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.

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

2001 ◽  
Vol 38 (3) ◽  
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.

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

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

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

scholarly journals Characterizing non-exponential growth and bimodal cell size distributions in Schizosaccharomyces pombe: an analytical approach

2021 ◽  
Author(s):  
Chen Jia ◽  
Abhyudai Singh ◽  
Ramon Grima
Keyword(s):  
Cell Cycle ◽  
Fission Yeast ◽  
Cell Size ◽  
Control Strategy ◽  
Size Control ◽  
Birth Size ◽  
Size Distributions ◽  
Cell Size Distribution ◽  
A Cell ◽  
Cell Size Control

Unlike many single-celled organisms, the growth of fission yeast cells within a cell cycle is not exponential. It is rather characterized by three distinct phases (elongation, septation and fission), each with a different growth rate. Experiments also show that the distribution of cell size in a lineage is often bimodal, unlike the unimodal distributions measured for the bacterium Escherichia coli. Here we construct a detailed stochastic model of cell size dynamics in fission yeast. The theory leads to analytic expressions for the cell size and the birth size distributions, and explains the origin of bimodality seen in experiments. In particular our theory shows that the left peak in the bimodal distribution is associated with cells in the elongation phase while the right peak is due to cells in the septation and fission phases. We show that the size control strategy, the variability in the added size during a cell cycle and the fraction of time spent in each of the three cell growth phases have a strong bearing on the shape of the cell size distribution. Furthermore we infer all the parameters of our model by matching the theoretical cell size and birth size distributions to those from experimental single cell time-course data for seven different growth conditions. Our method provides a much more accurate means of determining the cell size control strategy (timer, adder or sizer) than the standard method based on the slope of the best linear fit between the birth and division sizes. We also show that the variability in added size and the strength of cell size control of fission yeast depend weakly on the temperature but strongly on the culture medium.

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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