Some results for general cell-size-dependent branching processes

1973 ◽  
Vol 10 (2) ◽  
pp. 289-298 ◽  
Author(s):  
Aidan Sudbury ◽  
Peter Clifford
Keyword(s):  
Growth Rate ◽  
Cell Size ◽  
Wide Class ◽  
General Model ◽  
Branching Processes ◽  
Size Dependent ◽  
Sister Cells

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.

Some results for general cell-size-dependent branching processes

1973 ◽  
Vol 10 (02) ◽  
pp. 289-298
Author(s):  
Aidan Sudbury ◽  
Peter Clifford
Keyword(s):  
Growth Rate ◽  
Cell Size ◽  
Wide Class ◽  
General Model ◽  
Branching Processes ◽  
Size Dependent ◽  
Sister Cells

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.

scholarly journals On the Extinction of a Class of Population-Size-Dependent Bisexual Branching Processes

2005 ◽  
Vol 42 (01) ◽  
pp. 175-184 ◽  
Author(s):  
Yongsheng Xing ◽  
Yongjin Wang
Keyword(s):  
Growth Rate ◽  
Population Size ◽  
Branching Processes ◽  
Suitable Condition ◽  
Size Dependent ◽  
Offspring Distribution ◽  
Bisexual Branching Processes ◽  
The Law ◽  
Mating Unit

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.

scholarly journals Hybrid systems approach to modeling stochastic dynamics of cell size

2016 ◽  
Author(s):  
Cesar Augusto Vargas-Garcia ◽  
Abhyudai Singh
Keyword(s):  
Growth Rate ◽  
Cell Size ◽  
Size Variation ◽  
Model Parameters ◽  
Constant Growth Rate ◽  
Division Rate ◽  
Size Dependent ◽  
Daughter Cells ◽  
Constant Growth ◽  
Over Time

A ubiquitous feature of all living cells is their growth over time followed by division into two daughter cells. How a population of genetically identical cells maintains size homeostasis, i.e., a narrow distribution of cell size, is an intriguing fundamental problem. We model size using a stochastic hybrid system, where a cell grows exponentially over time and probabilistic division events are triggered at discrete time intervals. Moreover, whenever these events occur, size is randomly partitioned among daughter cells. We first consider a scenario, where a timer (i.e., cell-cycle clock) that measures the time since the last division event regulates cellular growth and the rate of cell division. Analysis reveals that such a timer-driven system cannot achieve size homeostasis, in the sense that, the cell-to-cell size variation grows unboundedly with time. To explore biologically meaningful mechanisms for controlling size we consider three different classes of models: i) a size-dependent growth rate and timer-dependent division rate; ii) a constant growth rate and size-dependent division rate and iii) a constant growth rate and division rate that depends both on the cell size and timer. We show that each of these strategies can potentially achieve bounded intercellular size variation, and derive closed-form expressions for this variation in terms of underlying model parameters. Finally, we discuss how different organisms have adopted the above strategies for maintaining cell size homeostasis.

The linear cell-size-dependent branching process

1972 ◽  
Vol 9 (04) ◽  
pp. 687-696 ◽  
Author(s):  
Peter Clifford ◽  
Aidan Sudbury
Keyword(s):  
Cell Size ◽  
Correlation Coefficient ◽  
Branching Process ◽  
Branching Processes ◽  
Linear Case ◽  
Size Dependent ◽  
Rate Of Growth ◽  
Linear Cell

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.

scholarly journals On the Extinction of a Class of Population-Size-Dependent Bisexual Branching Processes

2005 ◽  
Vol 42 (1) ◽  
pp. 175-184 ◽  
Author(s):  
Yongsheng Xing ◽  
Yongjin Wang
Keyword(s):  
Growth Rate ◽  
Population Size ◽  
Branching Processes ◽  
Suitable Condition ◽  
Size Dependent ◽  
Offspring Distribution ◽  
Bisexual Branching Processes ◽  
The Law ◽  
Mating Unit

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.

The linear cell-size-dependent branching process

1972 ◽  
Vol 9 (4) ◽  
pp. 687-696 ◽  
Author(s):  
Peter Clifford ◽  
Aidan Sudbury
Keyword(s):  
Cell Size ◽  
Correlation Coefficient ◽  
Branching Process ◽  
Branching Processes ◽  
Linear Case ◽  
Size Dependent ◽  
Rate Of Growth ◽  
Linear Cell

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.

Spindle scaling mechanisms

2020 ◽  
Vol 64 (2) ◽  
pp. 383-396
Author(s):  
Lara K. Krüger ◽  
Phong T. Tran
Keyword(s):  
Cell Size ◽  
Spindle Assembly ◽  
Dependent Manner ◽  
Post Translational Modification ◽  
Size Dependent ◽  
A Cell ◽  
Chromosome Separation ◽  
Spindle Elongation ◽  
Protein Gradients ◽  
Spindle Structure

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.

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