Cortical pyramidal cells as non-linear oscillators: Experiment and spike-generation theory

Brain Research

Volumn 1171, Issue 1, 2007, Pages 122-137

  Brumberg, Joshua C ^a   Gutkin, Boris S ^b,c  

^a CITY UNIVERSITY OF NEW YORK   (United States)

^b ECOLE NORMALE SUPÉRIEURE   (France)

^c INSTITUT PASTEUR   (France)

Author keywords

Bifurcation theory; Devil's staircase; Endogenous oscillator

Indexed keywords

ACTION POTENTIAL; ANIMAL TISSUE; ARTICLE; BRAIN SLICE; CONDUCTANCE; FEMALE; FERRET; MALE; MATHEMATICAL MODEL; NERVE POTENTIAL; NONHUMAN; OSCILLATION; PRIORITY JOURNAL; PYRAMIDAL NERVE CELL; THEORY;

ACTION POTENTIALS; ADAPTATION, PHYSIOLOGICAL; ANIMALS; BIOLOGICAL CLOCKS; DOSE-RESPONSE RELATIONSHIP, RADIATION; ELECTRIC STIMULATION; FEMALE; FERRETS; MALE; MODELS, NEUROLOGICAL; NONLINEAR DYNAMICS; PHOTIC STIMULATION; PYRAMIDAL CELLS; VISUAL CORTEX;

EID: 34548632479     PISSN: 00068993     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.brainres.2007.07.028     Document Type: Article

References (53)

1. Alexander J.C., Doedel E.J., and Othmer H.G. On the resonance structure in a forced excitable system. SIAM J. Appl. Math. 50 5 (1990) 1373-1418
2. Amitai Y. Membrane potential oscillations underlying firing patterns in neocortical neurons. Neuroscience 63 1 (1994) 151-161
3. Borg-Graham L. Interpretations of data and mechanisms for hippocampal pyramidal cell models chapter in cerebral cortex. In: Ulinski P.S., Jones E.G., and Peters A. (Eds). Cortical Models vol. 13 (1998), Plenum Press
4. Brown E., Moehlis J., and Holmes P. On the phase reduction and response dynamics of neural oscillator populations. Neural Comput. 16 4 (2004) 673-715 (Apr)
5. Brumberg J.C. Firing pattern modulation by oscillatory input in supragranular pyramidal neurons. Neuroscience 114 (2002) 239-246
6. Brumberg J.C., Nowak L.G., and McCormick D.A. Ionic mechanisms underlying repetitive high frequency burst firing in cortical neurons. J. Neurosci. 20 (2000) 4829-4843
7. Carandini M., Mechler F., Leonard C.S., and Movshon J.A. Spike train encoding by regular-spiking cells of the visual cortex. J. Neurophysiol. 76 (1996) 3425-3441
8. Coombes S., and Bressloff P.C. Mode locking and Arnold tongues in integrate-and-fire neural oscillators. Phys. Rev., E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60 (1999) 2086-2096
9. Desmaisons D., Vincent J.D., and Lledo P.M. Control of action potential timing by intrinsic subthreshold oscillations in olfactory bulb output neurons. J. Neurosci. 15 19(24) (1999) 10727-10737
10. Destexhe A., and Pare D. Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. J. Neurophysiol. 81 (1999) 1531-1547
11. Destexhe A., Contreras D., Steriade M., Sejnowski T.J., and Huguenard J.R. In vivo, in vitro, and computational analysis of dendritic calcium currents in thalamic reticular neurons. J. Neurosci. 16 (1996) 169-185
12. Ermentrout G.B. Type I membranes, phase resetting curves and synchrony. Neural Comput. 8 5 (1996) 979-1003
13. Ermentrout G.B. Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students (2002), SIAM books
14. Ermentrout G.B., and Kopell N. Frequency plateaus in a chain of weakly coupled oscillators, I. SIAM. J. Math. Anal. 15 2 (1984) 215-237
15. Ermentrout B., Pascal M., and Gutkin B. The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators. Neural Comput. 13 6 (2001) 1285-1310
16. Fellous J.-M., Houweling A.R., Modi R.H., Rao R.P.N., Tiesinga P.H.E., and Sejnowski T.J. Frequency dependence of spike timing reliability in cortical pyramidal neurons and interneurons. J. Neurophysiol. 85 (2001) 1782-1787
17. Fourcaud-Trocme N., Hansel D., van Vreeswijk C., and Brunel N. How spike generation mechanisms determine the neuronal response to fluctuating inputs. J. Neurosci. 23 37 (2003) 11628-11640
18. Gerstner W., and Kistler W.M. Spiking Neuron Models: Single Neurons, Populations, Plasticity (2002), Cambridge University Press, Cambridge UK
19. Glass L., and Mackey M.C. From Clocks to Chaos (1988), Princeton University Press, Princeton
20. Glass L., Graves C., Petrillo G.A., and Mackey M.C. Unstable dynamics of a periodically driven oscillator in the presence of noise. J. Theor. Biol. 86 (1980) 455-475
21. Gupta A., Wang Y., and Markram H. Organizing principles for a diversity of GABAergic interneurons and synapses in the neocortex. Science 287 (2000) 273-278
22. Gutkin, B.S. 1999. A Theory of Action Potential Generation in Cortical Neurons and its Implication for Neural Activity, Doctoral Dissertation, University of Pittsburgh.
23. Gutkin B.S., and Ermentrout G.B. Dynamics of membrane excitability determine interspike interval variability: a link between spike generation mechanisms and cortical spike train statistics. Neural Comput. 10 5 (1998) 1047-1065
24. Gutkin B.S., and Ermentrout G.B. Θ-neuron, a 1-dimensional spiking model that reproduces in vitro and in vivo spiking characteristics of cortical neurons. In: Paton H.A. (Ed). Information Processing in Cells and Tissues (1998), Plenum Press, New York 57-68
25. Gutkin B.S., Ermentrout G.B., and Reyes A. Phase-response curves give the responses of neurons to transient inputs. J. Neurophysiol. 94 2 (2005) 1623-1635
26. Guttman R., Feldman L., and Jakobson E. Frequency entrainment of squid axon membrane. J. Membr. Biol. 56 (1980) 9-18
27. Hansen A.J. Effect of anoxia on ion distribution in the brain. Physiol. Rev. 65 (1985) 101-148
28. Hayashi H., and Ishizuka S. Chaotic nature of bursting discharges in the Onchidium pacemaker neuron. J. Theor. Biol. 156 (1992) 269-291
29. Hodgkin A.L. The local electric changes associated with repetitive action I a non-medullated axon. J. Physiol. (London) 107 (1948) 165-181
30. Holden A.V. The response of excitable membrane models to a cyclic input. Biol. Cybern. 21 1 (1976) 1-7
31. Hoppensteadt F.C., and Izhikevich E.M. Weakly Connected Neural Networks (1997), Springer-Verlag, New York
32. Hunter J.D., Milton J.G., Thomas P.J., and Cowan J.D. Resonance effect for neural spike time reliability. J. Neurophysiol. 80 (1998) 1427-1438
33. Hutcheon B., and Yarom Y. Resonance, oscillation and the intrinsic frequency preferences of neurons. Trends Neurosci. 23 5 (2000) 216-222 (Related Articles)
34. Hutcheon B., Miura R.M., and Puil E. Subthreshold membrane resonance in neocortical neurons. J. Neurophysiol. 76 (1996) 683-698
35. Izhikevich E.M. Neural excitability, spiking and bursting. Int. J. Bifurc. Chaos Appl. Sci. Eng. 10 (2000) 1171-1266
36. Izhikevich E.M. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (2007), MIT press
37. Lampl L., and Yarom Y. Subthreshold oscillations of the membrane potential and resonant behavior: two manifestations of the same mechanism. Neuroscience 78 (1997) 325-341
38. Llinas R.R., Grace A.A., and Yarom Y. In vitro neuron in mammalian cortical layer 4 exhibit intrinsic oscillatory activity in the 10- to 50-Hz range. PNAS 88 (1991) 897-901
39. Mainen Z.F., Joerges J., Huguenard J., and Sejnowski T.J. A model of spike initiation in neocortical pyramidal neurons. Neuron 15 (1995) 1427-1439
40. McCormick D.A., Connors B.W., Lighthall J.W., and Prince D.A. Comparative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex. J. Neurophysiol. 54 (1985) 782-806
41. Naundorf B., Geisel T., and Wolf F. Action potential onset dynamics and the response speed of neuronal populations. J. Comput. Neurosci. 18 3 (2005) 297-309
42. Naundorf B., Wolf F., and Volgushev M. Unique features of action potential initiation in cortical neurons. Nature 440 7087 (2006) 1060-1063
43. Nowak L.G., Sanchez-Vives M.V., and McCormick D.A. Influence of low and high frequency inputs on spike timing in visual cortical neurons. Cereb. Cortex 7 (1997) 487-501
44. Nowak L.G., Azouz R., Sanchez-Vives M.V., Gray C.M., and McCormick D.A. Electrophysiological classes of cat primary visual cortical neurons in vivo as revealed by quantitative analyses. J. Neurophysiol. 89 (2003) 1541-1566
45. Pare D., Shink E., Gaudreau H., Destexhe A., and Lang E.J. Impact of spontaneous synaptic activity on the resting properties of cat neocortical pyramidal neurons in vivo. J. Neurophysiol. 79 (1998) 1450-1460
46. Parmananda P., Mena C.H., and Baier G. Resonant forcing of a silent Hodgkin-Huxley neuron. Phys. Rev., E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 66 (2002)
47. Richardson M.J., Brunel N., and Hakim V. From subthreshold to firing-rate resonance. J. Neurophysiol. 89 5 (2003) 2538-2554 (May)
48. Rinzel J., and Ermentrout B. Analysis of neural excitability and oscillations. In: Koch C., and Segev I. (Eds). Methods in Neuronal Modelling (1998), The MIT Press, Cambridge 251-291
49. + channels designed for high-frequency repetitive firing. Trends Neurosci. 24 (2001) 517-526
50. Schaus M.J., and Moehlis J. On the response of neurons to sinusoidal current stimuli: phase response curves and phase-locking. Proceedings of the IEEE 45th Conf. on Decision and Control (2006) 2376-2381
51. Smith G.D., Cox C.L., Sherman S.M., and Rinzel J. Fourier analysis of sinusoidally driven thalamocortical relay neurons and a minimal integrate-and-fire-or-burst model. J. Neurophysiol. 83 (2000) 588-610
52. Traub R.D., Jefferys J.G., and Whittington M.A. Fast oscillations in cortical circuits (1999), MIT Press, Cambridge, MA
53. Volgushev M., Chistakova M., and Singer W. Modification of discharge patterns of neocortical neurons by induced oscillations of the membrane potential. Neuroscience 83 (1998) 15-25