Leaders of neuronal cultures in a quorum percolation model

Frontiers in Computational Neuroscience

Volumn 4, Issue SEP, 2010, Pages

  Eckmann, Jean Pierre ^a   Moses, Elisha ^b   Stetter, Olav ^c,d   Tlusty, Tsvi ^b   Zbinden, Cyrille ^a  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^c MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

^d Bernstein Center for Computational Neuroscience (BCCN)   (Germany)

Author keywords

Activation dynamics; Graph theory; Leaders of activity; Neuronal cultures; Percolation; Quorum; Statistical mechanics of networks

Indexed keywords

ACTIVATION DYNAMICS; DEGREE DISTRIBUTIONS; EXCITATORY NEURONS; IN-DEGREE DISTRIBUTION; NEURONAL CULTURES; PERCOLATION MODELS; QUORUM; THEORETICAL FRAMEWORK;

GRAPH THEORY; NEURAL NETWORKS; PERCOLATION (SOLID STATE); SOLVENTS; STATISTICAL MECHANICS;

NEURONS;

EID: 84890879220     PISSN: 16625188     EISSN: None     Source Type: Journal    
DOI: 10.3389/fncom.2010.001322008     Document Type: Article

References (20)

1. Alvarez-Lacalle, E., and Moses, E. (2009). Slow and fast pulses in 1-d cultures of excitatory neurons. J. Comput. Neurosci. 26, 475-493.
2. Amit, D. J., Gutfreund, H., and Sompolinsky, H. (1985). Spin-glass models of neural networks. Phys. Rev. A 32, 1007-1018.
3. Bollobas, B. (1998). Modern Graph Theory. New York: Springer.
4. Breskin, I., Soriano, J., Moses, E., and Tlusty, T. (2006). Percolation in living neural networks. Phys. Rev. Lett. 97, 188102.
5. Cohen, O., Keselman, A., Moses, E., Rodriguez-Martinez, M., Soriano, J., and Tlusty, T. (2010). Quorum percolation in living neural networks. Europhys. Lett. 89, 18008.
6. Eckmann, J.-P., Jacobi, S., Marom, S., Moses, E., and Zbinden, C. (2008). Leader neurons in population bursts of 2d living neural networks. New J. Phys. 10, 015011.
7. Eytan, D., and Marom, S. (2006). Dynamics and effective topology underlying synchronization in networks of cortical neurons. J. Neurosci. 26, 8465-8476.
8. Feinerman, O., Segal, M., and Moses, E. (2005). Signal propagation along unidimensional neuronal networks. J. Neurophysiol. 94, 3406-3416.
9. Feinerman, O., Segal, M., and Moses, E. (2007). Identification and dynamics of spontaneous burst initiation zones in unidimensional neuronal cultures. J. Neurophysiol. 97, 2937-2948.
10. Golomb, D., and Ermentrout, G. B. (1999). Continuous and lurching traveling pulses in neuronal networks with delay and spatially decaying connectivity. Proc. Natl. Acad. Sci. U.S.A. 96, 13480-13485.
11. Golomb, D., and Ermentrout, G. B. (2002). Slow excitation supports propagation of slow pulses in networks of excitatory and inhibitory populations. Phys. Rev. E 65, 061911.
12. Jacobi, S., and Moses, E. (2007). Variability and corresponding amplitude-velocity relation of activity propagating in one-dimensional neural cultures. J. Neurophysiol. 97, 3597-3606.
13. Maeda, E., Robinson, H. P., and Kawana, A. (1995). The mechanisms of generation and propagation of synchronized bursting in developing networks of cortical neurons. J. Neurosci. 15, 6834-6845.
14. Osan, R., and Ermentrout, B. G. (2002). The evolution of synaptically generated waves in one- and two-dimensional domains. Physica D 163, 217-235.
15. Provost, J. P., and Vallee, G. (1983). Ergodicity of the coupling constants and the symmetric n-replicas trick for a class of mean-field spin-glass models. Phys. Rev. Lett. 50, 598-600.
16. Soriano, J., Rodriguez-Martinez, M., Tlusty, T., and Moses, E. (2008). Development of input connections in neural cultures. Proc. Natl. Acad. Sci. U.S.A. 105, 13758-13763.
17. Streit, J., Tscherter, A., Heuschkel, M. O., and Renaud, P. (2001). The generation of rhythmic activity in dissociated cultures of rat spinal cord. Eur. J. Neurosci. 14, 191.
18. Tlusty, T., and Eckmann, J.-P. (2009). Remarks on bootstrap percolation in metric networks. J. Phys. A 42, 205004.
19. van Hemmen, J. L. (1982). Classical spin-glass model. Phys. Rev. Lett. 49, 409-412.
20. Zbinden, C. (2010). Leader Neurons in Living Neural Networks and in Leaky Integrate and Fire Neuron Models. PhD thesis, University of Geneva, Geneva. Available at http://archive-ouverte.unige.ch/unige:5451.