The response of a classical Hodgkin-Huxley neuron to an inhibitory input pulse.
A population of uncoupled neurons can often be brought close to synchrony by a single strong inhibitory input pulse affecting all neurons equally. This mechanism is thought to underlie some brain rhythms, in particular gamma frequency (30-80 Hz) oscillations in the hippocampus and neocortex. Here we show that synchronization by an inhibitory input pulse often fails for populations of classical Hodgkin-Huxley neurons. Our reasoning suggests that in general, synchronization by inhibitory input pulses can fail when the transition of the target neurons from rest to spiking involves a Hopf bifurcation, especially when inhibition is shunting, not hyperpolarizing. Surprisingly, synchronization is more likely to fail when the inhibitory pulse is stronger or longer-lasting. These findings have potential implications for the question which neurons participate in brain rhythms, in particular in gamma oscillations.
Börgers
Christoph
C
Department of Mathematics, Tufts University, Medford, MA 02155, USA. cborgers@tufts.edu
Krupa
Martin
M
Gielen
Stan
S
D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D001683:Biological Clocks / Q000502:physiology; D002540:Cerebral Cortex / Q000166:cytology / Q000502:physiology*; D003198:Computer Simulation; D003344:Cortical Synchronization; D004558:Electric Stimulation; D006801:Humans; D007395:Interneurons / Q000502:physiology; D009433:Neural Inhibition / Q000502:physiology*; D009434:Neural Pathways / Q000502:physiology; D009474:Neurons / Q000502:physiology*; D017966:Pyramidal Cells / Q000502:physiology; D009435:Synaptic Transmission / Q000502:physiology*
J Physiol. 1998 Nov 15;513 ( Pt 1):117-26
9782163
Nat Rev Neurosci. 2004 Oct;5(10):793-807
15378039
J Neurophysiol. 2008 Dec;100(6):3030-42
18829848
PLoS Comput Biol. 2008 Oct;4(10):e1000198
18846205
Neural Comput. 2005 Mar;17(3):557-608
15802007
J Neurosci. 2004 Nov 17;24(46):10369-78
15548651
Proc Natl Acad Sci U S A. 2005 May 10;102(19):7002-7
15870189
Neural Comput. 1995 Mar;7(2):307-37
8974733
J Neurosci. 2004 Oct 13;24(41):9127-37
15483131
Nature. 1995 Feb 16;373(6515):612-5
7854418
J Neurosci. 1996 Oct 15;16(20):6402-13
8815919
Trends Neurosci. 2007 Jul;30(7):317-24
17499860
Nat Rev Neurosci. 2007 Jan;8(1):45-56
17180162
Neuron. 2003 Jan 23;37(2):311-22
12546825
J Physiol. 2001 Aug 15;535(Pt 1):125-31
11507163
J Neurophysiol. 1997 Sep;78(3):1199-211
9310412
Nature. 1980 Feb 14;283(5748):673-6
6965523
J Neurosci. 1995 Apr;15(4):2638-55
7722619
Neuron. 2006 Jan 5;49(1):107-17
16387643
J Comput Neurosci. 1994 Dec;1(4):313-21
8792237
Eur J Neurosci. 2007 Jun;25(11):3429-41
17553012
PLoS One. 2008;3(12):e3947
19079601
Nature. 1998 Jul 9;394(6689):186-9
9671302
Hippocampus. 2007;17(3):210-9
17294460
Proc Natl Acad Sci U S A. 2004 Oct 26;101(43):15482-7
15489269
J Neurophysiol. 2004 Oct;92(4):2283-94
15381746
Neural Comput. 2007 Mar;19(3):706-29
17298230
Neural Comput. 1998 May 15;10(4):837-54
9573408
J Comput Neurosci. 1997 Apr;4(2):141-50
9154520
J Neurophysiol. 2005 Mar;93(3):1197-208
15525802
Nat Neurosci. 2005 Dec;8(12):1677-83
16261136
Neural Comput. 1998 Jul 1;10(5):1047-65
9654767
Neural Comput. 2001 Jun;13(6):1285-310
11387047
Phys Rev Lett. 2005 Apr 22;94(15):158101
15904191
J Neurosci. 2001 Dec 1;21(23):9478-86
11717382
Proc Natl Acad Sci U S A. 1998 Feb 3;95(3):1259-64
9448319
Int J Psychophysiol. 2000 Dec 1;38(3):315-36
11102670
J Neurophysiol. 1999 Nov;82(5):2476-89
10561420
J Neurosci. 2000 Oct 15;20(20):7846-54
11027250
J Comput Neurosci. 1998 Mar;5(1):5-16
9580271
Neural Comput. 2003 Mar;15(3):509-38
12620157
J Neurosci. 2003 Oct 29;23(30):9761-9
14586003
Proc Natl Acad Sci U S A. 2003 Sep 16;100(19):11047-52
12960382
J Comput Neurosci. 2009 Apr;26(2):289-301
18784991
Eur J Neurosci. 2000 Nov;12(11):4093-106
11069606
J Neurosci. 2009 Aug 26;29(34):10533-40
19710306
Biophys J. 1981 Jul;35(1):193-213
7260316
J Physiol. 2005 Jan 1;562(Pt 1):9-26
15539390
Proc Natl Acad Sci U S A. 2008 Nov 18;105(46):18023-8
19004759
Neuron. 2005 Jan 6;45(1):105-17
15629706
J Theor Biol. 1978 Apr 6;71(3):401-20
642538
J Neurosci. 2008 Dec 17;28(51):13828-44
19091973
J Physiol. 1952 Aug;117(4):500-44
12991237
Neural Comput. 1996 Jul 1;8(5):979-1001
8697231