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Functional Topology Classification of Biological Computing Networks

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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.

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Authors and Affiliations

  1. Department of Life Sciences, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel

    Pablo Blinder & Danny Baranes

  2. The National Institute for Biotechnology in the Negev, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel

    Pablo Blinder & Danny Baranes

  3. School of Physics and Astronomy, Tel Aviv University, 69978, Tel Aviv, Israel

    Itay Baruchi, Vladislav Volman & Eshel Ben Jacob

  4. Center for Theoretical Biological Physics, University of California, San Diego, La Jolla, CA, 92093, USA

    Herbert Levine & Eshel Ben Jacob

Authors
  1. Pablo Blinder
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  2. Itay Baruchi
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  3. Vladislav Volman
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  4. Herbert Levine
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  5. Danny Baranes
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  6. Eshel Ben Jacob
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Correspondence to Eshel Ben Jacob.

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Blinder, P., Baruchi, I., Volman, V. et al. Functional Topology Classification of Biological Computing Networks. Nat Comput 4, 339–361 (2005). https://doi.org/10.1007/s11047-005-3667-6

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  • DOI: https://doi.org/10.1007/s11047-005-3667-6

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