Cluster burst synchronization in a scale-free network of inhibitory bursting neurons

Cognitive Neurodynamics - Tập 14 Số 1 - Trang 69-94 - 2020
Sang-Yoon Kim1, Woochang Lim1
1Institute for Computational Neuroscience and Department of Science Education, Daegu National University of Education, Daegu, Korea

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Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97

Aronson DG, Golubitsky M, Krupa M (1991) Coupled arrays of Josephson junctions and bifurcation of maps with $$S_N$$ symmetry. Nonlinearity 4:861–902

Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512

Bassett DS, Bullmore E (2006) Small-world brain networks. Neuroscientist 12:512–523

Batista CAS, Batista AM, de Pontes JAC, Viana RL, Lopes SR (2007) Chaotic phase synchronization in scale-free networks of bursting neuron. Phys Rev E 76:016218

Batista CAS, Batista AM, de Pontes JAC, Lopes SR, Viana RL (2009) Bursting synchronization in scale-free networks. Chaos Soliton Fract 41:2220–2225

Batista CAS, Lopes SR, Viana RL, Batista AM (2010) Delayed feedback control of bursting synchronization in a scale-free neuronal network. Neural Netw 23:114–124

Batista CA, Lameu EL, Batista AM, Lopes SR, Pereira T, Zamora-Lopez G, Kurths J, Viana RL (2012) Phase synchronization of bursting neurons in clustered small-world networks. Phys Rev E 86:016211

Bazhenov M, Timofeev I (2006) Thalamocortical oscillations. Scholarpedia 1(6):1319

Belykh I, Hasler M (2011) Mesoscale and clusters of synchrony in networks of bursting neurons. Chaos 21:016106

Belykh VN, Osipov GV, Petrov VS, Suykens JAK, Vandewalle J (2008) Cluster synchronization in oscillatory networks. Chaos 18:037106

Bevan M, Magill P, Terman D, Bolam J, Wilson C (2002) Move to the rhythm: oscillations in the subthalamic nucleus-external globus pallidus network. Trends Neurosci 25:525–531

Bonifazi P, Goldin M, Picardo MA, Jorquera I, Cattani A, Bianconi G, Represa A, Ben-Ari Y, Cossart R (2009) GABAergic hub neurons orchestrate synchrony in developing hippocampal networks. Science 326:1419–1424

Brown P (2007) Abnormal oscillatory synchronisation in the motor system leads to impaired movement. Cur Opin Neurobiol 17:656–664

Brunel N, Wang XJ (2003) What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance. J Neurophysiol 90:415–430

Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10:186–198

Butera RJ, Rinzel J, Smith JC (1999) Models of respiratory rhythm generation in the pre-Botzinger complex. I. Bursting pacemaker neurons. J Neurophysiol 82:382–397

Buzsáki G, Geisler C, Henze DA, Wang XJ (2004) Interneuron diversity series: circuit complexity and axon wiring economy of cortical interneurons. Trends Neurosci 27:186–193

Chay TR, Keizer J (1983) Minimal model for membrane oscillations in the pancreatic $$\beta $$-cell. Biophys J 42:181–190

Chik DTW, Coombes S, Wang ZD (2004) Clustering through postinhibitory rebound in synaptically coupled neurons. Phys Rev E 70:011908

Chklovskii DB, Mel BW, Svoboda K (2004) Cortical rewiring and information storage. Nature 431:782–788

Connors BW, Gutnick MJ (1990) Intrinsic firing patterns of diverse neocortical neurons. Trends Neurosci 13:99–104

Coombes S, Bressloff PC (eds) (2005) Bursting: the genesis of rhythm in the nervous system. World Scientific, Singapore

Del Negro CA, Hsiao CF, Chandler SH, Garfinkel A (1998) Evidence for a novel bursting mechanism in rodent trigeminal neurons. Biophys J 75:174–182

Dhamala M, Jirsa V, Ding M (2004) Transitions to synchrony in coupled bursting neurons. Phys Rev Lett 92:028101

Duan L, Fan D, Lu Q (2013) Hopf bifurcation and bursting synchronization in an excitable systems with chemical delayed coupling. Cogn Neurodyn 7:341–349

Eguíluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV (2005) Scale-free brain functional networks. Phys Rev Lett 94:018102

Elson RC, Selverston AI, Huerta R, Rulkov NF, Rabinovich MI, Abarbanel HDI (1998) Synchronous behavior of two coupled biological neurons. Phys Rev Lett 81:5691–5695

Felleman DJ, Van Essen DC (1991) Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex 1:1–47

Ferrari FAS, Viana RL, Lopes SR, Stoop R (2015) Phase synchronization of coupled bursting neurons and the generalized Kuramoto model. Neural Netw 66:107–118

Fisher R, van Emde BW, Blume W, Elger C, Genton P, Lee P, Engel J (2005) Epileptic seizures and epilepsy: definitions proposed by the International League Against Epilepsy (ILAE) and the International Bureau for Epilepsy (IBE). Epilepsia 46:470–472

Gais S, Plihal W, Wagner U, Born J (2000) Early sleep triggers memory for early visual discrimination skills. Nat Neurosci 3:1335–1339

Golomb D, Rinzel J (1994) Clustering in globally coupled inhibitory neurons. Phys D 72:259–282

Gray CM, McCormick DA (1996) Chattering cells: superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex. Science 274:109–113

Hammond C, Bergman H, Brown P (2007) Pathological synchronization in Parkinson’s disease: networks, models and treatments. Trends Neurosci 30:357–364

Hindmarsh JL, Rose RM (1982) A model of the nerve impulse using two first-order differential equations. Nature 296:162–164

Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond Ser B 221:87–102

Ivanchenko MV, Osipov GV, Shalfeev VD, Kurths J (2004) Phase synchronization in ensembles of bursting oscillators. Phys Rev Lett 93:134101

Izhikevich EM (2000) Neural excitability, spiking and bursting. Int J Bifurcat Chaos 10:1171–1266

Izhikevich EM (2004) Which model to use for cortical spiking neurons? IEEE Trans Neural Netw 15:1063–1070

Izhikevich EM (2006) Bursting. Scholarpedia 1(3):1300

Izhikevich EM (2007) Dynamical systems in neuroscience. MIT Press, Cambridge

Izhikevich EM, Desai NS, Walcott EC, Hoppensteadt FC (2003) Bursts as a unit of neural information: selective communication via resonance. Trends Neurosci 26:161–167

Kaiser M, Martin R, Andras P, Young MP (2007) Simulation of robustness against lesions of cortical networks. Eur J Neurosci 25:3185–3192

Kim SY, Lim W (2015a) Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons. Cogn Neurodyn 9:179–200

Kim SY, Lim W (2015b) Thermodynamic order parameters and statistical-mechanical measures for characterization of the burst and spike synchronizations of bursting neurons. Phys A 438:544–559

Kim SY, Lim W (2016) Effect of network architecture on burst and spike synchronization in a scale-free network of bursting neurons. Neural Netw 79:53–77

Kim SY, Lim W (2018) Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network. Cogn Neurodyn 12:315–342

Kinard TA, de Vries G, Sherman A, Satin LS (1999) Modulation of the bursting properties of single mouse pancreatic $$\beta $$-cells by artificial conductances. Biophys J 76:1423–1435

Kiss IZ, Zhai Y, Hudson H (2005) Predicting mutual entrainment of oscillators with experiment-based phase models. Phys Rev Lett 94:248301

Krahe R, Gabbian F (2004) Burst firing in sensory system. Nat Rev Neurosci 5:13–23

Lameu EL, Batista CAS, Batista AM, Larosz K, Viana RL, Lopes SR, Kurths J (2012) Suppression of bursting synchronization in clustered scale-free (rich-club) neuronal networks. Chaos 22:043149

Langdon AJ, Breakspear M, Coombes S (2012) Phase-locked cluster oscillations in periodically forced integrate-and-fire-or-burst neuronal populations. Phys Rev E 86:061903

Larimer P, Strowbridge BW (2008) Nonrandom local circuits in the dentate gyrus. J Neurosci 28:12212–12223

Lee SH, Govindaiah G, Cox CL (2007) Heterogeneity of firing properties among rat thalamic reticular nucleus neurons. J Physiol 582:195–208

Li X, Ouyang G, Usami A, Ikegaya Y, Sik A (2010) Scale-free topology of the CA3 hippocampal network: a novel method to analyze functional neuronal assemblies. Biophys J 98:1733–1741

Lisman J (1997) Bursts as a unit of neural information: making unreliable synapse reliable. Trends Neurosci 20:38–43

Llinás RL, Jahnsen H (1982) Electrophysiology of mammalian thalamic neurons in vitro. Nature 297:406–408

Longtin A (1997) Autonomous stochastic resonance in bursting neurons. Phys Rev E 55:868–876

McCormick DA, Huguenard JR (1992) A Model of the electrophysiological properties of thalamocortical relay neurons. J Neurophysiol 8:1384–1400

Meng P, Wang Q, Lu Q (2013) Bursting synchronization dynamics of pancreatic $$\beta $$-cells with electrical and chemical coupling. Cogn Neurodyn 7:197–212

Miyakawa K, Okano T, Yamazaki S (2013) Cluster synchronization in a chemical oscillator network with adaptive coupling. J Phy Soc Jpn 82:034005

Moon SJ, Cook KA, Rajendran K, Kevrekidis KG, Cisternas J, Liang CR (2015) Coarse-grained clustering dynamics of heterogeneously coupled neurons. J Math Neurosci 5:2

Morgan RJ, Soltesz I (2008) Nonrandom connectivity of the epileptic dentate gyrus predicts a major role for neuronal hubs in seizures. Proc Natl Acad Sci USA 105:6179–6184

Park C, Worth RM, Rubchinsky LL (2010) Fine temporal structure of beta oscillations synchronization in subthalamic nucleus in Parkinson’s disease. J Neurophysiol 103:2707–2716

Pereira T, Baptista M, Kurths J (2007) Multi-time-scale synchronization and information processing in bursting neuron networks. Eur Phys J Spec Top 146:155–168

Pernarowski M, Miura RM, Kevorkian J (1992) Perturbation techniques for models of bursting electrical activity in pancreatic $$\beta $$-cells. SIAM J Appl Math 52:1627–1650c

Plant RE (1981) Bifurcation and resonance in a model for bursting nerve cells. J Math Biol 11:15–32

Prado TdeL, Lopes SR, Batista CAS, Kurths J, Viana RL (2014) Synchronization of bursting Hodgkin-Huxley-type neurons in clustered networks. Phys Rev E 90:032818

Rose RM, Hindmarsh JL (1985) A model of a thalamic neuron. Proc R Soc Lond Ser B 225:161–193

Rinzel J (1985) Bursting oscillations in an excitable membrane model. In: Sleeman BD, Jarvis RJ (eds) Lecture notes in mathematics, vol 1151. Ordinary and partial differential equations. Springer, Berlin, pp 304–316

Rinzel J (1987) A formal classification of bursting mechanisms in excitable systems. In: Teramoto E, Yamaguti M (eds) Lecture notes in biomathematics, vol 71. Mathematical topics in population biology, morphogenesis, and neurosciences. Springer, Berlin, pp 267–281

San Miguel M, Toral R (2000) Stochastic effects in physical systems. In: Martinez J, Tiemann R, Tirapegui E (eds) Instabilities and nonequilibrium structures VI. Kluwer Academic Publisher, Dordrecht, pp 35–130

Scannell JW, Blakemore C, Young MP (1995) Analysis of connectivity in the cat cerebral cortex. J Neurosci 15:1463–1483

Scannell JW, Burns GAPC, Hilgetag CC, O’Neil MA, Young MP (1999) The connectional organization of the cortico-thalamic system of the cat. Cereb Cortex 9:277–299

Sejnowski TJ, Destexhe A (2000) Why do we sleep? Brain Res 886:208–223

Shi X, Lu Q (2005) Firing patterns and complete synchronization of coupled Hindmarsh-Rose neurons. Chin Phys 14:77–85

Shi X, Lu Q (2009) Burst synchronization of electrically and chemically coupled map-based neurons. Phys A 388:2410–2419

Shilnikov A, Cymbalyuk G (2005) Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe. Phys Rev Lett 94:048101

Shimazaki H, Shinomoto S (2010) Kernel bandwidth optimization in spike rate estimation. J Comput Neurosci 29:171–182

Song S, Sjöström PJ, Reigl M, Nelson S, Chklovskii DB (2005) Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biol 3:e68

Sporns O (2011) Networks of the brain. MIT Press, Cambridge

Sporns O, Honey CJ (2006) Small worlds inside big brains. Proc Natl Acad Sci USA 103:19219–19220

Sporns O, Tononi G, Edelman GM (2000) Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb Cortex 10:127–141

Sporns O, Chialvo DR, Kaiser M, Hilgetag CC (2004) Organization, development and function of complex brain networks. Trends Cogn Sci 8:418–425

Steriade M, McCormick DA, Sejnowski TJ (1993) Thalamocortical oscillations in the sleeping and aroused brain. Science 262:679–685

Stern EA, Jaeger D, Wilson CJ (1998) Membrane potential synchrony of simultaneously recorded striatal spiny neurons in vivo. Nature 394:475–478

Su H, Alroy G, Kirson ED, Yaari Y (2001) Extracellular calcium modulates persistent sodium current-dependent burst-firing in hippocampal pyramidal neurons. J Neurosci 21:4173–4182

Sun X, Lei J, Perc M, Kurths J, Chen G (2011) Burst synchronization transitions in a neuronal network of subnetworks. Chaos 21:016110

Tanaka G, Ibarz B, Sanjuan MA, Aihara K (2006) Synchronization and propagation of bursts in networks of coupled map neurons. Chaos 16:013113

Taylor AF, Kapetanopoulos P, Whitaker BJ, Toth R, Bull L, Tinsley MR (2008) Clusters and switchers in globally coupled photochemical oscillators. Phys Rev Lett 100:214101

Uhlhaas PJ, Singer W (2006) Neural synchrony in brain disorders: relevance for cognitive dysfunctions and pathophysiology. Neuron 52:155–168

Varona P, Torres JJ, Abarbanel HDI, Rabinovych MI, Elson RC (2001) Dynamics of two electrically coupled chaotic neurons: experimental observations and model analysis. Biol Cybern 84:91–101

van Vreeswijk C, Hansel D (2001) Patterns of synchrony in neural networks with spike adaptation. Neural Comput 13:959–992

Wang Q, Perc M, Duan Z, Chen G (2009) Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. Phys Rev E 80:026206

Wang QY, Murks A, Perc M, Lu QS (2011a) Taming desynchronized bursting with delays in the Macaque cortical network. Chin Phys B 20:040504

Wang Q, Chen G, Perc M (2011b) Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling. PLoS One 6:e15851

Wang H, Wang Q, Lu Q, Zheng Y (2013) Equilibrium analysis and phase synchronization of two coupled HR neurons with gap junction. Cogn Neurodyn 7:121–131

Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442

Wiedemann C (2010) Neuronal networks: a hub of activity. Nat Rev Neurosci 11:74

Wisenfeld K, Colet P, Wisenfeld S (1996) Synchronization transitions in a disordered Josephson series array. Phys Rev Lett 76:404–407

Womack MD, Khodakhah K (2002) Active contribution of dendrites to the tonic and trimodal patterns of activity in cerebellar Purkinje neurons. J Neurosci 22:10603–10612

Young MP (1993) The organization of neural systems in the primate cerebral cortex. Philos Trans R Soc 252:13–18

Young MP, Scannell JW, Burns GA, Blakemore C (1994) Analysis of connectivity: neural systems in the cerebral cortex. Rev Neurosci 5:227–250

Yu H, Wang J, Deng B, Wei X, Wong YK, Chan WL, Tsang KM, Yu Z (2011) Chaotic phase synchronization in small-world networks of bursting neurons. Chaos 21:013127

Zhang J, Yuan Z, Zhou T (2009) Synchronization and clustering of synthetic genetic networks: a role for cis-regulatory modules. Phys Rev E 79:041903