1973 ◽  
Vol 10 (2) ◽  
pp. 289-298 ◽  
Author(s):  
Aidan Sudbury ◽  
Peter Clifford

A general model for the growth and division of cells in which the growth rate and division probability at any instant depend only on their size at that time is introduced. Conditions under which (a) the distribution of cell-size at division converges ergodically, (b) the sizes tend to 0 or ∞, are exhibited, and bounds to the correlation between the sizes at division of sister cells are given in a wide class of cases.


1972 ◽  
Vol 9 (04) ◽  
pp. 687-696 ◽  
Author(s):  
Peter Clifford ◽  
Aidan Sudbury

In this paper is developed a theory of branching processes in which the division probability and rate of growth of cells depend only on their ‘size’ and in which ‘size’ is shared between daughters. Specific results are obtained in a linear case including the calculation of the correlation coefficient for the life spans of sisters.


1973 ◽  
Vol 10 (02) ◽  
pp. 289-298
Author(s):  
Aidan Sudbury ◽  
Peter Clifford

A general model for the growth and division of cells in which the growth rate and division probability at any instant depend only on their size at that time is introduced. Conditions under which (a) the distribution of cell-size at division converges ergodically, (b) the sizes tend to 0 or ∞, are exhibited, and bounds to the correlation between the sizes at division of sister cells are given in a wide class of cases.


1972 ◽  
Vol 9 (4) ◽  
pp. 687-696 ◽  
Author(s):  
Peter Clifford ◽  
Aidan Sudbury

In this paper is developed a theory of branching processes in which the division probability and rate of growth of cells depend only on their ‘size’ and in which ‘size’ is shared between daughters. Specific results are obtained in a linear case including the calculation of the correlation coefficient for the life spans of sisters.


2020 ◽  
Vol 64 (2) ◽  
pp. 383-396
Author(s):  
Lara K. Krüger ◽  
Phong T. Tran

Abstract The mitotic spindle robustly scales with cell size in a plethora of different organisms. During development and throughout evolution, the spindle adjusts to cell size in metazoans and yeast in order to ensure faithful chromosome separation. Spindle adjustment to cell size occurs by the scaling of spindle length, spindle shape and the velocity of spindle assembly and elongation. Different mechanisms, depending on spindle structure and organism, account for these scaling relationships. The limited availability of critical spindle components, protein gradients, sequestration of spindle components, or post-translational modification and differential expression levels have been implicated in the regulation of spindle length and the spindle assembly/elongation velocity in a cell size-dependent manner. In this review, we will discuss the phenomenon and mechanisms of spindle length, spindle shape and spindle elongation velocity scaling with cell size.


2021 ◽  
Author(s):  
Shixuan Liu ◽  
Ceryl Tan ◽  
Chloe Melo-Gavin ◽  
Kevin G. Mark ◽  
Miriam Bracha Ginzberg ◽  
...  

Proliferating animal cells maintain a stable size distribution over generations despite fluctuations in cell growth and division size. This tight control of cell size involves both cell size checkpoints (e.g., delaying cell cycle progression for small cells) and size-dependent compensation in rates of mass accumulation (e.g., slowdown of cellular growth in large cells). We previously identified that the mammalian cell size checkpoint is mediated by a selective activation of the p38 MAPK pathway in small cells. However, mechanisms underlying the size-dependent compensation of cellular growth remain unknown. In this study, we quantified global rates of protein synthesis and degradation in naturally large and small cells, as well as in conditions that trigger a size-dependent compensation in cellular growth. Rates of protein synthesis increase proportionally with cell size in both perturbed and unperturbed conditions, as well as across cell cycle stages. Additionally, large cells exhibit elevated rates of global protein degradation and increased levels of activated proteasomes. Conditions that trigger a large-size-induced slowdown of cellular growth also promote proteasome-mediated global protein degradation, which initiates only after growth rate compensation occurs. Interestingly, the elevated rates of global protein degradation in large cells were disproportionately higher than the increase in size, suggesting activation of protein degradation pathways. Large cells at the G1/S transition show hyperactivated levels of protein degradation, even higher than similarly sized or larger cells in S or G2, coinciding with the timing of the most stringent size control in animal cells. Together, these findings suggest that large cells maintain cell size homeostasis by activating global protein degradation to induce a compensatory slowdown of growth.


1981 ◽  
Vol 18 (01) ◽  
pp. 65-75 ◽  
Author(s):  
Aidan Sudbury

In cell-size-dependent growth the probabilistic rate of division of a cell into daughter-cells and the rate of increase of its size depend on its size. In this paper the expected number of cells in the population at time t is calculated for a variety of models, and it is shown that population growths slower and faster than exponential are both possible. When the cell sizes are bounded conditions are given for exponential growth.


1991 ◽  
Vol 28 (03) ◽  
pp. 512-519 ◽  
Author(s):  
Fima C. Klebaner

Sufficient conditions for survival and extinction of multitype population-size-dependent branching processes in discrete time are obtained. Growth rates are determined on the set of divergence to infinity. The limiting distribution of a properly normalized process can be generalized gamma, normal or degenerate.


2005 ◽  
Vol 42 (01) ◽  
pp. 175-184 ◽  
Author(s):  
Yongsheng Xing ◽  
Yongjin Wang

In this paper, we study a class of bisexual Galton-Watson branching processes in which the law of offspring distribution is dependent on the population size. Under a suitable condition on the offspring distribution, we prove that the limit of mean growth-rate per mating unit exists. Based on this limit, we give a criterion to identify whether the process admits ultimate extinction with probability one.


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