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Impact of individual nodes in Boolean network dynamics Fakhteh Ghanbarnejad, Konstantin Klemm Bioinformatics group, Universitt Leipzig, Germany arXiv:1111.5334v1 Dresden, May 2012 Impact of individual nodes in Boolean network dynamics P.

  1. Impact of individual nodes in Boolean network dynamics Fakhteh Ghanbarnejad, Konstantin Klemm Bioinformatics group, Universität Leipzig, Germany arXiv:1111.5334v1 Dresden, May 2012

  2. Impact of individual nodes in Boolean network dynamics P. Oliveri, E. H. Davidson Current Opinion in Genetics & Development - 2004

  3. Regulatory Dynamics M.H. Jensen, K. Sneppen, G. Tiana, FEBS Letters 541, 176 (2003)

  4. Regulatory Dynamics  parameters: production delay, production rates, binding threshold, characteristic degradation times Hes1 & rna  six parameters for a single gene  larger systems?!!!

  5. Discrete Abstract Model  ON/Off States  Interactions Network  Dynamics (time evolution of states): Logical Operators

  6. Attractors A A A B C B C B C A A ABC 00 011 A B C B C 01 011 10 011 B C 11 100 A A A B C B C B C

  7. Activity & Sensitivity F F F F 00 0 F 0 10 F 2 00 1 F 0 10 F 0 01 0 F 1 11 F 3 01 0 F 1 11 F 3 10 1 F 2 00 F 0 10 1 F 2 00 F 2 11 1 F 3 01 F 1 11 1 F 3 01 F 1

  8. Impact of individual nodes in Boolean network dynamics Short term Long term Fakhteh Ghanbarnejad, Konstantin Klemm arXiv:1111.5334v1

  9. Computing the dynamical impact of nodes nand 0 0 1 0 0 1 1 1 1 0 0 and and 1 0 1 0 1 0 0 Flip: 0  1 1 1 1  0 0 0 1 1

  10. Variation of dynamical impact across nodes in random Boolean networks

  11. Predicting of dynamical impact • Why ? S. Bornholdt. Science Vol. 310 no. 5747 pp. 449-451

  12. Predicting of dynamical impact • How ? Fakhteh Ghanbarnejad, Konstantin Klemm arXiv:1111.5334v1

  13. Probabilistic description of damage spreading in a Boolean dynamics

  14. Impact of individual nodes in Boolean network dynamics Centrality measures considered as predictors for the dynamical impact Range Adjacency matrix Activity matrix local out-degree strength global eigenvector eigenvector Fakhteh Ghanbarnejad, Konstantin Klemm arXiv:1111.5334v1

  15. Results for random Boolean networks Range Adjacency matrix Activity matrix local out-degree strength global eigenvector eigenvector

  16. Results for random Boolean networks Range Adjacency matrix Activity matrix local out-degree strength global eigenvector eigenvector

  17. More cases • Asynchronous updating • Attractor switching • With small perturbations

  18. fibroblast signal transduction Dynamical impact in a real network T. Helikaret al; PNAS 105, 1913 (2008)

  19. Impact of individual nodes in Boolean network dynamics • Linear algebra • Random Boolean networks • Empirical Boolean networks Range Adjacency matrix Activity matrix local out-degree strength global eigenvector eigenvector Fakhteh Ghanbarnejad, Konstantin Klemm arXiv:1111.5334v1

  20. Thanks! To be continued …

  21. Fakhteh Ghanbarnejad Konstantin Klemm Impact of individual nodes in Boolean network dynamics arXiv:1111.5334v1 Stability of Boolean and continuous dynamics Phys. Rev. Lett. 107.188701

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