Methods of Information Geometry in Computational System Biology (Consistency between Chemical and Biological Evolution)

  • Vadim Astakhov
Part of the Methods in Molecular Biology™ book series (MIMB, volume 569)


Interest in simulation of large-scale metabolic networks, species development, and genesis of various diseases requires new simulation techniques to accommodate the high complexity of realistic biological networks. Information geometry and topological formalisms are proposed to analyze information processes. We analyze the complexity of large-scale biological networks as well as transition of the system functionality due to modification in the system architecture, system environment, and system components.

The dynamic core model is developed. The term dynamic core is used to define a set of causally related network functions. Delocalization of dynamic core model provides a mathematical formalism to analyze migration of specific functions in biosystems which undergo structure transition induced by the environment. The term delocalization is used to describe these processes of migration. We constructed a holographic model with self-poetic dynamic cores which preserves functional properties under those transitions. Topological constraints such as Ricci flow and Pfaff dimension were found for statistical manifolds which represent biological networks. These constraints can provide insight on processes of degeneration and recovery which take place in large-scale networks. We would like to suggest that therapies which are able to effectively implement estimated constraints, will successfully adjust biological systems and recover altered functionality. Also, we mathematically formulate the hypothesis that there is a direct consistency between biological and chemical evolution. Any set of causal relations within a biological network has its dual reimplementation in the chemistry of the system environment.

Key words

System biology Metabolic network Biological networks Information geometry Complexity Dynamic systems 


  1. 1.
    Bernhard O. Palsson, System Biology. Cambridge University Press, CambridgeGoogle Scholar
  2. 2.
    Andrei L. Osterman, Tadhg P. Begley, A Subsystems-Based Approach to the Identification of Drug Targets in Bacterial Pathogens. Progress in Drug Research, Vol. 64Google Scholar
  3. 3.
    Anti De Sitter Space and Holography. Edward Witten (
  4. 4.
  5. 5.
    Grisha Perelman (November 11, 2002) “The Entropy Formula for the Ricci Flow and its Geometric Applications”. arXiv:math.DG/0211159Google Scholar
  6. 6.
    Pedro Lauridsen, Ribeiro Renormalization Group Flow in Algebraic Holography
  7. 7.
    Sebastian de Haro, Kostas Skenderis, Sergey N. Solodukhin, Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
  8. 8.
    Sergey N. Solodukhin, Entanglement entropy and the Ricci flow
  9. 9.
    Robert M. Kiehn, (1990) “Topological Torsion, Pfaff Dimension and Coherent Structures”, in: H. K. Moffatt and T. S. Tsinober eds., Topological Fluid Mechanics. Cambridge University Press, Cambridge, 449–458 Google Scholar
  10. 10.
    Gerald Edelman (2006) Theories and Measures of Consciousness: An Extended Framework. 10.1073/pnas.0604347103Google Scholar
  11. 11.
    Giulio Tononi, Olaf Sporns (2003) Measuring Information Integration., BMC Neuroscience, 4:31PubMedCrossRefGoogle Scholar
  12. 12.
    Ilya Prigogine, Dilip Kondepudi (1998) Modern Thermodynamics: From Heat Engines to Dissipative Structures. Wiley, ChichesterGoogle Scholar

Copyright information

© Humana Press, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Vadim Astakhov
    • 1
  1. 1.Biomedical Informatics Research Network Coordination Center, The Center for Research in Biological Systems (CRBS), UCSDLa JollaUSA

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