Formulas for intrinsic noise evaluation in oscillatory genetic networks

Journal of Theoretical Biology

Volumn 267, Issue 2, 2010, Pages 223-234

  Ito, Yohei ^a   Uchida, Kenko ^a  

^a WASEDA UNIVERSITY   (Japan)

Author keywords

Circadian oscillation; Floquet Lyapunov theory; Linear noise approximation

Indexed keywords

CIRCADIAN RHYTHM; COVARIANCE ANALYSIS; GENETIC ANALYSIS; PERIODICITY; REGULATORY APPROACH; SIMULATION; STOCHASTICITY;

AMPLITUDE MODULATION; ARTICLE; CIRCADIAN RHYTHM; CONTROLLED STUDY; GENE EXPRESSION REGULATION; GENE REGULATORY NETWORK; INTERMETHOD COMPARISON; MATHEMATICAL COMPUTING; MONTE CARLO METHOD; OSCILLATION; PLOTS AND CURVES; PRIORITY JOURNAL; PROCESS MODEL; STOCHASTIC MODEL; STRUCTURAL EQUATION MODELING; STRUCTURE ANALYSIS; VALIDITY;

CIRCADIAN RHYTHM; COMPUTER SIMULATION; GENE REGULATORY NETWORKS; HUMANS; MODELS, GENETIC; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 77956372809     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2010.08.025     Document Type: Article

References (22)

1. Anou-Kandil H., Freiling G., Ionescu V., Jank G. Matrix Riccati Equations in Control and Systems Theory 2003, Birkhauser Verlag.
2. Chabot J.R., Pedraza J.M., Luitel P., van Oudenaarden A. Stochastic gene expression out-of-steady-state in the cyanobacterial circadian clock. Nature 2007, 450:1249-1252.
3. Coddington E.A., Levinson N. Theory of Ordinary Differential Equations 1955, McGraw-Hill, (Paperback, McGraw-Hill Education, 1984).
4. Elf J., Ehrenberg M. Fast evaluation of fluctuations in biochemical networks with the linear noise approximation. Genome Res. 2003, 13:2475-2484.
5. Gillespie D.T. Exact stochastic simulations of coupled chemical reactions. J. Phys. Chem. 1997, 81(25):2340-2361.
6. Gillespie D.T. Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 2001, 115:1716-1733.
7. Goldbeter A. A model for circadian oscillations in the Drosophila period protein (PER). Proc. R. Soc. London 1995, B261:319-324.
8. Gonze D., Halloy L., Goldbeter A. Robustness of circadian rhythms with respect to molecular noise. Proc. Natl. Acad. Sci. USA 2002, 99:673-678.
9. Gonze D., Goldbeter A. Circadian rhythms and molecular noise. Chaos 16, 026110 2006, 1-11.
10. Kepler T.B., Elston T.C. Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. Biophys. J. 2001, 81:3116-3136.
11. Lestas I., Paulsson J., Ross N.E., Vinnicombe G. Noise in gene regulatory networks. IEEE Trans. Autom. Control, Special Issue Syst. Biol. 2008, 189-200.
12. Miura S., Shimokawa T., Nomura T. Stochastic simulations on a model of circadian rhythm generation. BioSystems 2008, 93:133-140.
13. Montagnier P., Spiter R.J., Angeles J. The control of linear time-periodic systems using Floquet-Lyapunov theory. Int. J. Control 2004, 77(5):472-490.
14. Ogawa K., Takekawa N., Hinohara T., Uchida K., Shibata S. On robust stability and sensitivity of circadian rhythms. Asian J. Control 2006, 8(3):281-289.
15. Paulsson J. Models of stochastic gene expression. Phys. Life Rev. 2005, 2:157-175.
16. Scott M., Ingalls B., Kaern M. Estimations of intrinsic and extrinsic noise in models of nonlinear genetic networks. Chaos 16, 026107 2006, 1-15.
17. Swain P.S., Elowitz M.B., Siggia E.D. Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc. Natl. Acad. Sci. USA 2002, 99:12795-12800.
18. Thattai M., van Oudenaarden A. Intrinsic noise in gene regulatory networks. Proc. Natl. Acad. Sci. USA 2001, 98:3614-3619.
19. Tian T., Burrage K. Binominal leap methods orsimuling chemical kinetics. J. Chem. Phys. 2004, 121:1035-1036.
20. Tomioka R., Kimura H., Kobayashi T.J., Aihara K. Multivariate analysis of noise in genetic regulatory networks. J. Theor. Biol. 2004, 229:501-521.
21. Tomita K., Ohta T., Tomita H. Irreversible circulation and orbital revolution-hard mode instability in far-from-equilibrium situation. Prog. Theor. Phys. 1974, 52:1744-1765.
22. van Kampen N.G. Stochastic Processes in Physics and Chemistry 1997, Elsevier Science, The Netherlands.