Journal of Computational Neuroscience

, Volume 31, Issue 2, pp 285–304 | Cite as

Leader neurons in leaky integrate and fire neural network simulations

  • Cyrille Zbinden


In this paper, we highlight the topological properties of leader neurons whose existence is an experimental fact. Several experimental studies show the existence of leader neurons in population bursts of activity in 2D living neural networks (Eytan and Marom, J Neurosci 26(33):8465–8476, 2006; Eckmann et al., New J Phys 10(015011), 2008). A leader neuron is defined as a neuron which fires at the beginning of a burst (respectively network spike) more often than we expect by chance considering its mean firing rate. This means that leader neurons have some burst triggering power beyond a chance-level statistical effect. In this study, we characterize these leader neuron properties. This naturally leads us to simulate neural 2D networks. To build our simulations, we choose the leaky integrate and fire (lIF) neuron model (Gerstner and Kistler 2002; Cessac, J Math Biol 56(3):311–345, 2008), which allows fast simulations (Izhikevich, IEEE Trans Neural Netw 15(5):1063–1070, 2004; Gerstner and Naud, Science 326:379–380, 2009). The dynamics of our lIF model has got stable leader neurons in the burst population that we simulate. These leader neurons are excitatory neurons and have a low membrane potential firing threshold. Except for these two first properties, the conditions required for a neuron to be a leader neuron are difficult to identify and seem to depend on several parameters involved in the simulations themselves. However, a detailed linear analysis shows a trend of the properties required for a neuron to be a leader neuron. Our main finding is: A leader neuron sends signals to many excitatory neurons as well as to few inhibitory neurons and a leader neuron receives only signals from few other excitatory neurons. Our linear analysis exhibits five essential properties of leader neurons each with different relative importance. This means that considering a given neural network with a fixed mean number of connections per neuron, our analysis gives us a way of predicting which neuron is a good leader neuron and which is not. Our prediction formula correctly assesses leadership for at least ninety percent of neurons.


Simulation Model Neuron Burst Leader Integrate and fire 



I would like to thank Jean-Pierre Eckmann, my PhD advisor at the University of Geneva, Switzerland, for his continuous useful help along this study. This paper could not have been without the help of Elisha Moses, Weizmann Institute of Science, Israel. During all this research, I was supported by the Fonds National Suisse. Finally I would like to thank Sonia Iva Zbinden.


  1. Alvarez-Lacalle, E., & Moses, E. (2007). Slow and fast pulses in 1-D cultures of excitatory neurons. Journal of Computational Neuroscience, 26(3), 475–493.CrossRefGoogle Scholar
  2. Brette, R., & Gerstner, W. (2005). Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. Journal of Neurophysiology, 94, 3637–3642.PubMedCrossRefGoogle Scholar
  3. Cessac, B. (2008). A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics. Journal of Mathematical Biology, 56(3), 311–345.PubMedCrossRefGoogle Scholar
  4. Cessac, B., Rochel, O., & Viéville, T. (2008). Introducing numerical bounds to event-based neural network simulation. arXiv:0810.3992.
  5. Cessac, B., & Samuelides, M. (2007). From neuron to neural network dynamics. EPJ Special Topics, 142(1), 7–88.CrossRefGoogle Scholar
  6. Cohen, O., Keselman, A., Moses, E., Rodriguez Martinez, M., Soriano, J., & Tlusty, T. (2009). Quorum percolation in living neural networks. A Letters Journal Exploring the Frontiers of Physics, 89. doi: 10.1209/0295-5075/89/18008.
  7. Droge, M. H., Gross, G. W., Hightower, M. H., & Czisny, L. E. (1986). Multielectrode analysis of coordinated, multisite, rhythmic bursting in cultured CNS monolayer networks. Journal of Neuroscience, 6(6), 1583–1592.PubMedGoogle Scholar
  8. Eckmann, J.-P., Feinerman, O., Gruendlinger, L., Moses, E., Soriano, J., & Tlusty, T. (2007). The physics of living neural networks. Physics Reports, 449, 54–76.CrossRefGoogle Scholar
  9. Eckmann, J.-P., Jacobi, S., Marom, S., Moses, E., & Zbinden, C. (2008). Leader neurons in population bursts of 2D living neural networks. New Journal of Physics, 10(015011).CrossRefGoogle Scholar
  10. Eckmann, J.-P., Moses, E., Stetter, O., Tlusty, T., & Zbinden, C. (2010). Leaders of neuronal cultures in a quorum percolation model. Frontiers in Computational Neuroscience, 4(132).CrossRefGoogle Scholar
  11. Eckmann, J.-P., & Tlusty, T. (2009). Remarks on bootstrap percolation in metric networks. Journal of Physics A: Mathematical and Theoretical, 42(205004).CrossRefGoogle Scholar
  12. Eytan, D., & Marom, S. (2006). Dynamics and effective topology underlying synchronization in networks of cortical neurons. Journal of Neuroscience, 26(33), 8465–8476.PubMedCrossRefGoogle Scholar
  13. Gerstner, W., & Kistler, W. M. (2002). Spiking neuron models. Single neurons, populations, plasticity. Cambridge: Cambridge University Press.Google Scholar
  14. Gerstner, W., & Naud, R. (2009). How good are neuron models? Science, 326, 379–380.PubMedCrossRefGoogle Scholar
  15. Golub, G. H., & Van Loan, C. F. (1996). Matrix computations (3rd ed.). Baltimore: The Johns Hopkins University Press.Google Scholar
  16. Izhikevich, E. M. (2004). Which model to use for cortical spinking neurons? IEEE Transactions on Neural Networks, 15(5), 1063–1070.PubMedCrossRefGoogle Scholar
  17. Luscher, H.-R., Jolivet, R., Rauch, A., & Gerstner, W. (2006). Predicting spike timing of neocortical pyramidal neurons by simple threshold models. Journal of Computational Neuroscience, 21, 35–49.PubMedCrossRefGoogle Scholar
  18. Maeda, E., Robinson, H. P., & Kawana, A. (1995). The mechanisms of generation and propagation of synchronized bursting in developing networks of cortical neurons. Journal of Neuroscience, 15(10), 6834–6845.PubMedGoogle Scholar
  19. Naud, R., Marcille, N., Clopath, C., & Gerstner, W. (2008). Firing patterns in the adaptive exponential integrate-and-fire model. Biological Cybernetics, 99, 335–347.PubMedCrossRefGoogle Scholar
  20. Rudolph, M., & Destexhe, A. (2007). How much can we trust neural simulation strategies? Neurocomputing, (70), 1966–1969.CrossRefGoogle Scholar
  21. Soriano, J., Rodriguez Martinez, M., Tlusty, T., & Moses, E. (2008). Development of input connections in neural cultures. Proceedings of the National Academy of Sciences of the United States of America, 105(37), 13758–13763.PubMedCrossRefGoogle Scholar
  22. Tscherter, A., Heuschkel, M. O., Renaud, P., & Streit, J. (2001). Spatiotemporal characterization of rhythmic activity in rat spinal cord slice cultures. European Journal of Neuroscience, 14(2), 179–190.PubMedCrossRefGoogle Scholar
  23. Wagenaar, D. A., Pine, J., & Potter, S. M. (2006a). An extremely rich repertoire of bursting patterns during the development of cortical cultures. BMC Neuroscience, 7(11).Google Scholar
  24. Wagenaar, D. A., Pine, J., & Potter, S. M. (2006b). Searching for plasticity in dissociated cortical cultures on multi-electrode arrays. Journal of Negative Results in Biomedicine, 5(1), 16.PubMedCrossRefGoogle Scholar
  25. Wilkinson, J. H., & Reinsch, C. (1971). Linear algebra. Berlin: Springer.Google Scholar
  26. Zbinden, C. (2010). Leader neurons in living neural networks and in leaky integrate and fire neuron models. PhD thesis, University of Geneva.

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Département de Physique ThéoriqueUniversité de GenèveGenève 4Switzerland

Personalised recommendations