Population mixture model for nonlinear telomere dynamics

Itzkovitz, Shalev; Shlush, Liran I.; Glück, Dan; Skorecki, Karl

doi:10.1103/physreve.78.060902

Cited by 7 publications

(19 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We find that fitting this same data with our Hayflick limit model leads to a small reduction (6%) in the mean square differences of the data and fitted functions relative to Ref. [14]. Other interesting biological information contained in these fits (rate constants in units of inverse weeks) are as follows.…”

Section: Application To Leukocyte Datamentioning

confidence: 84%

“…[14]. In the former model one accounts for the presence of stem cells as being the progenitors of new cells with chromosomes having full-length telomeres, whereas in the latter model the replenishment via stem cells is not considered.…”

Section: Summary and Discussionmentioning

confidence: 98%

“…For example, the work of Itzkovitz et al [14] advanced that of the previous subsection by including a population of stem cells that replenish the population of cells under study. The modification of the above model in one sense is very minor, namely the equations of motion now becomė…”

Section: Model With Stem Cells Without the Hayflick Limitmentioning

confidence: 97%

“…In Ref. [14] their so-called two-compartment model with fixed population size was compared to experimental data [15] for 3 different baboons (subjects 17891, 17927 and 18760) for 3 different leukocytes-B cells, T cells, and granulocytes. (Note that we confirmed numerically that this model represents an improvement over the no stem cells model presented in Section 2.1.)…”

Section: Application To Leukocyte Datamentioning

confidence: 99%

“…In Ref. [14] it was assumed that all new cells produced by stem cells have telomeres of length L o , and α was chosen to maintain a constant cell population size (independent of the distribution of telomere lengths), this condition corresponding to…”

Section: Model With Stem Cells Without the Hayflick Limitmentioning

confidence: 99%

See 4 more Smart Citations

Examining a scaled dynamical system of telomere shortening

Cyrenne

Gooding

2015

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

a b s t r a c tA model of telomere dynamics is proposed and examined. Our model, which extends a previously introduced model that incorporates stem cells as progenitors of new cells, imposes the Hayflick limit, the maximum number of cell divisions that are possible. This new model leads to cell populations for which the average telomere length is not necessarily a monotonically decreasing function of time, in contrast to previously published models. We provide a phase diagram indicating where such results would be expected via the introduction of scaled populations, rate constants and time. The application of this model to available leukocyte baboon data is discussed.

show abstract

Section: Application To Leukocyte Datamentioning

confidence: 84%

Section: Summary and Discussionmentioning

confidence: 98%

Section: Model With Stem Cells Without the Hayflick Limitmentioning

confidence: 97%

Section: Application To Leukocyte Datamentioning

confidence: 99%

Section: Model With Stem Cells Without the Hayflick Limitmentioning

confidence: 99%

See 3 more Smart Citations

Examining a scaled dynamical system of telomere shortening

Cyrenne

Gooding

2015

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

Modelling the regulation of telomere length: the effects of telomerase and G-quadruplex stabilising drugs

2013

View full text Add to dashboard Cite

Telomeres are guanine-rich sequences at the end of chromosomes which shorten during each replication event and trigger cell cycle arrest and/or controlled death (apoptosis) when reaching a threshold length. The enzyme telomerase replenishes the ends of telomeres and thus prolongs the life span of cells, but also causes cellular immortalisation in human cancer. G-quadruplex (G4) stabilising drugs are a potential anticancer treatment which work by changing the molecular structure of telomeres to inhibit the activity of telomerase. We investigate the dynamics of telomere length in different conformational states, namely t-loops, G-quadruplex structures and those being elongated by telomerase. By formulating deterministic differential equation models we study the effects of various levels of both telomerase and concentrations of a G4-stabilising drug on the distribution of telomere lengths, and analyse how these effects evolve over large numbers of cell generations. As well as calculating numerical solutions, we use quasicontinuum methods to approximate the behaviour of the system over time, and predict the shape of the telomere length distribution. We find those telomerase and G4-concentrations where telomere length maintenance is successfully regulated. Excessively high levels of telomerase lead to continuous telomere lengthening, whereas large concentrations of the drug lead to progressive telomere erosion. Furthermore, our models predict a positively skewed distribution of telomere lengths, that is, telomeres accumulate over lengths shorter than the mean telomere length at equilibrium. Our model results for telomere length distributions of telomerase-positive cells in drug-free assays are in good agreement with the limited amount of experimental data available.

show abstract

Critical telomerase activity for uncontrolled cell growth

2016

View full text Add to dashboard Cite

The lengths of the telomere regions of chromosomes in a population of cells are modelled using a chemical master equation formalism, from which the evolution of the average number of cells of each telomere length is extracted. In particular, the role of the telomere-elongating enzyme telomerase on these dynamics is investigated. We show that for biologically relevant rates of cell birth and death, one finds a critical rate, R crit, of telomerase activity such that the total number of cells diverges. Further, R crit is similar in magnitude to the rates of mitosis and cell death. The possible relationship of this result to replicative immortality and its associated hallmark of cancer is discussed.

show abstract

Population mixture model for nonlinear telomere dynamics

Cited by 7 publications

References 25 publications

Examining a scaled dynamical system of telomere shortening

Examining a scaled dynamical system of telomere shortening

Modelling the regulation of telomere length: the effects of telomerase and G-quadruplex stabilising drugs

Critical telomerase activity for uncontrolled cell growth

Contact Info

Product

Resources

About