Bifurcation phenomena arising in the cell cycle networks
Abstract
Time-dependent regulation by the network of intracellular proteins that leads a cell to its duplication through cell-division can be modeled by nonlinear autonomous coupled ordinary differential equations. Two such models restricted to different phases of the cell cycle are presented. Numerical simulations of these models that represent biological events are addressed. Results of bifurcation analysis performed on these models that leads to two special phenomena, hysteresis and period doubling, are included and the biological significance is discussed.
References
[1]
1. Aguda, B.D. (1999). A quantitative analysis of the kinetics of the G2 DNA damage checkpoint system, Proc. Natl. Acad. Sci. USA, v.96, pp. 11352-11357.
[2]
2. Lev Bar-Or, R, Maya, R, Segel, L.A, Alon, U, Levine, A.J, & Oren, M. (2000). Generation of oscillations by the p53-Mdm2 feedback loop: A theoretical and experimental study, Proc. Natl. Acad. Sci. USA; v.97, pp.11250-11255.
[3]
3. Romond, P.C., Guilmot, J.M, & Goldbeter, A. (1994). The mitotic oscillator: Temporal self-organization in a phosphorylation-dephosphorylationenzymatic cascade, Ber. Bunsenges Phys.Chem.; v. 98, pp. 1152-1159.
[4]
4. Thron, C.D. (1994). Theoretical dynamics of the cyclin B--MPF system: a possible role for p13sucl, BioSys, v. 32, pp. 97-109.
[5]
5. Tyson, J.J, Chen, K, & Novak, B.(2001). Network dynamics in cell physiology. Nature Reviews Molecular Cell Biology, v. 2, pp. 908-916.
[6]
6. Tyson, J.J, & Novak, B. (1999). Regulation of the eukaryotic cell cycle: molecular antagonism, hysteresis, and irreversible transitions, J theor Biol., v. 210, pp. 249-263.
[7]
7. Obeyesekere, M.N, Zimmerman, S.O, Tecarro, E.S, & Auchmuty, G. (1999). A model of cell cycle behavior dominated by kinetics of a pathway stimulated by growth factors, Bull. Math. Biol., v. 61, pp. 917-34.
[8]
8. Hatakeyama, M, Brill, J.A, Fink, G.R, & Weinberg, R.A. (1994). Collaboration of G1 cyclins in the functional inactivation of the retinoblastoma protein, Genes Dev., v. 8, pp. 1759-1771.
[9]
9. Zarkowska,T, & Mittnacht, S. (1997). Differential phosphorylation of the retinoblastoma protein by G1/S cyclin-dependent kinases, J. Biol. Chem., v. 272, pp. 12738-12746.
[10]
10. Campanero, M.R, & Flemington, E.K.(1997). Regulation of E2F through ubiquitin-proteasome-dependent degradation: stabilization by the pRB tumor suppressor protein, Proc. Natl. Acad. Sci. USA, v.94, pp. 2221-2226.
[11]
11. Vandel, L, & Kouzarides, T. (1999). Residues phosphorylated by TFIIH are required for E2F-1 degradation during S-phase, EMBO, v. 18, pp. 4280-4291.
[12]
12. Doedel, E.J, Champneys, A.R, Fairgrieve, T.F, Kuznetsov, Y.A, Sandstede, B, & Wang X. (1997). AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont).
[13]
13. Hale, J. K, & Kocak, H. (1991). Dynamics and bifurcation, Springer-Verlag, New York.
[14]
14. Ohtsubo, M, Theodoras, A.M, Schumacher, J, Roberts, J.M, & Pagano, M. (1995). Human cyclin E, a nuclear protein essential for the G1-to-S phase transition., Mol. Cell. Biol., v. 15, pp. 2612-2624.
[15]
15. Goodrich, D.W, Wang, N.P, Qian, Y.W, Lee, E.Y, & Lee W.H. (1991). The retinoblastoma gene product regulates progression through the G1 phase of the cell cycle, Cell, v. 67, pp. 293-302.
[16]
16. Templeton, D.J, Park, S.H, Lanier, L, & Weinberg, R.A. (1991). Nonfunctional mutants of the retinoblastoma protein arc characterized by defects in phosphorylation, viral oncoprotein association, and nuclear tethering, Proc. Natl. Acad. Sci. USA, v. 88, pp.3033-3037.
[17]
17. Qin, X.Q, Chittenden, T, Livingston, D.M, & Kaelin, W.G. Jr., (1992). Identification of a growth suppression domain within the retinoblastoma gcne product, Genes Dev., v. 6, pp. 953-964.
[18]
18. Hinds, P. W, Mittnacht, S, Dulic, V, Arnold, A, Reed, S. I, & Weinberg, R. A. (1992). Regulation of retinoblastoma protein functions by ectopic expression of human cyclins, Cell, v.70, pp. 993-1006.
[19]
19. Qin, X.Q, Livingston, D.M, Ewen, M., Sellers, W.R, Arany, Z., & Kaelin, W.G. Jr. (1995). The transcription factor E2F-1 is a downstream target of RB action, Mol. Cel. Biol., v. 15, pp. 742-755.
[20]
20. Bai, S, Goodrich, D, Thron, C. D, Tecarro, E, and Obeyesekere, M.N. (2003). Theoretical and experimental evidence for hysteresis in cell proliferation, Cell Cycle, v. 2; pp. 38-44.
Index Terms
- Bifurcation phenomena arising in the cell cycle networks
Recommendations
Codimension two bifurcations of discrete Bonhoeffer–van der Pol oscillator model
AbstractThe non-degeneracy is one of the conditions to check for bifurcation analysis. Therefore, we need to compute the critical normal form coefficients to verify the non-degeneracy of the listed bifurcations. Using the critical normal form coefficients ...
Codimension 2 bifurcation of twisted double homoclinic loops
A local active coordinates approach is employed to obtain bifurcation equations of twisted double homoclinic loops. Under the condition of one twisted orbit, we obtain the existence and uniqueness and of the 1-1 double homoclinic loop, 2-1 double ...
Two-parameter bifurcation analysis of firing activities in the Chay neuronal model
The parameter regions for different firing patterns in the Chay neuronal model are presented and classified by using both two-parameter bifurcations and fast-slow dynamics analysis. Firing arises via a supercritical Hopf bifurcation of the whole system ...
Comments
Information & Contributors
Information
Published In
Publisher
Dynamic Publishers, Inc.
United States
Publication History
Published: 01 September 2003
Author Tags
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 04 Feb 2025