Advertisement

Natural Computing

, Volume 4, Issue 4, pp 339–361 | Cite as

Functional Topology Classification of Biological Computing Networks

  • Pablo Blinder
  • Itay Baruchi
  • Vladislav Volman
  • Herbert Levine
  • Danny Baranes
  • Eshel Ben JacobEmail author
Article

Abstract

Current analyses of complex biological networks focus either on their global statistical connectivity properties (e.g. topological path lengths and nodes connectivity ranks) or the statistics of specific local connectivity circuits (motifs). Here we present a different approach – Functional Topology, to enable identification of hidden topological and geometrical fingerprints of biological computing networks that afford their functioning – the form-function fingerprints. To do so we represent the network structure in terms of three matrices: 1. Topological connectivity matrix – each row (i) is the shortest topological path lengths of node i with all other nodes; 2. Topological correlation matrix – the element (i,j) is the correlation between the topological connectivity of nodes (i) and (j); and 3. Weighted graph matrix – in this case the links represent the conductance between nodes that can be simply one over the geometrical length, the synaptic strengths in case of neural networks or other quantity that represents the strengths of the connections. Various methods (e.g. clustering algorithms, random matrix theory, eigenvalues spectrum etc.), can be used to analyze these matrices, here we use the newly developed functional holography approach which is based on clustering of the matrices following their collective normalization. We illustrate the approach by analyzing networks of different topological and geometrical properties: 1. Artificial networks, including – random, regular 4-fold and 5-fold lattice and a tree-like structure; 2. Cultured neural networks: A single network and a network composed of three linked sub-networks; and 3. Model neural network composed of two overlapping sub-networks. Using these special networks, we demonstrate the method’s ability to reveal functional topology features of the networks.

Keywords

connectivity networks functional topology graph theory information processing scale free networks small word networks topological correlations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amaral, LAN, Scala, A, Barthelemy, M, Stanley, HE 2000Classes of small-world networksProceedings of the National Academy of Sciences of the United States of America971114911152CrossRefGoogle Scholar
  2. Ashkenasy, G, Jagasia, R, Yadav, M, Ghadiri, MR 2004Design of a directed molecular networkProceedings of the National Academy of Sciences of the United States of America1011087210877CrossRefGoogle Scholar
  3. Baranes, D, LopezGarcia, JC, Chen, M, Bailey, CH, Kandel, ER 1996Reconstitution of the hippocampal mossy fiber and associational-commissural pathways in a novel dissociated cell culture systemProceedings of the National Academy of Sciences of the United States of America9347064711CrossRefGoogle Scholar
  4. Baruchi I and Ben-Jacob E (2004) Functional holography of recorded neuronal networks activity. Neuroinformatics, 333–352Google Scholar
  5. Baruchi, I, Towle, VL, Ben-Jacob, E 2005Functional holography of complex networks activity – from cultures to the human brainComplexity103851CrossRefGoogle Scholar
  6. Berg, J, Lassig, M 2004Local graph alignment and motif search in biological networksProceedings of the National Academy of Sciences of the United States of America1011468914694CrossRefGoogle Scholar
  7. Cove J, Blinder P, Abi-Jaoude E, Lafreniere-Roula M, Devroye L and Baranes D (2005) Growth of neurites toward neurite-neurtie contact sites increases synaptic clustering and secretion and is regulated by synaptic activity. Cerebral Cortex pp. bhi086Google Scholar
  8. Costa, L, Barbosa, MS, Coupez, V 2004A direct approach to neuronal connectivityPhysica A: Statistical Mechanics and Its Applications341618628MathSciNetGoogle Scholar
  9. Fuente, A, Bing, N, Hoeschele, I, Mendes, P 2004Discovery of meaningful associations in genomic data using partial correlation coefficientsBioinformatics2035653574Google Scholar
  10. Dorogovtsev, SN, Mendes, JFF 2002Evolution of networksAdvances in Physics5110791187CrossRefGoogle Scholar
  11. Eguiluz, VM, Chiavalo, DR, Cecchi, GA, Baliki, M, Apkarian, VA 2005Scale-free brain functional networksPhysical Review Letters94018102Google Scholar
  12. Goldberg, DS, Roth, FP 2003Assessing experimentally derived interactions in a small worldProceedings of the National Academy of Sciences of the United States of America10043724376MathSciNetGoogle Scholar
  13. Gong, P, Leeuwen, C 2004Evolution to a small-world network with chaotic unitsEurophysics Letters67328333CrossRefGoogle Scholar
  14. Hanisch, D, Zien, A, Zimmer, R, Lengauer, T 2002Co-clustering of biological networks and gene expression dataBioinformatics18S145154Google Scholar
  15. Jeong, H, Tombor, B, Albert, R, Oltvai, ZN, Barabasi, AL 2000The large-scale organization of metabolic networksNature407651654Google Scholar
  16. Jia, LC, Sano, M, Lai, PY, Chan, CK 2004Connectivities and synchronous firing in cortical neuronal networksPhysical Review Letters93088101Google Scholar
  17. Kalisman, N, Silberberg, G, Markram, H 2003Deriving physical connectivity from neuronal morphologyBiological Cybernetics88210218CrossRefGoogle Scholar
  18. Kashtan, N, Itzkovitz, S, Milo, R, Alon, U 2004Topological generalizations of network motifsPhysical Review E: Statistical, Nonlinear and Soft Matter Physics70031909Google Scholar
  19. Kavalali, ET, Klingauf, J, Tsien, RW 1999Activity-dependent regulation of synaptic clustering in a hippocampal culture systemProceedings of the National Academy of Sciences of the United States of America961289312900CrossRefGoogle Scholar
  20. Koch, C, Segev, I 2000The role of single neurons in information processingNature Neuroscience311711177Google Scholar
  21. Lago-Fernandes, LF, Huerta, R, Corbacho, F, Siguenza, JA 2000Fast response and temporal coherent oscillations in small-world networksPhysical Review Letters8427582760Google Scholar
  22. Latora, V, Marchiori, M 2003Economic small-world behaviour in weighted networksEuropean Physical Journal B32249263Google Scholar
  23. Lin, YC, Huang, ZH, Jan, IS, Yeh, CC, Wu, HJ, Chou, YC, Chang, YC 2002Development of excitatory synapses in cultured neurons dissociated from the cortices of rat embryos and rat pups at birthJournal of Neuroscience Research67484493CrossRefGoogle Scholar
  24. Liu, G, Tsien, RW 1995Properties of synaptic transmission at single hippocampal synaptic boutonsNature375404408Google Scholar
  25. LopezGarcia, JC, Arancio, O, Kandel, ER, Baranes, D 1996A presynaptic locus for long-term potentiation of elementary synaptic transmission at mossy fiber synapses in cultureProceedings of the National Academy of Sciences of the United States of America9347124717Google Scholar
  26. Mao, BQ, Hamzei-Sichani, F, Aronov, D, Froemke, RC, Yuste, R 2001Dynamics of spontaneous activity in neocortical slicesNeuron32883898CrossRefGoogle Scholar
  27. Milo, R, Shen-Orr, S, Itzkovitz, S, Kashtan, N, Chklovskii, D, Alon, U 2002Network motifs: simple building blocks of complex networksScience298824827CrossRefGoogle Scholar
  28. Morita, S, Oshio, K, Osana, Y, Funabashi, Y, Oka, K, Kawamura, K 2001Geometrical structure of the neuronal network of Caenorhabditis elegansPhysica A298553561CrossRefGoogle Scholar
  29. Netoff, TI, Clewley, R, Arno, S, Keck, T, White, JA 2004Epilepsy in small-world networksJournal of Neuroscience2480758083CrossRefGoogle Scholar
  30. Newman, MEJ 2004Analysis of weighted networksPhysical Review E70056131Google Scholar
  31. Nishikawa, T, Motter, AE, Lai, YC, Hoppensteadt , FC 2002Smallest small-world networkPhysical Review E66046139CrossRefGoogle Scholar
  32. Ormerod, P, Roach, APAP 2004The Medieval inquisition: scale-free networks and the suppression of heresyPhysica A: Statistical Mechanics and its Applications339645652CrossRefMathSciNetGoogle Scholar
  33. Polsky, A, Mel, BW, Schiller, J 2004Computational subunits in thin dendrites of pyramidal cellsNature Neuroscience7621627CrossRefGoogle Scholar
  34. Reka, A, Barabasi, A-L 2002Statistical mechanics of complex networksReviews of Modern Physics744751MathSciNetGoogle Scholar
  35. Rice, JJ, Tu, Y, Stolovitzky, G 2004Reconstructing biological networks using conditional correlation analysisBioinformatics7765773Google Scholar
  36. Scala, A, Amaral, LAN, Barthelemy, M 2001Small-world networks and the conformation space of a short lattice polymer chainEurophysics Letters55594600CrossRefGoogle Scholar
  37. Seaton, KA, Hackett, LMLM 2004Stations, trains and small-world networksPhysica A: Statistical Mechanics and its Applications339635644CrossRefMathSciNetGoogle Scholar
  38. Segev, R, Benveniste, M, Shapira, Y, Ben-Jacob, E 2003Formation of electrical active clusterized neuronal networksPhysical Review Letters90168101CrossRefGoogle Scholar
  39. Segev, R, Shapira, Y, Benveniste, M, Ben-Jacob, E 2001Observations and modeling of synchronized bursting in two-dimensional neural networksPhysical Review E: Statistical, Nonlinear and Soft Matter Physics64011920Google Scholar
  40. Shefi O, Golding I, Segev R, Ben-Yakov E and Ayali A (2002) Morphological characterization of in vitro neuronal networks. Physical Review E 021905Google Scholar
  41. Sytnyk, V, Leshchyns’ka, I, Delling, M, Dityateva, G, Dityatev, A, Schachner, M 2002Neural cell adhesion molecule promotes accumulation of TGN organelles at sites of neuron-to-neuron contactsThe Journal of Cell Biology159649661CrossRefGoogle Scholar
  42. Volman, V, Baruchi, I, Persi, E, Ben-jacob, E 2004Generative modelling of regulated activity in cultured neuronal networksPhysica A: Statistical Mechanics and its Applications335249278CrossRefMathSciNetGoogle Scholar
  43. Volman, V, Baruchi, I, Ben-Jacob, E 2005Manifestation of function-follow-form in cultured neuronal networksPhysical Biology298110CrossRefGoogle Scholar
  44. Watts, DJ, Strogatz, SH 1998Collective dynamics of ‘small-world’ networksNature393440442CrossRefGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Pablo Blinder
    • 1
    • 2
  • Itay Baruchi
    • 3
  • Vladislav Volman
    • 3
  • Herbert Levine
    • 4
  • Danny Baranes
    • 1
    • 2
  • Eshel Ben Jacob
    • 3
    • 4
    Email author
  1. 1.Department of Life SciencesBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.The National Institute for Biotechnology in the NegevBen-Gurion University of the NegevBeer-ShevaIsrael
  3. 3.School of Physics and AstronomyTel Aviv UniversityTel AvivIsrael
  4. 4.Center for Theoretical Biological PhysicsUniversity of CaliforniaSan Diego, La JollaUSA

Personalised recommendations