/fy0830/93006166-d.html
31. T Tateno A Harsch HPC Robinson 2004 Threshold firing frequency-current relationships of neurons in rat somatosensory cortex: type 1 and type 2 dynamics J Neurophysiol 92 4 2283 2294 10.1152/jn.00109.2004
32. M Toledo-Rodriguez B Blumenfeld C Wu J Luo B Attali P Goodman H Markram 2004 Correlation maps allow neuronal electrical properties to be predicted from single-cell gene expression profiles in rat neocortex Cereb Cortex 14 12 1310 1327 10.1093/cercor/bhh092
33. J Touboul 2008 Bifurcation analysis of a general class of nonlinear integrate-and-fire neurons SIAM J Appl Math 68 4 1045 1079
34. Touboul J, Brette R (2008) Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. Biol Cybernet. doi: 10.1007/s00422-008- 0267-4
35. MC Vanier JM Bower 1999 A comparative survey of automated parameter-search methods for compartmental neural models J Comput Neurosci 7 2 149 171
36. Y Wang A Gupta M Toledo-Rodriguez CZ Wu H Markram 2002 Anatomical, physiological, molecular and circuit properties of nest basket cells in the developing somatosensory cortex Cereb Cortex 12 4 395 410