Neuroinformatics

, Volume 9, Issue 4, pp 347–369 | Cite as

Models and Simulation of 3D Neuronal Dendritic Trees Using Bayesian Networks

  • Pedro L. López-Cruz
  • Concha Bielza
  • Pedro Larrañaga
  • Ruth Benavides-Piccione
  • Javier DeFelipe
Article
First Online:

Abstract

Neuron morphology is crucial for neuronal connectivity and brain information processing. Computational models are important tools for studying dendritic morphology and its role in brain function. We applied a class of probabilistic graphical models called Bayesian networks to generate virtual dendrites from layer III pyramidal neurons from three different regions of the neocortex of the mouse. A set of 41 morphological variables were measured from the 3D reconstructions of real dendrites and their probability distributions used in a machine learning algorithm to induce the model from the data. A simulation algorithm is also proposed to obtain new dendrites by sampling values from Bayesian networks. The main advantage of this approach is that it takes into account and automatically locates the relationships between variables in the data instead of using predefined dependencies. Therefore, the methodology can be applied to any neuronal class while at the same time exploiting class-specific properties. Also, a Bayesian network was defined for each part of the dendrite, allowing the relationships to change in the different sections and to model heterogeneous developmental factors or spatial influences. Several univariate statistical tests and a novel multivariate test based on Kullback–Leibler divergence estimation confirmed that virtual dendrites were similar to real ones. The analyses of the models showed relationships that conform to current neuroanatomical knowledge and support model correctness. At the same time, studying the relationships in the models can help to identify new interactions between variables related to dendritic morphology.

Keywords

Pyramidal cells Virtual dendrites Morphology simulation Dendritic structure Bayesian networks 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

This work has been supported by Spanish Science and Innovation Ministry, Cajal Blue Brain Project (C080020-09), TIN2010-20900-C04-04 Project and Consolider Ingenio 2010-CSD2007-00018. PL-C is supported by a FPU Fellowship from the Spanish Education Ministry.

References

  1. Anwar, H., Riachi, I., Hill, S., Schürmann, F., & Markram, H. (2009). An approach to capturing neuron morphological diversity. In E. De Schutter (Ed.), Computational modeling methods for neuroscientists (pp. 211–232). The MIT Press.Google Scholar
  2. Ascoli, G. A. (2007). Successes and rewards in sharing digital reconstructions of neuronal morphology. Neuroinformatics, 5, 154–160.PubMedCrossRefGoogle Scholar
  3. Ascoli, G. A., & Krichmar, J. L. (2000). L-neuron: A modeling tool for the efficient generation and parsimonious description of dendritic morphology. Neurocomputing, 32–33, 1003–1011.CrossRefGoogle Scholar
  4. Ascoli, G. A., Krichmar, J. L., Nasuto, S., & Senft, S. (2001). Generation, description and storage of dendritic morphology data. Philosophical transactions of the Royal Society of London. Series B, Biological Sciences, 356, 1131–1145.PubMedCrossRefGoogle Scholar
  5. Ascoli, G. A., Donohue, D. E., & Halavi, M. (2007). Neuromorpho.org: A central resource for neuronal morphologies. Journal of Neuroscience, 27(35), 9247–9251.PubMedCrossRefGoogle Scholar
  6. Ascoli, G. A., Alonso-Nanclares, L., Anderson, S., Barrionuevo, G., Benavides-Piccione, R., Burkhalter, A., et al. (2008). Petilla terminology: Nomenclature of features of gabaergic interneurons of the cerebral cortex. Nature Reviews. Neuroscience, 9(7), 557–568.PubMedCrossRefGoogle Scholar
  7. Ballesteros-Yáñez, I., Benavides-Piccione, R., Bourgeois, J., Changeux, J., & DeFelipe, J. (2010). Alterations of cortical pyramidal neurons in mice lacking high-affinity nicotinic receptors. Proceedings of the National Academy of Sciences of the United States of America, 107(25), 11,567–11,572.CrossRefGoogle Scholar
  8. Benavides-Piccione, R., Ballesteros-Yáñez, I., Martínez de Legrán, M., Elston, G., Estivill, X., Fillat, C., et al. (2004). On dendrites in Down syndrome and DS murine models: A spiny way to learn. Progress in Neurobiology, 74, 111–126.PubMedCrossRefGoogle Scholar
  9. Benavides-Piccione, R., Hamzei-Sichani, F., Ballesteros-Yáñez, I., DeFelipe, J., & Yuste, R. (2006). Dendritic size of pyramidal neurons differs among mouse cortical regions. Cerebral Cortex, 16, 990–1001.PubMedCrossRefGoogle Scholar
  10. Brown, K. M., Gillette, T. A., & Ascoli, G. A. (2008). Quantifying neuronal size: Summing up trees and splitting the branch difference. Seminars in Cell & Developmental Biology, 19, 485–493.CrossRefGoogle Scholar
  11. Cannon, R., Turner, D., Pyapali, G., & Wheal, H. (1998). An on-line archive of reconstructed hippocampal neurons. Journal of Neuroscience Methods, 84, 49–54.PubMedCrossRefGoogle Scholar
  12. Chen, J. Y. (2009). A simulation study investigating the impact of dendritic morphology and synaptic topology on neuronal firing patterns. Neural Computation, 22(4), 1086–1111.CrossRefGoogle Scholar
  13. Cline, H. (2001). Dendritic arbor development and synaptogenesis. Current Opinion in Neurobiology, 11(1), 118–126.PubMedCrossRefGoogle Scholar
  14. Cooper, G., & Herskovits, E. (1992). A Bayesian method for the induction of probabilistic networks from data. Machine Learning, 9, 309–347.Google Scholar
  15. DeFelipe, J. (2008). The neuroanatomist’s dream, the problems and solutions, and the ultimate aim. Frontiers in Neuroscience,, 2, 10–12.PubMedCrossRefGoogle Scholar
  16. DeFelipe, J., & Fariñas, I. (1992). The pyramidal neuron of the cerebral cortex: Morphological and chemical characteristics of the synaptic inputs. Progress in Neurobiology, 39, 563–607.PubMedCrossRefGoogle Scholar
  17. Devaud J. M., Quenet, B., Gascuel, J., & Masson, C. (2000). Statistical analysis and parsimonious modelling of dendrograms of in vitro neurones. Bulletin of Mathematical Biology, 62, 657–674.PubMedCrossRefGoogle Scholar
  18. Ding, B., Gentleman, R., & Carey, V. (2010). bioDist: Different distance measures. R package version 1.18.0.Google Scholar
  19. Donohue, D. E., & Ascoli, G. A. (2005a). Local diameter fully constrains dendritic size in basal but not apical trees of CA1 pyramidal neurons. Journal of Computational Neuroscience, 19(2), 223–238.PubMedCrossRefGoogle Scholar
  20. Donohue, D. E., & Ascoli, G. A. (2005b). Models of neuronal outgrowth. In S. Koslow, & S. Subramaniam (Eds.), Databasing the brain: From data to knowledge (pp. 303–326). New York: Wiley.Google Scholar
  21. Donohue, D. E., & Ascoli, G. A. (2008). A comparative computer simulation of dendritic morphology. PLoS Computational Biology, 4(6). doi: 10.1371/journal.pcbi.1000089.
  22. Efron, B., & Tibshirani, R. (1986). Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statistical Science, 1(1), 54–75.CrossRefGoogle Scholar
  23. Elston, G. (2007). Specializations in pyramidal cell structure during primate evolution. In J. Kaas, & T. Preuss (Eds.), Evolution of nervous systems (pp. 191–242). Academic: Oxford.CrossRefGoogle Scholar
  24. Elston, G., & Rosa, M. (1997). The occipito-parietal pathway of the macaque monkey: Comparison of pyramidal cell morphology in layer III of functionally related cortical visual areas. Cerebral Cortex, 7(5), 432–452.PubMedCrossRefGoogle Scholar
  25. Fay, M. P., & Proschan, M. A. (2010). Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules. Statistics Surveys, 4, 1–39.PubMedCrossRefGoogle Scholar
  26. Feldman, M. (1984). Morphology of the neocortical pyramidal neuron. In A. Peters, & E. Jones (Eds.), Cerebral cortex. Cellular components of the cerebral cortex (Vol. 1, pp. 201–253). New York: Plenum Press.Google Scholar
  27. Friedman, N., & Yakhini, Z. (1996). On the sample complexity of learning Bayesian networks. In Proceedings of the twelfth conference on uncertainty in artificial intelligence (UAI 96) (pp. 274–282).Google Scholar
  28. Friedman, N., Goldszmith, M., & Wyner, A. (1999). Data analysis with Bayesian networks: A bootstrap approach. In Proceedings of the fifteenth conference on uncertainty in artificial intelligence (UAI 99) (pp. 196–205).Google Scholar
  29. Geiger, D., & Heckerman, D. (1996). Knowledge representation and inference in similarity networks and Bayesian multinets. Artificial Intelligence, 82, 45–74.CrossRefGoogle Scholar
  30. Glaser, J., & Glaser, E. (1990). Neuron imaging with neurolucida—a PC-based system for image combining microscopy. Computerized Medical Imaging and Graphics, 14(5), 307–317.PubMedCrossRefGoogle Scholar
  31. Hamilton, P. (1993). A language to describe the growth of neurites. Biological Cybernetics, 68(6), 559–565.PubMedCrossRefGoogle Scholar
  32. Häusser, M., & Mel, B. (2003). Dendrites: Bug or feature? Current Opinion in Neurobiology, 13(3), 372–383.PubMedCrossRefGoogle Scholar
  33. Heckerman, D. (1996). A tutorial on learning with Bayesian networks. Tech. Rep. MSR-TR-95-06, Microsoft Corporation.Google Scholar
  34. Hentschel, H. G., & van Ooyen, A. (1999). Models of axon guidance and bundling during development. Proceedings of the Royal Society of London. Series B, Biological Sciences, 266, 2231–2238.CrossRefGoogle Scholar
  35. Heumann, H., & Wittum, G. (2009). The tree-edit-distance, a measure for quantifying neuronal morphology. Neuroinformatics, 7(3), 179–190.PubMedCrossRefGoogle Scholar
  36. Hillman, D. (1979). Neuronal shape parameters and substructures as a basis of neuronal form. In F Schmitt (Ed.), The neurosciences, 4th study program (pp. 477–498). MIT Press.Google Scholar
  37. Jacobs, B., & Scheibel, A. (2002). Regional dendritic variation in primate cortical pyramidal cells. In A. Schüz, & R. Miller (Eds.), Cortical areas: Unity and diversity (pp. 111–131). CRC Press.Google Scholar
  38. Kaufmann, W. E., & Moser, H. W. (2000). Dendritic anomalies in disorders associated with mental retardation. Cerebral Cortex, 10(10), 981–991.PubMedCrossRefGoogle Scholar
  39. Koch, C., & Segev, I. (2000). The role of single neurons in information processing. Nature Neuroscience, 3, 1171–1177.PubMedCrossRefGoogle Scholar
  40. Koch, C., Poggio, T., & Torres, V. (1982). Retinal ganglion cells: A functional interpretation of dendritic morphology. Proceedings of the Royal Society of London. Series B, Biological Sciences, 298(1090), 227–263.Google Scholar
  41. Koene, R. A., Tijms, B., van Hees, P., Postma, F., de Ridder, A., Ramakers, G. J., et al. (2009). Netmorph: A framework for the stochastic generation of large scale neuronal networks with realistic neuron morphologies. Neuroinformatics, 7(3), 195–210.PubMedCrossRefGoogle Scholar
  42. Koller, D., & Friedman, N. (2009). Probabilistic graphical models. Principles and techniques. The MIT Press.Google Scholar
  43. Krause, P. J. (1998). Learning probabilistic networks. Knowledge Engineering Review, 13(4), 321–351.CrossRefGoogle Scholar
  44. Kullback, S., & Leibler, R. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22(1), 79–86.CrossRefGoogle Scholar
  45. Larkman, A. (1991). Dendritic morphology of pyramidal neurones of the visual cortex of the rat: I. Branching patterns. Journal of Comparative Neurology, 306(2), 307–319.PubMedCrossRefGoogle Scholar
  46. Leray, P., & Francois, O. (2006). BNT structure learning package: Documentation and experiments. Tech. Rep. FRE CNRS 2645, Laboratoire PSI—INSA Rouen.Google Scholar
  47. Li, G. H., & Qin, C. D. (1996). A model for neurite growth and neuronal morphogenesis. Mathematical Biosciences, 132(1), 97–110.PubMedCrossRefGoogle Scholar
  48. Lindsay, K. A., Maxwell, D. J., Rosenberg, J. R., & Tucker, G. (2007). A new approach to reconstruction models of dendritic branching patterns. Mathematical Biosciences, 205(2), 271–296.PubMedCrossRefGoogle Scholar
  49. Luczak, A. (2006). Spatial embedding of neuronal trees modeled by diffusive growth. Journal of Neuroscience Methods, 157(1), 132–141.PubMedCrossRefGoogle Scholar
  50. Mainen, Z. F., & Sejnowski, T. J. (1996). Influence of dendritic structure on firing pattern in model neocortical neurons. Nature, 382, 363–366.PubMedCrossRefGoogle Scholar
  51. Markram, H. (2006). The blue brain project. Nature Reviews. Neuroscience, 7(2), 153–160.PubMedCrossRefGoogle Scholar
  52. McAllister, A. K. (2000). Cellular and molecular mechanisms of dendrite growth. Cerebral Cortex, 10(10), 963–973.PubMedCrossRefGoogle Scholar
  53. Miina, J., & Pukkala, T. (2002). Application of ecological field theory in distance-dependent growth modelling. Forest Ecology and Management, 161, 101–107.CrossRefGoogle Scholar
  54. Murphy, K. (2001). The Bayes net toolbox for Matlab. In E. Wegman, A. Braverman, A. Goodman, & P Smyth (Eds.), Computing science and statistics. Proceedings of the 33rd symposium on the interface (Vol. 33, pp. 331–350).Google Scholar
  55. Pearl, J. (1988). Probabilistic reasoning in intelligent systems. Morgan Kaufmann.Google Scholar
  56. Pourret, O., Naïm, P., & Marcot, B. (2008). Bayesian networks: A practical guide to applications. Wiley.Google Scholar
  57. R Development Core Team (2009). R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria.Google Scholar
  58. Robert, M. E., & Sweeney, J. D. (1997). Computer model: Investigating the role of filopodia-based steering in experimental neurite galvanotropism. Journal of Theoretical Biology, 188(3), 277–288.PubMedCrossRefGoogle Scholar
  59. Romero, V., Rumí, R., & Salmerón, A. (2006). Learning hybrid Bayesian networks using mixtures of truncated exponentials. International Journal of Approximate Reasoning, 42, 54–68.CrossRefGoogle Scholar
  60. Rozenberg, G., & Salomaa, A. (1980). The mathematical theory of L-systems. New York: Academic Press.Google Scholar
  61. Samsonovich, A. V., & Ascoli, G. A. (2003). Statistical morphological analysis of hippocampal principal neurons indicates cell-specific repulsion of dendrites from their own cell. Journal of Neuroscience Research, 71(2), 173–187.PubMedCrossRefGoogle Scholar
  62. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6(2), 461–464.CrossRefGoogle Scholar
  63. Scott, E. K., & Luo, L. (2001). How do dendrites take their shape? Nature Neuroscience, 4(4), 359–365.PubMedCrossRefGoogle Scholar
  64. Shepherd, G. M. (ed) (2004). The synaptic organization of the brain (5th edn). Oxford University Press.Google Scholar
  65. Spruston, N. (2008). Pyramidal neurons: Dendritic structure and synaptic integration. Nature Reviews. Neuroscience, 9(3), 206–221.PubMedCrossRefGoogle Scholar
  66. Steuber, V., De Schutter, E., & Jaeger, D. (2004). Passive models of neurons in the deep cerebellar nuclei: The effect of reconstruction errors. Neurocomputing, 58–60, 563–568.CrossRefGoogle Scholar
  67. Sumida, A., Terazawa, I., Togashi, A., & Komiyama, A. (2002). Spatial arrangement of branches in relation to slope and neighbourhood competition. Annals of Botany, 82, 301–310.CrossRefGoogle Scholar
  68. Torben-Nielsen, B., Tuyls, K., & Postma, E. O. (2006). Shaping realistic neuronal morphologies: An evolutionary computation method. In International joint conference on neural networks (IJCNN2006) (pp. 573–580). Vancouver, Canada.Google Scholar
  69. Torben-Nielsen, B., Tuyls, K., & Postma, E. O. (2007). On the neuronal morphology-function relationship: A synthetic approach. In Knowledge discovery and emergent complexity in bioinformatics, LNBI. (Vol. 4366, pp. 135–149). Springer.Google Scholar
  70. Torben-Nielsen, B., Tuyls, K., & Postma, E. O. (2008a). Evol-neuron: Neuronal morphology generation. Neurocomputing, 71, 963–972.CrossRefGoogle Scholar
  71. Torben-Nielsen, B., Vanderlooy, S., & Postma, E. O. (2008b). Non-parametric algorithmic generation of neuronal morphologies. Neuroinformatics, 6, 257–277.PubMedCrossRefGoogle Scholar
  72. Uylings, H. B., & van Pelt, J. (2002). Measures for quantifying dendritic arborizations. Network: Computation in Neural Systems, 13, 397–414.CrossRefGoogle Scholar
  73. Uylings, H. B., Ruiz-Marcos, A., & Van Pelt, J. (1986). The metric analysis of three-dimensional dendritic tree patterns: A methodological review. Journal of Neuroscience Methods, 18, 127–151.PubMedCrossRefGoogle Scholar
  74. Van Pelt, J., & Uylings, H. B. (1999). Modeling the natural variability in the shape of dendritic trees: Application to basal dendrites of small rat cortical layer 5 pyramidal neurons. Neurocomputing, 26–27, 305–311.Google Scholar
  75. Van Pelt, J., & Uylings, H. B. (2005). Natural variability in the geometry of dendritic branching patterns. In G. Reeke, R. Poznanski, K. Lindsay, J. Rosenberg, & O. Sporns (Eds.), Modeling in the neurosciences: From biological systems to neuromimetic robotics (pp. 89–116). CRC Press.Google Scholar
  76. Van Pelt, J., van Ooyen, A., & Uylings, H. B. (2001). Modeling dendritic geometry and the development of nerve connections. In E. De Schutter (Ed.), Computational neuroscience: Realistic modeling for experimentalists (pp. 179–208). CRC Press.Google Scholar
  77. Van Veen, M. P., & Van Pelt, J. (1993). Terminal and intermediate segment lengths in neuronal trees with finite length. Bulletin of Mathematical Biology, 55, 277–294.PubMedCrossRefGoogle Scholar
  78. Verwer, R., van Pelt, J., & Uylings, H. B. (1992). An introduction to topological analysis of neurones. In M Stewart (Ed.), Quantitative methods in neuroanatomy (pp. 292–323). John Wiley and Sons.Google Scholar
  79. Vetter, P., Roth, A., & Häusser, M. (2001). Propagation of action potentials in dendrites depends on dendritic morphology. Journal of Neurophysiology, 85(2), 926–937.PubMedGoogle Scholar
  80. Wang, Q., Kulkarni, S. R., & Verdú, S. (2006). A nearest-neighbor approach to estimating divergence between continuous random vectors. In IEEE international symposium on information theory (ISIT 2006) (pp. 242–246).Google Scholar
  81. Wen, Q., Stepanyants, A., Elston, G., Grosberg, A., & Chklovskii, D. (2009). Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors. Proceedings of the National Academy of Sciences of the United States of America, 106(30), 12,536–12,541.CrossRefGoogle Scholar
  82. White, E. (1989). Cortical circuits: Synaptic organization of the cerebral cortex. structure, function and theory. Boston: Birkhauser.Google Scholar
  83. Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin 1(6), 80–83.CrossRefGoogle Scholar
  84. Yuste, R., & Bonhoeffer, T. (2004). Genesis of dendritic spines: Insights from ultrastructural and imaging studies. Nature Reviews. Neuroscience, 5, 24–34.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Pedro L. López-Cruz
    • 1
  • Concha Bielza
    • 1
  • Pedro Larrañaga
    • 1
  • Ruth Benavides-Piccione
    • 2
  • Javier DeFelipe
    • 2
  1. 1.Departamento de Inteligencia Artificial, Facultad de InformáticaUniversidad Politécnica de MadridMadridSpain
  2. 2.Laboratorio Cajal de Circuitos CorticalesUniversidad Politécnica de Madrid and Instituto Cajal (CSIC)MadridSpain

Personalised recommendations