The rational parameterisation theorem for multisite post-translational modification systems

Journal of Theoretical Biology

Volumn 261, Issue 4, 2009, Pages 626-636

  Thomson, Matthew ^a   Gunawardena, Jeremy ^b  

^a HARVARD UNIVERSITY   (United States)

^b HARVARD MEDICAL SCHOOL   (United States)

Author keywords

Algebraic geometry; King Altman; Matrix Tree theorem; Multisite PTM; Rational variety; Systems biology

Indexed keywords

CONCENTRATION (COMPOSITION); ENZYME ACTIVITY; GEOMETRY; MATRIX; NUMERICAL METHOD; PARAMETERIZATION; PROTEIN; REACTION KINETICS;

ARTICLE; BIOCHEMISTRY; ENZYME MECHANISM; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MOLECULAR BIOLOGY; PRIORITY JOURNAL; PROTEIN PROCESSING; STEADY STATE; ANIMAL; BIOLOGICAL MODEL; HUMAN; KINETICS; MATHEMATICS; SYSTEMS BIOLOGY;

ANIMALS; HUMANS; KINETICS; MATHEMATICS; MODELS, BIOLOGICAL; PROTEIN PROCESSING, POST-TRANSLATIONAL; SYSTEMS BIOLOGY;

EID: 70350575331     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2009.09.003     Document Type: Article

References (45)

1. Angeli D., Ferrell J.E., and Sontag E.D. Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems. Proc. Natl. Acad. Sci. USA 101 (2004) 1822-1827
2. Christopher C.J., and Lloyd N.G. Polynomial systems: a lower bound for the Hilbert numbers. Proc. Roy. Soc. London A 450 (1995) 219-224
3. Chung, F.R.K., 1997. Spectral graph theory. In: Regional Conference Series in Mathematics, vol. 92. American Mathematical Society, Providence, RI.
4. Ciliberto A., Capuani F., and Tyson J.J. Modeling networks of coupled enzymatic reactions using the total quasi-steady state approximation. PLoS Comput. Biol. 3 (2007) e45
5. Cornish-Bowden A. Fundamentals of Enzyme Kinetics. second ed (1995), Portland Press, London, UK
6. Cox D., Little J., and O'Shea D. Ideals, Varieties and Algorithms. second ed (1997), Springer, Berlin
7. Craciun, G., Dickenstein, A., Shiu, A., Sturmfels, B., 2009. Toric dynamical systems. J. Symbolic Comput. 44, 1551-1565.
8. Craciun G., Tang Y., and Feinberg M. Understanding bistability in complex enzyme-driven reaction networks. Proc. Natl. Acad. Sci. USA 103 (2006) 8697-86102
9. Feinberg, M., 1979. Lectures on Chemical Reaction Networks, Lecture Notes, Mathematics Research Center, University of Wisconsin, 1979. 〈www.che.eng.ohio-state.edu/∼feinberg/research/〉.
10. Ferrarese A., Marin O., Bustos V.H., Venerando A., Antonelli M., Allende J.E., and Pinna L.A. Chemical dissection of the APC Repeat 3 multistep phosphorylation by the concerted action of protein kinases CK1 and GSK3. Biochemistry 46 (2007) 11902-11910
11. Ferrell J.E., and Bhatt R.R. Mechanistic studies of the dual phosphorylation of mitogen-activated protein kinase. J. Biol. Chem. 272 (1997) 19008-19016
12. Fischer E.H. Protein phosphorylation and cellular regulation, II. In: Ringertz N. (Ed). Nobel Lectures, Physiology or Medicine 1991-1995 (1997), World Scientific, Singapore
13. Gatermann K., and Huber B. A family of sparse polynomial systems arising in chemical reaction systems. J. Symbolic Comput. 33 (2002) 273-305
14. Goldbeter A., and Koshland D.E. An amplified sensitivity arising from covalent modification in biological systems. Proc. Natl. Acad. Sci. USA 78 11 (1981) 6840-6844
15. Gunawardena, J., 2003. Chemical Reaction Network Theory for in-silico biologists, Lecture Notes, Harvard University, 2003. 〈vcp.med.harvard.edu/papers/crnt.pdf〉.
16. Gunawardena J. Multisite protein phosphorylation makes a good threshold but can be a poor switch. Proc. Natl. Acad. Sci. USA 102 (2005) 14617-14622
17. Gunawardena J. Distributivity and processivity in multisite phosphorylation can be distinguished through steady-state invariants. Biophys. J. 93 (2007) 3828-3834
18. Gunawardena J. Models in systems biology: the parameter problem and the meanings of robustness. In: Lodhi H., and Muggleton S. (Eds). Elements of Computational Systems Biology. Wiley Book Series on Bioinformatics (2009), Wiley, New York
19. Herstein I. Topics in Algebra (1975), Wiley, New York
20. Hunter T. The age of crosstalk: phosphorylation, ubiquitination and beyond. Mol. Cell 28 (2007) 730-738
21. Jenuwein T., and Allis C.D. Translating the histone code. Science 293 (2001) 1074-1080
22. Kim S.Y., and Ferrell J.E. Substrate competition as a source of ultrasensitivity in the inactivation of Wee1. Cell 128 (2007) 1133-1145
23. King E.L., and Altman C. A schematic method of deriving the rate laws for enzyme-catalyzed reactions. J. Phys. Chem. 60 (1956) 1375-1378
24. Krebs E.G. Protein phosphorylation and cellular regulation, I. In: Ringertz N. (Ed). Nobel Lectures, Physiology or Medicine 1991-1995 (1997), World Scientific, Singapore
25. Kruse J.-P., and Gu W. SnapShot: p53 posttranslational modifications. Cell 133 (2008) 930
26. Lisman J.E. A mechanism for memory storage insensitive to molecular turnover: a bistable autophosphorylating kinase. Proc. Natl. Acad. Sci. USA 82 (1985) 3055-3057
27. Manrai A., and Gunawardena J. The geometry of multisite phosphorylation. Biophys. J. 95 (2008) 5533-5543
28. Markevich N.I., Hoek J.B., and Kholodenko B.N. Signalling switches and bistability arising from multisite phosphorylation in protein kinase cascades. J. Cell Biol. 164 (2004) 353-359
29. Moon, J.W., 1970. Counting labelled trees. In: Canadian Mathematical Monographs, vol. 1. Canadian Mathematical Congress.
30. Nakajima M., Imai K., Ito H., Nishiwaki T., Murayama Y., Iwasaki H., Oyama T., and Kondo T. Reconstitution of circadian oscillation of cyanobacterial KaiC phosphorylation in vitro. Science 308 (2005) 414-415
31. Park K.-S., Mohapatra D.P., Misonou H., and Trimmer J.S. Graded regulation of the Kv2.1 potassium channel by variable phosphorylation. Science 313 (2006) 976-979
32. Pesavento J.J., Bullock C.R., LeDuc R.D., Mizzen C.A., and Kelleher N.L. Combinatorial modification of human histone H4 quantitated by two-dimensional liquid chromatography coupled with top down mass spectrometry. J. Biol. Chem. 283 (2008) 14927-14937
33. Phanstiel D., Brumbaugh J., Berggren W.T., Conrad K., Feng X., Levenstein M.E., McAllister G.C., Thomson J.A., and Coon J.J. Mass spectrometry identifies and quantifies 74 unique histone H4 isoforms in differentiating human embryonic stem cells. Proc. Natl. Acad. Sci. USA 105 (2008) 4093-4098
34. Pufall M.A., Lee G.M., Nelson M.L., Kang H.-S., Velyvis A., Kay L.E., McIntosh L.P., and Graves B.J. Variable control of Ets-1 DNA binding by multiple phosphates in an unstructured region. Science 309 (2005) 142-145
35. Roach P.J. Multisite and hierarchal protein phosphorylation. J. Biol. Chem. 266 (1991) 14139-14142
36. Rust M.J., Markson J.S., Lane W.S., Fisher D.S., and O'Shea E. Ordered phosphorylation governs oscillation of a three-protein circadian clock. Science 318 (2007) 809-812
37. Salazar C., and Höfer T. Versatile regulation of multisite protein phosphorylation by the order of phosphate processing and protein-protein interactions. FEBS J. 274 (2007) 1046-1060
38. Shacter-Noiman E., Chock P.B., and Stadtman E.R. Protein phosphorylation as a regulatory device. Philos. Trans. R. Soc. London B 302 (1983) 157-166
39. Soulé C. Graphic requirements for multistationarity. ComPlexUs 1 (2003) 123-133
40. Strogatz S.H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering (2001), Perseus Books
41. Thomson, M., Gunawardena, J., 2009. Unlimited multistability in multisite phosphorylation systems. Nature 460, 274-277.
42. Turner B. Cellular memory and the histone code. Cell 111 (2002) 285-291
43. Tutte W.T. The dissection of equilateral triangles into equilateral triangles. Proc. Cambridge Philos. Soc. 44 (1948) 463-482
44. Walsh, C.T., 2006. Posttranslational Modification of Proteins. Roberts and Company, Englewood, Colorado.
45. Wu R.C., Qin J., Yi P., Wong J., Tsai S.Y., Tsai M.J., and O'Malley B.W. Selective phosphorylations of the SRC-3/AIB1 coactivator integrate genomic responses to multiple cellular signaling pathways. Mol. Cell 15 (2004) 937-949