TY - JOUR
T1 - Asymptotic limit in a cell differentiation model with consideration of transcription
AU - Friedman, Avner
AU - Kao, Chiu Yen
AU - Shih, Chih-Wen
PY - 2012/5/15
Y1 - 2012/5/15
N2 - T cells of the immune system, upon maturation, differentiate into either Th1 or Th2 cells that have different functions. The decision to which cell type to differentiate depends on the concentrations of transcription factors T-bet (x 1) and GATA-3 (x 2). These factors are translated by the mRNA whose levels of expression, y 1 and y 2, depend, respectively, on x 1 and x 2 in a nonlinear nonlocal way. The population density of T cells, φ(t, x 1, x 2, y 1, y 2), satisfies a hyperbolic conservation law with coefficients depending nonlinearly and nonlocally on (t, x 1, x 2, y 1, y 2), while the x i, y i satisfy a system of ordinary differential equations. We study the long time behavior of φ and show, under some conditions on the parameters of the system of differential equations, that the gene expressions in the T-cell population aggregate at one, two or four points, which connect to various cell differentiation scenarios.
AB - T cells of the immune system, upon maturation, differentiate into either Th1 or Th2 cells that have different functions. The decision to which cell type to differentiate depends on the concentrations of transcription factors T-bet (x 1) and GATA-3 (x 2). These factors are translated by the mRNA whose levels of expression, y 1 and y 2, depend, respectively, on x 1 and x 2 in a nonlinear nonlocal way. The population density of T cells, φ(t, x 1, x 2, y 1, y 2), satisfies a hyperbolic conservation law with coefficients depending nonlinearly and nonlocally on (t, x 1, x 2, y 1, y 2), while the x i, y i satisfy a system of ordinary differential equations. We study the long time behavior of φ and show, under some conditions on the parameters of the system of differential equations, that the gene expressions in the T-cell population aggregate at one, two or four points, which connect to various cell differentiation scenarios.
KW - Cell differentiation
KW - Conservation law
KW - Integro-differential equation
KW - MRNA
KW - Multistationary
KW - Th1/Th2 cells
KW - Transcription factors
UR - http://www.scopus.com/inward/record.url?scp=84858285873&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2012.02.006
DO - 10.1016/j.jde.2012.02.006
M3 - Article
AN - SCOPUS:84858285873
SN - 0022-0396
VL - 252
SP - 5679
EP - 5711
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 10
ER -