Effects of Hebbian learning on the dynamics and structure of random networks with inhibitory and excitatory neurons

Journal of Physiology Paris

Volumn 101, Issue 1-3, 2007, Pages 136-148

  Siri, Benoît ^a   Quoy, Mathias ^b   Delord, Bruno ^c   Cessac, Bruno ^d,e   Berry, Hugues ^a  

^a INRIA   (France)

^b UNIVERSITÉ DE CERGY PONTOISE   (France)

^c SORBONNE UNIVERSITÉ   (France)

^d INSTITUT NON LINÉAIRE DE NICE   (France)

^e INRIA   (France)

Author keywords

Chaotic dynamics; Hebbian learning; Network structure; Random recurrent neural networks

Indexed keywords

ARTICLE; BRAIN FUNCTION; CHAOTIC DYNAMICS; ENTROPY; LEARNING; MATHEMATICAL MODEL; NERVE CELL; NERVE CELL NETWORK; SYNAPSE;

ANIMALS; CEREBRAL CORTEX; COMPUTER SIMULATION; HUMANS; NEURAL NETWORKS (COMPUTER); NEURONAL PLASTICITY; NEURONS; NONLINEAR DYNAMICS; SYNAPSES;

EID: 36649020961     PISSN: 09284257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jphysparis.2007.10.003     Document Type: Article

References (61)

1. Abraham W.C., and Bear M.F. Metaplasticity: the plasticity of synaptic plasticity. Trends Neurosci. 19 (1996) 126-130
2. Achard S., Salvador R., Whitcher B., Suckling J., and Bullmore E. A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. J. Neurosci. 26 (2006) 63-72
3. Aizenman C., Manis P., and Linden D. Polarity of long-term synaptic gain change is related to postsynaptic spike firing at a cerebellar inhibitory synapse. Neuron 21 (1998) 827-835
4. Atay F., Biyikoglu T., and Jost J. Network synchronization: Spectral versus statistical properties. Physica D 224 (2006) 35-41
5. Barahona M., and Pecora L. Synchronization in small-world systems. Phys. Rev. Lett. 89 (2002) 054101
6. Bassett D., and Bullmore E. Small-world brain networks. The Neuroscientist 12 (2006) 512-523
7. Berry H., and Quoy M. Structure and dynamics of random recurrent neural networks. Adaptive Behavior 14 (2006) 129-137
8. Bertschinger N., and Natschlager T. Real-time computation at the edge of chaos in recurrent neural networks. Neural Comp. 16 (2004) 1413-1436
9. Bettencourt L., Stephens G., Ham M., and Gross G. Functional structure of cortical neuronal networks grown in vitro. Phys. Rev. E 75 (2007) 021915
10. Bienenstock E., Cooper L., and Munro P. Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J. Neurosci. 2 (1982) 32-48
11. Binzegger T., Douglas R.J., and Martin K.A.C. A quantitative map of the circuit of cat primary visual cortex. J. Neurosci. 24 (2004) 8441-8453
12. Bliss T.V.P., and Collingridge G.L. A synaptic model of memory: long-term potentiation in the hippocampus. Nature 361 (1993) 31-39
13. Boccaletti S., Latora V., Moreno Y., Chavez M., and Hwang D.U. Complex networks: Structure and dynamics. Phys. Reports 424 (2006) 175-308
14. Brager D., Cai X., and Thompson S. Activity-dependent activation of presynaptic protein kinase c mediates post-tetanic potentiation. Nature Neurosci. 6 (2003) 551-552
15. Cessac B., and Samuelides M. From neuron to neural networks dynamics. EPJ Special Topics: Topics in Dynamical Neural Networks 142 (2007) 7-88
16. Daoudal G., and Debanne D. Long-term plasticity of intrinsic excitability: learning rules and mechanisms. Learn. Mem. 10 (2003) 456-465
17. Dauce E., Quoy M., Cessac B., Doyon B., and Samuelides M. Self-organization and dynamics reduction in recurrent networks: stimulus presentation and learning. Neural Networks 11 (1998) 521-533
18. Daucé E., Quoy M., and Doyon B. Resonant spatio-temporal learning in large random neural networks. Biol. Cybern. 87 (2002) 185-198
19. Delord B., Berry H., Guigon E., and Genet S. A new principle for information storage in an enzymatic pathway model. PLoS Comput. Biol. 3 (2007) e124
20. Doyere V., Errington M., Laroche S., and Bliss T. Low-frequency trains of paired stimuli induce long-term depression in area ca1 but not in dentate gyrus of the intact rat. Hippocampus 6 (1996) 52-57
21. Doyon B., Cessac B., Quoy M., and Samuelides M. Chaos in neural networks with random connectivity. Int. J. Bifurication Chaos 3 (1993) 279-291
22. Eckmann J., and Ruelle D. Ergodic theory of strange attractors. Rev. Mod. Phys. 57 (1985) 617-656
23. Eguiluz V., Chialvo D., Cecchi G., and Apkarian A. Scale-free brain functional networks. Phys. Rev. Lett. 94 (2005) 018102
24. Freeman W. Simulation of chaotic eeg pattern with a dynamic model of the olfactory system. Biol. Cyber. 56 (1987) 139-150
25. Freeman W., Yao Y., and Burke B. Central pattern generating and recognizing in olfactory bulb: a correlation learning rule. Neural Networks 1 (1988) 277-288
26. Gabbott P.L.A., and Somogyi P. Quantitative distribution of GABA-immunoreactive neurons in the visual cortex (area 17) of the cat. Exp. Brain Res. 61 (1986) 323-331
27. Gouzé J. Positive and negative circuits in dynamical systems. J. Biol. Syst. 6 (1998) 11-15
28. Grinstein G., and Linsker R. Synchronous neural activity in scale-free network models versus random network models. PNAS 28 (2005) 9948-9953
29. Hasegawa H. Synchronisations in small-world networks of spiking neurons: Diffusive versus sigmoid couplings. Phys. Rev. E. 72 (2005) 056139
30. He, Y., Chen, Z., Evans, A., 2007. Small-world anatomical networks in the human brain revealed by cortical thickness from MRI. Cerebral Cortex. Advance access published online January 4.
31. Heynen A., Quinlan E., Bae D., and Bear M. Bidirectional, activity-dependent regulation of glutamate receptors in the adult hippocampus in vivo. Neuron 28 (2000) 527-536
32. Hirsch M. Convergent activation dynamics in continuous time networks. Neural Networks 2 (1989) 331-349
33. Holtmaat A., Trachtenberg J., Wilbrecht L., Shepherd G., Zhang X., Knott G., and Svoboda K. Transient and persistent dendritic spines in the neocortex in vivo. Neuron 45 (2005) 279-291
34. Hong H., Kim B., Choi M., and Park H. Factors that predict better synchronizability on complex networks. Phys. Rev. E 65 (2002) 067105
35. Kalisman N., Silberberg G., and Markram H. The neocortical microcircuit as a tabula rasa. Proc. Natl. Acad. Sci. USA 102 (2005) 880-885
36. Kano M. Plasticity of inhibitory synapses in the brain: a possible memory mechanism that has been overlooked. Neurosci. Res. 21 (1995) 177-182
37. Kwok H.F., Jurica P., Raffone A., and van Leeuwen C. Robust emergence of small-world structure in networks of spiking neurons. Cogn. Neurodyn. 1 (2007) 39-51
38. Lago-Fernández L.F., Huerta R., Corbacho F., and Sigüenza J.A. Fast response and temporal coherent oscillations in small-world networks. Phys. Rev. Lett. 84 (2000) 2758-2761
39. Linsker R. From Basic Network Principles to Neural Architecture: Emergence of Orientation-Selective Cells. Proc. Natl. Acad. Sci. USA 83 (1986) 8390-8394
40. Markram H., Lübke J., Frotscher M., Roth A., and Sakmann B. Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. J. Physiol. 500 (1997) 409-440
41. Micheloyannis S., Pachou E., Stam C., Vourkas M., Erimaki S., and Tsirka V. Using graph theoretical analysis of multi channel eeg to evaluate the neural efficiency hypothesis. Neurosci. Lett 402 (2006) 273-277
42. Montague P.R., and Sejnowski T.J. The predictive brain: temporal coincidence and temporal order in synaptic learning mechanisms. Learn. Mem. 1 (1994) 1-33
43. Nishikawa T., Motter A.E., Lai Y.C., and Hoppensteadt F.C. Heterogeneity in oscillator networks: are smaller worlds easier to synchronize ?. Phys. Rev. Lett. (2003) 91
44. Nishiyama M., Hong K., Mikoshiba K., Poo M., and Kato K. Calcium stores regulate the polarity and input specificity of synaptic modification. Nature 30 (2000) 584-588
45. Nugent F.S., Penick E.C., and Kauer J.A. Opioids block long-term potentiation of inhibitory synapses. Nature 446 (2007) 1086-1090
46. Racine R., Milgram N., and Hafner S. Long-term potentiation phenomena in the rat limbic forebrain. Brain Res. 260 (1983) 217-231
47. Shefi O., Golding I., Segev R., Ben-Jacob E., and Ayali A. Morphological characterization of in vitro neuronal networks. Phys. Rev. E 66 (2002) 021905
48. Shin C.W., and Kim S. Self-organized criticality and scale-free properties in emergent functional neural networks. Phys. Rev. E 74 (2006) 045101
49. Siri, B., Berry, H., Cessac, B., Delord, B., Quoy, M., 2006. Topological and dynamical structures induced by Hebbian learning in random neural networks. In: International Conference on Complex Systems. Boston.
50. Siri, B., Berry, H., Cessac, B., Delord, B., Quoy, M., 2007. A mathematical analysis of the effects of Hebbian learning rules on the dynamics and structure of discrete-time random recurrent neural networks. e-print: arXiv:0705.3690v1.
51. Skarda C., and Freeman W. How brains make chaos in order to mahe sense of the world. Behav. Brain Sci. 10 (1987) 161-195
52. Soto-Trevino C., Thoroughman K.A., Marder E., and Abbott L. Activity-dependent modification of inhibitory synapses in models of rhythmic neural networks. Nat. Neurosci. 4 (2001) 297-303
53. Soula, H., Alwan, A., Beslon, G., 2005. Learning at the edge of chaos: Temporal coupling of spiking neurons controller for autonomous robotics. In: AAAI Spring Symposium on Developmental Robotics. Stanford, CA, USA.
54. Sporns O., and Zwi J. The small world of the cerebral cortex. Neuroinformatics 2 (2004) 145-162
55. Stam C. Functional connectivity patterns of human magnetoencephalographic recordings: a 'small-world' network?. Neurosci. Lett. 355 (2004) 25-28
56. Stepanyants A., Hof P.R., and Chklovskii D.B. Geometry and structural plasticity of synaptic connectivity. Neuron 34 (2002) 275-288
57. Tao H., Zhang L., Bi G., and Poo M. Selective presynaptic propagation of long-term potentiation in defined neural networks. J. Neurosci. 20 (2000) 3233-3243
58. Thomas, R., 1981. On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations, Numerical methods in the study of critical phenomena, Springer-Verlag in Synergetics, 1981, pp. 180-193.
59. Volianskis A., and Jensen M. Transient and sustained types of long-term potentiation in the ca1 area of the rat hippocampus. J. Physiol. 550 (2003) 459-492
60. Von Bremen H., Udwadia F., and Proskuroswki W. An efficient QR based method for the computation of lyapunov exponents. Physica D 101 (1985) 1-6
61. Watts D., and Strogatz S. Collective dynamics of "small-world" networks. Nature 393 (1998) 440-442