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Cellular Automata Models of Complex Biochemical Systems

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Complexity in Chemistry, Biology, and Ecology

5. General Summary

The linkage between complex, dynamic systems and cellular automata is made quite clear in this monograph. The dynamic portrayal of many phenomena has been shown to mirror reality in several important ways among the studies described. We aver that cellular automata belongs on the pantheon of methods of probing, modeling and even predicting events associated with complex systems, emerging phenomena and hierarchical patterns.

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References

  1. H. Gutfreund, Kinetics for the Life Sciences: Receptors, Transmitters, and Catalysts, Cambridge University, Cambridge, U.K. (1995).

    Book  Google Scholar 

  2. M. A. Savageau, Biochemical Systems Analysis, Addison-Wesley, Reading, MA (1976).

    MATH  Google Scholar 

  3. D. L. Beveridge and W. L. Jorgensen, Computer Simulation of Chemical and Biomolecular Systems, Vol. 482, Annals of the New York Academy of Sciences, New York (1986).

    Google Scholar 

  4. L. A. Segel (ed.), Biological Kinetics, Cambridge University, Cambridge, UK (1991).

    MATH  Google Scholar 

  5. S. A. Levin (ed.), Frontiers in Mathematical Biology, Springer, Berlin (1994).

    MATH  Google Scholar 

  6. T. M. Witten, Computational Medicine, in Encyclopedia of Computer Science 4th edition, A. Ralston, E. D. Reilly, and D. Hemmendinger (eds.), Macmillan Reference, London and Grove’s Dictionaries, New York (2000).

    Google Scholar 

  7. P.W. Anderson, K. J. Arrow, and D. Pines (eds.), The Economy as an Evolving Complex System, Santa Fe Institute, Studies in the Sciences of Complexity, Addison-Wesley, Redwood City, CA (1988).

    MATH  Google Scholar 

  8. M. S. Townend, Mathematics in Sport. Ellis Horwood, Chichester, UK (1984).

    MATH  Google Scholar 

  9. C. Renfrew and K. L. Cooke, Transformations: Mathematical Approaches to Culture Change, Academic Press, New York (1979).

    MATH  Google Scholar 

  10. A. S. Mikhailov and V. Calenbuhr, From Cells to Societies: Models of Complex Coherent Interaction, Springer, Berlin (2002).

    Google Scholar 

  11. W. Sulis and A. Combs, Nonlinear Dynamics in Human Behavior, World Scientific, Singapore (1996).

    MATH  Google Scholar 

  12. T. M. Witten, Bull. Math. Biol. 42, 267–272 (1980).

    MathSciNet  Google Scholar 

  13. T. M. Witten, Bull. Math. Biol. 44, 572–584 (1982).

    Google Scholar 

  14. TM Witten, Computational Medicine, in: Encyclopedia of Computer Science, 4th ed., A. Ralston, E. D. Reilly, and D. Hemmendinger (eds.), Macmillan Reference, London, UK, and Grove’s Dictionaries, New York (2000).

    Google Scholar 

  15. National Science Foundation. Grand Challenges: High Performance Computing and Communications. The FY 1992 US Research and Development Program (1992).

    Google Scholar 

  16. National Science Foundation. Grand Challenges: High Performance Computing and Communications. The FY 1993 US Research and Development Program (1993).

    Google Scholar 

  17. T. M. Witten, Supercomputing Review 3, 34–40 (1990).

    Google Scholar 

  18. T. M. Witten, Supercomputer, 8, 37–53 (1991).

    Google Scholar 

  19. T. M. Witten, Future Generation Computer Systems 10, 223–232 (1994).

    Article  MathSciNet  Google Scholar 

  20. J. M. Haile, Molecular Dynamics Simulation: Elementary Methods, Wiley, New York (1992).

    Google Scholar 

  21. A. R. Leach, Molecular Modelling: Principles and Applications, Longman, Harlow, UK (1996).

    Google Scholar 

  22. M. P. Allen and D. J. Tildesley, Computer Simulation in Chemical Physics, Kluwer Academic, Boston (1998).

    Google Scholar 

  23. D. J. Tildesley, The Molecular Dynamics Method, In: ibid, p. 23–47.

    Google Scholar 

  24. M. P. Allen, Introduction to Monte Carlo Simulations, in Observation, Prediction and Simulation of Phase Transitions in Complex Fluids, M. Baus, L. F. Rull, J.-P. Ryckaert (eds.), Kluwer Academic, Boston (1995) pp. 339–356.

    Google Scholar 

  25. W. L. Jorgensen, Monte Carlo Simulations for Liquids, in Encyclopedia of Computational Chemistry, P. V. Ragué Schleyer (ed.), Wiley, New York (1998) pp. 1754–1763.

    Google Scholar 

  26. W. L. Jorgensen and J. Tirado-Rives, J. Phys. Chem. 100, 14508–14513 (1996).

    Article  CAS  Google Scholar 

  27. R. K. Belew and Mmitchell (eds.), Adaptive Individuals in Evolving Populations: Models and Algorithms, Santa Fe Institute Studies in the Sciences of Complexity, Addison-Wesley, Reading, MA (1996).

    Google Scholar 

  28. T. F. H. Allen and T. B Starr, Hierarchy: Perspectives for Ecological Complexity, The University of Chicago, Chicago, IL (1982).

    Google Scholar 

  29. S. N. Salthe, Evolving Hierarchical Systems: Their Structure and Representation. Columbia University, New York (1985).

    Google Scholar 

  30. Y. Bar-Yam, Dynamics of Complex Systems. Studies in Nonlinearity. Perseus, Reading, MA (1997).

    Google Scholar 

  31. N. MacDonald, Trees and Networks in Biological Systems. Wiley, Chichester, UK (1983).

    Google Scholar 

  32. N. Rashevsky, Organismic Sets, Clowes and Sons, London, U.K. (1972).

    Google Scholar 

  33. R. Rosen, Bull Math. Biol. 20, 245–260 (1958).

    Google Scholar 

  34. R. Rosen, Bull Math. Biol. 20, 317–341(1958).

    Google Scholar 

  35. R. Rosen, Bull Math. Biol. 21, 109–128 (1959).

    Google Scholar 

  36. R. Rosen, Bull Math. Biol. 27, 11–14 (1965).

    Google Scholar 

  37. T. M. Witten, Mech. Aging and Dev., 27, 323–340 (1984).

    Article  CAS  Google Scholar 

  38. E. H. Davidson, JP Rast, P. Oliveri, Science 295, 1669–1678 (2002).

    Article  PubMed  ADS  CAS  Google Scholar 

  39. R. Satorras-Pastor, E. Smith, and R. V. Sole, J. Theor. Biol. 222, 199–210 (2003).

    Article  CAS  Google Scholar 

  40. E. Ravasz, A. L. Somera, D. A. Mongru, Z. N. Oltvai, and A.-L. Barabasi, Science 297, 1551–1555 (2002).

    Article  PubMed  ADS  CAS  Google Scholar 

  41. A. L. Barabasi and R. Albert, Science 286, 509–512 (1999).

    Article  PubMed  MathSciNet  Google Scholar 

  42. J. M. Montoya and R. V. Sole, J. Theor. Biol. 214, 405–412 (2002).

    Article  PubMed  Google Scholar 

  43. R. Albert and A.-L. Barabasi, Rev. Mod.Phys. 74, 47–97 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  44. J.-P. Eckmann, E. Moses, and D. Sergi, Dialog in E-Mail traffic. E-print archives, http://xxx.aps.org/arXiv:cond-mat/0304433 (2003).

    Google Scholar 

  45. D. Bonchev, Overall Connectivity and Molecular Complexity, in Topological Indices and Related Descriptors, J. Devillers and A. T. Balaban (eds.), Gordon and Breach, Reading, UK (1999) pp. 361–401.

    Google Scholar 

  46. D. Bonchev, The Wiener Number. Some Applications and New Developments, in Topology in Chemistry. Discrete Mathematics of Molecules, D. H. Rouvray and R. B. King (eds.), Horwood, Chichester, UK (2002) pp. 58–88.

    Google Scholar 

  47. E. Ravesz, A. L. Somera, D. A. Mongru, Z. N. Oltvai, and A.-L. Barabasi, Science 297, 1551–1555 (2002).

    Article  ADS  Google Scholar 

  48. R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Allon, Science 298, 824–827 (2002).

    Article  PubMed  ADS  CAS  Google Scholar 

  49. M. M. Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos. New York, NY, Simon and Schuster (1992).

    Google Scholar 

  50. P. Decker, Spatial, Chiral, and Temporal Self-Organization Through Bifurcation in “Bioids,” Open Systems Capable of a Generalized Darwinian Evolution, in Bifurcation Theory and Applications in Scientific Disciplines, O. Gurel, and O. E. Rossler (eds.), Annals of the New York Academy of Science, New York, NY (1979) Vol. 316.

    Google Scholar 

  51. L. F. Olsen and H. Degn, Nature 267, 177 (1977).

    Article  PubMed  ADS  CAS  Google Scholar 

  52. E. E. Selkov, Eur. J. Biochem. 4, 79 (1967).

    Article  Google Scholar 

  53. B. Hess and T. Plesser, Temporal and Spatial Order in Biochemical Systems, in Bifurcation Theory and Applications in Scientific Disciplines, O. Gurel and O. E. Rossler (eds.), Annals of the New York Academy of Science, New York, NY (1979) Vol. 316.

    Google Scholar 

  54. K. R. Sharma and R. M. Noyes, J. Amer. Chem. Soc. 98, 4345 (1976).

    Article  ADS  CAS  Google Scholar 

  55. G. Nicolis and I. Prigogine, Exploring Complexity: An Introduction. New York, NY, Freeman (1989).

    Google Scholar 

  56. U. S. Bhalla and R. Iyengar, Science 283, 381–387 (1999).

    Article  PubMed  ADS  CAS  Google Scholar 

  57. L. B. Kier, B. Testa and P. A. Carrupt, Med. Res. Rev. 17, 303–326 (1997).

    Article  PubMed  Google Scholar 

  58. B. Testa, and L. B. Kier, Drug Res. 30, 1–14 (1997).

    Article  CAS  Google Scholar 

  59. H. G. Wells, J. S. Huxley, and G. P. Wells, The Science of Life: The Literary Guild, New York (1934) p. 1475.

    Google Scholar 

  60. S. M. Ulam, Proc. Int. Congr. Math. 2, 264 (1952).

    MathSciNet  Google Scholar 

  61. S. M. Ulam, Adventures of a Mathematician, Charles Scribner’s Sons, New York (1976).

    MATH  Google Scholar 

  62. J. von Neumann, Theory of Self-Replicating Automata, A. Burks (ed.), Univ. of Illinois Press, Urbana (1966).

    Google Scholar 

  63. K. Zuse, Int. J. Theoret. Phys 21, 589–600 (1982).

    Article  Google Scholar 

  64. T. Toffoli and N. Margolus, Cellular Automata Machines, MIT Press, Cambridge, MA (1987).

    Google Scholar 

  65. M. Schroeder, Fractals, Chaos, Power Laws,W. H. Freeman, New York (1991) p. 371.

    MATH  Google Scholar 

  66. G. Y. Vichniac, Physica D, 10, 96–116 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  67. T. Toffoli, Physica D, 10, 117–127 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  68. S. Wolfram, Rev. Mod. Phys. 55, 601–644 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  69. L. B. Kier and C. K. Cheng, J. Chem. Inf. Comp. Sci. 34,1334-1337 (1994).

    Google Scholar 

  70. L. B. Kier and C. K. Cheng, Pharm. Res. 12, 1521–1525 (1995).

    Article  PubMed  CAS  Google Scholar 

  71. L. B. Kier and C. K. Cheng, J. Math. Chem., 21, 71–81 (1997).

    Article  CAS  Google Scholar 

  72. L. B. Kier, C. K. Cheng, B. Testa, and P. A. Carrupt, Pharm. Res. 12, 615–620 (1995).

    Article  PubMed  CAS  Google Scholar 

  73. C. K. Cheng and L. B. Kier, J. Chem. Inf. & Comput. Sci. 35, 1054–1059 (1995).

    Article  CAS  Google Scholar 

  74. L. B. Kier and C. K. Cheng, in Lipophilicity in Drug Research, Pliska, Testa, and Waterbeemd (eds.), VCH (1996).

    Google Scholar 

  75. L. B. Kier, C. K. Cheng, B. Testa and P. A. Carrupt, Pharm. Res. 13, 1419–1422 (1996).

    Article  PubMed  CAS  Google Scholar 

  76. L. B. Kier, C. K. Cheng, B. Testa and P. A. Carrupt, J. Pharm. Sci. 86, 774–779 (1997).

    Article  PubMed  CAS  Google Scholar 

  77. L. B. Kier and C. K. Cheng, J. Theor. Biol. 186, 75–80 (1997).

    Article  CAS  Google Scholar 

  78. L. B. Kier, C. K Cheng, M. Tute, and P. G. Seybold, J. Chem. Inf. Comp. Sci. 38, 271–280 (1998).

    Article  CAS  Google Scholar 

  79. L. B. Kier, C. K. Cheng and B. Testa, J. Chem. Inf. Comp. Sci. 39, 326–332 (1999).

    Article  CAS  Google Scholar 

  80. L. B. Kier, C. K. Cheng and B. Testa, Fut. Gen. Comput. Sys. 16, 273–289 (1999).

    Article  Google Scholar 

  81. L. B. Kier, C. K. Cheng and P. Seybold, SAR QSAR Environ. Res. 11, 79–102 (2000).

    Article  PubMed  CAS  Google Scholar 

  82. L. B. Kier, C. K. Cheng and P. Seybold, Rev. Comp. Chem. 17, 205–254 (2001).

    Article  CAS  Google Scholar 

  83. L. B. Kier and C. K. Cheng, J. Chem. Inf. Comp. Sci. 34, 647–652 (1994).

    Article  CAS  Google Scholar 

  84. L. B. Kier, Cheng and B. Testa, J. Theoret. Biol. 214, 415–426 (2002).

    Article  CAS  Google Scholar 

  85. G. R. Welch, Biosystems 38, 147–153 (1996).

    Article  PubMed  CAS  Google Scholar 

  86. G. Adam and M. Delbruck, in Structural Chemistry and Molecular Biology, A. Rich and N. Davidson (eds.), Freeman, San Fransisco (1968).

    Google Scholar 

  87. M. Eigen, in Quantum Statistical Mechanics in the Natural Sciences, S. L. Mintz and S. M. Widemeyer (eds.), Plenum, New York (1974).

    Google Scholar 

  88. G. R. Welch, J. Theoret Biol. 68, 267–271 (1977).

    Article  CAS  Google Scholar 

  89. L. B. Kier and B. Testa, Complexity, 1, 37–41 (1996).

    Google Scholar 

  90. C. H. Waddington, The Strategy of the Genes, George Allen & Urwin Ltd., London, UK (1957).

    Google Scholar 

  91. L. B. Kier, AANA Journal 71, 422–426 (2003).

    PubMed  Google Scholar 

  92. D. Bonchev, Complexity of Protein-Protein Interaction Networks, Complexes and Pathways, in Handbook of Proteomics Methods, M. Conn (ed.), Humana, New York, (2003), pp. 451–462.

    Chapter  Google Scholar 

  93. L. B. Kier, D. Bonchev and G. A. Buck. Chem. & Biodiv., 2, 233–243 (2005).

    Article  Google Scholar 

  94. C. Y. F. Huang and J. E. Ferell, Proc. Natl. Acad. Sci. USA 93, 10078–10083 (1996).

    Article  PubMed  ADS  CAS  Google Scholar 

  95. L. B. Kier, C. K. Cheng, and B. Testa, J. Molec. Graphics 14, 227–231 (1996).

    Article  CAS  Google Scholar 

  96. L. B. Kier and C. K. Cheng, J. Molec. Graphics 18, 29–32 (2000).

    Article  CAS  Google Scholar 

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Kier, L.B., Witten, T.M. (2005). Cellular Automata Models of Complex Biochemical Systems. In: Bonchev, D., Rouvray, D.H. (eds) Complexity in Chemistry, Biology, and Ecology. Springer, Boston, MA. https://doi.org/10.1007/0-387-25871-X_6

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