title: Mechanisms of very fast oscillations in networks of axons coupled by gap junctions.
abstract: Because electrical coupling among the neurons of the brain is much faster than chemical synaptic coupling, it is natural to hypothesize that gap junctions may play a crucial role in mechanisms underlying very fast oscillations (VFOs), i.e., oscillations at more than 80 Hz. There is now a substantial body of experimental and modeling literature supporting this hypothesis. A series of modeling papers, starting with work by Roger Traub and collaborators, have suggested that VFOs may arise from expanding waves propagating through an "axonal plexus", a large random network of electrically coupled axons. Traub et al. also proposed a cellular automaton (CA) model to study the mechanisms of VFOs in the axonal plexus. In this model, the expanding waves take the appearance of topologically circular "target patterns". Random external stimuli initiate each wave. We therefore call this kind of VFO "externally driven". Using a computational model, we show that an axonal plexus can also exhibit a second, distinctly different kind of VFO in a wide parameter range. These VFOs arise from activity propagating around cycles in the network. Once triggered, they persist without any source of excitation. With idealized, regular connectivity, they take the appearance of spiral waves. We call these VFOs "re-entrant". The behavior of the axonal plexus depends on the reliability with which action potentials propagate from one axon to the next, which, in turn, depends on the somatic membrane potential V (s) and the gap junction conductance g (gj). To study these dependencies, we impose a fixed value of V (s), then study the effects of varying V (s) and g (gj). Not surprisingly, propagation becomes more reliable with rising V (s) and g (gj). Externally driven VFOs occur when V (s) and g (gj) are so high that propagation never fails. For lower V (s) or g (gj), propagation is nearly reliable, but fails in rare circumstances. Surprisingly, the parameter regime where this occurs is fairly large. Even a single propagation failure can trigger re-entrant VFOs in this regime. Lowering V (s) and g (gj) further, one finds a third parameter regime in which propagation is unreliable, and no VFOs arise. We analyze these three parameter regimes by means of computations using model networks adapted from Traub et al., as well as much smaller model networks.
authors.affiliation: Department of Mathematics and Center for Biodynamics, Boston University, Boston, MA 02215, USA. ecmun@bu.edu
authors.forename: Erin
authors.initials: E
authors.lastname: Munro
authors.forename: Christoph
authors.initials: C
authors.lastname: Börgers
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D001369:Axons / Q000502:physiology*; D001683:Biological Clocks / Q000502:physiology; D001921:Brain / Q000502:physiology*; D003198:Computer Simulation; D017629:Gap Junctions / Q000502:physiology*; D006801:Humans; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D009434:Neural Pathways / Q000502:physiology; D011930:Reaction Time / Q000502:physiology; D013997:Time Factors
references.citation: Neuron. 2008 Jun 12;58(5):775-88
references.pmid: 18549788
references.citation: Epilepsy Curr. 2003 May;3(3):77-79
references.pmid: 15309064
references.citation: J Neurophysiol. 2001 Oct;86(4):1884-98
references.pmid: 11600648
references.citation: Epilepsia. 2004 Sep;45(9):1017-23
references.pmid: 15329064
references.citation: J Neurosci. 2008 Jun 11;28(24):6104-10
references.pmid: 18550752
references.citation: Neuroscience. 1999;92(2):407-26
references.pmid: 10408594
references.citation: Network. 2000 Nov;11(4):299-320
references.pmid: 11128169
references.citation: J Clin Neurophysiol. 2005 Oct;22(5):330-42
references.pmid: 16357637
references.citation: J Neurosci. 1997 Sep 1;17(17):6783-97
references.pmid: 9254689
references.citation: Eur J Neurosci. 2008 Oct;28(8):1603-16
references.pmid: 18973579
references.citation: Brain. 2007 Sep;130(Pt 9):2354-66
references.pmid: 17626037
references.citation: Proc Natl Acad Sci U S A. 2007 Jan 16;104(3):702-7
references.pmid: 17210922
references.citation: J Physiol. 2003 Aug 1;550(Pt 3):873-87
references.pmid: 12807984
references.citation: Epilepsia. 2001 Feb;42(2):153-70
references.pmid: 11240585
references.citation: Proc Natl Acad Sci U S A. 2007 Jul 24;104(30):12548-53
references.pmid: 17640909
references.citation: J Neurosci. 2000 Mar 15;20(6):2086-93
references.pmid: 10704482
references.citation: Neuron. 2008 Jun 12;58(5):763-74
references.pmid: 18549787
references.citation: Proc Natl Acad Sci U S A. 2003 Feb 4;100(3):1370-4
references.pmid: 12525690
references.citation: Eur J Neurosci. 2004 Oct;20(8):2141-8
references.pmid: 15450093
references.citation: Epilepsia. 2009 Apr;50(4):598-604
references.pmid: 19055491
references.citation: Brain. 2004 Jul;127(Pt 7):1496-506
references.pmid: 15155522
references.citation: J Neurophysiol. 2003 Feb;89(2):841-52
references.pmid: 12574462
references.citation: Proc Natl Acad Sci U S A. 2010 Jan 5;107(1):338-43
references.pmid: 19966298
references.citation: Ann Neurol. 2004 Jul;56(1):108-15
references.pmid: 15236407
references.citation: J Physiol. 2005 Mar 15;563(Pt 3):663-70
references.pmid: 15661820
references.citation: Nature. 1998 Jul 9;394(6689):189-92
references.pmid: 9671303
references.citation: Epilepsia. 1999 Feb;40(2):127-37
references.pmid: 9952257
references.citation: J Neurophysiol. 2007 Dec;98(6):3450-60
references.pmid: 17913989
references.citation: Am Heart J. 1964 Feb;67:200-20
references.pmid: 14118488
references.citation: Brain. 2007 Nov;130(Pt 11):2868-78
references.pmid: 17615093
references.citation: CMAJ. 2004 Sep 28;171(7):755-60
references.pmid: 15451840
references.citation: Epilepsia. 2008 Nov;49(11):1893-907
references.pmid: 18479382
references.citation: J Neurosci. 2008 Jul 9;28(28):7165-73
references.pmid: 18614686
references.citation: Proc Natl Acad Sci U S A. 2003 Sep 16;100(19):11047-52
references.pmid: 12960382
references.citation: J Neurosci. 2002 Mar 1;22(5):2012-21
references.pmid: 11880532
references.citation: Epilepsia. 2010 Aug;51(8):1587-97
references.pmid: 20002152
references.citation: Eur J Neurosci. 2007 Jun;25(11):3347-58
references.pmid: 17553003
references.citation: Eur J Neurosci. 2000 Nov;12(11):4093-106
references.pmid: 11069606
references.citation: J Neurosci. 1995 Jan;15(1 Pt 1):30-46
references.pmid: 7823136
references.citation: Neuron. 2001 Sep 13;31(5):831-40
references.pmid: 11567620
references.citation: J Clin Neurophysiol. 1992 Jul;9(3):441-8
references.pmid: 1517412