Asymptotic limit in a cell differentiation model with consideration of transcription

Journal of Differential Equations

Volumn 252, Issue 10, 2012, Pages 5679-5711

  Friedman, Avner ^a   Kao, Chiu Yen ^a,b   Shih, Chih Wen ^c  

^a OHIO STATE UNIVERSITY   (United States)

^b CLAREMONT MCKENNA COLLEGE   (United States)

^c NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

Cell differentiation; Conservation law; Integro differential equation; MRNA; Multistationary; Th1 Th2 cells; Transcription factors

Indexed keywords

EID: 84858285873     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2012.02.006     Document Type: Article

References (10)

1. Aguda B.D., Friedman A. Models of Cellular Regulation 2008, Oxford University Press.
2. Friedman A., Kao C.-Y., Shih C.-W. Asymptotic phases in a cell differentiation model. J. Differential Equations 2009, 247(3):736-769.
3. Gustafsson B., Kreiss H.-O., Oliger J. Time-Dependent Problems and Difference Methods 1995, Wiley-Interscience, New York.
4. Hale J. Ordinary Differential Equations 1980, Robert E. Krieger Publishing Company.
5. Hale J. Asymptotic Behavior of Dissipative Systems. Math. Surveys Monogr. 1988, vol. 25. Amer. Math. Soc., Providence, RI.
6. Hale J., Kocak H. Dynamics and Bifurcations 1991, Springer-Verlag.
7. LeVeque R.J. Numerical Methods for Conservation Laws 1990, Birkhäuser-Verlag, Basel.
8. Magal P., Zhao X.-Q. Global attractors and steady states for uniformly persistent dynamical systems. SIAM J. Math. Anal. 2005, 37(1):251-275.
9. Mariani L., Lohning M., Radbruch A., Hofer T. Transcriptional control networks of cell differentiation: insights from helper T lymphocytes. Biophys. Mol. Biol. 2004, 86:45-76.
10. Yates A., Callard R., Stark J. Combining cytokine signaling with T-bet and GATA-3 regulation in Th1 and Th2 differentiation: a model for cellular decision-making. J. Theoret. Biol. 2004, 231:181-196.