Advertisement

Theoretical Neuroanatomy:Analyzing the Structure, Dynamics,and Function of Neuronal Networks

  • Anil K. Seth
  • Gerald M. Edelman
Part IV Biological Networks
Part of the Lecture Notes in Physics book series (LNP, volume 650)

Abstract

The mammalian brain is an extraordinary object: its networks give rise to our conscious experiences as well as to the generation of adaptive behavior for the organism within its environment. Progress in understanding the structure, dynamics and function of the brain faces many challenges. Biological neural networks change over time, their detailed structure is difficult to elucidate, and they are highly heterogeneous both in their neuronal units and synaptic connections. In facing these challenges, graph-theoretic and information-theoretic approaches have yielded a number of useful insights and promise many more.

Keywords

Mutual Information Adaptive Behavior Network Type Connection Strength Head Direction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1. G.M. Edelman. The remembered present. Basic Books, Inc., New York, NY, 1989.Google Scholar
  2. 2. A. Clark. Being there: Putting brain, body, and world together again. MIT Press, Cambridge, MA, 1997.Google Scholar
  3. 3. D. Buonomano and M. Merzenich. Cortical plasticity: From synapses to maps. Annual Review of Neuroscience, 21:149–186, 1998.Google Scholar
  4. 4. K. Friston. Functional and effective connectivity in neuroimaging: A synthesis. Human Brain Mapping, 2:56–78, 1994.Google Scholar
  5. 5. S.L. Bressler. Large-scale cortical networks and cognition. Brain Research Reviews, 20:288–304, 1995.Google Scholar
  6. 6. R.S.J. Frackowiak, K.J. Friston, C.D. Frith, R.J. Dolan, and J.C. Mazziotta. Human brain function. Academic Press, San Diego, CA, 1997.Google Scholar
  7. 7. F. Varela, J.-P Lachaux, E. Rodriguez, and J. Martiniere. The brainweb: Phase synchronization and large-scale integration. Nature Reviews Neuroscience, 2:229–239, 2001.Google Scholar
  8. 8. R. Cummins. Functional analysis. Journal of Philosophy, 72:741–764, 1975.Google Scholar
  9. 9. F. Harary. Graph theory. Addison-Wesley, Reading, MA, 1969.Google Scholar
  10. 10. B. Bollobás. Random graphs. Academic Press, London, 1985.Google Scholar
  11. 11. B. Jouve, P. Rosentiehl, and M. Imbert. A mathematical approach to the connectivity between the cortical visual areas of the macaque monkey. Cerebral Cortex, 8:28–39, 1998.Google Scholar
  12. 12. C.C. Hilgetag, R. Kötter, K.E. Stephan, and O. Sporns. Computational methods for the analysis of brain connectivity. In G.A. Ascoli, editor, Computational neuroanatomy: Principles and methods, pages 295–331. Humana Press, Totowa, NJ, 2002.Google Scholar
  13. 13. O. Sporns. Graph theory methods for the analysis of neural connectivity patterns. In R. Kötter, editor, Neuroscience Databases. A Practical Guide, pages 169–183. Kluwer Publishers, Boston, MA, 2002.Google Scholar
  14. 14. O. Sporns, G. Tononi, and G.M. Edelman. Theoretical neuroanatomy: Relating anatomical and functional connectivity in graphs and cortical connection matrices. Cerebral Cortex, 10:127–141, 2000.Google Scholar
  15. 15. R. Albert, H. Jeong, and A.-L. Barábasi. Diameter of the world wide web. Nature, 401:130–131, 1999.Google Scholar
  16. 16. D.J. Watts and S.H. Strogatz. Collective dynamics of ‘small world’ networks. Nature, 393:440–442, 1998.Google Scholar
  17. 17. S.H. Strogatz. Exploring complex networks. Nature, 410:268–276, 2001.Google Scholar
  18. 18. M.E.J. Newman. The structure and function of complex networks. SIAM Review, 45(2):167–256, 2003.Google Scholar
  19. 19. G.Q. Bi and M.M. Poo. Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. Journal of Neuroscience, 18:10464–10472, 1998.Google Scholar
  20. 20. Y.X. Fu, K. Djupsund, H. Gao B. Hayden, K. Shen, and Y. Dan. Temporal specificity in the cortical plasticity of visual space representation. Science, 296:1999–2003, 2002.Google Scholar
  21. 21. W. Bialek, I. Nemenman, and N. Tishby. Predictability, complexity, and learning. Neural Computation, 13:2409–2463, 2001.Google Scholar
  22. 22. M. Costa, A.L. Goldberger, and C.K. Peng. Multiscale entropy analysis of complex physiological time series. Physical Review Letters, 89:681–682, 2002.Google Scholar
  23. 23. L. Paninski. Estimation of entropy and mutual information. Neural Computation, 15:1191–1253, 2003.Google Scholar
  24. 24. G.N. Reeke and A.D. Coop. Estimating the temporal interval entropy of neuronal discharge. Neural Computation, in press.Google Scholar
  25. 25. G. Tononi, O. Sporns, and G.M. Edelman. A measure for brain complexity: Relating functional segregation and integration in the nervous system. Proceedings of the National Academy of Science (USA), 91:5033–5037, 1994.Google Scholar
  26. 26. A.K. Seth and G.M. Edelman. Environment and behavior influence the complexity of evolved neural networks. Adaptive Behavior, in press.Google Scholar
  27. 27. F. Crick and E. Jones. Backwardness of human neuroanatomy. Nature, 361:109–110, 1993.Google Scholar
  28. 28. D.J. Felleman and D.C. Van Essen. Distributed hierarchical processing in the primate cerebral cortex. Cerebral Cortex, 1:1–47, 1991.Google Scholar
  29. 29. M.P. Young. The organization of neural systems in the primate cerebral cortex. Philosophical Transactions of the Royal Society of London: Series B, 252:13–18, 1993.Google Scholar
  30. 30. J.W. Scannell, C. Blakemore, and M.P. Young. Analysis of connectivity in the cat cerebral cortex. Journal of Neuroscience, 15, 1995.Google Scholar
  31. 31. J.W. Scannell, G.A.P.C. Burns, C.C. Hilgetag, M.A. O’Neil, and M.P. Young. The connectional organization of the cortico-thalamic system of the cat. Cerebral Cortex, 9:277–299, 1999.Google Scholar
  32. 32. R. Kötter. Neuroscience databases: Tools for exploring brain structure-function relationships. Philosophical Transactions of the Royal Society of London: Series B, 356:1111–1120, 2001.Google Scholar
  33. 33. K.E. Stephan, L. Kamper, A. Bokzurt, G.A.P.C. Burns, M.P. Young, and R. Kötter. Advances in database methodology for the collation of connectivity data on the macaque brain (CoCoMac). Philosophical Transactions of the Royal Society of London: Series B, 356:1159–1186, 2001.Google Scholar
  34. 34. J.M.J. Murre and D.P.F. Sturdy. The connectivity of the brain: Multi-level quantitative analysis. Biological Cybernetics, 73:529–545, 1995.Google Scholar
  35. 35. A. Nicoll and C. Blakemore. Patterns of local connectivity in the neocortex. Neural Computation, 5:665–680, 1993.Google Scholar
  36. 36. C.C. Hilgetag. Mathematical approaches to the analysis of neural connectivity in the mammalian brain. PhD thesis, Faculty of Medicine, University of Newcastle upon Tyne, 1999.Google Scholar
  37. 37. L. Lagae, D.K. Xiao, S. Raiquel, H. Maes, and G.A. Orban. Position invariance of optic flow component selectivity differentiates monkey MST and FST cells from MT cells. Invest. Ophthamol. Vis. Sci., 32:823, 1991.Google Scholar
  38. 38. J.J. Gibson. The ecological approach to visual perception. Houghton-Mifflin, Boston, 1979.Google Scholar
  39. 39. D.J. Watts. Small worlds. Princeton University Press, Princeton, NJ, 1999.Google Scholar
  40. 40. P. Erdös and A. Rényi. On random graphs. Publicationes Mathematicae, 6:290–297, 1959.Google Scholar
  41. 41. R. Albert and A.-L. Barábasi. Statistical mechanics of complex networks. Reviews of Modern Physics, 74:47–97, 2002.Google Scholar
  42. 42. H. Jeong, B. Tombor, R. Albert, Z. Oltvai, and A.-L. Barábasi. The large-scale organization of metabolic networks. Nature, 407:651–654, 2000.Google Scholar
  43. 43. G.M. Edelman. Neural Darwinism. Basic Books, New York, 1987.Google Scholar
  44. 44. G. Tononi, O. Sporns, and G.M. Edelman. Reentry and the problem of integrating multiple cortical areas: Simulation of dynamic integration in the visual system. Cerebral Cortex, 2(4):31–35, 1992.Google Scholar
  45. 45. G.M. Edelman. Selection and reentrant signaling in higher brain function. Neuron, 10:115–125, 1993.Google Scholar
  46. 46. G.M. Edelman and G. Tononi. A universe of consciousness: How matter becomes imagination. Basic Books, New York, 2000.Google Scholar
  47. 47. A.K. Seth, J.L. McKinstry, G.M. Edelman, and J.L. Krichmar. Visual binding through reentrant connectivity and dynamic synchronization in a brain-based device. Cerebral Cortex, in press.Google Scholar
  48. 48. G. Mitchison. Neuronal branching patterns and the economy of cortical wiring. Proceedings of the Royal Society of London: Series B. Biological Sciences., 245:151–158, 1991.Google Scholar
  49. 49. C. Cherniak. Component placement optimization in the brain. Journal of Neuroscience, 14:2418–2427, 1994.Google Scholar
  50. 50. C. Cherniak. Optimal-wiring models of neuroanatomy. In G.A. Ascoli, editor, Computational neuroanatomy: Principles and methods, pages 71–83. Humana Press, Totowa, NJ, 2002.Google Scholar
  51. 51. C. Cherniak, Z. Mokhtarzada, R. Rodriguez-Esteban, and K. Changizi. Global optimization of cerebral cortex layout. Proceedings of the National Academy of Sciences, USA, 101(4):1081–1086, 2004.Google Scholar
  52. 52. J.B. Kruskal. Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29:115–129, 1964.Google Scholar
  53. 53. J.B. Kruskal. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29:1–27, 1964.Google Scholar
  54. 54. M.P. Young, J.W. Scannell, M.A. O’Neill, C.C. Hilgetag, G.A.P.C. Burns, and C. Blakemore. Non-metric multidimensional scaling in the analysis of neuroanatomical connection data and the organization of the primate visual system. Philosophical Transactions of the Royal Society of London: Series B, 348:281–308, 1995.Google Scholar
  55. 55. L.G. Ungerleider and J.V. Haxby. ‘what’ and ‘where’ in the human brain. Current Opinion in Neurobiology, 4:157–165, 1994.Google Scholar
  56. 56. C.C. Hilgetag, G.A.P.C. Burns, M.A. O’Neill, and M.P. Young. Cluster structure of cortical systems in mammalian brains. In J.M. Bower, editor, Computational neuroscience, pages 41–46. Plenum Press, New York, 1998.Google Scholar
  57. 57. G. Tononi, G.M. Edelman, and O. Sporns. Complexity and coherency: Integrating information in the brain. Trends in Cognitive Science, 2:474–484, 1998.Google Scholar
  58. 58. O. Sporns and G. Tononi. Classes of network connectivity and dynamics. Complexity, 7(1):28–38, 2002.Google Scholar
  59. 59. S. Zeki. Functional specialization in the visual cortex of the Rhesus monkey. Nature, 274:423–428, 1978.Google Scholar
  60. 60. S. Zeki. A vision of the brain. Blackwell, Oxford, 1993.Google Scholar
  61. 61. W. Vanduffel, B.R. Payne, S.G. Lomber, and G.A. Orban. Functional impact of cerebral connections. Proceedings of the National Academy of Science (USA), 94:7617–7620, 1997.Google Scholar
  62. 62. A. Papoulis and S.U. Pillai. Probability, random variables, and stochastic processes. McGraw-Hill, New York, NY, 2002. 4th edition.Google Scholar
  63. 63. D.S. Jones. Elemenary information theory. Clarendon Press, 1979.Google Scholar
  64. 64. G. Tononi and G.M. Edelman. Consciousness and complexity. Science, 282:1846–1851, 1998.Google Scholar
  65. 65. G. Tononi, A.R. McIntosh, D.P. Russell, and G.M. Edelman. Functional clustering: identifying strongly interactive brain regions in neuroimaging data. Neuroimage, 7:133–149, 1998.Google Scholar
  66. 66. S.E. Petersen, P.T. Fox, M.I. Posner, M. Mintun, and M. Raichle. Positron emission tomographic studies of the cortical anatomy of single-word processing. Nature, 331:585–589, 1988.Google Scholar
  67. 67. R. Hari, S. Levänen, and T. Raij. Timing of human cortical functions during cognition: role of MEG. Trends in Cognitive Science, 4(12):455–461, 2000.Google Scholar
  68. 68. G. Tononi, O. Sporns, and G.M. Edelman. A complexity measure for selective matching of signals by the brain. Proceedings of the National Academy of Science (USA), 93:3422–3427, 1996.Google Scholar
  69. 69. G. Tononi, O. Sporns, and G.M. Edelman. Measures of degeneracy and redundancy in biological networks. Proceedings of the National Academy of Science (USA), 96:3257–3262, 1999.Google Scholar
  70. 70. G.M. Edelman and J. Gally. Degeneracy and complexity in biological systems. Proceedings of the National Academy of Sciences, USA, 98(24):13763–13768, 2001.Google Scholar
  71. 71. A.K. Seth. On the relations between behaviour, mechanism, and environment: Explorations in artificial evolution. PhD thesis, University of Sussex, 2000.Google Scholar
  72. 72. M. Mitchell. An introduction to genetic algorithms. MIT Press, Cambridge, MA, 1997.Google Scholar
  73. 73. V. Latora and M. Marchiori. Efficient behavior of small-world networks. Physical Review Letters, 87(19):198701–4, 2001.Google Scholar
  74. 74. C. Cannings and C. Penman. Random graphs. In C.R. Rao and D.N. Shanbhag, editors, Stochastic processes: Modelling and simulation, Vol. 21. Handbook of Statistics series. Elsevier, 2002.Google Scholar
  75. 75. M. E. J. Newman Who is the best connected scientist? A study of scientific coauthorship networks Physical Review E, 64:016131, 2001.Google Scholar
  76. 76. A.R. McIntosh and F. Gonzalez-Lima. Structural equation modeling and its application to network analysis in functional brain imaging. Human Brain Mapping, 2:2–22, 1994.Google Scholar
  77. 77. A.R. McIntosh, C.L. Grady, L.G. Ungerleider, J.V. Haxby, S.I. Rapoport, and B. Horwitz. Network analysis of cortical visual pathways mapped with PET. Journal of Neuroscience, 14:655–666, 1994.Google Scholar
  78. 78. M.S. Pinsker. Information and information stability of random variables and processes. Holden-Day, San Francisco, 1964.Google Scholar
  79. 79. R.M. Gray. Probability, random processes, and ergodic properties. Springer-Verlag, Berlin, 1988.Google Scholar
  80. 80. M. Doppelmayr, W. Klimesch, J. Schwaiger, and T. Winkler. Theta synchronization in human EEG and episodic retrieval. Neuroscience Letters, 257(1):41–4, 1998.Google Scholar
  81. 81. J.L. Cantero, M. Atienza, and R.M. Salas. Human alpha oscillations in wakefulness, drowsiness period, and REM sleep: different electroencephalographic phenomena within the alpha band. Neurophysiol. Clin., 32(1):54–71, 2002.Google Scholar
  82. 82. W. Singer and C. Gray. Visual feature integration and the temporal correlation hypothesis. Annual Review of Neuroscience, 18:555–586, 1995.Google Scholar
  83. 83. C. Gray. The temporal correlation hypothesis: still alive and well. Neuron, 24:31–47, 1999.Google Scholar
  84. 84. L.F. Lago-Fernandez, R. Huerta, F. Corbacho, and J. Siguenza. Fast response and temporal coherent oscillations in small-world networks. Physical Review Letters, 84:2758–2761, 2000.Google Scholar
  85. 85. G.M. Edelman. Naturalizing consciousness: A theoretical framework. Proceedings of the National Academy of Sciences, USA, 100(9):5520–5524, 2003.Google Scholar
  86. 86. J.L. Krichmar and G.M. Edelman. Machine psychology: Autonomous behavior, perceptual categorization and conditioning in a brain-based device. Cerebral Cortex, 12(8):818–30, 2002.Google Scholar

Authors and Affiliations

  • Anil K. Seth
    • 1
  • Gerald M. Edelman
    • 1
  1. 1.The Neurosciences Institute, 10640 John Jay Hopkins Drive, San Diego, CA 92121USA

Personalised recommendations