Principal difference between stability and structural stability (robustness) as used in systems biology

Nonlinear Dynamics, Psychology, and Life Sciences

Volumn 11, Issue 4, 2007, Pages 413-433

  Nikolov, Svetoslav ^a,d   Yankulova, Elka ^b   Wolkenhauer, Olaf ^c   Petrov, Valko ^a  

^a BULGARIAN ACADEMY OF SCIENCES   (Bulgaria)

^b UNIVERSITY OF SOFIA   (Bulgaria)

^c UNIVERSITY OF ROSTOCK   (Germany)

^d INSTITUTE OF MECHANICS   (Bulgaria)

Author keywords

Robustness; Stability; Systems biology

Indexed keywords

BIOLOGICAL MODEL; CONFERENCE PAPER; HUMAN; SYSTEMS BIOLOGY;

HUMANS; MODELS, BIOLOGICAL; SYSTEMS BIOLOGY;

EID: 35248896405     PISSN: 10900578     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (80)

1. Allada, R. (2003). Circadian clocks: An tale of two feedback loops. Cell, 112, 284-286.
2. Alligood, K., Sauer, T., & Yorke, J. (1996). Chaos: An introduction to dynamical systems. New York: Springer.
3. Andronov, A., & Pontryagin, L. (1937). Systems grossieres. Dokladi Academii Nauk USSR, 14, 247-251.
4. th ed.). Igevsk: Institute for Computer Investigations.
5. Arnold, V., Afraimovich, V., Iliaschenko, Y., & Shilnikov, L. (1986). Bifurcation theory. Moscow: Nauka.
6. Bachvarov, S. (2001). Mechanics. Part I: Statics and Kinematics. Sofia: Standart Printing House LTD.
7. Bagley, R., & Glass, L. (1996). Counting and classifying attractors in high dimensional dynamical systems. Journal of Theoretical Biology, 183, 269-284.
8. Barkai, N., & Leibier, S. (1997). Robustness in simple biochemical networks. Nature, 387, 913-917.
9. Bloom, J., Labthavikul, S., Otey, C., & Arnold, F. (2006). Protein stability promotes evolvabiliry. Proceedings of the National Academy of Sciences, 103, 5869-5874.
10. st-century biologists. Science, 303, 788-790.
11. Butenin, N., Neimark, Y., & Fufaev, N. (1976). Introduction to the theory of nonlinear oscillations. Moscow: Nauka.
12. Carlson, J., & Doyle, J. (2000). Highly optimized tolerance: robustness and design in complex systems. Physics Review Letters, 84, 2529-2532.
13. Chen, L., & Wang, R. (2004). Dynamics of gene regulatory networks with cell division cycle. Physics Review E, 70, 011909-13.
14. Chetaev, N. (1965). Stability of motion. Moscow: Nauka.
15. Csete, M., & Doyle, J. (2002). Reverse Engineering of Biological Complexity. Science, 295, 1664-1669.
16. Dawes, J., & Tsai, T. (2006). Frequency locking and complex dynamics near a periodically forced robust heteroclinic cycle, Physics Review E, 74, 055201-5(R).
17. Eldar, A., Dorfman, R., Weiss, D., Ashe, H., Shilo, B. & Barkai, N. (2002). Robustness of the BMP morphogen gradient in drosophila embryonic patterning. Nature, 419, 304-308.
18. Elowitz, M., Levine, A., Siggia, E., & Swain, P. (2002). Stochastic Gene Expression in a Single Cell. Science, 297, 1183-1186.
19. Ein-Dor, L., Zuk, O., & Domany, E. (2006). Thousands of simples are needed to generate a robust gene list for predicting outcome in cancer, Proceedings of the National Academy of Sciences, 103, 5923-5928.
20. Endy, D., & Brent, R. (2001). Modelling Cellular behaviour, Nature, 409, 391-396.
21. Fellenberg, M. (2003). Developing integrative bioinformatics systems. Biosilico, 1, 177-183.
22. Freeman, M. (2000). Feedback control of intercellular signalling in development. Nature, 408, 313-319.
23. Friedman, N. (2004). Inferring cellular networks using probabilistic graphical models. Science, 303, 799-806.
24. Fall, C., Marland, E., Wagner, J., & Tyson, J. (2002). Computational cell biology. New York: Springer-Verlag.
25. Glass, L., & Mackey, M. (1988). From clocks to chaos: The rhythms of life, Princeton, NJ: Princeton University Press.
26. Gierer, A., Meinhardt, H. (1972). A theory of biological pattern formation. Kybernetik, 12, 30-39.
27. Guckenheimer, J., & Holmes, P. (1993). Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, New York: Springer-Verlag.
28. Guet, C., Elowitz, M., Hsing, W., & Leibler, S. (2002). Combinatorial synthesis of genetic networks. Science, 296, 1466-1470.
29. Hartwell, L. (2004). Robust interactions. Science, 303, 774-775.
30. Hasty, J., Dolnik, M., Rottschafer, V., & Collins, J. (2002). Synthetic gene network for entraining and amplifying cellular oscillations, Physics Review Letters, 88, 148101-4.
31. Hoffman, A., Levchenko, A., Scott, M., & Baltimore, D. (2002). The IkB-NF-kB signaling module: temporal control and selective gene activation. Science, 298, 1241-1245.
32. Kacser, H., & Burns, J. (1981). The molecular basis of dominance. Genetics, 97, 639-666.
33. Kitano, H. (2002). Systems biology: A brief overview. Science, 295, 1662-1664.
34. Kitano, H. (2004). Biological robustness. Genetics 5, 826-837.
35. Krupa, M. (1997). Robust heteroclinic cycles. Journal of Nonlinear Science, 7, 129-176.
36. Lefschetz, S. (1957). Differential equations: Geometric theory. London: Interscience Publisher LTD.
37. Leontovich, E., & Mayer, A. (1937). On trajectories which definite the qualitative separation of sphere of trajectories. Dokladi Academii Nauk USSR, 14, 251-254.
38. Luscomble, N., Babu, M., Yu, H., Snyder, M., Teichmann, S., & Gerstein, M. (2004). Genomic analysis of regulatory network dynamics reveals large topological changes. Nature, 431, 308-312.
39. Lyapunov, A. (1966). Stability of motion. New York: Academic Press.
40. Malkin, I. (1952). Theory of stability of motion. [Translation Series, Report No. AEC-tr-3352]. Washington, DC: US Atomic Energy Commision.
41. Meinhardt, H. (1994). Biological pattern formation: new observations provide support for theoretical predictions. Bioessays, 16, 627-632.
42. May, R. (2004). Uses and abuses of mathematics in biology. Science, 303, 790-794.
43. Miguez, D., Izus, G., Minuzuri, A. (2006). Robustness and stability of flow-anddiffusion structures, Physics Review E, 73, 016207-13.
44. Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D. & Alou, U. (2002). Network motifs: simple building blocks of complex networks. Science, 298, 824-827.
45. Morohashi, M., Winn, A., Borisuk, M., Bolouri, H., Doyle, J. & Kitano, H. (2002). Robustness as a measure of plausibility in models of biochemical networks. Journal of Theoretical Biology, 216, 19-30.
46. Murray, J. (2002). Mathematical biology, I: An introduction, Third Edition, New York: Springer-Verlag.
47. Neimark, Yu. (1972). Method of point map in the theory of nonlinear oscillations. Moscow: Nauka.
48. Neimark, Yu., & Landa, P. (1992). Stochastic and chaotic oscillations. Dordrecht: Kluwer Academic Publishers.
49. Nikolov, S., Kotev, V., & Petrov, V. (2005a). An alternative approach to investigating a time delay model of JAK-STAT signalling pathway. Comptes rendus de l'Academie Bulgare des Sciences, 58, 889-896.
50. Nikolov, S., Kotev, V., & Petrov, V. (2005b, September). Analysis of dynamic behavior of a time delay model of JAK-STAT signaling pathway. Paper presented to the X National Congress of Theoretical and Applied Mechanics, Varna.
51. Nikolov, S., Yankulova, E., Nikolova, A., & Petrov, V. (2006). Stability and structural stability (robustness) in computational systems biology. Journal of the Bulgarian Academy of Sciences, 69, 21-29.
52. Nikolov, S. (2006a). Structural stability analysis and bifurcation behavior of phase synchronized systems. Engineering Mechanics, 13, 413-423.
53. Nikolov, S. (2006b). Estimating of bifurcations and chaotic behavior in a four-dimensional system. Journal of the Calcutta Mathematical Society, 2, 17-28.
54. Pali, J., & Smale, S. (1969). Structure stability theorems. Mathematics, 13, 145-155.
55. Panchev, S. (2001). Theory of chaos. Sofia: Academic Publisher "prof. Marin Drinov".
56. Petterson, M., Andersson, D., Roth, J., & Berg, O. (2005). The amplification model for adaptive mutation: simulations and analysis. Genetics, 169, 1105-1115.
57. Petrov, V., Georgiev, N., & Nikolova, E. (2005). Computational systems biology of cell signaling. Journal of the Bulgarian Academy of Sciences, 68, 45-51.
58. Poston, T., & Stewart, I. (1978). Catastrophe theory and its applications. London: Pitman.
59. Prill, R., Iglesias, P., & Levchenko, A. (2005). Dynamic properties of network motifs contribute to biological network organization. PLoS Biology, 3, e343.
60. Ravasz, E., Somera, A., Mongru, D., Oltvai, Z., & Barabasi, A. (2002). Hierarchical organization of modularity in metabolic networks. Science, 297, 1551-1555.
61. Sasaki, J., Sasaki, T., Matsumoto, W., Opavsky, A., Cheng, M., et. al. (2001). CD45 is a JAK phosphatase and negative regulates cytokine receptor signaling. Nature, 409, 349-354.
62. Schibler, U. (2003). Liver regeneration clocks on. Science, 302, 234-235.
63. Shilnikov, L. (1969). On a new type of bifurcation of multi-dimensional dynamical systems. Dokladi Academii Nauk USSR, 189, 59-62.
64. Shilnikov, L. (1970). A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type. MathematicalUSSR Sbornik, 81, 92-103.
65. Shilnikov, L., Shilnikov, A., Turaev, D., & Chua, L. (2001). Methods of qualitative theory in nonlinear dynamics, Part II. Singapore: World Scientific.
66. Sonechkin, D. (1984). Stochasticity in the models of general circulation atmosphere. Leningrad: Gidrometeoizdat.
67. Starr, R., Willson, T., Viney, E., Murray, L., Rayner, J., et al. (1997). A family of cytokine-inducible inhibitors of signaling. Nature, 387, 917-921.
68. Stelling, J., Sauer, U., Szallasi, Z., Doyle, F., & Doyle, J. (2004). Robustness of cellular functions. Cell, 118, 675-685.
69. Swameye, I., Muller, T., Timmer, J., Sandra, O., & Klingmuller, U. (2003). Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by databased modeling', Cell Biology, 100, 1028-1033.
70. Tiana, G., Jensen, M., & Sneppen, K. (2002). Time delay as a key to apoptosis induction in the p53 network. European Physical Journal, B29, 135-140.
71. Timmer, J., Muller, T, Swameye, I., Sandra, O., & Klingmuller, U. (2004). Modeling the nonlinear dynamics of cellular signal transduction', International Journal of Bifurcation and Chaos, 14, 2069-2079.
72. Tong, A., Lesage, G., Bader, G., Ding, H., Xu, H., et al. (2004). Global mapping of the yeast genetic interaction networks. Science, 303, 808-813.
73. Turing, A. (1952). The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London, B237, 37-72.
74. Uitni, H. (1969). Peculiarities of map in Euclidian space, Mathematics, 13, 105-123.
75. van Swinderen, B., & Greenspan, R. (2005). Flexibility in a gene network affecting a simple behavior in Drosophila melanogaster, Genetics, 169, 2151-2163.
76. Wagner, A. (2005). Robustness and evolvability in living systems, Princeton NJ: Princeton University Press.
77. Wolkenhauer, O., Sreenath, S., Wellstead, P., Ullah, M., & Cho, K. H. (2005). A systems- and signal-oriented approach to intracellular dynamics. Biochemical Society Transactions, 33, Part 3, 507-515.
78. Waddington, C. (1942). Canalization of development and the inheritance of acquired characters. Nature, 150, 563-565.
79. Wu, F., Zhang, W., & Kusalik, A. (2004). State-space model with time delays for gene regulatory networks. Journal of Biological Systems, 12, 483-500.
80. Zhu, X., Yin, L., Hood, L., & Ao, P. (2004). Robustness, stability and efficiency of phage A. gene regulatory network: dynamical structure analysis. Journal of Bioinformatics and Computaional Biology, 2, 785-819.