title: Small modifications to network topology can induce stochastic bistable spiking dynamics in a balanced cortical model.
abstract: Directed random graph models frequently are used successfully in modeling the population dynamics of networks of cortical neurons connected by chemical synapses. Experimental results consistently reveal that neuronal network topology is complex, however, in the sense that it differs statistically from a random network, and differs for classes of neurons that are physiologically different. This suggests that complex network models whose subnetworks have distinct topological structure may be a useful, and more biologically realistic, alternative to random networks. Here we demonstrate that the balanced excitation and inhibition frequently observed in small cortical regions can transiently disappear in otherwise standard neuronal-scale models of fluctuation-driven dynamics, solely because the random network topology was replaced by a complex clustered one, whilst not changing the in-degree of any neurons. In this network, a small subset of cells whose inhibition comes only from outside their local cluster are the cause of bistable population dynamics, where different clusters of these cells irregularly switch back and forth from a sparsely firing state to a highly active state. Transitions to the highly active state occur when a cluster of these cells spikes sufficiently often to cause strong unbalanced positive feedback to each other. Transitions back to the sparsely firing state rely on occasional large fluctuations in the amount of non-local inhibition received. Neurons in the model are homogeneous in their intrinsic dynamics and in-degrees, but differ in the abundance of various directed feedback motifs in which they participate. Our findings suggest that (i) models and simulations should take into account complex structure that varies for neuron and synapse classes; (ii) differences in the dynamics of neurons with similar intrinsic properties may be caused by their membership in distinctive local networks; (iii) it is important to identify neurons that share physiological properties and location, but differ in their connectivity.
authors.affiliation: Computational and Theoretical Neuroscience Laboratory, Institute for Telecommunications Research, University of South Australia, Mawson Lakes, South Australia, Australia.
authors.forename: Mark D
authors.initials: MD
authors.lastname: McDonnell
authors.affiliation: Department of Psychology and Brain Research Centre, University of British Columbia, Vancouver, British Columbia, Canada.
authors.forename: Lawrence M
authors.initials: LM
authors.lastname: Ward
mesh_terms: D001921:Brain / Q000166:cytology*; D025461:Feedback, Physiological; D008564:Membrane Potentials; D008959:Models, Neurological; D009415:Nerve Net / Q000166:cytology*; D009474:Neurons / Q000166:cytology*; D013269:Stochastic Processes
references.citation: Trends Neurosci. 2004 Apr;27(4):186-93
references.pmid: 15046877
references.citation: J Neurosci. 1998 May 15;18(10):3870-96
references.pmid: 9570816
references.citation: Proc Natl Acad Sci U S A. 2008 Apr 22;105(16):6179-84
references.pmid: 18375756
references.citation: PLoS Comput Biol. 2012 Jan;8(1):e1002354
references.pmid: 22275859
references.citation: J Neurosci. 2012 Jul 18;32(29):9817-23
references.pmid: 22815496
references.citation: Science. 2011 Dec 16;334(6062):1569-73
references.pmid: 22075724
references.citation: Neuron. 2006 Jan 5;49(1):119-30
references.pmid: 16387644
references.citation: Nat Methods. 2013 Jun;10(6):491-3
references.pmid: 23722207
references.citation: Nature. 2012 Oct 11;490(7419):293-8
references.pmid: 23060196
references.citation: PLoS Comput Biol. 2011 May;7(5):e1002059
references.pmid: 21625580
references.citation: J Neurosci. 2011 Apr 27;31(17):6263-5
references.pmid: 21525265
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Sep;86(3 Pt 2):036103
references.pmid: 23030976
references.citation: Front Comput Neurosci. 2011 Mar 08;5:8
references.pmid: 21556129
references.citation: Nature. 1998 Jun 4;393(6684):440-2
references.pmid: 9623998
references.citation: Cereb Cortex. 1997 Apr-May;7(3):237-52
references.pmid: 9143444
references.citation: Physiol Rev. 2010 Jul;90(3):1195-268
references.pmid: 20664082
references.citation: Nat Rev Neurosci. 2007 Jan;8(1):45-56
references.pmid: 17180162
references.citation: Neuron. 2010 Dec 22;68(6):1043-50
references.pmid: 21172607
references.citation: J Neurosci. 2009 Aug 19;29(33):10234-53
references.pmid: 19692598
references.citation: PLoS Comput Biol. 2012 Aug;8(8):e1002596
references.pmid: 23133368
references.citation: Neuron. 2009 Apr 16;62(1):17-29
references.pmid: 19376064
references.citation: PLoS Comput Biol. 2012;8(3):e1002408
references.pmid: 22457608
references.citation: Nature. 2011 Mar 10;471(7337):177-82
references.pmid: 21390124
references.citation: J Neurophysiol. 2003 Jul;90(1):415-30
references.pmid: 12611969
references.citation: Proc Natl Acad Sci U S A. 2002 Jun 11;99(12):7821-6
references.pmid: 12060727
references.citation: PLoS Comput Biol. 2011 Feb 03;7(2):e1001066
references.pmid: 21304930
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Aug;76(2 Pt 2):026107
references.pmid: 17930104
references.citation: Front Comput Neurosci. 2012 Jul 10;6:41
references.pmid: 22787446
references.citation: PLoS Biol. 2012;10(10):e1001411
references.pmid: 23109909
references.citation: PLoS Biol. 2004 Nov;2(11):e369
references.pmid: 15510229
references.citation: Front Comput Neurosci. 2011 Feb 08;5:5
references.pmid: 21369354
references.citation: Sci Rep. 2012;2:485
references.pmid: 22761993
references.citation: Front Comput Neurosci. 2011 Oct 12;5:41
references.pmid: 22016730
references.citation: Neural Comput. 2007 Jan;19(1):1-46
references.pmid: 17134316
references.citation: J Comput Neurosci. 2004 Mar-Apr;16(2):159-75
references.pmid: 14758064
references.citation: Annu Rev Neurosci. 2005;28:357-76
references.pmid: 16022600
references.citation: J Neurosci. 2012 Mar 21;32(12):4049-64
references.pmid: 22442071
references.citation: Nat Rev Neurosci. 2009 Mar;10(3):186-98
references.pmid: 19190637
references.citation: J Neurophysiol. 2007 Feb;97(2):1566-87
references.pmid: 17093119
references.citation: PLoS Comput Biol. 2005 Sep;1(4):e42
references.pmid: 16201007
references.citation: J Neurosci. 2008 May 28;28(22):5696-709
references.pmid: 18509031
references.citation: Nat Neurosci. 2011 Jul 17;14(8):1045-52
references.pmid: 21765421
references.citation: Nat Neurosci. 2012 Nov;15(11):1498-505
references.pmid: 23001062
references.citation: Trends Neurosci. 2005 Jun;28(6):304-9
references.pmid: 15927686
references.citation: Front Comput Neurosci. 2011 Mar 10;5:11
references.pmid: 21441986
references.citation: J Neurophysiol. 2005 Dec;94(6):4344-61
references.pmid: 16093332
references.citation: Front Comput Neurosci. 2011 Jul 08;5:28
references.pmid: 21779239
references.citation: Science. 1996 Dec 6;274(5293):1724-6
references.pmid: 8939866
references.citation: Nat Neurosci. 2011 Jan;14(1):100-7
references.pmid: 21076426
references.citation: Science. 2012 Jul 27;337(6093):437-44
references.pmid: 22837521
references.citation: J Comput Neurosci. 2010 Feb;28(1):137-54
references.pmid: 19866352
references.citation: Nature. 2004 Oct 14;431(7010):782-8
references.pmid: 15483599
references.citation: PLoS Comput Biol. 2010 Apr 22;6(4):e1000748
references.pmid: 20421990
references.citation: PLoS Comput Biol. 2012 Jan;8(1):e1002311
references.pmid: 22291581
references.citation: Brain Res. 2012 Jan 24;1434:162-77
references.pmid: 22000590
references.citation: Neuroimage. 2010 Sep;52(3):1059-69
references.pmid: 19819337
references.citation: Phys Rev Lett. 2004 May 14;92(19):198101
references.pmid: 15169447
references.citation: Proc Natl Acad Sci U S A. 2011 Mar 29;108(13):5419-24
references.pmid: 21383177
references.citation: Chaos. 2008 Mar;18(1):015113
references.pmid: 18377094
references.citation: J Comput Neurosci. 2011 Oct;31(2):229-45
references.pmid: 21222148
references.citation: Phys Rev Lett. 2008 Mar 21;100(11):118703
references.pmid: 18517839
references.citation: Bioinformatics. 2009 Jul 1;25(13):1680-5
references.pmid: 19389738
references.citation: PLoS Comput Biol. 2008 Dec;4(12):e1000239
references.pmid: 19079571
references.citation: PLoS Comput Biol. 2012 Jan;8(1):e1002334
references.pmid: 22291583
references.citation: Nat Neurosci. 2009 Apr;12(4):483-91
references.pmid: 19305402
references.citation: Nature. 2011 Jul 27;477(7363):171-8
references.pmid: 21796121
references.citation: J Comput Neurosci. 2010 Jun;28(3):579-94
references.pmid: 20490645
references.citation: Neuron. 2009 Apr 30;62(2):171-89
references.pmid: 19409263
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Apr;85(4 Pt 2):045102
references.pmid: 22680529
references.citation: Neural Comput. 2007 Jun;19(6):1437-67
references.pmid: 17444756
references.citation: Front Comput Neurosci. 2011 Jan 19;5:1
references.pmid: 21267396
references.citation: J Neurosci. 2004 Sep 29;24(39):8441-53
references.pmid: 15456817