scholarly journals A Multi-stage Representation of Cell Proliferation as a Markov Process

2017 ◽  
Vol 79 (12) ◽  
pp. 2905-2928 ◽  
Author(s):  
Christian A. Yates ◽  
Matthew J. Ford ◽  
Richard L. Mort
Keyword(s):  
Cell Cycle ◽  
Cell Proliferation ◽  
Markov Process ◽  
Cycle Time ◽  
Time Distribution ◽  
Cellular Proliferation ◽  
Gillespie Algorithm ◽  
Biological Processes ◽  
Cell Cycle Time ◽  
Gillespie’S Algorithm

Abstract The stochastic simulation algorithm commonly known as Gillespie’s algorithm (originally derived for modelling well-mixed systems of chemical reactions) is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well-mixed scenarios at the sub-cellular level it is often reasonable to assume that times between successive reaction/interaction events are exponentially distributed and can be appropriately modelled as a Markov process and hence simulated by the Gillespie algorithm. However, Gillespie’s algorithm is routinely applied to model biological systems for which it was never intended. In particular, processes in which cell proliferation is important (e.g. embryonic development, cancer formation) should not be simulated naively using the Gillespie algorithm since the history-dependent nature of the cell cycle breaks the Markov process. The variance in experimentally measured cell cycle times is far less than in an exponential cell cycle time distribution with the same mean. Here we suggest a method of modelling the cell cycle that restores the memoryless property to the system and is therefore consistent with simulation via the Gillespie algorithm. By breaking the cell cycle into a number of independent exponentially distributed stages, we can restore the Markov property at the same time as more accurately approximating the appropriate cell cycle time distributions. The consequences of our revised mathematical model are explored analytically as far as possible. We demonstrate the importance of employing the correct cell cycle time distribution by recapitulating the results from two models incorporating cellular proliferation (one spatial and one non-spatial) and demonstrating that changing the cell cycle time distribution makes quantitative and qualitative differences to the outcome of the models. Our adaptation will allow modellers and experimentalists alike to appropriately represent cellular proliferation—vital to the accurate modelling of many biological processes—whilst still being able to take advantage of the power and efficiency of the popular Gillespie algorithm.

scholarly journals A multi-stage representation of cell proliferation as a Markov process

2017 ◽  
Author(s):  
Christian A. Yates ◽  
Matthew J. Ford ◽  
Richard L. Mort
Keyword(s):  
Cell Cycle ◽  
Cell Proliferation ◽  
Markov Process ◽  
Cycle Time ◽  
Time Distribution ◽  
Cellular Proliferation ◽  
Gillespie Algorithm ◽  
Biological Processes ◽  
Cell Cycle Time ◽  
Gillespie’S Algorithm

AbstractThe stochastic simulation algorithm commonly known as Gillespie’s algorithm (originally derived for modelling well-mixed systems of chemical reactions) is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well mixed scenarios at the sub-cellular level it is often reasonable to assume that times between successive reaction/interaction events are exponentially distributed and can be appropriately modelled as a Markov process and hence simulated by the Gillespie algorithm. However, Gillespie’s algorithm is routinely applied to model biological systems for which it was never intended. In particular, processes in which cell proliferation is important (e.g. embryonic development, cancer formation) should not be simulated naively using the Gillespie algorithm since the history-dependent nature of the cell cycle breaks the Markov process. The variance in experimentally measured cell cycle times is far less than in an exponential cell cycle time distribution with the same mean.Here we suggest a method of modelling the cell cycle that restores the memoryless property to the system and is therefore consistent with simulation via the Gillespie algorithm. By breaking the cell cycle into a number of independent exponentially distributed stages we can restore the Markov property at the same time as more accurately approximating the appropriate cell cycle time distributions. The consequences of our revised mathematical model are explored analytically as far as possible. We demonstrate the importance of employing the correct cell cycle time distribution by recapitulating the results from two models incorporating cellular proliferation (one spatial and one non-spatial) and demonstrating that changing the cell cycle time distribution makes quantitative and qualitative differences to the outcome of the models. Our adaptation will allow modellers and experimentalists alike to appropriately represent cellular proliferation - vital to the accurate modelling of many biological processes - whilst still being able to take advantage of the power and efficiency of the popular Gillespie algorithm.

CHANGES IN CELL PROLIFERATION RATE IN MOUSE UTERINE EPITHELIUM DURING CONTINUOUS OESTROGEN TREATMENT

1974 ◽  
Vol 61 (1) ◽  
pp. 117-121 ◽  
Author(s):  
AUDREY E. LEE ◽  
L. A. ROGERS ◽  
GAIL TRINDER
Keyword(s):  
Cell Cycle ◽  
Cell Proliferation ◽  
Dna Synthesis ◽  
Mitotic Index ◽  
Cycle Time ◽  
Luminal Epithelium ◽  
Cell Cycle Time ◽  
Oestrogen Treatment ◽  
Probability Of Transition ◽  
The Mean

SUMMARY Fraction of labelled mitoses (FLM) curves were constructed for mouse uterine luminal epithelium during oestradiol treatment; on day 2 when mitosis was high, and on days 4 and 9 when mitosis was low. No difference was found between the duration of DNA synthesis on these 3 days. The distance between the first and second peaks, usually taken as an estimate of the mean cell cycle time, did not change significantly between days 2 and 4, although the labelling index fell from 38 to 8%. The second peaks of the FLM curves became progressively lower on the three days examined, which was consistent with the interpretation that there was a reduction in the probability of transition of cells from G1 (the post-mitotic period) into the replicative phase of the cell cycle, resulting in the observed fall in mitotic index.

scholarly journals Connexin 37 profoundly slows cell cycle progression in rat insulinoma cells

2008 ◽  
Vol 295 (5) ◽  
pp. C1103-C1112 ◽  
Author(s):  
Janis M. Burt ◽  
Tasha K. Nelson ◽  
Alexander M. Simon ◽  
Jennifer S. Fang
Keyword(s):  
Cell Cycle ◽  
Cell Proliferation ◽  
Cycle Time ◽  
Cell Cycle Progression ◽  
Serum Deprivation ◽  
Cell Cycle Time ◽  
Cycle Progression ◽  
Suppressive Function ◽  
Connexin 37 ◽  
Rat Insulinoma

In addition to providing a pathway for intercellular communication, the gap junction-forming proteins, connexins, can serve a growth-suppressive function that is both connexin and cell-type specific. To assess its potential growth-suppressive function, we stably introduced connexin 37 (Cx37) into connexin-deficient, tumorigenic rat insulinoma (Rin) cells under the control of an inducible promoter. Proliferation of these iRin37 cells, when induced to express Cx37, was profoundly slowed: cell cycle time increased from 2 to 9 days. Proliferation and cell cycle time of Rin cells expressing Cx40 or Cx43 did not differ from Cx-deficient Rin cells. Cx37 suppressed Rin cell proliferation irrespective of cell density at the time of induced expression and without causing apoptosis. All phases of the cell cycle were prolonged by Cx37 expression, and progression through the G1/S checkpoint was delayed, resulting in accumulation of cells at this point. Serum deprivation augmented the effect of Cx37 to accumulate cells in late G1. Cx43 expression also affected cell cycle progression of Rin cells, but its effects were opposite to Cx37, with decreases in G1 and increases in S-phase cells. These effects of Cx43 were also augmented by serum deprivation. Cx-deficient Rin cells were unaffected by serum deprivation. Our results indicate that Cx37 expression suppresses cell proliferation by significantly increasing cell cycle time by extending all phases of the cell cycle and accumulating cells at the G1/S checkpoint.

Comparison of Multiple Injections with Continuous Infusion of Tritiated Thymidine, and Estimation of the Cell Cycle Time

1969 ◽  
Vol 5 (3) ◽  
pp. 575-582
Author(s):  
W. K. BLENKINSOPP ◽  
C. W. GILBERT
Keyword(s):  
Cell Cycle ◽  
Cell Proliferation ◽  
Continuous Infusion ◽  
Cycle Time ◽  
Squamous Epithelium ◽  
Tritiated Thymidine ◽  
Intraperitoneal Administration ◽  
Cell Cycle Time ◽  
Multiple Injections ◽  
Stratified Squamous Epithelium

Labelled nuclei were counted in stratified squamous epithelium in mice killed after 24 h intraperitoneal administration of tritiated thymidine to label cells synthesizing deoxyribonucleic acid. Multiple injections produced the same result as an infusion of tritiated thymidine given after 24 h infusion of saline, but infusion of tritiated thymidine alone produced a different result. Thus, cell proliferation was depressed during the first 24 h of continuous infusion but was normal during the second 24 h. Comparison of proliferation of the oesophageal epithelium at the level of the thyroid and at the level of the diaphragm showed no difference between the two. Comparison of male with female mice given 72-h infusions of tritiated thymidine showed that cell proliferation occurred at the same rate in both. The cell cycle time was estimated in the epithelium of the oesophagus and tongue by comparison of mice given a single injection with mice given multiple injections of tritiated thymidine.

Nuclear DNA content and minimum generation time in herbaceous plants

1972 ◽  
Vol 181 (1063) ◽  
pp. 109-135 ◽  
Keyword(s):  
Cell Cycle ◽  
Dna Content ◽  
Cycle Time ◽  
Generation Time ◽  
Nuclear Dna ◽  
Nuclear Dna Content ◽  
Annual Species ◽  
Cell Cycle Time ◽  
Developmental Processes ◽  
The Mean

Many components of cell and nuclear size and mass are correlated with nuclear DNA content in plants, as also are the durations and rates of such developmental processes as mitosis and meiosis. It is suggested that the multiple effects of the mass of nuclear DNA which affect all cells and apply throughout the life of the plant can together determine the minimum generation time for each species. The durations of mitosis and of meiosis are both positively correlated with nuclear DNA content and, therefore, species with a short minimum generation time might be expected to have a shorter mean cell cycle time and mean meiotic duration, and a lower mean nuclear DNA content, than species with a long mean minimum generation time. In tests of this hypothesis, using data collated from the literature, it is shown that the mean cell cycle time and the mean meiotic duration in annual species is significantly shorter than in perennial species. Furthermore, the mean nuclear DNA content of annual species is significantly lower than for perennial species both in dicotyledons and monocotyledons. Ephemeral species have a significantly lower mean nuclear DNA content than annual species. Among perennial monocotyledons the mean nuclear DNA content of species which can complete a life cycle within one year (facultative perennials) is significantly lower than the mean nuclear DNA content of those which cannot (obligate perennials). However, the mean nuclear DNA content of facultative perennials does not differ significantly from the mean for annual species. It is suggested that the effects of nuclear DNA content on the duration of developmental processes are most obvious during its determinant stages, and that the largest effects of nuclear DNA mass are expressed at times when development is slowest, for instance, during meiosis or at low temperature. It has been suggested that DNA influences development in two ways, directly through its informational content, and indirectly by the physical-mechanical effects of its mass. The term 'nucleotype' is used to describe those conditions of the nucleus which effect the phenotype independently of the informational content of the DNA. It is suggested that cell cycle time, meiotic duration, and minimum generation time are determined by the nucleotype. In addition, it may be that satellite DNA is significant in its nucleotypic effects on developmental processes.

p27(Kip1) links cell proliferation to morphogenesis in the developing organ of Corti

Development ◽  
1999 ◽  
Vol 126 (8) ◽  
pp. 1581-1590 ◽  
Author(s):  
P. Chen ◽  
N. Segil
Keyword(s):  
Cell Cycle ◽  
Cell Proliferation ◽  
Inner Ear ◽  
Hair Cells ◽  
Cellular Proliferation ◽  
Adult Life ◽  
Organ Of Corti ◽  
Morphological Development ◽  
Supporting Cells ◽  
P27 Kip1

Strict control of cellular proliferation is required to shape the complex structures of the developing embryo. The organ of Corti, the auditory neuroepithelium of the inner ear in mammals, consists of two types of terminally differentiated mechanosensory hair cells and at least four types of supporting cells arrayed precisely along the length of the spiral cochlea. In mice, the progenitors of greater than 80% of both hair cells and supporting cells undergo their terminal division between embryonic day 13 (E13) and E14. As in humans, these cells persist in a non-proliferative state throughout the adult life of the animal. Here we report that the correct timing of cell cycle withdrawal in the developing organ of Corti requires p27(Kip1), a cyclin-dependent kinase inhibitor that functions as an inhibitor of cell cycle progression. p27(Kip1) expression is induced in the primordial organ of Corti between E12 and E14, correlating with the cessation of cell division of the progenitors of the hair cells and supporting cells. In wild-type animals, p27(Kip1) expression is downregulated during subsequent hair cell differentiation, but it persists at high levels in differentiated supporting cells of the mature organ of Corti. In mice with a targeted deletion of the p27(Kip1) gene, proliferation of the sensory cell progenitors continues after E14, leading to the appearance of supernumerary hair cells and supporting cells. In the absence of p27(Kip1), mitotically active cells are still observed in the organ of Corti of postnatal day 6 animals, suggesting that the persistence of p27(Kip1) expression in mature supporting cells may contribute to the maintenance of quiescence in this tissue and, possibly, to its inability to regenerate. Homozygous mutant mice are severely hearing impaired. Thus, p27(Kip1) provides a link between developmental control of cell proliferation and the morphological development of the inner ear.

scholarly journals Broussoflavonol B from Broussonetia kazinoki Siebold Exerts Anti-Pancreatic Cancer Activity through Downregulating FoxM1

Molecules ◽  
2020 ◽  
Vol 25 (10) ◽  
pp. 2328
Author(s):  
Ji Hye Jeong ◽  
Jae-Ha Ryu
Keyword(s):  
Cell Cycle ◽  
Pancreatic Cancer ◽  
Cell Proliferation ◽  
Cell Migration ◽  
Cellular Proliferation ◽  
Cyclin B1 ◽  
Human Pancreatic Cancer ◽  
Migration And Invasion ◽  
Cell Migration And Invasion ◽  
Cancer Activity

Pancreatic cancer has a high mortality rate due to poor rates of early diagnosis. One tumor suppressor gene in particular, p53, is frequently mutated in pancreatic cancer, and mutations in p53 can inactivate normal wild type p53 activity and increase expression of transcription factor forkhead box M1 (FoxM1). Overexpression of FoxM1 accelerates cellular proliferation and cancer progression. Therefore, inhibition of FoxM1 represents a therapeutic strategy for treating pancreatic cancer. Broussoflavonol B (BF-B), isolated from the stem bark of Broussonetia kazinoki Siebold has previously been shown to inhibit the growth of breast cancer cells. This study aimed to investigate whether BF-B exhibits anti-pancreatic cancer activity and if so, identify the underlying mechanism. BF-B reduced cell proliferation, induced cell cycle arrest, and inhibited cell migration and invasion of human pancreatic cancer PANC-1 cells (p53 mutated). Interestingly, BF-B down-regulated FoxM1 expression at both the mRNA and protein level. It also suppressed the expression of FoxM1 downstream target genes, such as cyclin D1, cyclin B1, and survivin. Cell cycle analysis showed that BF-B induced the arrest of G0/G1 phase. BF-B reduced the phosphorylation of extracellular signal-regulated kinase ½ (ERK½) and expression of ERK½ downstream effector c-Myc, which regulates cell proliferation. Furthermore, BF-B inhibited cell migration and invasion, which are downstream functional properties of FoxM1. These results suggested that BF-B could repress pancreatic cancer cell proliferation by inactivation of the ERK/c-Myc/FoxM1 signaling pathway. Broussoflavonol B from Broussonetia kazinoki Siebold may represent a novel chemo-therapeutic agent for pancreatic cancer.

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