title: Extending transfer entropy improves identification of effective connectivity in a spiking cortical network model.
abstract: Transfer entropy (TE) is an information-theoretic measure which has received recent attention in neuroscience for its potential to identify effective connectivity between neurons. Calculating TE for large ensembles of spiking neurons is computationally intensive, and has caused most investigators to probe neural interactions at only a single time delay and at a message length of only a single time bin. This is problematic, as synaptic delays between cortical neurons, for example, range from one to tens of milliseconds. In addition, neurons produce bursts of spikes spanning multiple time bins. To address these issues, here we introduce a free software package that allows TE to be measured at multiple delays and message lengths. To assess performance, we applied these extensions of TE to a spiking cortical network model (Izhikevich, 2006) with known connectivity and a range of synaptic delays. For comparison, we also investigated single-delay TE, at a message length of one bin (D1TE), and cross-correlation (CC) methods. We found that D1TE could identify 36% of true connections when evaluated at a false positive rate of 1%. For extended versions of TE, this dramatically improved to 73% of true connections. In addition, the connections correctly identified by extended versions of TE accounted for 85% of the total synaptic weight in the network. Cross correlation methods generally performed more poorly than extended TE, but were useful when data length was short. A computational performance analysis demonstrated that the algorithm for extended TE, when used on currently available desktop computers, could extract effective connectivity from 1 hr recordings containing 200 neurons in ∼5 min. We conclude that extending TE to multiple delays and message lengths improves its ability to assess effective connectivity between spiking neurons. These extensions to TE soon could become practical tools for experimentalists who record hundreds of spiking neurons.
authors.affiliation: Department of Physics, Indiana University, Bloomington, Indiana, United States of America. itos@indiana.edu
authors.forename: Shinya
authors.initials: S
authors.lastname: Ito
authors.forename: Michael E
authors.initials: ME
authors.lastname: Hansen
authors.forename: Randy
authors.initials: R
authors.lastname: Heiland
authors.forename: Andrew
authors.initials: A
authors.lastname: Lumsdaine
authors.forename: Alan M
authors.initials: AM
authors.lastname: Litke
authors.forename: John M
authors.initials: JM
authors.lastname: Beggs
mesh_terms: D000200:Action Potentials; D000465:Algorithms; D003198:Computer Simulation; D019277:Entropy; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D013569:Synapses / Q000502:physiology*
references.citation: Phys Rev Lett. 2008 Apr 18;100(15):158101
references.pmid: 18518155
references.citation: J Comp Physiol A Neuroethol Sens Neural Behav Physiol. 2006 Aug;192(8):777-84
references.pmid: 16550391
references.citation: PLoS One. 2009 Aug 04;4(8):e6482
references.pmid: 19652720
references.citation: Neural Comput. 2005 Sep;17(9):1927-61
references.pmid: 15992486
references.citation: Science. 1999 Oct 15;286(5439):509-12
references.pmid: 10521342
references.citation: J Neurophysiol. 1994 Feb;71(2):437-53
references.pmid: 8176419
references.citation: Science. 2002 Oct 25;298(5594):824-7
references.pmid: 12399590
references.citation: PLoS Biol. 2008 Jan;6(1):e16
references.pmid: 18232737
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Oct;72(4 Pt 2):046217
references.pmid: 16383522
references.citation: Nature. 2010 Oct 7;467(7316):673-7
references.pmid: 20930838
references.citation: Nature. 1998 Jun 4;393(6684):440-2
references.pmid: 9623998
references.citation: Neural Comput. 2007 Apr;19(4):910-33
references.pmid: 17348767
references.citation: J Neurosci. 1999 Nov 1;19(21):9497-507
references.pmid: 10531452
references.citation: Biol Cybern. 1997 Mar;76(3):217-27
references.pmid: 9151419
references.citation: J Neurophysiol. 1985 Oct;54(4):782-806
references.pmid: 2999347
references.citation: J Neurosci Methods. 2009 Mar 15;177(2):386-96
references.pmid: 19027792
references.citation: Phys Rev Lett. 2004 Mar 19;92(11):118102
references.pmid: 15089177
references.citation: J Neurosci. 2008 Jan 9;28(2):505-18
references.pmid: 18184793
references.citation: J Comput Neurosci. 2007 Jun;22(3):301-12
references.pmid: 17226088
references.citation: Trends Neurosci. 2003 Mar;26(3):161-7
references.pmid: 12591219
references.citation: Phys Rev Lett. 2000 Jul 10;85(2):461-4
references.pmid: 10991308
references.citation: Biol Cybern. 2000 Feb;82(2):111-21
references.pmid: 10664098
references.citation: Brain Res. 2006 Jun 6;1093(1):41-53
references.pmid: 16712817
references.citation: PLoS Comput Biol. 2006 Oct 27;2(10):e144
references.pmid: 17069456
references.citation: PLoS Biol. 2005 Mar;3(3):e68
references.pmid: 15737062
references.citation: J Neurosci Methods. 2008 Jul 15;172(1):79-93
references.pmid: 18508128
references.citation: J Neurophysiol. 2000 Feb;83(2):828-35
references.pmid: 10669497
references.citation: J Neural Eng. 2010 Oct;7(5):056001
references.pmid: 20720282
references.citation: Neuroimage. 2008 Jun;41(2):354-62
references.pmid: 18394927
references.citation: Biol Cybern. 2001 Aug;85(2):145-57
references.pmid: 11508777
references.citation: Biol Cybern. 1999 Jan;80(1):45-55
references.pmid: 9951397
references.citation: J Neural Eng. 2007 Jun;4(2):54-67
references.pmid: 17409480
references.citation: Trends Cogn Sci. 2004 Sep;8(9):418-25
references.pmid: 15350243
references.citation: Neural Comput. 2002 Jan;14(1):43-80
references.pmid: 11747534
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Feb;75(2 Pt 1):021915
references.pmid: 17358375
references.citation: Invest Radiol. 1979 Mar-Apr;14(2):109-21
references.pmid: 478799
references.citation: Biol Cybern. 2006 Jun;94(6):469-82
references.pmid: 16544165
references.citation: Biophys J. 1967 Jul;7(4):419-40
references.pmid: 4292792
references.citation: Neuroimage. 2008 Aug 15;42(2):799-806
references.pmid: 18599316
references.citation: Neuroscience. 2007 Aug 10;148(1):294-303
references.pmid: 17614210
references.citation: J Neurosci. 2006 Aug 16;26(33):8465-76
references.pmid: 16914671
references.citation: Annu Int Conf IEEE Eng Med Biol Soc. 2007;2007:1445-8
references.pmid: 18002238
references.citation: Biophys J. 2010 May 19;98(9):1733-41
references.pmid: 20441736
references.citation: PLoS Comput Biol. 2010 Sep 16;6(9):
references.pmid: 20862355
references.citation: Neural Comput. 2006 Feb;18(2):245-82
references.pmid: 16378515
references.citation: Trends Neurosci. 1997 Jan;20(1):38-43
references.pmid: 9004418
references.citation: Proc Natl Acad Sci U S A. 2007 Jun 12;104(24):10240-5
references.pmid: 17548818
references.citation: Eur J Neurosci. 1999 Oct;11(10):3517-30
references.pmid: 10564360
references.citation: Neuroscience. 2008 Jun 2;153(4):1354-69
references.pmid: 18448256
references.citation: J Neurosci. 1995 Oct;15(10):6834-45
references.pmid: 7472441
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Feb;77(2 Pt 2):026103
references.pmid: 18352086
references.citation: J Physiol. 2003 Aug 15;551(Pt 1):139-53
references.pmid: 12813147
references.citation: J Neurophysiol. 1985 Nov;54(5):1346-62
references.pmid: 4078619
references.citation: Nature. 1989 Mar 23;338(6213):334-7
references.pmid: 2922061
references.citation: Nature. 2008 Aug 21;454(7207):995-9
references.pmid: 18650810
references.citation: Science. 2009 Dec 4;326(5958):1419-24
references.pmid: 19965761
references.citation: Front Neuroeng. 2010 May 10;3:4
references.pmid: 20485465
references.citation: J Neurophysiol. 1987 Oct;58(4):752-64
references.pmid: 3681393
references.citation: Biophys J. 1970 Sep;10(9):876-900
references.pmid: 4322240
references.citation: J Neurosci. 2004 Jun 2;24(22):5216-29
references.pmid: 15175392
references.citation: IEEE Trans Biomed Eng. 2006 Sep;53(9):1802-12
references.pmid: 16941836
references.citation: Neural Comput. 2009 Feb;21(2):450-77
references.pmid: 19431266
references.citation: Neuroimage. 2006 Apr 15;30(3):794-812
references.pmid: 16364661
references.citation: Neuroinformatics. 2005;3(3):243-62
references.pmid: 16077161
references.citation: Nat Neurosci. 2000 Sep;3(9):919-26
references.pmid: 10966623
references.citation: J Neurosci Methods. 2006 Apr 15;152(1-2):210-9
references.pmid: 16269188
references.citation: J Comput Neurosci. 1998 Jul;5(3):267-84
references.pmid: 9663552
references.citation: J Neurophysiol. 2007 Mar;97(3):2533-43
references.pmid: 17202243
references.citation: J Physiol. 1983 Sep;342:181-215
references.pmid: 6631731
references.citation: PLoS One. 2008 Oct 07;3(10):e3355
references.pmid: 18839039
references.citation: Curr Opin Neurobiol. 2002 Oct;12(5):587-92
references.pmid: 12367640
references.citation: Proc Natl Acad Sci U S A. 2010 Jun 1;107(22):10244-9
references.pmid: 20479225
references.citation: J Neurophysiol. 1989 May;61(5):900-17
references.pmid: 2723733
references.citation: IEEE Trans Neural Netw. 2003;14(6):1569-72
references.pmid: 18244602
references.citation: Neural Comput. 1997 Aug 15;9(6):1265-75
references.pmid: 9248062