Characterizing the Relationship between Steady State and Response Using Analytical Expressions for the Steady States of Mass Action Models

PLoS Computational Biology

Volumn 9, Issue 2, 2013, Pages

  Loriaux, Paul Michael ^a,b,c   Tesler, Glenn ^b   Hoffmann, Alexander ^a,c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c University of California San Diego   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

SIGNAL TRANSDUCTION;

ANALYTICAL EXPRESSIONS; CELLULAR RESPONSE; DIAGNOSTIC MARKERS; KING-ALTMAN METHODS; MASS ACTION MODELS; PARAMETRIC EXPRESSIONS; PROCASPASE; STEADY RESPONSE; STEADY STATE; STEADY-STATE MEASUREMENTS;

CELL DEATH;

BAR PROTEIN; CASPASE 8; DULANERMIN; PROCASPASE 8; TUMOR NECROSIS FACTOR RELATED APOPTOSIS INDUCING LIGAND; UNCLASSIFIED DRUG;

APOPTOSIS; ARTICLE; BIOTRANSFORMATION; CELL DEATH; CELL FUNCTION; CONTROLLED STUDY; DRUG SENSITIVITY; ENZYME ACTIVATION; ENZYME SUBSTRATE; HUMAN; HUMAN CELL; KING ALTMAN METHOD; MASS ACTION; MATHEMATICAL MODEL; PROTEIN EXPRESSION; SIGNAL TRANSDUCTION; STEADY STATE; STOICHIOMETRY; SUBSTITUTION REACTION; VELOCITY;

EID: 84874771424     PISSN: 1553734X     EISSN: 15537358     Source Type: Journal    
DOI: 10.1371/journal.pcbi.1002901     Document Type: Article

References (60)

1. Werner SL, Barken D, Hoffmann A, (2005) Stimulus specificity of gene expression programs determined by temporal control of IKK activity. Science 309: 1857-61.
2. Nakakuki T, Birtwistle MR, Saeki Y, Yumoto N, Ide K, et al. (2010) Ligand-specific c-Fos expression emerges from the spatiotemporal control of ErbB network dynamics. Cell 141: 884-96.
3. Batchelor E, Loewer A, Mock C, Lahav G, (2011) Stimulus-dependent dynamics of p53 in single cells. Molecular Systems Biology 7: 488.
4. Miller-Jensen K, Janes Ka, Wong YL, Griffith LG, Lauffenburger Da, (2006) Adenoviral vector saturates Akt pro-survival signaling and blocks insulin-mediated rescue of tumor necrosis-factorinduced apoptosis. Journal of Cell Science 119: 3788-98.
5. O'Dea EL, Kearns JD, Hoffmann A, (2008) UV as an amplifier rather than inducer of NF-kappaB activity. Molecular Cell 30: 632-41.
6. Spencer SL, Gaudet S, Albeck JG, Burke JM, Sorger PK, (2009) Non-genetic origins of cell-to-cell variability in TRAIL-induced apoptosis. Nature 459: 428-32.
7. Ashkenazi A, Herbst RS, (2008) To kill a tumor cell: the potential of proapoptotic receptor agonists. The Journal of Clinical Investigation 118: 1979-90.
8. Mahalingam D, Oldenhuis CNaM, Szegezdi E, Giles FJ, de Vries EGE, et al. (2011) Targeting TRAIL towards the clinic. Current Drug Targets 12: 2079-90.
9. Niepel M, Spencer SL, Sorger PK, (2009) Non-genetic cell-to-cell variability and the consequences for pharmacology. Current Opinion in Chemical Biology 13: 556-61.
10. Tyson JJ, Chen KC, Novak B, (2003) Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. Current Opinion in Cell Biology 15: 221-31.
11. Goldstein B, Faeder JR, Hlavacek WS, (2004) Mathematical and computational models of immune-receptor signalling. Nature Reviews Immunology 4: 445-56.
12. Cheong R, Hoffmann A, Levchenko A, (2008) Understanding NF-kappaB signaling via mathematical modeling. Molecular Systems Biology 4: 192.
13. Kearns JD, Hoffmann A, (2009) Integrating computational and biochemical studies to explore mechanisms in NF-fkappagB signaling. The Journal of Biological Chemistry 284: 5439-43.
14. Albeck JG, Burke JM, Spencer SL, Lauffenburger DA, Sorger PK, (2008) Modeling a snap-action, variable-delay switch controlling extrinsic cell death. PLoS Biology 6: 2831-52.
15. Monroe JG, (2004) Ligand-independent tonic signaling in B-cell receptor function. Current Opinion in Immunology 16: 288-95.
16. Gough DJ, Messina NL, Clarke CJ, Johnstone RW, Levy DE, (2012) Constitutive Type I Interferon Modulates Homeostatic Balance through Tonic Signaling. Immunity 36: 166-174.
17. Macia J, Regot S, Peeters T, Conde N, Solé R, et al. (2009) Dynamic signaling in the Hog1 MAPK pathway relies on high basal signal transduction. Science Signaling 2: ra13.
18. Artomov M, Kardar M, Chakraborty AK, (2010) Only signaling modules that discriminate sharply between stimulatory and nonstimulatory inputs require basal signaling for fast cellular responses. The Journal of Chemical Physics 133: 105101.
19. Singh DK, Ku CJ, Wichaidit C, Steininger RJ, Wu LF, et al. (2010) Patterns of basal signalling heterogeneity can distinguish cellular populations with different drug sensitivities. Molecular Systems Biology 6: 369.
20. Hoffmann A, Levchenko A, Scott ML, Baltimore D, (2002) The IkappaB-NF-kappaB signalling module: temporal control and selective gene activation. Science 298: 1241-5.
21. King E, Altman C, (1956) A schematic method of deriving the rate laws for enzyme-catalyzed reactions. The Journal of Physical Chemistry 60: 1375-1378.
22. Thomson M, Gunawardena J, (2009) The rational parameterization theorem for multisite posttranslational modification systems. Journal of Theoretical Biology 261: 626-36.
23. Volkenstein M, Goldstein B, (1966) A new method for solving the problems of the stationary kinetics of enzymological reactions. Biochimica et Biophysica Acta 115: 471-477.
24. Cha S, (1968) A simple method for derivation of rate equations for enzyme-catalyzed reactions under the rapid equilibrium assumption or combined assumptions of equilibrium and steady state. The Journal of Biological Chemistry 243: 820-5.
25. Lam CF, Priest DG, (1972) Enzyme kinetics. Systematic generation of valid King-Altman patterns. Biophysical Journal 12: 248-56.
26. Qi F, Dash RK, Han Y, Beard Da, (2009) Generating rate equations for complex enzyme systems by a computer-assisted systematic method. BMC Bioinformatics 10: 238.
27. Dickenstein A, Shiu A, (2011) Chemical Reaction Systems with Toric Steady States. Bulletin of Mathematical Biology pp. 1-29.
28. Feliu E, Knudsen M, Andersen LN, Wiuf C, (2012) An algebraic approach to signaling cascades with N layers. Bulletin of Mathematical Biology 74: 45-72.
29. Feliu E, Wiuf C, (2012) Variable elimination in post-translational modification reaction networks with mass-action kinetics. Journal of Mathematical Biology 66: 281-310.
30. Sreenath SN, Cho KH, Wellstead P, (2008) Modelling the dynamics of signalling pathways. Essays in Biochemistry 45: 1-28.
31. Palsson BO (2006) Systems Biology: Properties of Reconstructed Networks. Cambridge: Cambridge University Press. 334 pp.
32. Oberhardt MA, Chavali AK, Papin JA, (2009) Flux balance analysis: interrogating genome-scale metabolic networks. Methods in Molecular Biology 500: 61-80.
33. Gianchandani EP, Chavali AK, Papin Ja, (2010) The application of ux balance analysis in systems biology. Wiley Interdisciplinary Reviews Systems Biology And Medicine 2: 372-82.
34. Orth JD, Thiele I, Palsson BO, (2010) What is flux balance analysis? Nature Biotechnology 28: 245-8.
35. Famili I, Mahadevan R, Palsson BO, (2005) k-Cone analysis: determining all candidate values for kinetic parameters on a network scale. Biophysical Journal 88: 1616-25.
36. Jamshidi N, Palsson BO, (2008) Formulating genome-scale kinetic models in the post-genome era. Molecular Systems Biology 4: 171.
37. Fromm SJ, Fromm HJ, (1999) A two-step computer-assisted method for deriving steady-state rate equations. Biochemical and Biophysical Research Communications 265: 448-52.
38. Poland D, (1989) King-Altman-Hill diagram method for open systems. The Journal of Physical Chemistry 93: 3605-3612.
39. Cox D, Little J, OShea D (2007) Ideals, Varieties, and Algorithms. Undergraduate Texts in Mathematics. Third edition. New York, NY: Springer New York. 551 pp. doi:10.1007/978-0-387-35651-8. URL http://www.springerlink.com/index/10.1007/978-0-387-35651-8.
40. Manrai AK, Gunawardena J, (2008) The geometry of multisite phosphorylation. Biophysical journal 95: 5533-43.
41. Martínez-Forero I, Peláez-López A, Villoslada P, (2010) Steady state detection of chemical reaction networks using a simplified analytical method. PloS One 5: e10823.
42. Hansen JN, Dinovo EC, Boyer PD, (1969) Initial and equilibrium 18O, 14C, 3H, and 2H exchange rates as probes of the fumarase reaction mechanism. The Journal of Biological Chemistry 244: 6270-9.
43. Mühlenbeck F, Haas E, Schwenzer R, Schubert G, Grell M, et al. (1998) TRAIL/Apo2L activates c-Jun NH2-terminal kinase (JNK) via caspase-dependent and caspase-independent pathways. The Journal of Biological Chemistry 273: 33091-8.
44. Gaudet S, Spencer SL, Chen WW, Sorger PK, (2012) Exploring the Contextual Sensitivity of Factors that Determine Cell-to-Cell Variability in Receptor-Mediated Apoptosis. PLoS Computational Biology 8: e1002482.
45. Schwanhäusser B, Busse D, Li N, Dittmar G, Schuchhardt J, et al. (2011) Global quantification of mammalian gene expression control. Nature 473: 337-42.
46. Zhang L, Fang B, (2005) Mechanisms of resistance to TRAIL-induced apoptosis in cancer. Cancer Gene Therapy 12: 228-37.
47. Zhang H, Xu Q, Krajewski S, Krajewska M, Xie Z, et al. (2000) BAR: An apoptosis regulator at the intersection of caspases and Bcl-2 family proteins. Proceedings of the National Academy of Sciences of the United States of America 97: 2597-602.
48. Eggert A, Grotzer MA, Zuzak TJ, Wiewrodt BR, Ho R, et al. (2001) Resistance to tumor necrosis factor-related apoptosis-inducing ligand (TRAIL)-induced apoptosis in neuroblastoma cells correlates with a loss of caspase-8 expression. Cancer Research 61: 1314-9.
49. Ganten TM, Haas TL, Sykora J, Stahl H, Sprick MR, et al. (2004) Enhanced caspase-8 recruitment to and activation at the DISC is critical for sensitisation of human hepatocellular carcinoma cells to TRAIL-induced apoptosis by chemotherapeutic drugs. Cell Death and Differentiation 11 Suppl 1: S86-96.
50. Schliemann M, Bullinger E, Borchers S, Allgower F, Findeisen R, et al. (2011) Heterogeneity Reduces Sensitivity of Cell Death for TNF-Stimuli. BMC Systems Biology 5: 204.
51. Knudsen M, Feliu E, Wiuf C, (2012) Exact analysis of intrinsic qualitative features of phosphorelays using mathematical models. Journal of Theoretical Biology 300: 7-18.
52. Shinar G, Feinberg M, (2010) Structural sources of robustness in biochemical reaction networks. Science 327: 1389-91.
53. Thomson M, Gunawardena J, (2009) Unlimited multistability in multisite phosphorylation systems. Nature 460: 274-7.
54. Gunawardena J, (2007) Distributivity and processivity in multisite phosphorylation can be distinguished through steady-state invariants. Biophysical Journal 93: 3828-34.
55. Segel LA, (1988) On the validity of the steady state assumption of enzyme kinetics. Bulletin of mathematical biology 50: 579-93.
56. Bailey JE, (2001) Complex biology with no parameters. Nature Biotechnology 19: 503-4.
57. Purvis JE, Radhakrishnan R, Diamond SL, (2009) Steady-state kinetic modeling constrains cellular resting states and dynamic behavior. PLoS Computational Biology 5: e1000298.
58. Chen WW, Schoeberl B, Jasper PJ, Niepel M, Nielsen UB, et al. (2009) Input-output behaviour of ErbB signaling pathways as revealed by a mass action model trained against dynamic data. Molecular Systems Biology 5: 239.
59. Aldridge BB, Gaudet S, Lauffenburger Da, Sorger PK, (2011) Lyapunov exponents and phase diagrams reveal multi-factorial control over TRAIL-induced apoptosis. Molecular Systems Biology 7: 553.
60. Huang CY, Ferrell JE, (1996) Ultrasensitivity in the mitogen-activated protein kinase cascade. Proceedings of the National Academy of Sciences of the United States of America 93: 10078-83.