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Information Theory in Living Systems, Methods, Applications, and Challenges

Bulletin of Mathematical Biology volume 69, pages 635–657 (2007)Cite this article

Abstract

Living systems are distinguished in nature by their ability to maintain stable, ordered states far from equilibrium. This is despite constant buffeting by thermodynamic forces that, if unopposed, will inevitably increase disorder. Cells maintain a steep transmembrane entropy gradient by continuous application of information that permits cellular components to carry out highly specific tasks that import energy and export entropy. Thus, the study of information storage, flow and utilization is critical for understanding first principles that govern the dynamics of life. Initial biological applications of information theory (IT) used Shannon’s methods to measure the information content in strings of monomers such as genes, RNA, and proteins. Recent work has used bioinformatic and dynamical systems to provide remarkable insights into the topology and dynamics of intracellular information networks. Novel applications of Fisher-, Shannon-, and Kullback–Leibler informations are promoting increased understanding of the mechanisms by which genetic information is converted to work and order. Insights into evolution may be gained by analysis of the the fitness contributions from specific segments of genetic information as well as the optimization process in which the fitness are constrained by the substrate cost for its storage and utilization. Recent IT applications have recognized the possible role of nontraditional information storage structures including lipids and ion gradients as well as information transmission by molecular flux across cell membranes. Many fascinating challenges remain, including defining the intercellular information dynamics of multicellular organisms and the role of disordered information storage and flow in disease.

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References

  • Adami, C., Ofria, C., Collier, T.C., 2000. Evolution of biological complexity. Proc. Natl. Acad. Sci. 97, 4463–4468.

    Article  Google Scholar 

  • Albert, R., Barabasi, A.-L., 2002. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97.

    Article  MathSciNet  Google Scholar 

  • Albert, R., Jeong, H., Barabasi, A.-L., 2000. Error and attack tolerance of complex networks. Nature 406, 378–382.

    Article  Google Scholar 

  • Alberts, B., 1998. The cell as a collection of protein machines:preparing the next generation of molecular biologists. Cell 92, 291–294.

    Article  Google Scholar 

  • Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., Watson, J.D., 1994. Molecular Biology of the Cell. Garland Publishing Inc., New York.

    Google Scholar 

  • Brooks, D.R., Leblond, P.H., Cumming, D.D., 1984. Information and entropy in a simple evolution model. J. Theor. Biol. 109, 77–93.

    MathSciNet  Google Scholar 

  • Callaway, D.S., Hopcraft, J.E., Kleinberg, J.M., Newman, M.E., Strogatz, S.H., 2000. Network robustness and fragility: Percolation on random graphs. Phys. Rev. Lett. 85, 5468–5471.

    Article  Google Scholar 

  • Chamaraux, F., Fache, S., Bruckert, F., Fourcade, B., 2005. Kinetics of cell spreading. Phys. Rev. Lett. 94, 158102–158110.

    Article  Google Scholar 

  • Dehnert, M., Helm, W.E., Hutt, M.-T., 2005. Information theory reveals large-scale synchronization of statistical correlations in eukaryote genomes. Gene 345, 81–90.

    Article  Google Scholar 

  • Dockery, J.D., Keener, J.P., 2001. A mathematical model for quorum sensing in Pseudomonas aeruginosa. Bull. Math. Biol. 63, 95–116.

    Article  Google Scholar 

  • Ebeling, W., Frommel, C., 1998. Entropy and predictability of information carriers. Biosystem 46, 47–55.

    Article  Google Scholar 

  • Eigen, M., Schuster, P., 1977. The hypercycle. A principle of natural self-organization. Part A: Emergence of the hypercycle. Naturwissenschaften 64, 541–565.

    Article  Google Scholar 

  • Fath, B.D., Cabezas, H., Pawlowski, W., 2003. Regime changes in ecological systems: an information theory approach. J. Theor. Biol. 222, 517–530.

    MathSciNet  Google Scholar 

  • Fisher, R.A., 1925. Theory of statistical estimation. Proc. Cambridge Phil. Soc. 22, 700–725.

    MATH  Article  Google Scholar 

  • Fisher, R.A., 1959. Statistical methods and scientific inference, 2nd edition. Oliver and Boyd, London, pp. 1–112

    Google Scholar 

  • Franca-Koh, J., Devreotes, P.N., 2004. Moving forward: Mechanisms of chemoattractant gradient sensing. Physiology 19, 300–308.

    Article  Google Scholar 

  • Frieden, B.R., 2001. Probability, Statistical Optics and Data Testing, 3rd edition. Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • Frieden, B.R., 2004. Science from Fisher Information, 2nd edition. Cambridge University Press, Cambridge, U.K.

    MATH  Google Scholar 

  • Garcia, S.B., Novelli, M., Wright, N.A., 2000. The clonal origin and clonal evolution of epithelial tumors. Int. J. Exp. Path. 81, 89–116.

    Article  Google Scholar 

  • Gatenby, R.A., Frieden, B.R., 2002. Application of information theory and extreme physical information to carcinogenesis. Cancer Res. 62, 3675–3684.

    Google Scholar 

  • Gatenby, R.A., Frieden, B.R., 2005a. Information dynamics in carcinogenesis and tumor growth. Mutat. Res. 568(2), 259–227.

    Google Scholar 

  • Gatenby, R.A., Frieden, B.R., 2005b. The role of non-genomic information in maintaining thermodynamic stability in living systems. Math. Biosci. Eng. 2(1), 43–51.

    MATH  Google Scholar 

  • Gilbert, E.N., 1966. Information theory after 18 years. Science 152, 320–326.

    Article  Google Scholar 

  • Grunenfelder, B., Winzeler, E.A., 2002. Treasures and traps in genome-wide data sets: Case examples from yeast. Nat. Rev. Genet. 3, 653–661.

    Article  Google Scholar 

  • Han, J-D., et al., 2004. Evidence for dynamically organized modularity in the yeast protein-protein interaction network. Nature 430, 88–93.

    Article  Google Scholar 

  • Hariri, A., Weber, B., Olmsted, J., 1990. On the validity of Shannon-information calculations for molecular biological sequences. J. Theor. Biol. 147, 235–254.

    Google Scholar 

  • Jeong, H., et al., 2001. Lethality and centrality in protein networks. Nature 411, 41–45.

    Article  MathSciNet  Google Scholar 

  • Jeong, H., et al., 2000. The large-scale organization of metabolic networks. Nature 407, 651–654.

    Article  Google Scholar 

  • Johnson, H.A., 1970. Information theory in biology after 18 years. Science 168, 1545–1550.

    Article  Google Scholar 

  • Kaiser, D., 2001. Building a multicellular organism. Annu. Rev. Genet. 35, 103–123.

    Article  Google Scholar 

  • Keener, J.P., 2005. A model for length control of flagellar hooks of Salmonella typhimurium. J. Theor. Biol. 234, 263–275.

    Article  MathSciNet  Google Scholar 

  • Kendal, W.S., 1990. The use of information theory to analyze genomic changes in neoplasia. Math. Biosc. 100, 143–159.

    MATH  Article  Google Scholar 

  • Kullback, S., 1959 Information Theory and Statistics. Wiley, New York.

    MATH  Google Scholar 

  • Lahoz-Beltra, R., 1997. Molecular automata assembly: Principles and simulation of bacterial membrane construction. Biosys. 44, 209–229.

    Article  Google Scholar 

  • Li, S., Armstrong, C.M., Bertin, N., et al., 2004. A map of the interactome network of the metazoan C. elegans. Nature 303, 540–543.

    Google Scholar 

  • Loeb, L.A., 2001. A mutator phenotype in cancer. Cancer Res. 61, 3230–3239.

    Google Scholar 

  • Luscombe, N.M., Babu, M.M., Yu, H., Snyder, M., Teichmann, S.A., Gerstein, M., 2004. Genomic analysis of regulatory network dynamics reveals large topological changes. Nature 431, 308–312.

    Article  Google Scholar 

  • Maxwell, J.C., 1880. Theory of Heat, 6th edition. D. Appleton Co., New York.

    Google Scholar 

  • Morowitz, H.J., 1955. Some order-disorder considerations in living systems. Bull. Math. Biophys. 17, 81–86.

    Article  Google Scholar 

  • Morris, J.A., 2001. Information theory: A guide to the investigation of disease. J. Biosci. 26, 15–23.

    Google Scholar 

  • Pierce, J.R., 1980. Information theory and physics, in introduction to information theory. symbols, signals, and noise. 2nd edition. Dover Publications, New York, pp. 184–207.

    Google Scholar 

  • Prigogine, I., 1965. Steady states and entropy production. Physica 31, 719–724.

    MATH  Article  Google Scholar 

  • Reza, F.M., 1961. An Introduction to Information Theory. McGraw-Hill, New York.

    Google Scholar 

  • Schneider, T.D., 2003. Evolution of biological information. Nucleic Acids Res. 28, 2794–2785.

    Article  Google Scholar 

  • Schneider, T.D., 1997. Information content of individual genetic sequences. J. Theor. Biol. 189, 427–441.

    Article  Google Scholar 

  • Schneider, T.D., 1991a. Theory of molecular machines. I. Channel capacity of molecular machines. J. Theor. Biol. 148, 83–123.

    Article  Google Scholar 

  • Schneider, T.D., 1991b. Theory of molecular machines II. Energy dissipation from molecular machines. J. Theor. Biol. 148, 125–137.

    Article  Google Scholar 

  • Schrodinger, E., 1944. What is Life? Cambridge University Press, Cambridge, U.K.

    Google Scholar 

  • Segre, D., Ben-Eli, D., Lancet, D., 2000. Compositional genomes: Prebiotic information transfer in mutually catalytic non-covalent assemblies. Proc. Natl Acad. Sci. 97, 4112–4117.

    Article  Google Scholar 

  • Shannon, C.E., 1948. A mathematical theory of communication. Bell System Tech. J. 27, 379–623.

    MATH  MathSciNet  Google Scholar 

  • Sole, R.V., Deisboeck, T.S., 2004. An error catastrophe in cancer? J. Theor. Biol. 228, 47–54.

    Article  Google Scholar 

  • Strait, B.J., Dewey, T.G., 1996. The Shannon information entropy of protein sequences. J. Biophys. 71, 148–155.

    Article  Google Scholar 

  • Surette, M.G., Miller, M.B., Bassler, B.L., 1999. Quorum sensing in Escherichia coli, Salmonella typhimurium, and Vibrio harveyi: A new family of genes responsible for autoinducer production. Proc. Natl. Acad Sci. 96, 1639–1644.

    Article  Google Scholar 

  • Szilard, L., 1929. On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings. Z. Physik. 53, 840–848.

    Article  Google Scholar 

  • Taga, M.E., Bassler, B.L., 2003. Chemical communication among bacteria. Proc. Natl. Acad. Sci. 100, 14549–14554.

    Article  Google Scholar 

  • Trincher, K.S., 1965. Biology and Information: Elements of Biological Thermodynamics. Consultants Bureau, New York.

  • Ulanowicz, R.E., 2001. Information theory in ecology. Comput. Chem. 25, 393–399.

    Article  Google Scholar 

  • von Mering, C., Krause, R., Snel, B., Cornell, M., Oliver, S.G., Fields, S., Bork, P., 2002. Comparative assessment of large-scale data sets of protein-protein interactions. Nature 417, 399–403.

    Article  Google Scholar 

  • Wagner, A., Fell, D., 2000. Technical Report No. 00-07-041. Santa Fe Inst.

  • Wallace, R., Wallace, R.G., 1998. Information theory, scaling laws and the thermodynamics of evolution. J. Theor. Biol. 192, 545–559.

    Article  Google Scholar 

  • Weiss, O., Jimenez-Montano, M.A., Herzel, H., 2000. Information content of protein sequence. J. Theor. Biol. 206, 379–386.

    Article  Google Scholar 

  • Yeger-Lotem, E., Sattath, S., Kashtan, N., Itzkovitz, S., Milo, R., Pinter, R.Y., Alon, U., Margalit, H., 2004. Network motifs in integrated cellular networks of transcription and protein-protein interactions. Proc. Nat. Acad. Sci. 101, 5934–5939.

    Article  Google Scholar 

  • Yook, S-H., Oltvai, Z.N., Barabasi, A.-L., 2004. Functional and topological characterization of protein interaction networks. Proteomics 4, 928–942.

    Article  Google Scholar 

  • Zhang, L.-H., Dong, Y.-H., 2004. Quorum sensing and signal interference:diverse implications. Mol. Micro. 53, 1563–1571.

    Article  Google Scholar 

  • Zeeberg, B., 2002. Shannon information theoretic computation of synonymous codon usage biases in coding regions of human and mouse genomes. Genome. Res. 1944–1955.

  • Zhao, L., Park, K., Lai, Y.-C., 2004. Attack vulnerability of scale-free networks due to cascading breakdown. Phys. Rev. E. 70, 1–4.

    Google Scholar 

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Affiliations

  1. Department of Radiology, University Medical Center, University of Arizona, 1501 North Campbell Avenue, Tucson, Arizona, 85724, USA

    Robert A. Gatenby

  2. Department of Applied Mathematics, University of Arizona, 1501 North Campbell Avenue, Tucson, Arizona, 85724, USA

    Robert A. Gatenby

  3. Department of Optical Science, University of Arizona, Tucson, Arizona, 85724, USA

    B. Roy Frieden

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  1. Robert A. Gatenby
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  2. B. Roy Frieden
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Correspondence to Robert A. Gatenby.

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Gatenby, R.A., Frieden, B.R. Information Theory in Living Systems, Methods, Applications, and Challenges. Bull. Math. Biol. 69, 635–657 (2007). https://doi.org/10.1007/s11538-006-9141-5

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  • DOI: https://doi.org/10.1007/s11538-006-9141-5

Keywords

  • Information theory
  • Entropy
  • Shannon information