Journal of Computational Neuroscience

, Volume 21, Issue 3, pp 227–241 | Cite as

An integrate-and-fire model for synchronized bursting in a network of cultured cortical neurons

  • D. A. FrenchEmail author
  • E. I. Gruenstein


It has been suggested that spontaneous synchronous neuronal activity is an essential step in the formation of functional networks in the central nervous system. The key features of this type of activity consist of bursts of action potentials with associated spikes of elevated cytoplasmic calcium. These features are also observed in networks of rat cortical neurons that have been formed in culture. Experimental studies of these cultured networks have led to several hypotheses for the mechanisms underlying the observed synchronized oscillations. In this paper, bursting integrate-and-fire type mathematical models for regular spiking (RS) and intrinsic bursting (IB) neurons are introduced and incorporated through a small-world connection scheme into a two-dimensional excitatory network similar to those in the cultured network.

This computer model exhibits spontaneous synchronous activity through mechanisms similar to those hypothesized for the cultured experimental networks. Traces of the membrane potential and cytoplasmic calcium from the model closely match those obtained from experiments. We also consider the impact on network behavior of the IB neurons, the geometry and the small world connection scheme.


Integrate-and-fire Cultured cortical network Spontaneous synchronized oscillations 


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  1. Butts, Feller (1999) J. Comp. Neurosci. 19:3580Google Scholar
  2. Chagnac-Amitai Y, Connors BW (1989) Synchronized excitation and inhibition driven by intrinsically bursting neurons in the neocortex. J. Neurophysiol. 62: 1149–1162.Google Scholar
  3. Chow CC, Kopell N (2000) Dynamics of spiking neurons with electrical coupling. Neural Comput. 12: 1643–78.Google Scholar
  4. Compte A, Sanchez-Vives MV, McCormick DA, Wang X-J (2003) Cellular and network mechanisms of slow oscillatory activitiy (<1 Hz) and wave propagations in a cortical network model. J. Neurophysiol. 89: 2707–2725.Google Scholar
  5. Connors BW, Gutnick MJ, Prince DA (1982) Electrophysical properties of neocortical neurons in vitro. J. Neurophysiol. 48: 1302–1320.Google Scholar
  6. Coombs S, Owen MR, Smith GD (2001) Mode locking in a periodically forced integrate-and-fire-or-burst neuron model. Phys. Rev. E 64: 041914.Google Scholar
  7. Fall CP, Marland ES, Wagner JM, Tyson JL, (2002) Computational Cell Biology, Springer-Verlag.Google Scholar
  8. Feller MB (1999) Spontaneous correlated activity in developing neural circuits. Neuron 22: 653–656.Google Scholar
  9. Feller MB, Butts DA, Aaron HL, Rokhsar DS, Shatz CJ (1997) Dynamic processes shape spatiotemporal properties of retinal waves. Neuron 19: 293–306.Google Scholar
  10. Golomb D (1998) Models of neuronal transient synchrony during propagation of activity through neocortical circuitry. J. Neurophysiol. 79: 1–12.Google Scholar
  11. Golomb D, Amitai Y (1997) Propagating neuronal discharges in neocortical slices: computational study. J. Neurophys. 78: 1199–1211.Google Scholar
  12. Golomb D, Ermentrout GB (1999) Continuous and lurching traveling pulses in neuronal networks with delay and spatially decaying connectivity. PNAS 96: 13480–13485.Google Scholar
  13. Humphries MD, Gurney KN (2001) A pulsed neural network model of bursting in the basal ganglia. Neural Netw. 14: 845–863.Google Scholar
  14. Katz LC, Schatz CJ (1996) Synaptic activity and the construction of cortical circuits. Science 274: 1133–1138.Google Scholar
  15. Laing CR, Longtin A (2002) A two variable model of somatic-dendritic interations in a bursting neuron. Bull. Math. Biol. 64: 829–860.Google Scholar
  16. Liu Y-H, Wang X-J (2001) Spike-frequency adaptation of a generalized leaky integrate-and-fire model neuron. J. Comput. Neurosci. 10: 25–45.Google Scholar
  17. Maeda E, Robinson HPC A, Kawana K (1995) The mechanisms of generation and propagation of synchronized bursting in developing networks of cortical neurons. J. Neurosci. 15: 6834–6845.Google Scholar
  18. Mittmann T, Linton SM, Schwindt P, Crill W (1997) Evidence for persistant Na+ current in apical dendrites of rat neocortical neurons form imaging of +-sensitive dye. J. Neurophysiol. 78: 1188–1192.Google Scholar
  19. Murphy TH, Blatter LA, Wier WG, Baraban JM (1992) Spontaneous synchronous synaptic calcium transients in cultured cortical neurons. J. Neurosci. 12: 4834–4845.Google Scholar
  20. McCormick DA, Connors BW, Lighthall JW, Prince DA (1985) Comparative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex. J. Neurophysiol. 54: 782–806.Google Scholar
  21. Netoff TI, Clewley R, Arno S, Keck T, White JA (2004) Epilepsy in small-world networks. J. Neurosci. 24: 8075–8083.Google Scholar
  22. Opitz T, de Lima AD, Voigt T (2002) Spontaneous development of synchronous oscillatory activity during maturation of cortical networks in vitro. J. Neurophysiol. 88: 2196–2206.Google Scholar
  23. Pinsky PF, J. Rinzel J (1994) Intrinsic and network rhythmogenesis in a reduced Traub model. J. Comput. Neurosci. 1: 39–60.Google Scholar
  24. Robinson HPC, Kawahara, Jimbo MY, Torimitsu K, Kuroda Y, Kawana A (1993a) Periodic synchronized bursting and intracellular calcium transients elicited by low magnesium in cultured cortical neurons. J. Neurophysiol. 70: 1606–1616.Google Scholar
  25. Robinson HPC, Torimitsu K, Jimbo Y, Kuroda Y, Kawana A (1993b) Periodic bursting of cultured neurons in low magnesium: cellular and network mechanisms. Jap. J. Physiol. 43(Suppl. 1): S125–S130.Google Scholar
  26. Schwindt P, Crill W (1999) Mechanisms underlying burst and regular spiking evoked by dendritic depolarization in layer 5 cortical pyramidal neurons. J. Neurophysiol. 81: 1341–1354.Google Scholar
  27. Shefi O, Golding E, Segev, R, Eshel B-J, Ayali A (2002) Morphological characterization of in vitro neuronal networks. Phys. Rev. E 66: 021905(5).Google Scholar
  28. Strogatz SH (2001) Exploring complex networks. Nature 410: 268–276.Google Scholar
  29. Tabak J, Senn W, O'Donovan MJ, Rinzel J (2000) Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network. J. Neurosci. 20: 3041–3056.Google Scholar
  30. Traub RD, Buhl EH, Gloveli T, Whittington MA (2003) Fast rhythmic bursting can be induced in layer 2/3 cortical neurons by enhancing persistent Na+ conductance or by blocking BK channels. J. Neurophysiol. 89: 909–921.Google Scholar
  31. van Vreeswijk C, Hansel D (2001) Patterns of synchrony in neural networks with spike adaptation. Neural Comput. 13: 959–992.Google Scholar
  32. Voigt T, Opitz T, de Lima AD (2001) Synchronous oscillatory activity in immature cortical network is driven by GABAergic preplate neurons. J. Neurosci. 21: 8895–8905.Google Scholar
  33. Wang X-J (1998) Calcium coding and adaptive temporal computation in cortical pyramidal neurons. J. Neurophysiol. 79: 1549–1566.Google Scholar
  34. Wang X-S, Gruenstein E (1997) Mechanism of synchronized calcium oscillations in cortical neurons. Brain Res. 767: 239–249.Google Scholar
  35. Watts DJ, Stogatz SH (1998) Collective dynamics of ‘small world’ networks. Nature 393: 440–442.Google Scholar
  36. Wilson HR (1999) Simplified dynamics of human and mammalian neocortical neurons. J. Theor. Biol. 200: 375–388.Google Scholar
  37. Wiedemann UA, Lüthi A (2003) Timing of synchronization by refractory mechanisms. J. Neurophysiol. 90: 3902–3911.Google Scholar

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© Springer Science Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  2. 2.College of MedicineUniversity of CincinnatiCincinnatiUSA

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