Asymptotic Analysis of a Cell Cycle Model Based on Unequal Division

1987 ◽  
Vol 47 (1) ◽  
pp. 128-145 ◽  
Author(s):  
Ovide Arino ◽  
Marek Kimmel
Keyword(s):  
Cell Cycle ◽  
Asymptotic Analysis ◽  
Cycle Model ◽  
Unequal Division ◽  
Model Based ◽  
A Cell

Analysis of a cell cycle model based on unequal division of metabolic constituents to daughter cells during cytokinesis

1984 ◽  
Vol 110 (4) ◽  
pp. 637-664 ◽  
Author(s):  
Marek Kimmel ◽  
Zbigniew Darzynkiewicz ◽  
Ovide Arino ◽  
Frank Traganos
Keyword(s):  
Cell Cycle ◽  
Cycle Model ◽  
Daughter Cells ◽  
Unequal Division ◽  
Model Based ◽  
A Cell

A Cell Cycle Model Based on the Estrogen-Stimulated Uterus

1984 ◽  
Vol 87 (3/4) ◽  
pp. 151
Author(s):  
Lynn A. Lavia ◽  
Robert W. Kelly ◽  
Daniel K. Roberts
Keyword(s):  
Cell Cycle ◽  
Cycle Model ◽  
Model Based ◽  
A Cell

A cell cycle model and translation semigroups

1997 ◽  
Vol 54 (1) ◽  
pp. 135-153 ◽  
Author(s):  
Larbi Alaoui
Keyword(s):  
Cell Cycle ◽  
Cycle Model ◽  
A Cell ◽  
Translation Semigroups

Simulation of a cell cycle model of slowly growing Eschericha coli cells

1973 ◽  
Vol 13 (2) ◽  
pp. 131-139
Author(s):  
W. A. Knorre ◽  
H. Müller ◽  
Z. Simon
Keyword(s):  
Cell Cycle ◽  
Cycle Model ◽  
A Cell

scholarly journals A Cell Cycle Model for Somitogenesis: Mathematical Formulation and Numerical Simulation

2000 ◽  
Vol 207 (3) ◽  
pp. 305-316 ◽  
Author(s):  
J.R. COLLIER ◽  
D. MCINERNEY ◽  
S. SCHNELL ◽  
P.K. MAINI ◽  
D.J. GAVAGHAN ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Cell Cycle ◽  
Mathematical Formulation ◽  
Cycle Model ◽  
A Cell

On the existence of the stable birth-type distribution in a general branching process cell cycle model with unequal cell division

2001 ◽  
Vol 38 (03) ◽  
pp. 685-695 ◽  
Author(s):  
Marina Alexandersson
Keyword(s):  
Cell Cycle ◽  
Branching Process ◽  
Critical Size ◽  
Birth Size ◽  
Cycle Model ◽  
Frobenius Theorem ◽  
Type Distribution ◽  
A Cell ◽  
Cell Cycle Models ◽  
Birth Type

We use multi-type branching process theory to construct a cell population model, general enough to include a large class of such models, and we use an abstract version of the Perron-Frobenius theorem to prove the existence of the stable birth-type distribution. The generality of the model implies that a stable birth-size distribution exists in most size-structured cell cycle models. By adding the assumption of a critical size that each cell has to pass before division, called the nonoverlapping case, we get an explicit analytical expression for the stable birth-type distribution.

scholarly journals Coupling of proadipocyte growth arrest and differentiation. II. A cell cycle model for the physiological control of cell proliferation.

1982 ◽  
Vol 94 (2) ◽  
pp. 400-405 ◽  
Author(s):  
R E Scott ◽  
B J Hoerl ◽  
J J Wille ◽  
D L Florine ◽  
B R Krawisz ◽  
...  
Keyword(s):  
Cell Cycle ◽  
Cell Proliferation ◽  
Growth Arrest ◽  
Biological Processes ◽  
Cycle Model ◽  
Physiological Control ◽  
Physiological Factors ◽  
Regulatory Processes ◽  
A Cell

Experimental evidence is presented that supports a cell cycle model showing that there are five distinct biological processes involved in proadipocyte differentiation. These include: (a) growth arrest at a distinct state in the G1 phase of the cell cycle; (b) nonterminal differentiation; (c) terminal differentiation; (d) loss of the differentiated phenotype; and (e) reinitiation of cell proliferation. Each of these events is shown to be regulated by specific human plasma components or other physiological factors. At two states designated GD and GD', coupling of growth arrest and differentiation is shown to occur. We propose that these mechanisms for the coupling of growth arrest and differentiation are physiologically significant and mimic the regulatory processes that control stem cell proliferation in vivo.

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