The asymptotic behaviour of an invasion process

1977 ◽  
Vol 14 (3) ◽  
pp. 584-590 ◽  
Author(s):  
F. P. Kelly

Black and white cells are positioned at the vertices of a rectangular lattice. When a cell division occurs, the daughter cells are of the same colour as the parent cell; one of them replaces an adjacent cell and the other remains in the position of the parent cell. In one variant of the model it is assumed that whenever a white cell appears at the origin it is transformed into a black cell; apart from this the black and white cells are equally competitive and in particular they divide at the same rate. Initially, only the cell at the origin is black. The asymptotic behaviour of the black clone is investigated.

1977 ◽  
Vol 14 (03) ◽  
pp. 584-590 ◽  
Author(s):  
F. P. Kelly

Black and white cells are positioned at the vertices of a rectangular lattice. When a cell division occurs, the daughter cells are of the same colour as the parent cell; one of them replaces an adjacent cell and the other remains in the position of the parent cell. In one variant of the model it is assumed that whenever a white cell appears at the origin it is transformed into a black cell; apart from this the black and white cells are equally competitive and in particular they divide at the same rate. Initially, only the cell at the origin is black. The asymptotic behaviour of the black clone is investigated.


1981 ◽  
Vol 18 (03) ◽  
pp. 732-737
Author(s):  
D. Y. Downham ◽  
S. B. Fotopoulos

Normal and abnormal cells are positioned at the vertices of a regular two-dimensional lattice. Abnormal cells divide k times as fast as normal cells. Whenever a cell divides, the daughter is the same type as the parent and replaces an adjacent cell. The Kolmogorov forwards and backwards equations are derived, and then used to obtain bounds for the distribution function of the time when all the abnormal cells are forced from the plane. These bounds are used to comment on the non-asymptotic variance of the number of abnormal cells at a given time and on a method of estimating k.


1981 ◽  
Vol 18 (3) ◽  
pp. 732-737 ◽  
Author(s):  
D. Y. Downham ◽  
S. B. Fotopoulos

Normal and abnormal cells are positioned at the vertices of a regular two-dimensional lattice. Abnormal cells divide k times as fast as normal cells. Whenever a cell divides, the daughter is the same type as the parent and replaces an adjacent cell. The Kolmogorov forwards and backwards equations are derived, and then used to obtain bounds for the distribution function of the time when all the abnormal cells are forced from the plane. These bounds are used to comment on the non-asymptotic variance of the number of abnormal cells at a given time and on a method of estimating k.


2010 ◽  
Vol 192 (16) ◽  
pp. 4134-4142 ◽  
Author(s):  
Jennifer R. Juarez ◽  
William Margolin

ABSTRACT The Min system regulates the positioning of the cell division site in many bacteria. In Escherichia coli, MinD migrates rapidly from one cell pole to the other. In conjunction with MinC, MinD helps to prevent unwanted FtsZ rings from assembling at the poles and to stabilize their positioning at midcell. Using time-lapse microscopy of growing and dividing cells expressing a gfp-minD fusion, we show that green fluorescent protein (GFP)-MinD often paused at midcell in addition to at the poles, and the frequency of midcell pausing increased as cells grew longer and cell division approached. At later stages of septum formation, GFP-MinD often paused specifically on only one side of the septum, followed by migration to the other side of the septum or to a cell pole. About the time of septum closure, this irregular pattern often switched to a transient double pole-to-pole oscillation in the daughter cells, which ultimately became a stable double oscillation. The splitting of a single MinD zone into two depends on the developing septum and is a potential mechanism to explain how MinD is distributed equitably to both daughter cells. Septal pausing of GFP-MinD did not require MinC, suggesting that MinC-FtsZ interactions do not drive MinD-septal interactions, and instead MinD recognizes a specific geometric, lipid, and/or protein target at the developing septum. Finally, we observed regular end-to-end oscillation over very short distances along the long axes of minicells, supporting the importance of geometry in MinD localization.


Development ◽  
1993 ◽  
Vol 118 (4) ◽  
pp. 1267-1277 ◽  
Author(s):  
B. Goldstein

The gut of C. elegans derives from all the progeny of the E blastomere, a cell of the eight cell stage. Previous work has shown that gut specification requires an induction during the four cell stage (Goldstein, B. (1992) Nature 357, 255–257). Blastomere isolation and recombination experiments were done to determine which parts of the embryo can respond to gut induction. Normally only the posterior side of the EMS blastomere contacts the inducing cell, P2. When P2 was instead placed in a random position on an isolated EMS, gut consistently differentiated from the daughter of EMS contacting P2, indicating that any side of EMS can respond to gut induction. Additionally, moving P2 around to the opposite side of EMS in an otherwise intact embryo caused EMS's two daughter cells to switch lineage timings, and gut to differentiate from the descendents of what normally would be the MS blastomere. The other cells of the four cell stage, ABa, ABp, and P2, did not form gut when placed in contact with the inducer. To determine whether any other inductions are involved in gut specification, timed blastomere isolations were done at the two and eight cell stages. In the absence of cell contact at the two cell stage, segregation of gut fate proceeded normally at both the two and four cell stages. Gut fate also segregated properly in the absence of cell contact at the eight cell stage. A model is presented for the roles of lineage-dependent mechanisms and cell interactions in establishing gut fate in the E lineage.


Cells ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 271 ◽  
Author(s):  
Roberta Fraschini

The duplication cycle is the fascinating process that, starting from a cell, results in the formation of two daughter cells and it is essential for life. Cytokinesis is the final step of the cell cycle, it is a very complex phase, and is a concert of forces, remodeling, trafficking, and cell signaling. All of the steps of cell division must be properly coordinated with each other to faithfully segregate the genetic material and this task is fundamental for generating viable cells. Given the importance of this process, molecular pathways and proteins that are involved in cytokinesis are conserved from yeast to humans. In this review, we describe symmetric and asymmetric cell division in animal cell and in a model organism, budding yeast. In addition, we illustrate the surveillance mechanisms that ensure a proper cell division and discuss the connections with normal cell proliferation and organs development and with the occurrence of human diseases.


PLoS ONE ◽  
2020 ◽  
Vol 15 (11) ◽  
pp. e0242547
Author(s):  
Tim Lijster ◽  
Christoffer Åberg

Several previous studies have shown that when a cell that has taken up nanoparticles divides, the nanoparticles are inherited by the two daughter cells in an asymmetrical fashion, with one daughter cell receiving more nanoparticles than the other. This interesting observation is typically demonstrated either indirectly using mathematical modelling of high-throughput experimental data or more directly by imaging individual cells as they divide. Here we suggest that measurements of the coefficient of variation (standard deviation over mean) of the number of nanoparticles per cell over the cell population is another means of assessing the degree of asymmetry. Using simulations of an evolving cell population, we show that the coefficient of variation is sensitive to the degree of asymmetry and note its characteristic evolution in time. As the coefficient of variation is readily measurable using high-throughput techniques, this should allow a more rapid experimental assessment of the degree of asymmetry.


2016 ◽  
Author(s):  
Mohammad Soltani ◽  
Abhyudai Singh

AbstractExpression of many genes varies as a cell transitions through different cell-cycle stages. How coupling between stochastic expression and cell cycle impacts cell-to-cell variability (noise) in the level of protein is not well understood. We analyze a model, where a stable protein is synthesized in random bursts, and the frequency with which bursts occur varies within the cell cycle. Formulas quantifying the extent of fluctuations in the protein copy number are derived and decomposed into components arising from the cell cycle and stochastic processes. The latter stochastic component represents contributions from bursty expression and errors incurred during partitioning of molecules between daughter cells. These formulas reveal an interesting trade-off: cell-cycle dependencies that amplify the noise contribution from bursty expression also attenuate the contribution from partitioning errors. We investigate existence of optimum strategies for coupling expression to the cell cycle that minimize the stochastic component. Intriguingly, results show that a zero production rate throughout the cell cycle, with expression only occurring just before cell division minimizes noise from bursty expression for a fixed mean protein level. In contrast, the optimal strategy in the case of partitioning errors is to make the protein just after cell division. We provide examples of regulatory proteins that are expressed only towards the end of cell cycle, and argue that such strategies enhance robustness of cell-cycle decisions to the intrinsic stochasticity of gene expression.


mBio ◽  
2017 ◽  
Vol 8 (6) ◽  
Author(s):  
Sónia Castanheira ◽  
Juan J. Cestero ◽  
Gadea Rico-Pérez ◽  
Pablo García ◽  
Felipe Cava ◽  
...  

ABSTRACT Bacterial cell division has been studied extensively under laboratory conditions. Despite being a key event in the bacterial cell cycle, cell division has not been explored in vivo in bacterial pathogens interacting with their hosts. We discovered in Salmonella enterica serovar Typhimurium a gene absent in nonpathogenic bacteria and encoding a peptidoglycan synthase with 63% identity to penicillin-binding protein 3 (PBP3). PBP3 is an essential cell division-specific peptidoglycan synthase that builds the septum required to separate daughter cells. Since S. Typhimurium carries genes that encode a PBP3 paralog—which we named PBP3SAL—and PBP3, we hypothesized that there are different cell division events in host and nonhost environments. To test this, we generated S. Typhimurium isogenic mutants lacking PBP3SAL or the hitherto considered essential PBP3. While PBP3 alone promotes cell division under all conditions tested, the mutant producing only PBP3SAL proliferates under acidic conditions (pH ≤ 5.8) but does not divide at neutral pH. PBP3SAL production is tightly regulated with increased levels as bacteria grow in media acidified up to pH 4.0 and in intracellular bacteria infecting eukaryotic cells. PBP3SAL activity is also strictly dependent on acidic pH, as shown by beta-lactam antibiotic binding assays. Live-cell imaging microscopy revealed that PBP3SAL alone is sufficient for S. Typhimurium to divide within phagosomes of the eukaryotic cell. Additionally, we detected much larger amounts of PBP3SAL than those of PBP3 in vivo in bacteria colonizing mouse target organs. Therefore, PBP3SAL evolved in S. Typhimurium as a specialized peptidoglycan synthase promoting cell division in the acidic intraphagosomal environment. IMPORTANCE During bacterial cell division, daughter cells separate by a transversal structure known as the division septum. The septum is a continuum of the cell wall and therefore is composed of membrane(s) and a peptidoglycan layer. To date, actively growing bacteria were reported to have only a “cell division-specific” peptidoglycan synthase required for the last steps of septum formation and consequently, essential for bacterial life. Here, we discovered that Salmonella enterica has two peptidoglycan synthases capable of synthesizing the division septum. One of these enzymes, PBP3SAL, is present only in bacterial pathogens and evolved in Salmonella to function exclusively in acidic environments. PBP3SAL is used preferentially by Salmonella to promote cell division in vivo in mouse target organs and inside acidified phagosomes. Our data challenge the concept of only one essential cell division-specific peptidoglycan synthase and demonstrate that pathogens can divide in defined host locations using alternative mechanisms. IMPORTANCE During bacterial cell division, daughter cells separate by a transversal structure known as the division septum. The septum is a continuum of the cell wall and therefore is composed of membrane(s) and a peptidoglycan layer. To date, actively growing bacteria were reported to have only a “cell division-specific” peptidoglycan synthase required for the last steps of septum formation and consequently, essential for bacterial life. Here, we discovered that Salmonella enterica has two peptidoglycan synthases capable of synthesizing the division septum. One of these enzymes, PBP3SAL, is present only in bacterial pathogens and evolved in Salmonella to function exclusively in acidic environments. PBP3SAL is used preferentially by Salmonella to promote cell division in vivo in mouse target organs and inside acidified phagosomes. Our data challenge the concept of only one essential cell division-specific peptidoglycan synthase and demonstrate that pathogens can divide in defined host locations using alternative mechanisms.


Author(s):  
Gerard A. Ateshian ◽  
Kevin D. Costa ◽  
Evren U. Azeloglu ◽  
Barclay Morrison ◽  
Clark T. Hung

A framework is formulated for continuum modeling of biological tissue growth that explicitly addresses cell division, using a homogenized representation of cells and the extracellular matrix (ECM). The essential elements of this model rely on the description of the cell as containing a solution of water and osmolytes, and having osmotically inactive solid constituents that may be generically described as a porous solid matrix. The division of a cell into two nearly identical daughter cells normally starts with the duplication of cell contents during the synthesis phase, followed by cell division during the mitosis phase. Thus, ultimately, cell division is equivalent to doubling of the cell solid matrix and osmolyte content, and a resulting increase in water uptake via osmotic effects. In a homogenized representation of the tissue, the geometry of individual cells is not modeled explicitly, but their solid matrix and intracellular osmolyte content can be suitably incorporated into the analysis of the tissue response, thereby accounting for their osmotic effects. Thus, cell division can be described by the growth of these cell constituents, including the accumulation of osmotically active content, and the resultant uptake of water.


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