Self-organized Cultured Neuronal Networks: Longitudinal Analysis and Modeling of the Underlying Network Structure

  • Daniel de Santos-Sierra
  • Inmaculada Leyva
  • Juan Antonio Almendral
  • Stefano Boccaletti
  • Irene Sendiña-NadalEmail author
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 20)


This work analyzes the morphological evolution of assemblies of living neurons, as they self-organize from collections of separated cells into elaborated, clustered, networks. In particular, we introduce and implement a graph-based unsupervised segmentation algorithm that automatically retrieves the whole network structure from large scale phase-contrast images taken at high resolution throughout the entire life of a cultured neuronal network. The network structure is represented by an adjacency matrix in which nodes are identified as neurons or clusters of neurons, and links are the reconstructed connections (neurites) between them. The algorithm is also able to extract all other relevant morphological information characterizing neurons and neurites. More importantly and at variance with other segmentation methods that require fluorescence imaging from immunocytochemistry techniques, our measures are non invasive and entitle us to carry out a fully longitudinal analysis during the maturation of a single culture. In turn, a systematic statistical analysis of a group of topological observables grants us the possibility of quantifying and tracking the progression of the main networks characteristics during the self-organization process of the culture. Our results point to the existence of a particular state corresponding to a small-world network configuration, in which several relevant graphs’ micro- and meso-scale properties emerge. Finally, we identify the main physical processes taking place during the cultures morphological transformations, and embed them into a simplified growth model that quantitatively reproduces the overall set of experimental observations.


  1. 1.
    Achard, S., Bullmore, E.: Efficiency and cost of economical brain functional networks. PLoS Comput. Biol. 3(2), e17 (2007)CrossRefGoogle Scholar
  2. 2.
    Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(1), 47–97 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Amaral, L.A., Scala, A., Barthelemy, M., Stanley, H.E.: Classes of small-world networks. Proc. Natl. Acad. Sci. USA 97(21), 11,149–11,152 (2000)CrossRefGoogle Scholar
  4. 4.
    Anava, S., Greenbaum, A., Ben Jacob, E., Hanein, Y., Ayali, A.: The regulative role of neurite mechanical tension in network development. Biophys. J. 96(4), 1661–1670 (2009)CrossRefGoogle Scholar
  5. 5.
    Ayali, A.: Editorial: models of invertebrate neurons in culture. J. Mol. Histol. 43(4), 379–81 (2012)CrossRefGoogle Scholar
  6. 6.
    Baker, B.J., Kosmidis, E.K., Vucinic, D., Falk, C.X., Cohen, L.B., Djurisic, M., Zecevic, D.: Imaging brain activity with voltage- and calcium-sensitive dyes. Cell. Mol. Neurobiol. 25(2), 245–282 (2005)CrossRefGoogle Scholar
  7. 7.
    Bakkum, D.J., Chao, Z.C., Gamblen, P., Ben-Ary, G., Shkolnik, A.G., DeMarse, T.B., Potter, S.M.: Embodying cultured networks with a robotic drawing arm. Conf. Proc. IEEE Eng. Med. Biol. Soc. 2007, 2996–2999 (2007)Google Scholar
  8. 8.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Baruchi, I., Jacob, E.B.: Towards neuro-memory-chip: imprinting multiple memories in cultured neural networks. Phys. Rev. E. 75(5), 050901(R) (2007)CrossRefGoogle Scholar
  10. 10.
    Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.U.: Complex networks: Structure and dynamics. Phys. Rep. 424, 175–308 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Boccaletti, S., Bianconi, G., Criado, R., del Genio, C., Gómez-Gardeñes, J., Romance, M., Sendiña-Nadal, I., Wang, Z., Zanin, M.: The structure and dynamics of multilayer networks. Phys. Rep. 544(1), 1–122 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Bollobás, B.: Random Graphs. Cambridge University Press, Cambridge (2001)Google Scholar
  13. 13.
    Bologna, L.L., Nieus, T., Tedesco, M., Chiappalone, M., Benfenati, F., Martinoia, S.: Low-frequency stimulation enhances burst activity in cortical cultures during development. Neuroscience 165(3), 692–704 (2010)CrossRefGoogle Scholar
  14. 14.
    Breskin, I., Soriano, J., Moses, E., Tlusty, T.: Percolation in living neural networks. Phys. Rev. Lett. 97, 188,102 (2006)CrossRefGoogle Scholar
  15. 15.
    Buice, M.A., Cowan, J.D.: Statistical mechanics of the neocortex. Prog. Biophys. Mol. Biol. 99, 53–86 (2009)CrossRefGoogle Scholar
  16. 16.
    Chatterjee, N., Sinha, S.: Understanding the mind of a worm: hierarchical network structure underlying nervous system function in C. elegans. Prog. Brain Res. 168, 145–153 (2007) (Elsevier)Google Scholar
  17. 17.
    Cohen, O., Keselman, A., Moses, E., Martnez, M.R., Soriano, J., Tlusty, T.: Quorum percolation in living neural networks. EPL 89(1), 18008 (2010)CrossRefGoogle Scholar
  18. 18.
    Demarse, T.B., Wagenaar, D.A., Blau, A.W., Potter, S.M.: The neurally controlled animat: Biological brains acting with simulated bodies. Auton. Robot. 11(3), 305–310 (2001)zbMATHCrossRefGoogle Scholar
  19. 19.
    Downes, J.H., Hammond, M.W., Xydas, D., Spencer, M.C., Becerra, V.M., Warwick, K., Whalley, B.J., Nasuto, S.J.: Emergence of a small-world functional network in cultured neurons. PLoS Comput Biol 8(5), e1002522 (2012)CrossRefGoogle Scholar
  20. 20.
    Eckmann, J.P., Feinerman, O., Gruendlinger, L., Moses, E., Soriano, J., Tlusty, T.: The physics of living neural networks. Phys. Rep. 449(13), 54–76 (2007) (Nonequilibrium physics: From complex fluids to biological systems III. Living systems)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Feldt, S., Bonifazi, P., Cossart, R.: Dissecting functional connectivity of neuronal microcircuits: experimental and theoretical insights. Trends Neurosci. 34(5), 225–236 (2011)CrossRefGoogle Scholar
  22. 22.
    Fuchs, E., Ayali, A., Robinson, A., Hulata, E., Ben-Jacob, E.: Coemergence of regularity and complexity during neural network development. Dev Neurobiol 67(13), 1802–1814 (2007)CrossRefGoogle Scholar
  23. 23.
    Fuchs, E., Ayali, A., Ben-Jacob, E., Boccaletti, S.: The formation of synchronization cliques during the development of modular neural networks. Phys. Biol. 6(3), 036018 (2009)CrossRefGoogle Scholar
  24. 24.
    Grienberger, C., Konnerth, A.: Imaging calcium in neurons. Neuron 73(5), 862–885 (2012)CrossRefGoogle Scholar
  25. 25.
    Harrison, R.G., Greenman, M.J., Mall, F.P., Jackson, C.M.: Observations of the living developing nerve fiber. Anat. Rec. 1(5), 116–128 (1907)CrossRefGoogle Scholar
  26. 26.
    Honey, C.J., Kötter, R., Breakspear, M., Sporns, O.: Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc. Natl. Acad. Sci. USA 104(24), 10,240–10,245 (2007)CrossRefGoogle Scholar
  27. 27.
    Honey, C.J., Sporns, O., Cammoun, L., Gigandet, X., Thiran, J.P., Meuli, R., Hagmann, P.: Predicting human resting-state functional connectivity from structural connectivity. Proc. Natl. Acad. Sci. USA 106(6), 2035–2040 (2009)CrossRefGoogle Scholar
  28. 28.
    Jacobi, S., Soriano, J., Moses, E.: BDNF and NT-3 increase velocity of activity front propagation in unidimensional hippocampal cultures. J. Neurophysiol. 104(6), 2932–2939 (2010)CrossRefGoogle Scholar
  29. 29.
    Latora, V., Marchiori, M.: Economic small-world behavior in weighted networks. EPJ B 32(2), 249–263 (2003)CrossRefGoogle Scholar
  30. 30.
    Li, D., Li, G., Kosmidis, K., Stanley, H.E., Bunde, A., Havlin, S.: Percolation of spatially constraint networks. EPL 93(6), 68004 (2011)CrossRefGoogle Scholar
  31. 31.
    Maeda, E., Robinson, H.P., Kawana, A.: The mechanisms of generation and propagation of synchronized bursting in developing networks of cortical neurons. J. Neurosci. 15(10), 6834–6845 (1995)CrossRefGoogle Scholar
  32. 32.
    Marom, S., Shahaf, G.: Development, learning and memory in large random networks of cortical neurons: lessons beyond anatomy. Q. Rev. Biophys. 35(1), 63–87 (2002)CrossRefGoogle Scholar
  33. 33.
    Meijering, E.: Neuron tracing in perspective. Cytometry A 77(7), 693–704 (2010)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Melli, G., Höke, A.: Dorsal root ganglia sensory neuronal cultures: a tool for drug discovery for peripheral neuropathies. Expert. Opin. Drug Discov. 4(10), 1035–1045 (2009)CrossRefGoogle Scholar
  35. 35.
    Morin, F.O., Takamura, Y., Tamiya, E.: Investigating neuronal activity with planar microelectrode arrays: achievements and new perspectives. J. Biosci. Bioeng. 100(2), 131–143 (2005)CrossRefGoogle Scholar
  36. 36.
    Newman, M.E.J.: Assortative mixing in networks. Phys. Rev. Lett. 89(20), 208701 (2002)CrossRefGoogle Scholar
  37. 37.
    Orlandi, J.G., Soriano, J., Alvarez-Lacalle, E., Teller, S., Casademunt, J.: Noise focusing and the emergence of coherent activity in neuronal cultures. Nat. Phys. 9, 582–590 (2013)CrossRefGoogle Scholar
  38. 38.
    Rad, A.A., Sendiña-Nadal, I., Papo, D., Zanin, M., Buldú, J.M., del Pozo, F., Boccaletti, S.: Topological measure locating the effective crossover between segregation and integration in a modular network. Phys. Rev. Lett. 108, 228,701 (2012)Google Scholar
  39. 39.
    de Santos, D., Lorente, V., de la Paz, F., Cuadra, J.M., Alvarez-Sánchez, J.R., Fernández, E., Ferrández, J.M.: A client-server architecture for remotely controlling a robot using a closed-loop system with a biological neuroprocessor. Robot. Auton. Syst. 58(12), 1223–1230 (2010)CrossRefGoogle Scholar
  40. 40.
    de Santos-Sierra, D., Arriaga-Gómez, M.F., Bailador, G., Avila, C.S.: Low computational cost multilayer graph-based segmentation algorithms for hand recognition on mobile phones. In: 2014 International Carnahan Conference on Security Technology (ICCST), pp. 1–5Google Scholar
  41. 41.
    de Santos-Sierra, D., Sendiña-Nadal, I., Leyva, I., Almendral, J.A., Anava, S., Ayali, A., Papo, D., Boccaletti, S.: Emergence of small-world anatomical networks in self-organizing clustered neuronal cultures. PLoS ONE 9(1), e85828 (2014)Google Scholar
  42. 42.
    de Santos-Sierra, D., Sendiña-Nadal, I., Leyva, I., Almendral, J.A., Ayali, A., Anava, S., Sánchez-Ávila, C., Boccaletti, S.: Graph-based unsupervised segmentation algorithm for cultured neuronal networks’ structure characterization and modeling. Cytometry A 87A, 513–523 (2015)CrossRefGoogle Scholar
  43. 43.
    de Sierra-Santos, D.: Self-organizing cultured neural networks: image analysis techniques for longitudinal tracking and modeling of the underlying network structure. PhD thesis, Technical University of Madrid (2015)Google Scholar
  44. 44.
    Schmeltzer, C., Soriano, J., Sokolov, I.M., Rüdiger, S.: Percolation of spatially constrained Erdős–Rényi networks with degree correlations. Phys. Rev. E 89, 012116 (2014)CrossRefGoogle Scholar
  45. 45.
    Segev, R., Benveniste, M., Shapira, Y., Ben-Jacob, E.: Formation of electrically active clusterized neural networks. Phys. Rev. Lett. 90(16), 168101 (2003)CrossRefGoogle Scholar
  46. 46.
    Sendiña-Nadal, I., Soriano, J.: Cultivos neuronales: sistemas modelo para comprender la dinámica y la conectividad en redes. In: Maestú, F., del Pozo, F., Pereda, E. (eds.) Conectividad funcional y anatómica en el cerebro humano: Análisis de señales y aplicaciones en ciencias de la salud, pp. 103–113. Elsevier, Amsterdam (2015)Google Scholar
  47. 47.
    Shefi, O., Ben-Jacob, E., Ayali, A.: Growth morphology of two-dimensional insect neural networks. Neurocomputing 44–46, 635–643 (2002)zbMATHCrossRefGoogle Scholar
  48. 48.
    Shefi, O., Golding, I., Segev, R., Ben-Jacob, E., Ayali, A.: Morphological characterization of in vitro neuronal networks. Phys. Rev. E 66, 021905 (2002)CrossRefGoogle Scholar
  49. 49.
    Sombati, S., Delorenzo, R.J.: Recurrent spontaneous seizure activity in hippocampal neuronal networks in culture. J. Neurophysiol. 73(4), 1706–1711 (1995)CrossRefGoogle Scholar
  50. 50.
    Soriano, J., Rodríguez Martínez, M., Tlusty, T., Moses, E.: Development of input connections in neural cultures. Proc. Natl. Acad. Sci. USA 105(37), 13758–13763 (2008)CrossRefGoogle Scholar
  51. 51.
    Sun, J.J., Kilb, W., Luhmann, H.J.: Self-organization of repetitive spike patterns in developing neuronal networks in vitro. Eur. J. Neurosci. 32(8), 1289–1299 (2010)CrossRefGoogle Scholar
  52. 52.
    Teller, S., Granell, C., De Domenico, M., Soriano, J., Gómez, S., Arenas, A.: Emergence of assortative mixing between clusters of cultured neurons. PLoS Comput. Biol. 10(9), e1003796 (2014)CrossRefGoogle Scholar
  53. 53.
    van Pelt, J., Vajda, I., Wolters, P.S., Corner, M.A., Ramakers, G.J.A.: Dynamics and plasticity in developing neuronal networks in vitro. Prog. Brain Res. 147, 173–188 (2005)Google Scholar
  54. 54.
    Watts, D., Strogatz, S.: Collective dynamics of “small-world” networks. Nature 393, 440–442 (1998)zbMATHCrossRefGoogle Scholar
  55. 55.
    Watts, D.J.: Small worlds: the dynamics of networks between order and randomness. Princeton University Press, Princeton, NJ (1999)zbMATHGoogle Scholar
  56. 56.
    White, J.G., Southgate, E., Thomson, J.N., Brenner, S.: The structure of the nervous system of the nematode caenorhabditis elegans. Philos. Trans. R. Soc. Lond. B Biol. Sci. 314(1165), 1–340 (1986)CrossRefGoogle Scholar
  57. 57.
    Wilson, S.W.: Knowledge growth in an artificial animal. In: Proceedings of the 1st International Conference on Genetic Algorithms, L. Erlbaum Associates Inc., Hillsdale, NJ, USA, pp. 16–23 (1985)Google Scholar
  58. 58.
    Woiterski, L., Claudepierre, T., Luxenhofer, R., Jordan, R., Kaes, J.: Stages of neuronal network formation. New. J. Phys. 15(025029), 1–15 (2013)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Daniel de Santos-Sierra
    • 1
  • Inmaculada Leyva
    • 1
    • 2
  • Juan Antonio Almendral
    • 1
    • 2
  • Stefano Boccaletti
    • 3
  • Irene Sendiña-Nadal
    • 1
    • 2
    Email author
  1. 1.Center for Biomedical TechnologyTechnical University of MadridMadridSpain
  2. 2.Center for Biomedical Technology, Technical University of MadridMadridSpain
  3. 3.CNR-Institute of Complex SystemsSesto Fiorentino, FlorenceItaly

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