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Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network

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Abstract

We consider an excitatory population of subthreshold Izhikevich neurons which cannot fire spontaneously without noise. As the coupling strength passes a threshold, individual neurons exhibit noise-induced burstings. This neuronal population has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). However, STDP was not considered in previous works on stochastic burst synchronization (SBS) between noise-induced burstings of sub-threshold neurons. Here, we study the effect of additive STDP on SBS by varying the noise intensity D in the Barabási–Albert scale-free network (SFN). One of our main findings is a Matthew effect in synaptic plasticity which occurs due to a positive feedback process. Good burst synchronization (with higher bursting measure) gets better via long-term potentiation (LTP) of synaptic strengths, while bad burst synchronization (with lower bursting measure) gets worse via long-term depression (LTD). Consequently, a step-like rapid transition to SBS occurs by changing D, in contrast to a relatively smooth transition in the absence of STDP. We also investigate the effects of network architecture on SBS by varying the symmetric attachment degree \(l^*\) and the asymmetry parameter \(\Delta l\) in the SFN, and Matthew effects are also found to occur by varying \(l^*\) and \(\Delta l\). Furthermore, emergences of LTP and LTD of synaptic strengths are investigated in details via our own microscopic methods based on both the distributions of time delays between the burst onset times of the pre- and the post-synaptic neurons and the pair-correlations between the pre- and the post-synaptic instantaneous individual burst rates (IIBRs). Finally, a multiplicative STDP case (depending on states) with soft bounds is also investigated in comparison with the additive STDP case (independent of states) with hard bounds. Due to the soft bounds, a Matthew effect with some quantitative differences is also found to occur for the case of multiplicative STDP.

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References

  • Abbott LF, Blum KI (1996) Functional significance of long-term potentiation for sequence learning and prediction. Cereb Cortex 6:406–416

    Article  CAS  PubMed  Google Scholar 

  • Abbott LF, Nelson SB (2000) Synaptic plasticity: taming the beast. Nat Neurosci 3:1178–1183

    Article  CAS  PubMed  Google Scholar 

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

    Article  Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • Bi GQ, Poo MM (1998) Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. J Neurosci 18:10464–10472

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Bi GQ, Poo MM (2001) Synaptic modification by correlated activity: Hebbs postulate revisited. Annu Rev Neurosci 24:139–166

    Article  CAS  PubMed  Google Scholar 

  • Bienenstock EL, Cooper LN, Munro PW (1982) Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J Neurosci 2:32–48

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Birtoli B, Ulrich D (2004) Firing mode-dependent synaptic plasticity in rat neocortical pyramidal neurons. J Neurosci 24:4935–4940

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Blum KI, Abbott LF (1996) A model of spatial map formation in the hippocampus of the rat. Neural Comput 8:85–93

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

  • Borges RR, Borges FS, Batista AM, Lameu EL, Viana RL, Iarosz KC, Caldas IL, Sanjuán MAF (2016) Effects of spike timing-dependent plasticity on the synchronization in a random Hodgkin–Huxley neuronal network. Commun Nonlinear Sci Numer Simulat 34:12–22

    Article  Google Scholar 

  • Borges RR, Borges FS, Lameu EL, Batista AM, Iarosz KC, Caldas IL, Antonopoulos CG, Batista MS (2017) Spike timing-dependent plasticity induces non-trivial topology in the brain. Neural Netw 88:58–64

    Article  CAS  PubMed  Google Scholar 

  • Braun HA, Wissing H, Schäfer K, Hirsh MC (1994) Oscillation and noise determine signal transduction in shark multimodal sensory cells. Nature 367:270–273

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

  • Buzsáki G (2006) Rhythms of the brain. Oxford University Press, New York

    Book  Google Scholar 

  • 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

    Article  PubMed  CAS  Google Scholar 

  • Buzsáki G, Wang XJ (2012) Mechanisms of gamma oscillations. Annu Rev Neurosci 35:203–225

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Caporale N, Dan Y (2008) Spike timing-dependent plasticity: a Hebbian learning rule. Annu Rev Neurosci 31:25–46

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

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

    Google Scholar 

  • Dan Y, Poo MM (2004) Spike timing-dependent plasticity of neural circuits. Neuron 44:23–30

    Article  CAS  PubMed  Google Scholar 

  • Dan Y, Poo MM (2006) Spike timing-dependent plasticity: from synapse to perception. Physiol Rev 86:1033–1048

    Article  PubMed  Google Scholar 

  • Debanne D, Gähwiler BH, Thompson SM (1998) Long-term synaptic plasticity between pairs of individual CA3 pyramidal cells in rat hippocampal slice cultures. J Physiol 507(1):237–247

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • 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

    Article  PubMed  PubMed Central  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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

    Article  PubMed  PubMed Central  Google Scholar 

  • Egger V, Feldmeyer D, Sakmann B (1999) Coincidence detection and changes of synaptic efficacy in spiny stellate neurons in rat barrel cortex. Nat Neurosci 2:1098–1105

    Article  CAS  PubMed  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • Elson RC, Selverston AI, Huerta R, Rulkov NF, Rabinovich MI, Abarbanel HDI (1998) Synchronous behavior of two coupled biological neurons. Phys Rev Lett 81:5692–5695

    Article  CAS  Google Scholar 

  • Feldman DE (2000) Timing-based LTP and LTD at vertical inputs to layer II/III pyramidal cells in rat barrel cortex. Neuron 27:45–56

    Article  CAS  PubMed  Google Scholar 

  • Feldman DE (2012) The spike-timing dependence of plasticity. Neuron 75:556–571

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

  • Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40:35–41

    Article  Google Scholar 

  • Freeman LC (1978) Centrality in social networks conceptual clarification. Soc Netw 1:215–239

    Article  Google Scholar 

  • Garcia-Rill E (2015) Waking and the reticular activating system in health and disease. Elsevier, London

    Google Scholar 

  • Gerstner W, Kempter R, van Hemmen JL, Wagner H (1996) A neuronal learning rule for sub-millisecond temporal coding. Nature 383:76–81

    Article  CAS  PubMed  Google Scholar 

  • Gray CM (1994) Synchronous oscillations in neuronal systems: mechanisms and functions. J Comput Neurosci 1:11–38

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

  • Gütig R, Aharonov R, Rotter S, Sompolinksy H (2003) Learning input correlations through nonlinear temporally asymmetric Hebbian plasticity. J Neurosci 23:3697–3714

    Article  PubMed  PubMed Central  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Harnett MT, Bernier BE, Ahn KC, Morikawa H (2009) Burst-timing-dependent plasticity of NMDA receptor-mediated transmission in midbrain dopamine neurons. Neuron 62:826–838

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Hebb DO (1949) The organization of behavior; a neuropsychological theory. Wiley, New York

    Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • Hodgkin AL (1948) The local electric changes associated with repetitive action in a non-medullated axon. J Physiol 107:165–181

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500–544

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Hu B, Zhou C (2000) Phase synchronization in coupled nonidentical excitable systems and array-enhanced coherence resonance. Phys Rev E 61:R1001–R1004

    Article  CAS  Google Scholar 

  • Huber MT, Braun HA (2006) Stimulus-response curves of a neuronal model for noisy subthreshold oscillations and related spike generation. Phys Rev E 73:041929

    Article  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

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

    Article  Google Scholar 

  • Izhikevich EM (2003) Simple model of spiking neurons. IEEE Trans Neural Netw 14:1569–1572

    Article  CAS  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

  • Ji D, Wilson M (2007) Coordinated memory replay in the visual cortex and hippocampus during sleep. Nat Neurosci 10:100–107

    Article  CAS  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Kepecs A, van Rossum MCW, Song S, Tegner J (2002) Spike-timing-dependent plasticity: common themes and divergent vistas. Biol Cybern 87:446–458

    Article  PubMed  Google Scholar 

  • Khodagholy D, Gelinas N, Buzsáki G (2017) Learning-enhanced coupling between ripple oscillations in association cortices and hippocampus. Science 358:369–372

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

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

    Article  Google Scholar 

  • Kim SY, Lim W (2015c) Fast sparsely synchronized brain rhythms in a scale-free neural network. Phys Rev E 92:022717

    Article  CAS  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

  • Kim SY, Lim W (2018) Stochastic spike synchronization in a small-world neural network with spike-timing-dependent plasticity. Neural Netw 97:92–106

    Article  PubMed  Google Scholar 

  • Kim SY, Kim Y, Hong DG, Kim J, Lim W (2012) Stochastic bursting synchronization in a population of subthreshold Izhikevich neurons. J Korean Phys Soc 60:1441–1447

    Article  Google Scholar 

  • 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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Kornoski J (1948) Conditional reflexes and neuron organization. Cambridge University Press, Cambridge

    Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • 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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    Article  Google Scholar 

  • Longtin A, Hinzer K (1996) Encoding with bursting, subthreshold oscillations and noise in mammalian cold receptors. Neural Comput 8:215–255

    Article  CAS  PubMed  Google Scholar 

  • Lourens MAJ, Schwab BC, Nirody JA, Meijer HGE, van Gils SA (2015) Exploiting pallidal plasticity for stimulation in Parkinsons disease. J Neural Eng 12:026005

    Article  PubMed  Google Scholar 

  • Markram H, Lübke J, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275:213–215

    Article  CAS  PubMed  Google Scholar 

  • Markram H, Gerstner W, Sjöström PJ (2012) Spike-timing-dependent plasticity: a comprehensive overview. Front Synaptic Neurosci 4:2

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  Google Scholar 

  • Mehta MR, Wilson M (2000) From hippocampus to V1: Effect of LTP on spatiotemporal dynamics of receptive fields. Neurocomputing 32:905–911

    Article  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Michalareas G, Vezoli J, van Pelt S, Schoffelen JM, Kennedy H, Fries P (2016) Alpha-beta and gamma rhythms subserve feedback and feedforward influences among human cortical areas. Neuron 89:384–397

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Miyawaki H, Diva K (2016) Regulation of hippocampal firing by network oscillations during sleep. Curr Biol 26:893–902

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • 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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Morrison A, Aertsen A, Diesmann M (2007) Spike-timing-dependent plasticity in balanced random networks. Neural Comput 19:1437–1467

    Article  PubMed  Google Scholar 

  • Nishikawa T, Motter AE, Lai YC, Hoppensteadt FC (2003) Heterogeneity in oscillator networks: are smaller worlds easier to synchronize? Phys Rev Lett 91:014101

    Article  PubMed  CAS  Google Scholar 

  • Oliva A, Fernández-Ruiz A, Buzsáki G, Berényi A (2016) Role of hippocampal CA2 region in triggering sharp-wave ripples. Neuron 91:1–14

    Article  CAS  Google Scholar 

  • Omelchenko I, Rosenblum M, Pikovsky A (2010) Synchronization of slow-fast systems. Eur Phys J 191:3–14

    CAS  Google Scholar 

  • 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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ploner M, Sorg C, Gross J (2017) Brain rhythms of pain. Trends Cogn Sci 21:100–110

    Article  PubMed  PubMed Central  Google Scholar 

  • Popovych OV, Tass PA (2012) Desynchronizing electrical and sensory coordinated reset neuromodulation. Front Hum Neurosci 6:58

    Article  PubMed  PubMed Central  Google Scholar 

  • Popovych OV, Yanchuk S, Tass PA (2013) Self-organized noise resistance of oscillatory neural networks with spike-timing-dependent plasticity. Sci Rep 3:2926

    Article  PubMed  PubMed Central  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Chapter  Google Scholar 

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

    Article  CAS  Google Scholar 

  • Roux L, Hu B, Eichler R, Stark E, Buzsáki G (2017) Sharp wave ripples during learning stabilize the hioppocampal map. Nat Neurosci 20:845–853

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Rubin JE (2007) Burst synchronization. Scholarpedia 2(10):1666

    Article  Google Scholar 

  • Rubin J, Lee DD, Sompolinsky H (2001) Equilibrium properties of temporally asymmetric Hebbian plasticity. Phys Rev Lett 86:364–367

    Article  CAS  PubMed  Google Scholar 

  • Saleem AB, Lien AD, Krumin M, Haider B, Rosón MR, Ayaz A, Reinhold K, Busse L, Carandini M, Harris KD (2017) Subcortical source and modulation of the narrowband gamma oscillation in mouse visual cortex. Neuron 93:315–322

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • 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

    Chapter  Google Scholar 

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

  • Sejnowski TJ (1977) Storing covariance with nonlinearly interacting neurons. J Math Biol 4:303–321

    Article  CAS  PubMed  Google Scholar 

  • Shatz CJ (1992) The developing brain. Sci Am 267:60–67

    Article  CAS  PubMed  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  • 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

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Shinohara Y, Kanamaru T, Suzuki H, Horita T, Aihara K (2002) Array-enhanced coherence resonance and forced dynamics in coupled FitzHugh–Nagumo neurons with noise. Phys Rev E 65:051906

    Article  CAS  Google Scholar 

  • Song S, Abbott LF (2001) Cortical development and remapping through spike timing-dependent plasticity. Neuron 32:339–350

    Article  CAS  PubMed  Google Scholar 

  • Song S, Miller KD, Abbott LF (2000) Competitive Hebbian learning through spike-timing-dependent plasticity synaptic plasticity. Nat Neurosci 3:919–926

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  PubMed  PubMed Central  CAS  Google Scholar 

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

    Google Scholar 

  • Sporns O, Betzel RF (2016) Modular brain networks. Annu Rev Psychol 67:19.1–19.28

    Article  Google Scholar 

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Stent GS (1973) A physiological mechanism for Hebbs postulate of learning. Proc Natl Acad Sci USA 70:997–1001

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Swann NC, de Hemptinne C, Miocinovic S, Qasim S, Wang SS, Ziman N, Ostrem JL, San Luciano M, Galifianakis NB, Starr PA (2017) Gamma Oscillations in the Hyperkinetic State Detected with Chronic Human Brain Recordings in Parkinson’s Disease. J Neurosci 36:6445–6458

    Article  CAS  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Taxidis J, Anastassiou CA, Diva K, Koch C (2015) Local field potentials encode place cell ensemble activation during hippocampal sharp wave ripples. Neuron 87:590–604

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Traub RD, Whittington MA (2010) Cortical oscillations in health and diseases. Oxford University Press, New York

    Book  Google Scholar 

  • Tzounopoulos T, Kim Y, Oertel D, Trussell LO (2004) Cell-specific, spike timing-dependent plasticities in the dorsal cochlear nucleus. Nat Neurosci 7:719–725

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Ujma PP, Bódizs R, Gombos F, Stintzing J, Konrad BN, Ginzel L, Steiger A, Dresler M (2015) Nap sleep spindle correlates of intelligence. Sci Rep 5:17159

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • 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

    Article  CAS  PubMed  Google Scholar 

  • Veit J, Hakim R, Jadi MP, Sejnowski TJ, Adesnik H (2017) Cortical gamma band synchronization through somatostatin interneurons. Nat Neurosci 20:951–959

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Vogels TP, Froemke RC, Doyon N, Gilson M, Haas JS, Liu R, Maffei A, Miller P, Wierenga CJ, Woodin MA, Zenke F, Sprekeler H (2013) Inhibitory synaptic plasticity: spike timing-dependence and putative network function. Front Neural Circuits 7:119

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • von der Malsburg C (1973) Self-organization of orientation sensitive cells in the striate cortex. Kybernetik 14:85–100

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Wang XJ (2010) Neurophysiological and computational principles of cortical rhythms in cognition. Physiol Rev 90:1195–1268

    Article  PubMed  Google Scholar 

  • Wang Y, Chik DTW, Wang ZD (2000) Coherence resonance and noise-induced synchronization in globally coupled Hodgkin-Huxley neurons. Phys Rev E 61:740–746

    Article  CAS  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Wittenberg GM, Wang SS (2006) Malleability of spike-timing-dependent plasticity at the CA3-CA1 synapse. J Neurosci 26:6610–6617

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • 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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    CAS  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • 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

    Article  PubMed  Google Scholar 

  • Zhang LI, Tao HW, Holt CE, Harris WA, Poo M (1998) A critical window for cooperation and competition among developing retinorectal synapses. Nature 395:37–44

    Article  CAS  PubMed  Google Scholar 

  • Zhou C, Kurths J (2002) Spatiotemporal coherence resonance of phase synchronization in weakly coupled chaotic oscillators. Phys Rev E 65:040101

    Article  CAS  Google Scholar 

  • Zhou C, Kurths J, Hu B (2001) Array-enhanced coherence resonance: nontrivial effects of heterogeneity and spatial independence of noise. Phys Rev Lett 87:098101

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 20162007688).

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  1. Institute for Computational Neuroscience and Department of Science Education, Daegu National University of Education, Daegu, 42411, Korea

    Sang-Yoon Kim & Woochang Lim

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  1. Sang-Yoon Kim
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Kim, SY., Lim, W. Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network. Cogn Neurodyn 12, 315–342 (2018). https://doi.org/10.1007/s11571-017-9470-0

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