Stability and structural constraints of random brain networks with excitatory and inhibitory neural populations

Journal of Computational Neuroscience

Volumn 27, Issue 1, 2009, Pages 81-101

  Gray, Richard T ^a,c   Robinson, Peter A ^a,b  

^a UNIVERSITY OF SYDNEY   (Australia)

^b University of Sydney   (Australia)

^c UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Brain dynamics; Complex networks; Cortical networks; Graph spectra; Random matrix theory; Stability analysis

Indexed keywords

BRAIN; COMPLEX NETWORKS; PHYSIOLOGICAL MODELS; PROBABILITY DISTRIBUTIONS; RANDOM VARIABLES; SPECTRAL DENSITY;

BRAIN DYNAMICS; BRAIN NETWORKS; CONNECTIONS STRENGTH; CORTICAL NETWORK; GRAPH SPECTRUM; NEURAL POPULATIONS; RANDOM MATRICES THEORY; STABILITY ANALYZE; STABILITY CONSTRAINTS; STRUCTURAL CONSTRAINTS;

STABILITY;

ARTICLE; ARTIFICIAL NEURAL NETWORK; CELL POPULATION; CELL STRUCTURE; EXCITATORY JUNCTION POTENTIAL; NERVE CELL NETWORK; PRIORITY JOURNAL; PROBABILITY; SPECTROMETRY; STIMULUS RESPONSE;

ALGORITHMS; ANIMALS; BRAIN; HUMANS; MODELS, NEUROLOGICAL; NEURAL INHIBITION; NEURAL PATHWAYS; NEURONS; PROBABILITY; SYNAPTIC TRANSMISSION;

EID: 68449084062     PISSN: 09295313     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10827-008-0128-0     Document Type: Article

References (58)

1. Attwell, D., & Laughlin, S. B. (2001). An energy budget for signaling in the grey matter of the brain. Journal of Cerebral Blood Flow and Metabolism, 121, 1133-1145.
2. Bassett, D. S., & Bullmore, E. (2006). Small-world brain networks. The Neuroscientist, 12, 1-12.
3. Bear, M. F., Connors, B. W., & Paradiso, M. A. (2001). Neuroscience: Exploring the brain, (2nd Ed.). Baltimore: Lippincott Williams and Wilkins.
4. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., & Hwang, D.-U. (2006). Complex networks: Structure and dynamics. Physics Reports, 424, 175-308.
5. Bollobás, B. (1985). Random graphs. London: Academic.
6. Breakspear, M. (2002). Nonlinear phase desynchronization in human electroncephalographic data. Human Brain Mapping, 15, 175-198.
7. Breakspear, M., Roberts, J. A., Terry, J. R., Rodrigues, S., Mahant, N., & Robinson, P. A. (2006). A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cerebral Cortex, 16, 1296-1313.
8. Breakspear, M., Terry, J. R., & Friston, K. J. (2003). Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a nonlinear model of neuronal dynamics. Neurocomputing, 52-54, 151-158.
9. Brede, M., & Sinha, S. (2005). Assortative mixing by degree makes a network more unstable. arXiv:cOnd-mat/0507710.
10. Bronk, B. V. (1964). Accuracy of the semicircle approximation for the density of eigenvalues of random matrices. Journal of Mathematical Physics, 5, 215-220.
11. Cherniak, C. (1994). Component placement optimization in the brain. Journal of Neuroscience, 14, 2418-2427.
12. Chklovskii, D. B., & Koulakov, A. A. (2004). Maps in the brain: What can we learn from them? Annual Reviews of Neuroscience, 27, 369-392.
13. Chklovskii, D. B., Schikorski, T., & Stevens, C. F. (2002). Wiring optimization in cortical circuits. Neuron, 34, 341-347.
14. Costa, L. da. F., & Sporns, O. (2005). Hierarchical features of large scale cortical connectivity. The European Physics Journal B, 48, 567-573.
15. Farkas, I. J., Derényi, I., Barabási, A.-L., & Vicsek, T. (2001). Spectra of "real-world" graphs: Beyond the semicircle law. Physical Review E, 64, 026704/1-12.
16. Felleman, D. J., & van Essen, D. C. (1991). Distributed hierarchical processing in the primate cerebral cortex. Cerebral Cortex, 1, 1-47.
17. Feng, J., Jirsa, V. K., & Ding, M. (2006). Synchronization in networks with random interactions: Theory and applications. Chaos, 16, 015109/1-21.
18. Füredi, Z., & Komlós, J. (1981). The eigenvalues of random symmetric matrices. Combinatorica, 1, 233-241.
19. Gray, R. T., & Robinson, P. A. (2007). Stability and spectra of randomly connected excitatory cortical networks. Neurocomputing, 70, 1000-1012.
20. Gray, R. T., & Robinson, P. A. (2008a). Stability and synchronization of random brain networks with a distribution of connection strengths. Neurocomputing, 71, 1373-1387.
21. Gray, R. T., & Robinson, P. A. (2008b). Stability of random brain networks with excitatory and inhibitory connections. Neurocomputing. doi: 10.1016/j.neucom.2008.06.001
22. Hilgetag, C. C., Burns, G. A. P. C., O'Neill, M. A., Scannell, J. W., & Young, M. P. (2000a). Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat. Philosophical Transactions of the Royal Society of London B, 355, 91-110.
23. Hilgetag, C. C., O'Neill, M. A., & Young, M. P. (2000b). Hierarchical organization of macaque and cat cortical sensory systems explored with a novel network processor. Philosophical Transactions of the Royal Society of London B, 355, 71-89.
24. Honey, C. J., Kötter, R., Breakspear, M., & Sporns, O. (2007). Network structure of cerebral cortex shapes functional connectivity on multiple time scales. In Proceedings of the National Academy of Science of the United States of America, 104, 10240-10245.
25. Jouve, B., Rosenstiehl, P., & Imbert, M. (1998). A mathematical approach to the connectivity between the cortical visual areas of the macaque monkey. Cerebral Cortex, 8, 28-39.
26. Kaiser, M., Görner, M., & Hilgetag, C. C. (2007). Criticality of spreading dynamics in hierarchical cluster networks with inhibition. New Journal of Physics, 9, 110.
27. Kaiser, M., & Hilgetag, C. C. (2006). Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems. PLoS Computational Biology, 2, e95/1-11.
28. Kim, J. W., & Robinson, P. A. (2007). Compact dynamical model of brain activity. Physical Review E, 75, 031907/1-10.
29. Klyachko, V. A., & Stevens, C. F. (2003). Connectivity optimization and the positioning of cortical areas. In Proceedings of the National Academy of Science of the United States of America, 100, 7937-7941.
30. Kristan, W. B. (2007). A push-me pull-me neural design. Science, 315, 339-340.
31. McCormick, D. A. (1992). Neurotransmitter actions in the thalamus and cerebral cortex and their role in neuromodulation of thalamocortical activity. Progress in Neurobiology, 39, 337-388.
32. Nunez, P. L. (1995). Towards a physics of neocortex. In P. L. Nunez (Ed.), Neocortical dynamics and human EEG rhythms (pp. 111). New York: Oxford University Press.
33. Prill, R. J., Iglesias, P. A., & Levchenko, A. (2005). Dynamic properties of network motifs contribute to biological network organization. PLoS Biology, 3, 1881-1892.
34. Rajan, K., & Abbott, L. F. (2006). Eigenvalue spectra of random matrices for neural networks. Physical Review Letters, 97, 188104/1-4.
35. Robinson, P. A. (2007). Visual gamma oscillations: Waves, correlations, and other phenomena, including comparison with experimental data. Biological Cybernetics, 97, 317-335.
36. Robinson, P. A., Rennie, C. J., Rowe, D. L., & O'Conner, S. C. (2004) Estimation of multiscale neurophysiologic parameters by electroencephalographic means. Human Brain Mapping, 23, 53-72.
37. Robinson, P. A., Rennie, C. J., & Rowe, D. L. (2002). Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Physical Review E, 65, 041924/1-9.
38. Robinson, P. A., Rennie, C. J., Rowe, D. L., & O'Connor, S. C. (2003). Neurophysical modeling of brain dynamics. Neuropsychopharmacology, 28, s74-s79.
39. Robinson, P. A., Rennie, C. J., & Wright, J. J. (1997). Propagation and stability of waves of electrical activity in the cerebral cortex. Physical Review E, 56, 826-840.
40. Robinson, P. A., Rennie, C. J., Wright, J. J., Bahramali, H., Gordon, E., & Rowe, D. L. (2001). Prediction of electroencephalographic spectra from neurophysiology. Physical Review E, 63, 0211903/1-18.
41. Robinson, P. A., Rennie, C. J., Wright, J. J., & Bourke, P. D. (1998). Steady states and global dynamics of electrical activity in the cerebral cortex. Physical Review E, 58, 3557-3571.
42. Salinas, E., & Sejnowski, T. J. (2001). Correlated neuronal activity and the flow of neural information. Nature Reviews Neuroscience, 2, 533-550.
43. Scannell, J. W., Blakemore, C., & Young, M. P. (1995). Analysis of connectivity in the cat cerebral cortex. Journal of Neuroscience, 15, 1463-1483.
44. Sommers, H. J., Crisanti, A., Sompolinsky, H., & Stein, Y. (1998). Spectrum of large random asymmetric matrices. Physical Review Letters, 60, 1895-1898.
45. Sporns, O. (2002). Graph theory methods for the analysis of neural connectivity patterns. In R. Kötter (Ed.), Neuroscience databases. A practical guide (pp. 169-183). Boston: Klüwer.
46. Sporns, O. (2003). Network analysis, complexity, and the brain function. Complexity, 8, 56-60.
47. Sporns, O., Chialvo, D. R., Kaiser, M., & Hilgetag, C. C. (2004). Organization, development and function of complex brain networks. Trends in Neuroscience, 8, 418-425.
48. Sporns, O., & Kötter, R. (2004). Motifs in brain networks. PLoS Biology, 2, 1910-1918.
49. Sporns, O., Tononi, G., & Edelman, G. M. (2000). Theoretical neuroanatomy: Relating anatomical and functional connectivity in graphs and cortical connection matrices. Cerebral Cortex, 10, 127-141.
50. Sporns, O., & Zwi, J. D. (2004). The small world of the cerebral cortex. Neuroinformatics, 2, 145-161.
51. Sporns, O., Tononi, G., & Kötter, R. (2005). The human connectome: A structural description of the human brain. PLoS Computational Biology, 1, e42/245-251.
52. Stam, C., Pijn, J. P. M., Suffczynski, P., & da Silva, F. H. L. (1999). Dynamics of the human alpha rhythm: Evidence for non-linearity? Clinical Neurophysiology, 110, 1801-1812.
53. Variano, E. A., McCoy, J. H., & Lipson, H. (2004). Networks, dynamics, and modularity. Physical Review Letters, 92, 188701/1-4.
54. Vreeswijk, C. V., & Sompolinsky, H. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science, 274, 1724-1726.
55. Wigner, E. (1967). Random matrices in physics. SIAM Review, 9, 1-23.
56. Wright, J. J., Robinson, P. A., Rennie, C. J., Gordan, E., Bourke, P. D., Chapman, C. L., et al. (2001). Towards an integrated continuum model of cerebral dynamics: The cerebral rhythms, synchronous oscillation and cortical stability. BioSystems, 63, 71-88.
57. Young, M. (2000). The architecture of visual cortex and inferential processes in vision. Spatial Vision, 13, 137-146.
58. Zhou, C., Zemanová, L., Hilgetag, C. C., & Kurths, K. (2006). Hierarchical organization unveiled by functional connectivity in complex brain networks. Physical Review Letter, 97, 238103.