Synchronization from second order network connectivity statistics

Frontiers in Computational Neuroscience

Volumn 5, Issue , 2011, Pages

  Zhao, Liqiong ^a   Beverlin, Bryce ^b   Netoff, Theoden ^b   Nykamp, Duane Q ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

^b University of Minnesota   (United States)

Author keywords

Common input; Correlations; Degree distribution; Maximum entropy; Neuronal networks; Synchrony

Indexed keywords

CHAINS; MAXIMUM ENTROPY METHODS; NEURONS;

COMMON INPUT; CORRELATIONS; DEGREE DISTRIBUTIONS; NEURONAL NETWORKS; SYNCHRONY;

NEURAL NETWORKS;

FIRING RATE; MODEL; NERVE CELL NETWORK; STATISTICS;

EID: 84936989057     PISSN: None     EISSN: 16625188     Source Type: Journal    
DOI: 10.3389/fncom.2011.00028     Document Type: Article

References (56)

1. Abbott, L. F., and van Vreeswijk, C. (1993). Asynchronous states in networks of pulse coupled oscillators. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 48, 1483-1490.
2. Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., and Zhou, C. (2008). Synchronization in complex networks. Phys. Rep. 469, 93-153.
3. Axmacher, N., Mormann, F., Fernández, G., Elger, C. E., and Fell, J. (2006). Memory formation by neuronal synchronization. Brain Res. Rev. 52, 170-182.
4. Bergman, H., Feingold, A., Nini, A., Raz, A., Slovin, H., Abeles, M., and Vaadia, E. (1998). Physiological aspects of information processing in the basal ganglia of normal and parkinsonian primates. Trends Neurosci. 21, 32-38
5. Bianconi, G., Gulbahce, N., and Motter, A. E. (2008). Local structure of directed networks. Phys. Rev. Lett. 100, 118701
6. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., and Hwang, D.-U. (2006). Complex networks: structure and dynamics. Phys. Rep. 424, 175-308
7. Brunel, N. (2000). Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J. Comp. Neurosci. 8, 183-208.
8. Cavazos, J. E., Golarai, G., and Sutula, T. P. (1991). Mossy fiber synaptic reorganization induced by kindling: time course of development, progression, and permanence. J. Neurosci. 11, 2795-2803.
9. Chow, C. C. (1998). Phase-locking in weakly heterogeneous neuronal networks. Physica A 118, 343-370.
10. Chung, F., and Lu, L. (2002). Connected components in random graphs with given expected degree sequences. Ann. Comb. 6, 125-145.
11. Denker, M., Timme, M., Diesmann, M., Wolf, F., and Geisel, T. (2004). Breaking synchrony by heterogeneity in complex networks. Phys. Rev. Lett. 92, 074103.
12. Diesmann, M., Gewaltig, M. O., and Aertsen, A. (1999). Stable propagation of synchronous spiking in cortical neural networks. Nature 402, 529-533
13. Erdős, P., and Rényi, A. (1959). On random graphs. I. Publ. Math. 6, 290-297
14. Ermentrout, G. B., and Kopell, N. (1991). Multiple pulse interactions and averaging in systems of coupled neural oscillators. J. Math. Biol. 29, 195-217
15. Hansel, D., Mato, G., and Meunier, C. (1995). Synchrony in excitatory neural networks. Neural Comput. 7, 307-337
16. Hansel, D., and Sompolinsky, H. (1992). Synchronization and computation in a chaotic neural network. Phys. Rev. Lett. 68, 718-721.
17. Hoffman, A. J., and Wielandt, H. W. (1953). The variation of the spectrum of a normal matrix. Duke Math. J. 20, 37-39.
18. Holmgren, C., Harkany, T., Svennenfors, B., and Zilberter, Y. (2003). Pyramidal cell communication within local networks in layer 2/3 of rat neocortex. J. Neurophysiol. 551, 139-153.
19. Jaynes, E. T. (1957). Information theory and statistical mechanics. Phys. Rev. 106, 62-79.
20. Kitano, K., and Fukai, T. (2007). Variability v.s. synchronicity of neuronal activity in local cortical network models with different wiring topologies. J. Comp. Neurosci. 23, 237-250.
21. Kramer, M. A., Chang, F. L., Cohen, M. E., Hudson, D., and Szeri, A. J. (2007). Synchronization measures of the scalp electroencephalogram can discriminate healthy from alzheimer’s subjects. Int. J. Neural Syst. 17, 61-69.
22. Kriener, B., Helias, M., Aertsen, A., and Rotter, S. (2009). Correlations in spiking neuronal networks with distance dependent connections. J. Comp. Neurosci. 27, 177-200.
23. Kuramoto, Y. (1984). Chemical Oscillations, Waves, and Turbulence. Berlin: Springer-Verlag.
24. LaMar, M. D., and Smith, G. D. (2010). Effect of node-degree correlation on synchronization of identical pulsecoupled oscillators. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81, 046206
25. Lefort, S., Tomm, C., Sarria, J.-C. F., and Petersen, C. C. (2009). The excitatory neuronal network of the C2 barrel column in mouse primary somatosensory cortex. Neuron 61, 301-316
26. Liu, C.-Y., and Nykamp, D. Q. (2009). A kinetic theory approach to capturing interneuronal correlation: the feedforward case. J. Comp. Neurosci. 26, 339-368.
27. Macke, J. H., Berens, P., Ecker, A. S., Tolias, A. S., and Bethge, M. (2009). Generating spike trains with specified correlation coefficients. Neural Comput. 21, 397-423.
28. Morris, C., and Lecar, H. (1981). Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 35, 193-213
29. Motter, A. E., Zhou, C., and Kurths, J. (2005). Network synchronization, diffusion, and the paradox of heterogeneity. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 016116.
30. Netoff, T. I., Clewley, R., Arno, S., Keck, T., and White, J. A. (2004). Epilepsy in small-world networks. J. Neurosci. 24, 8075-8083.
31. Netoff, T. I., and Schiff, S. J. (2002). Decreased neuronal synchronization during experimental seizures. J. Neurosci. 22, 7297-7307.
32. Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Rev. Soc. Ind. Appl. Math. 45, 167-256.
33. Nishikawa, T., and Motter, A. E. (2010). Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions. Proc. Natl. Acad. Sci. U.S.A. 107, 10342-10347
34. Ogata, K. (2010). Modern Control Engineering. Boston: Prentice-Hall
35. Oswald, A.-M. M., Doiron, B., Rinzel, J., and Reyes, A. D. (2009). Spatial profile and differential recruitment of GABAB modulate oscillatory activity in auditory cortex. J. Neurosci. 29, 10321-10334.
36. Parent, J. M., Yu, T. W., Leibowitz, R. T., Geschwind, D. H., Sloviter, R. S., and Lowenstein, D. H. (1997). Dentate granule cell neurogenesis is increased by seizures and contributes to aberrant network reorganization in the adult rat hippocampus. J. Neurosci. 17, 3727-3738.
37. Pecora, L. M., and Carroll, T. L. (1998). Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80, 2109-2112.
38. Perin, R., Berger, T. K., and Markram, H. (2011). A synaptic organizing principle for cortical neuronal groups. Proc. Natl. Acad. Sci. U.S.A. 108, 5419-5424
39. Renart, A., de la Rocha, J., Bartho, P., Hollender, L., Parga, N., Reyes, A., and Harris, K. D. (2010). The asynchronous state in cortical circuits. Science 327, 587-590.
40. Restrepo, J. G., Ott, E., and Hunt, B. R. (2006a). Emergence of coherence in complex networks of heterogeneous dynamical systems. Phys. Rev. Lett. 96, 254103.
41. Restrepo, J. G., Ott, E., and Hunt, B. R. (2006b). Emergence of synchronization in complex networks of interacting dynamical systems. Physica D 224, 114-122.
42. Restrepo, J. G., Ott, E., and Hunt, B. R. (2007). Approximating the largest eigenvalue of network adjacency matrices. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76, 056119.
43. Reyes, A. D. (2003). Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro. Nat. Neurosci. 6, 593-599.
44. Rosenbaum, R. J., Trousdale, J., and Josić, K. (2010). Pooling and correlated neural activity. Front Comput Neurosci 4:9. doi: 10.3389/fncom.2010.00009
45. Roxin, A. (2011). The role of degree distribution in shaping the dynamics in networks of sparsely connected spiking neurons. Front. Comput. Neurosci. 5:8. doi: 10.3389/fncom.2011.00008
46. Shadlen, M. N., and Newsome, W. T. (1998). The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J. Neurosci. 18, 3870-3896
47. Song, S., Sjostrom, P. J., Reigl, M., Nelson, S., and Chklovskii, D. (2005). Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biol. 3, e68. doi: 10.1371/journal.pbio.0030068
48. Strogatz, S. (2000). From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 143, 1-20
49. Strogatz, S. H., and Mirollo, R. E. (1991). Stability of incoherence in a population of coupled oscillators. J. Stat. Phys. 63, 613-635.
50. Tetzlaff, T., Buschermhle, M., Geisel, T., and Diesmann, M. (2003). The spread of rate and correlation in stationary cortical networks. Neurocomputing 52, 949-954.
51. Uhlhaas, P. J., and Singer, W. (2010). Abnormal neural oscillations and synchrony in schizophrenia. Nat. Rev. Neurosci. 11, 100-113.
52. Van Drongelen, W., Koch, H., Marcuccilli, C., Pena, F., and Ramirez, J.-M. (2003). Synchrony levels during evoked seizure-like bursts in mouse neocortical slices. J. Neurophysiol. 90, 1571-1580
53. van Rossum, M. C. W., Turrigiano, G. G., and Nelson, S. B. (2002). Fast propagation of firing rates through layered networks of noisy neurons. J. Neurosci. 22, 1956-1966.
54. Watts, D. J., and Strogatz, S. H. (1998). Collective dynamics of “small-world” networks. Nature 394, 440-442
55. Zeng, L. H., Xu, L., Rensing, N. R., Sinatra, P. M., Rothman, S. M., and Wong, M. (2007). Kainate seizures cause acute dendritic injury and actin depolymerization in vivo. J. Neurosci. 27, 11604-11613.
56. Zhan, C., Chen, G., and Yeung, L. F. (2010). On the distributions of Laplacian eigenvalues versus node degrees in complex networks. Physica A 389, 1779-1788.