Predicting single spikes and spike patterns with the Hindmarsh-Rose model

Biological Cybernetics

Volumn 99, Issue 4-5, 2008, Pages 349-360

  De Lange, Enno ^a   Hasler, Martin ^b  

^a EPFL   (Switzerland)

^b UNIVERSITY OF BERN   (Switzerland)

Author keywords

Bifurcation analysis; Hindmarsh Rose model; Neocortical neurons; Nonlinear dynamics; Nonlinear optimization; Parameter fitting; Quantitative neuron modeling; Spike timing

Indexed keywords

BIFURCATION (MATHEMATICS); DATABASE SYSTEMS; DYNAMICS; MILITARY OPERATIONS; NEURONS; RELAXATION OSCILLATORS; THREE DIMENSIONAL;

BIFURCATION ANALYSIS; HINDMARSH-ROSE MODEL; NEOCORTICAL NEURONS; NONLINEAR DYNAMICS; NONLINEAR OPTIMIZATION; PARAMETER FITTING; QUANTITATIVE NEURON MODELING; SPIKE-TIMING;

STOCHASTIC MODELS;

RATTUS;

ACTION POTENTIAL; ANIMAL; ARTICLE; BIOLOGICAL MODEL; NEOCORTEX; NERVE CELL; PHYSIOLOGY; RAT;

ACTION POTENTIALS; ANIMALS; MODELS, NEUROLOGICAL; NEOCORTEX; NEURONS; RATS;

EID: 56449090678     PISSN: 03401200     EISSN: 14320770     Source Type: Journal    
DOI: 10.1007/s00422-008-0260-y     Document Type: Article

References (34)

1. Arbib, M (eds) (2002) The handbook of brain theory and neural networks, 2nd edn. MIT Press, London
2. Bargas J, Galarraga E (2002) Ion channels: keys to neuronal specialization. In: Arbib M (eds) The handbook of brain theory and neural networks, 2nd edn. MIT Press, London, pp 496-501
3. I Belykh E de Lange M Hasler 2005 Synchronization of bursting neurons: what matters in the network topology Phys Rev Lett 94 18 8101
4. TR Chay 1996 Electrical bursting and luminal calcium oscillation in excitable cell models Biol Cybern 75 419 431
5. C Clopath R Jolivet A Rauch HR Lüscher W Gerstner 2007 Predicting neuronal activity with simple models of the threshold type: Adaptive exponential integrate-and-fire model with two compartments Neurocomputing 70 1668 1673
6. AR Conn NIM Gould PL Toint 1997 A globally convergent augmented Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds Math Comput 66 261 288
7. B Connors M Gutnick 1990 Intrinsic firing patterns of diverse neocortical neurons Trends Neurosci 17 3894 3906
8. A Destexhe M Rudolph JM Fellous TS 2001 Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons Neuroscience 107 13 24
9. Doedel E, Paffenroth R, Champneys A, Fairgrieve T, Kuznetsov Y, Sandstede B, Wang X (2001) Auto 2000: continuation and bifurcation software for ordinary differential equations (with homcont). Technical Reportr, Caltech
10. Fletcher R (1987) Practical methods of optimization. Wiley, New York
11. JM González-Miranda 2003 Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model Chaos 13 3 845
12. JM González-Miranda 2007 Complex bifurcation structures in the Hindmarsh-Rose neuron model Int J Bifurcations Chaos 17 9 3071 3083
13. A Gupta Y Wang H Markram 2000 Organizing principles for a diversity of GABAergic interneurons and synapses in the neocortex Science 287 5451 273 278
14. J Hindmarsh R Rose 1984 A model of neuronal bursting using three coupled first order differential equations Proc R Soc Lond Ser B 221 1222 87 102
15. AC Hindmarsh P Brown KE Grant SL Lee R Serban DE Shumaker CS Woodward 2005 Sundials, suite of nonlinear and differential/algebraic equation solvers ACM Trans Math Softw 31 363 396
16. Innocenti G, Morelli A, Genesio R, Torcini A (2007) Dynamical phases of the Hindmarsh-Rose neuronal model: studies of the transition from bursting to spiking chaos. Chaos 17:043,128
17. E Izhikevich 2000 Neural excitability, spiking and bursting Int J Bifurcation Chaos 10 6 1171 1266
18. Jolivet R, Rauch A, Lüscher HR, Gerstner W (2006a) Integrate-and-fire models with adaptation are good enough. In: Weiss Y, Schölkopf B, Platt J (eds) (2006) Advances in neural information processing systems, vol 18. MIT Press, Cambridge, pp 595-602
19. R Jolivet A Rauch HR Lüscher W Gerstner 2006 Predicting spike timing of neocortical pyramidal neurons by simple threshold models J Comput Neurosc 21 1 35 49
20. Y Kawaguchi Y Kubota 1997 GABAergic cell subtypes and their synaptic connections in rat frontal cortex Cereb Cortex 7 476 486
21. de Lange E (2006) Neuron models of the generic bifurcation type: Network analysis and data modeling. PhD thesis, Ecole Polytechnique F édérale de Lausanne
22. Z Mainen T Sejnowski 1995 Reliability of spike timing in neocortical neurons Science 268 1503 1506
23. H Markram M Toledo-Rodriguez Y Wang A Gupta G Silberberg C Wu 2004 Interneurons of the neocortical inhibitory system Nat Rev Neurosci 5 793 807
24. D McCormick B Connors J Lighthall D Prince 1985 Comparative electrophysiology of pyramidal and sparsely spiny neurons of the neocortex J Neurophysiol 54 782 806
25. A Rauch G La Camera H Lüscher W Senn S Fusi 2003 Neocortical pyramidal cells respond as Integrate-and-Fire neurons to in vivo-like input currents J Neurophysiol 90 1598 1612
26. AI Selverston MI Rabinovich HDI Abarbanel R Elson A Szücs RD Pinto R Huerta P Varona 2000 Reliable circuits from irregular neurons: a dynamical approach to understanding central pattern generators J Physiol (Paris) 94 357 374
27. M Steriade 2004 Neocortical cell classes are flexible entities Nat Rev Neurosci 5 121 134
28. Steur E (2006) Parameter estimation in Hindmarsh-Rose neurons. Technical Report DCT 2006.073, Technische Universiteit Eindhoven
29. Steur E, Tyukin I, Nijmeijer H, van Leeuwen C (2007) Reconstructing dynamics of spiking neurons form input-output measurements in vitro. In: Third international IEEE scientific conference on physics and control, Potsdam
30. M Storace D Linaro E de Lange 2008 The Hindmars-Rose neuron model: bifurcation analysis and piecewise-linear approximations Chaos 18 033128
31. Toledo-Rodriguez M, Gupta A, Wang Y, Wu C, Markram H (2002) Neocortex: basic neuron types. In: Arbib M (eds) The handbook of brain theory and neural networks, 2nd edn. MIT Press, London, pp 791-725
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
33. Tuckwel H (1988) Introduction to theoretical neurobiology. Linear cable theory and dendritic structure, vol 1. Cambridge University Press, Cambridge
34. Weiss, Y, Schölkopf, B, Platt, J (eds) (2006) Advances in neural information processing systems, vol 18. MIT Press, Cambridge