Integration of sensitivity and bifurcation analysis to detect critical processes in a model combining signalling and cell population dynamics

International Journal of Systems Science

Volumn 41, Issue 1, 2010, Pages 81-105

  Nikolov, S ^a   Lai, X ^b   Liebal, U W ^b   Wolkenhauer, O ^b   Vera, J ^b  

^a INSTITUTE OF MECHANICS   (Bulgaria)

^b UNIVERSITY OF ROSTOCK   (Germany)

Author keywords

Bifurcation analysis; Cell population dynamics; Epo; JAK2 STAT5; Sensitivity; Sensitivity analysis; Signalling pathways; Systems biology; Time delay systems

Indexed keywords

BIFURCATION ANALYSIS; CELL POPULATION DYNAMICS; SIGNALLING PATHWAYS; SYSTEMS BIOLOGY; TIME-DELAY SYSTEMS;

BIFURCATION (MATHEMATICS); CELL CULTURE; CELL PROLIFERATION; COORDINATION REACTIONS; DELAY CONTROL SYSTEMS; DYNAMICS; MATHEMATICAL MODELS; POPULATION DYNAMICS; REGRESSION ANALYSIS; TIME DELAY;

SENSITIVITY ANALYSIS;

EID: 77649267923     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207720903147746     Document Type: Article

References (61)

1. Aaronson, D.S., and Horvath, C.M. (2002), 'A Road Map for Those Who Don't Know JAK-STAT', Science, 296(5573), 1653-1655.
2. Adimy, M., and Crauste, F. (2004), 'Stability and Instability Induced by Time Delay in an Erythropoiesis Model', Monografias del Seminario Matematico Garcia de Galdeano, 31, 3-12.
3. Adimy, M., Crauste, F., and Ruan, S. (2006), 'Modelling Hematopoiesis Mediated by Growth Factors with Applications to Periodic Hematological Diseases', Bulletin of Mathematical Biology, 68(8), 2321-2351.
4. Andronov, A., Witt, A., and Chaikin, S. (1966), Theory of Oscillations, Reading. MA: Addison-Wesley.
5. Balsa-Canto, E., Alonso, A.A., and Banga, J.R. (2008), 'Computational Procedures for Optimal Experimental Design in Biological Systems', IET Systems Biology, 2(4), 163-172.
6. Barkai, N., and Leibler, S. (1997), 'Robustness in Simple Biochemical Networks', Nature, 387(6636), 913-917.
7. Bellman, R., and Cooke, K. (1963), Differential-Difference Equations, Academic Press: New York.
8. Bernard, S., Pujo-Menjouet, L., and Mackey, M.C. (2003), 'Analysis of Cell Kinetics Using a Cell Division Marker: Mathematical Modeling of Experimental Data', Biophysical Journal, 84(5), 3414-3424.
9. Chassagnole, C., Jackson, R.C., Hussain, N., Bashir, L., Derow, C., Savin, J., and Fell, D.A. (2006), 'Using a Mammalian Cell Cycle Simulation to Interpret Differential Kinase Inhibition in Anti-Tumour Pharmaceutical Development', Biosystems, 83(2-3), 91-97.
10. Chikkappa, G., Borner, G., Burlington, H., Chanana, A.D., Cronkite, E.P., Ohl, S., Pavelec, M., and Robertson, T.S. (1976), 'Periodic Oscillation of Blood Leukocytes, Platelets and Reticulocytes in a Patient with Chronic Myelocytic Leukemia', Blood, 47, 1023-1030.
11. Colijn, C., and Mackey, M.C. (2005a), 'A Mathematical Model of Hematopoiesis: I. Periodic Chronic Myelogenous Leukemia', Journal of Theoretical Biology, 237(2), 117-132.
12. Colijn, C., and Mackey, M.C. (2005b), 'A Mathematical Model of Hematopoiesis: II. Cyclical Neutropenia', Journal of Theoretical Biology, 237(2), 133-146.
13. Dale, D.C., and Hammond, W.P. (1988), 'Cyclic Neutropenia: A clinical review', Blood Reviews, 2, 178-185.
14. Danø, S., Madsen, M.F., Schmidt, H., and Cedersund, G. (2006), 'Reduction of a Biochemical Model with Preservation of its Basic Dynamic Properties', FEBS Journal, 273(21), 4862-4877.
15. Danø, S., Sorensen, P., and Hynne, F. (1999), 'Sustained Oscillations in Living cells', Nature, 402, 320-322.
16. Elsgolz, L., and Norkin, S. (1974), Introduction to Time Delay Equations, Nauka, Moscow (in Russian).
17. Erbe, L., Kong, Q., and Zhang, B. (1995), Oscillation Theory for Functional Differential Equations, New York: Marcel Dekker.
18. Ermentrout, B. (2002), Simulating, Analyzing, and Animating Dynamical Systems: A Guide to Xppaut for Researchers and Students, Philadelphia, PA: Society for Industrial Mathematics (SIAM).
19. Ferrell Jr, J.E. (2002), 'Self-Perpetuating States in Signal Transduction: Positive Feedback, Double-Negative Feedback and Bistability', Current Opinion in Cell Biology, 14, 140-148.
20. Fisher, J.W. (2003), 'Erythropoietin: Physiology and Pharmacology Update', Experimental Biology and Medicine (Maywood), 228(1), 1-14.
21. Frey, S., Millat, T., Hohmann, S., and Wolkenhauer, O. (2008), 'How Quantitative Measures Unravel Design Principles in Multi-Stage Phosphorylation Cascades', Journal of Theoretical Biology, 254, 27-36.
22. Goldbeter, A. (2007), 'Biological Rhythms as Temporal Dissipative Structures', Advances in Chemical Physics, 135, 253-295.
23. Guckenheimer, J., and Worfolk, P. (1993), 'Dynamical Systems: Some Computational Problems', in Bifurcations and Periodic Orbits of Vector Fields, Dordrecht: NATO ASI Series: Kluwer Academic Publishers, pp. 241-278.
24. Heinrich, R., Neel, B.G., and Rapoport, T.A. (2002), 'Mathematical models of protein kinase signal transduction', Molecular Cell, 9(5), 957-970.
25. Heinrich, R., and Schuster, S. (1996), The Regulation of Cellular Systems, New York: Chapman and Hall.
26. Jackson, R.C. (1989), 'The Problem of the Quiescent Cancer Cell', Advances in Enzyme Regulation, 29, 27-46.
27. Jelkmann, W. (2004), 'Molecular Biology of Erythropoietin', Internal Medicine, 43(8), 649-659.
28. Joo, J., Plimpton, S., Martin, S., Swiler, L., and Faulon, J.L. (2007), 'Sensitivity Analysis of a Computational Model of the IKK NF-kappaB IkappaBalpha A20 Signal Transduction Network', Annals of the New York Academy of Sciences, 1115, 221-239.
29. Jordan, J.D., Landau, E.M., and Iyengar, R. (2000), 'Signaling Networks: The Origins of Cellular Multitasking', Cell., 103(2), 193-200.
30. Khan, Q., and Greenhagh, D. (1999), 'Hopf Bifurcation in Epidemic Models with a Time Delay in Vaccination', IMA Journal of Mathematics Applied in Medicine and Biology, 16, 113-142.
31. Kholodenko, B.N. (2006), 'Cell-Signalling Dynamics in Time and Space', Nature Reviews Molecular Cell Biology, 7(3), 165-176.
32. Kisseleva, T., Bhattacharya, S., Braunstein, J., and Schindler, C.W. (2002), 'Signaling through the JAK/STAT Pathway, Recent Advances and Future Challenges', Gene, 285, 1-24.
33. Kitano, H. (2003), 'Cancer Robustness: Tumour Tactics', Nature, 426, 125.
34. Kitano, H. (2004), 'Biological Robustness', Nature Reviews Genetics, 5, 826-837.
35. Kopelman, R. (1988), 'Fractal Reaction Kinetics', Science, 241(4873), 1620-1626.
36. Lewis, R.S., and Ward, A.C. (2008), 'Stat5 as a Diagnostic Marker for Leukemia', Expert Review of Molecular Diagnostics, 8(1), 73-82.
37. Mackey, M.C. (1978), 'Unified Hypothesis for the Origin of Aplastic Anemia and Periodic Hematopoiesis', Blood, 51(5), 941-956.
38. Mahaffy, J.M., Belair, J., and Mackey, M.C. (1998), 'Hematopoietic Model with Moving Boundary Condition and State Dependent Delay: Applications in Erythropoiesis', Journal of Theoretical Biology, 190, 135-146.
39. Marsden, J., and McCracken, M. (1976), The Hopf Bifurcation and its Applications, New York: Springer-Verlag.
40. Nikolov, S. (2006), 'Estimating of Bifurcations and Chaotic Behavior in a Four-Dimensional System', Journal of the Calcutta Mathematical Society, 2(1), 17-28.
41. Nikolov, S. (2008), 'Stability and Bifurcation Behavior of Genetic Regulatory Systems with Two Delays', Comptes rendus de l'Academie Bulgare des Sciences, 61(5), 585-594.
42. Nikolov, S., Vera, J., Rath, O., Kolch, W., and Wolkenhauer, O. (2008), 'The Role of Inhibitory Proteins as Modulators of Oscillations in NFB Signalling', IET Systems Biology, 3(2), 59-76.
43. Nikolov, S., Vera, J., Kotev, V., Wolkenhauer, O., and Petrov, V. (2008), 'Dynamic Properties of a Delayed Protein Cross Talk Model', Biosystems, 91, 51-68.
44. Nová k, B., and Tyson, J.J. (2008), 'Design Principles of Biochemical Oscillators', Nature Reviews Molecular Cell Biology, 9(12), 981-991.
45. Orr, J.S., Kirk, J., Gray, K.G., and Anderson, J.R. (1968), 'A Study of the Interdependence of Red Cell and Bone Marrow Stem Cell Populations', British Journal of Haematology, 15, 23-34.
46. Pujo-Menjouet, L., and Mackey, M.C. (2004), 'Contribution to the Study of Periodic Chronic Myelogenous Leukemia', Comptes Rendus Biologies, 327(3), 235-244.
47. Savageau, M.A. (1998), 'Development of fractal kinetic theory for enzyme-catalysed reactions and implications for the design of biochemical pathways', Biosystems, 47(1-2), 9-36.
48. Schmidt, H., and Jirstrand, M. (2006) Systems Biology Toolbox for MATLAB: A Computational Platform for Research in Systems Biology, Bioinformatics, 22(4), 514-515 (www.sbtoolbox2.org).
49. Shilnikov, L., Shilnikov, A., Turaev, D., and Chua, L. (2001), Methods of Qualitative Theory in Nonlinear Dynamics, Part II, Singapore: World Scientific.
50. Swameye, I., Muller, T.G., Timmer, J., Sandra, O., and Klingmuller, U. (2003), 'Identification of Nucleocytoplasmic Cycling as a Remote Sensor in Cellular Signaling by Databased Modeling', in Proceedings of the National Academy of Sciences USA, 100(3), 1028-1033.
51. Tyson, J.J., Chen, K.C., and Novak, B. (2003), 'Sniffers, Buzzers, Toggles and Blinkers: Dynamics of Regulatory and Signaling Pathways in the Cell', Current Opinion in Cell Biology, 15, 221-231.
52. Tyson, J.J., Csikasz-Nagy, A., and Novak, B. (2002), 'The Dynamics of Cell Cycle Regulation', Bioessays, 24(12), 1095-1109.
53. Varma, A., Morbidelli, M., and Wu, H. (1999), Parametric Sensitivity in Chemical Systems, New York: Cambridge University Press.
54. Vera, J., Balsa-Canto, E., Wellstead, P., Banga, J.R., and Wolkenhauer, O. (2007b), 'Power-Law Models of Signal Transduction Pathways', Cellular Signalling, 19, 1531-1541.
55. Vera, J., Bachmann, J., Pfeifer, A.C., Becker, V., Hormiga, J., Torres Darias, N.V., Timmer, J., Klingmuller, U., and Wolkenhauer, O. (2008), 'A Systems Biology Approach to Analyse Amplification in the JAK2-STAT5 Signalling Pathway', BMC Systems Biology, 2, 38.
56. Vera, J., Curto, R., Cascante, M., and Torres, N.V. (2007a), 'Detection of Potential Enzyme Targets by Metabolic Modelling and Optimization: Application to a Simple Enzymopathy', Bioinformatics, 23(17), 2281-2289.
57. Vera, J., and Wolkenhauer, O. (2008), 'A System Biology Approach to Understand Functional Activity of Cell Communication Systems', Methods in Nano Cell Biology, 90, pp. 399-415.
58. Wang, Z., Gao, H., Cao, J., and Liu, X. (2008a), 'On Delayed Genetic Regulatory Networks with Polytopic Uncertainties: Robust Stability Analysis', IEEE Transactions on NanoBioscience, 7(2), 154-163. (Pubitemid 351835963)
59. Wang, Z., Lam, J., Wei, G., Fraser, K., and Liu, X. (2008b), 'Filtering for Nonlinear Genetic Regulatory Networks with Stochastic Disturbances', IEEE Transactions on Automatic Control, (ISSN 0018-9286), 53(10), 2448-2457.
60. Wolkenhauer, O. (2007), 'Defining Systems Biology: An Engineering Perspective', IET Systems Biology, 1(4), 1-4.
61. Yue, H., Brown, M., Knowles, J., Wang, H., Broomhead, D.S., and Kell, D.B. (2006), 'Insights into the Behaviour of Systems Biology Models from Dynamic Sensitivity and Identifiability Analysis: A Case Study of an NF-kappaB Signalling Pathway', Molecular BioSystems, 2(12), 640-649.