Journal of Computational Neuroscience

, Volume 19, Issue 3, pp 357–378 | Cite as

Modeling the Spontaneous Activity of the Auditory Cortex

  • E. Bart
  • S. Bao
  • D. Holcman


We present a rate model of the spontaneous activity in the auditory cortex, based on synaptic depression. A Stochastic integro-differential system of equations is derived and the analysis reveals two main regimes. The first regime corresponds to a normal activity. The second regime corresponds to epileptic spiking. A detailed analysis of each regime is presented and we prove in particular that synaptic depression stabilizes the global cortical dynamics. The transition between the two regimes is induced by a change in synaptic connectivity: when the overall connectivity is strong enough, an epileptic activity is spontaneously generated. Numerical simulations confirm the predictions of the theoretical analysis. In particular, our results explain the transition from normal to epileptic regime which can be induced in rats auditory cortex, following a specific pairing protocol. A change in the cortical maps reorganizes the synaptic connectivity and this transition between regimes is accounted for by our model. We have used data from recording experiments to fit synaptic weight distributions. Simulations with the fitted distributions are qualitatively similar to the real EEG recorded in vivo during the experiments.

We conclude that changes in the synaptic weight function in our model, which affects excitatory synapses organization and reproduces the changes in cortical map connectivity can be understood as the main mechanism to explain the transitions of the EEG from the normal to the epileptic regime in the auditory cortex.


modeling spontaneous activity auditory cortex stochastic equations epilepsy rate model synaptic depression 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Atzori M, Lei S, Evans DI, Kanold PO, Phillips-Tansey E, McIntyre O, McBain CJ (2001) Differential synaptic processing separates stationary from transient inputs to the auditory cortex. Nat Neurosci. 4(12): 1230–1237.CrossRefPubMedGoogle Scholar
  2. Aubin T (1998) Some nonlinear problems in riemannian geometry, springer monographs in mathematics. XVII, 395 pp.Google Scholar
  3. Bao S, Chan VT, Merzenich MM (2001) Cortical remodelling induced by activity of ventral tegmental dopamine neurons. Nature 412(6842): 79–83.Google Scholar
  4. Bao S, Chang EF, Davis JD, Gobeske KT, Merzenich MM (2003) Progressive degradation and subsequent refinement of acoustic representations in the adult auditory cortex. J Neurosci. 23(34): 10765–10775.PubMedGoogle Scholar
  5. Bao S, et al. (2004) Temporal plasticity in the primary auditory cortex induced by operant perceptual learning. Nat Neurosci. 7: 974–981.PubMedGoogle Scholar
  6. Bressloff P, Folias S (2004) Front bifurcations in an excitatory neural network. SIAM Journal on Applied Mathematics 65(1): 131–151.Google Scholar
  7. Byl NN, McKenzie A (2000) Treatment effectiveness for patients with a history of repetitive hand use and focal hand dystonia: a planned, prospective follow-up study. J Hand Ther. 13: 289–301.PubMedGoogle Scholar
  8. Blake DT, et al. (2002) Sensory representation abnormalities that parallel focal hand dystonia in a primate model. Somatosens Mot Res. 19: 347–357.CrossRefPubMedGoogle Scholar
  9. Buonomano DV, Merzenich MM (1998) Cortical plasticity: From synapses to maps. Annu Rev Neurosci. 21: 149–186.CrossRefPubMedGoogle Scholar
  10. Coq JO, Xerri C (1998) Environmental enrichment alters organizational features of the forepaw representation in the primary somatosensory cortex of adult rats. Exp Brain Res. 121: 191–204.CrossRefPubMedGoogle Scholar
  11. Cossart R, Aronov D, Yuste R (2003) Attractor dynamics of network UP states in the neocortex. Nature 423(6937): 283–288.CrossRefPubMedGoogle Scholar
  12. Ermentrout GB, Cowan JD (1980) Large scale spatially organized activity in neural nets. SIAM J. Appl. Math. 38(1): 1–21.CrossRefGoogle Scholar
  13. Friedman, A (1964) Partial differential equations of parabolic type. Prentice-Hall, Inc., Englewood Cliffs, N.J.Google Scholar
  14. Galassi M, Davies J, Theiler J, Gough B, Gerard J, Michael B, Fabrice R (2003) The GNU Scientific Library reference manual.Google Scholar
  15. Kilgard MP, Merzenich MM (1998) Cortical map reorganization enabled by nucleus basalis activity. Science. 279(5357): 1714–1718.CrossRefPubMedGoogle Scholar
  16. Kenet T, Bibitchkov D, Tsodyks M, Grinvald A, Arieli A (2003) Spontaneously emerging cortical representations of visual attributes. Nature. 425(6961): 954–956.CrossRefPubMedGoogle Scholar
  17. Loebel A, Tsodyks M (2002) Computation by ensemble synchronization in recurrent networks with synaptic depression. J Comput Neurosci. 13(2): 111–124.CrossRefPubMedGoogle Scholar
  18. Shu Y, Hasenstaub A, McCormick DA (2003) Turning on and off recurrent balanced cortical activity. Nature. 423(6937): 288–293.CrossRefPubMedGoogle Scholar
  19. Schuss Z (1980) Theory and applications of stochastic differential equations, wiley series in probability and statistics. John Wiley Sons, Inc., New York.Google Scholar
  20. Tsodyks M, Uziel A, Markram H (2000) Synchrony generation in recurrent networks with frequency-dependent synapses. J Neurosci. 20(1): 825–835.Google Scholar
  21. Tsodyks M, Pawelzik K, Markram H (1998) Neural networks with dynamic synapses. Neural Comput. 10(4): 821–835.Google Scholar
  22. Tsodyks MV, Markram H (1997) The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proc Natl Acad Sci USA 94(2): 719–723. Erratum in: Proc Natl Acad Sci USA 1997 May 13;94(10): 5495.CrossRefPubMedGoogle Scholar
  23. Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J. 12(1): 1–24.PubMedGoogle Scholar
  24. Wilson HR, Cowan JD (1973) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik. 13(2): 55–80.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • E. Bart
    • 1
  • S. Bao
    • 2
  • D. Holcman
    • 3
    • 4
  1. 1.Department of Applied Mathematics and Computer ScienceWeizmann Institute of ScienceRehovotIsrael
  2. 2.Helen Wills Neuroscience InstituteUniversity of CaliforniaBerkeleyUSA
  3. 3.Department of MathematicsWeizmann Institute of ScienceRehovotIsrael
  4. 4.Department of PhysiologyKeck-Center for Theoretical NeurobiologySan FranciscoUSA

Personalised recommendations