The role of theorem proving in systems biology

Journal of Theoretical Biology

Volumn 300, Issue , 2012, Pages 57-61

  Wolkenhauer, Olaf ^a,b   Shibata, Darryl ^c   Mesarović, Mihajlo D ^d  

^a UNIVERSITY OF ROSTOCK   (Germany)

^b STELLENBOSCH UNIVERSITY   (South Africa)

^c UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^d CASE WESTERN RESERVE UNIVERSITY   (United States)

Author keywords

Dynamical systems theory; Mathematical general systems theory; Multilevel systems; Tissue organization

Indexed keywords

BIOLOGY; CELLULAR AUTOMATON; NUMERICAL MODEL; THEORETICAL STUDY;

ANALYTIC METHOD; ARTICLE; CELLULAR, SUBCELLULAR AND MOLECULAR BIOLOGICAL PHENOMENA AND FUNCTIONS; DOMINANCE THEOREM; MATHEMATICAL GENERAL SYSTEMS THEORY; MATHEMATICAL MODEL; MECHANISTIC MODEL; ORGANIZATIONAL THEORY; PRIORITY JOURNAL; PYTHAGOREAN THEOREM; ROBUSTNESS THEOREM; STABILITY THEOREM; SYSTEMS BIOLOGY; THEORY VALIDATION;

ANIMALS; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; SYSTEMS BIOLOGY; SYSTEMS THEORY;

EID: 84856301558     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2011.12.023     Document Type: Article

References (28)

1. Alon U. An Introduction to Systems Biology, Design Principles of Biological Circuits 2006, Chapman and Hall/CRC.
2. Angeli D., Ferrell J.E., Sontag E.D. Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems. Proc. Natl. Assoc. Sci. 2004, 101(7):1822-1827.
3. Arrow K.J. A difficulty in the concept of social welfare. J. Political Econ. 1950, 58(4):328-346.
4. Arrow K.J. Social Choice and Individual Values 1963, John Wiley & Sons, New York. second ed.
5. Banaji M., Craciun G. Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems. Adv. Appl. Math. 2010, 44(2):168-184.
6. Systems Biology for Signaling Networks 2010, Springer. S. Choi (Ed.).
7. Dayarian A., Chaves M., Sontag E.D., Sengupta A.M. Shape, size, and robustness: feasible regions in the parameter space of biochemical networks. PLoS Comput. Biol. 2009, 5(1):e1000256.
8. Gunawardena J. Biological systems theory. Science 2010, 328:581-582.
9. Hanahan D., Weinberg R.A. The hallmarks of cancer. Science 2000, 100:57-70.
10. Hanahan D., Weinberg R.A. Hallmarks of cancer: the next generation. Cell 2011, 144:646-674.
11. Klipp E., Liebermeister W., Wierling C., Kowald A., Lehrach H., Herwig R. Systems Biology 2009, Wiley-VCH.
12. Kreeger P.K., Lauffenburger D.A. Cancer systems biology: a network modeling perspective. Carcinogenesis 2010, 31(1):2-8.
13. Lander A.D. The edges of understanding. BMC Biol. 2010, 8:40. 10.1186/1741-7007-8-40.
14. Mesarović M., Takahara Y. General Systems Theory: Mathematical Foundations 1975, Academic Press, New York.
15. Mesarović M., Macko D., Takahara Y. Theory of Hierarchical, Multilevel 1970, Systems, Academic Press, New York.
16. Mesarović M., Sreenath S., Keene J. Search for organizing principles: understanding in systems biology. IET Syst. Biol. 2004, 1(1):19-27.
17. Palsson B.O. Systems Biology-Simulation of Dynamic Network States 2011, Cambridge University Press, Cambridge.
18. Pomerening J.R., Sontag E.D., Ferrell J.E. Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2. Nat. Cell Biol. 2003, 5(4):346-351.
19. Russo G., di Bernardo M., Sontag E.D. Global entrainment of transcriptional systems to periodic inputs. PLoS Comput. Biol. 2010, 6(4):e1000739.
20. Soulé C. Graphic requirements for multistationarity. ComPlexUs 2003, 1:123-133.
21. Shinar G., Feinberg M. Structural sources of robustness in biochemical reaction networks. Science 2010, 327(5971):1389-1391.
22. Shinar G., Feinberg M. Design principles for robust biochemical reaction networks. Math. Biosci. 2011, 231:39-48.
23. Sen A.K. Collective Choice and Social Welfare 1979, North-Holland, Amsterdam.
24. Wolkenhauer O., Fell D., De Meyts P., Bluethgen N., Herzel H., Le Novere N., Hoefer T., Schürrle K., van Leeuwen I. SysBioMed report: advancing systems biology for medical application. IET Syst. Biol. 2009, 3(3):131-136.
25. Systems Biology 2008, Portland Press, London. O. Wolkenhauer, P. Wellstead, K.H. Cho (Eds.).
26. Wiggins S. Introduction to Applied Nonlinear Dynamical Systems and Chaos 2003, Springer, New York. second ed.
27. Wolkenhauer O., Shibata O., Mesarović M. A stem cell niche dominance theorem. BMC Syst. Biol. 2011, 5(4). 10.1186/1752-0509-5-4.
28. Wolkenhauer O., Auffray C., Baltrusch S., Blüthgen N., Byrne H., Cascante M., Ciliberto A., Dale T., Drasdo D., Fell D., Ferrell J.E., Gallahan D., Gatenby R., Günther U., Harms B.D., Herzel H., Junghanss C., Kunz M., Leeuwen I.v., Lenormand P., Levi F., Linnebacher M., Lowengrub J., Maini P.K., Malik A., Rateitschak K., Samsom O., Schäfer R., Schürrle K., Sers C., Schnell S., Shibata D., Tyson J., Vera J., White M., Zhivotovsky B., Jaster R. Systems biologists seek fuller integration of systems biology approaches in new cancer research programs. Cancer Res. 2009, 70(1):12-13.