Biological Cybernetics

, Volume 102, Issue 1, pp 71–80

Density-dependence of functional development in spiking cortical networks grown in vitro


    • Center for Nonlinear Studies and Applied Modern Physics P-21Los Alamos National Laboratory
  • Vadas Gintautas
    • Center for Nonlinear Studies and Applied Mathematics and Plasma PhysicsLos Alamos National Laboratory
  • Marko A. Rodriguez
    • Center for Nonlinear StudiesLos Alamos National Laboratory
  • Ryan A. Bennett
    • Center for Network Neuroscience and Department of PhysicsUniversity of North Texas
  • Cara L. Santa Maria
    • Center for Network Neuroscience and Department of BiologyUniversity of North Texas
  • Luìs M. A. Bettencourt
    • Theoretical DivisionLos Alamos National Laboratory
    • Santa Fe Institute
Original Paper

DOI: 10.1007/s00422-009-0351-4

Cite this article as:
Ham, M.I., Gintautas, V., Rodriguez, M.A. et al. Biol Cybern (2010) 102: 71. doi:10.1007/s00422-009-0351-4


During development, the mammalian brain differentiates into specialized regions with distinct functional abilities. While many factors contribute to functional specialization, we explore the effect of neuronal density on the development of neuronal interactions in vitro. Two types of cortical networks, namely, dense and sparse with 50,000 and 12,500 total cells, respectively, are studied. Activation graphs that represent pairwise neuronal interactions are constructed using a competitive first response model. These graphs reveal that, during development in vitro, dense networks form activation connections earlier than sparse networks. Link entropy analysis of dense network activation graphs suggests that the majority of connections between electrodes are reciprocal in nature. Information theoretic measures reveal that early functional information interactions (among three electrodes) are synergetic in both dense and sparse networks. However, during later stages of development, previously synergetic relationships become primarily redundant in dense, but not in sparse networks. Large link entropy values in the activation graph are related to the domination of redundant ensembles in late stages of development in dense networks. Results demonstrate differences between dense and sparse networks in terms of informational groups, pairwise relationships, and activation graphs. These differences suggest that variations in cell density may result in different functional specializations of nervous system tissue in vivo.


Activation graphCultured neural networksInformation theoryIn vitroDevelopmentNeuronal density

Copyright information

© Springer-Verlag 2009