Transient Processes in Cell Proliferation Kinetics

Yakovlev, Andrei; Yanev, Nikolaj M.

doi:10.1007/978-3-642-48702-6

Cited by 46 publications

(23 citation statements)

References 8 publications

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“…This distribution is the most popular choice in cell kinetics studies (12), because the gamma family is quite f lexible and ref lects a multistage structure of the cell cycle. Furthermore, in this case the functions M 1 (t) and M 2 (t), given by formulas 1 and 2, can be found in an explicit form.…”

Section: Results Of Data Analysismentioning

confidence: 99%

Quantitative insight into proliferation and differentiation of oligodendrocyte type 2 astrocyte progenitor cells in vitro

Yakovlev

Boucher²,

Mayer-Pröschel³

et al. 1998

Proc. Natl. Acad. Sci. U.S.A.

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As part of our attempts at understanding fundamental principles that underlie the generation of nondividing terminally differentiated progeny from dividing precursor cells, we have developed approaches to a quantitative analysis of proliferation and differentiation of oligodendrocyte type 2 astrocyte (O-2A) progenitor cells at the clonal level. Owing to extensive previous studies of clonal differentiation in this lineage, O-2A progenitor cells represent an excellent system for such an analysis. Previous studies have resulted in two competing hypotheses; one of them suggests that progenitor cell differentiation is symmetric, the other hypothesis introduces an asymmetric process of differentiation. We propose a general model that incorporates both such extreme hypotheses as special cases. Our analysis of experimental data has shown, however, that neither of these extreme cases completely explains the observed kinetics of O-2A progenitor cell proliferation and oligodendrocyte generation in vitro. Instead, our results indicate that O-2A progenitor cells become competent for differentiation after they complete a certain number of critical mitotic cycles that represent a period of symmetric development. This number varies from clone to clone and may be thought of as a random variable; its probability distribution was estimated from experimental data. Those O-2A cells that have undergone the critical divisions then may differentiate into an oligodendrocyte in each of the subsequent mitotic cycles with a certain probability, thereby exhibiting the asymmetric type of differentiation.Developing a quantitative analysis of the process(s) through which precursor cells generate appropriate numbers of differentiated progeny represents a major challenge in theoretical biology. This challenge has multiple components and includes both cellular biological and mathematical elements. Although the narrative description of biological events is required to generate hypotheses, the tools of quantitative analysis are indispensable for testing alternative descriptive hypotheses. Mathematical analyses have proven of great benefit to our understanding of such diverse topics as prey-predator interactions, population genetics, DNA sequence analysis, and kinetics of cell proliferation in normal and neoplastic tissues. Although there have been several attempts to analyze temporally regulated differentiation of cells, there remains a lack of models that have been tested quantitatively against experimental data. Moreover, there are relatively few cellular systems for which the analysis of differentiation has been carried out in such a detailed manner as to support extensive efforts to develop quantitative insights into the underlying processes.One of the problems in developing a quantitative analysis of differentiation is that although most analyses of this process are carried out at the level of populations, actual differentiation events occur at the level of individual cells that frequently share a clonal relationship with each other. T...

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Section: Results Of Data Analysismentioning

confidence: 99%

Quantitative insight into proliferation and differentiation of oligodendrocyte type 2 astrocyte progenitor cells in vitro

Yakovlev

Boucher²,

Mayer-Pröschel³

et al. 1998

Proc. Natl. Acad. Sci. U.S.A.

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“…Differentiating both sides of eqn. (4) with respect to u at u = 1 yields the following integral equation for the expectation of the process: (9) The second and third order factorial moments satisfy (10) and (11) Let (s) denote the Laplace transform of m k (t), k = 1, 2, 3. Taking the Laplace transform of both sides of eqns.…”

Section: Letmentioning

confidence: 99%

“…We have , defined for s ∈ (−κ j , ∞), but also extendable to s ∈ (−∞, −κ j ) ∪ (−κ j , ∞) by analytic continuation. The assumption of gamma distributed lifespan is frequently made in practice [3,9]. We obtain the Markov process of the previous section if ω j = 1, j ∈ (p).…”

Section: Gamma Distributed Lifespanmentioning

confidence: 99%

On Classes of Equivalence and Identifiability of Age-Dependent Branching Processes

Chen

Hyrien

2014

Adv. Appl. Probab.

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Age-dependent branching processes are increasingly used in analyses of biological data. Despite being central to most statistical procedures, the identifiability of these models has not been studied. In this paper, we partition a family of age-dependent branching processes into equivalence classes over which the distribution of the population size remains identical. This result is applicable to study identifiability of the offspring and lifespan distributions for parametric families of branching processes. For example, we identify classes of Markov processes that are not identifiable. We show that age-dependent processes with (non-exponential) gamma distributed lifespan are identifiable and that Smith-Martin processes are not always identifiable.

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“…As in Section 2.2 for the Cyton Model, with the distributions of K and {T , t) in equation (17). If K is unbounded and there is not a minimum time between cell divisions, then care needs to be taken to ensure that M is finite as explained in the example in Section 5.1.…”

Section: Cyton Model Variant 3 Generational Pgf Evolutionmentioning

confidence: 99%

On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics

Duffy

Subramanian

2008

J. Math. Biol.

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During an adaptive immune response, lymphocytes proliferate for five to twenty five cell divisions, then stop and die over a period of weeks. Based on extensive flow cytometry data, Hawkins et al. (PNAS, 2007, 104, 5032-5037) introduced a cell-level stochastic model of lymphocyte population dynamics, called the Cyton Model, that accurately captures mean lymphocyte population size as a function of time. In Subramanian et al. (J. Math. Biol., 2008, 56:6, 861-892), we performed a branching process analysis of the Cyton Model and deduced from parameterizations for in vitro and in vivo data that the immune response is predictable despite each cell's fate being highly variable.One drawback of flow cytometry data is that individual cells cannot be tracked, so that it is not possible to investigate dependencies in the fate of cells within family trees. In the absence of this information, while the Cyton Model abandons one of the usual assumptions of branching processes (the independence of lifetime and progeny number), it adopts another of the standard branching processes hypotheses: that the fates of progeny are stochastically independent. However, new experimental observations of lymphocytes show that the fates of cells in the same family tree are not stochastically independent. Hawkins et al. (2008, submitted for publication) report on ciné lapse photography experiments where every founding cell's family tree is recorded for a system of proliferating lymphocytes responding to a mitogenic stimulus. Data from these experiments demonstrate that the death-ordivision fates of collaterally consanguineous cells (those in the same generation within a founding cell's family tree) are strongly correlated, while there is little correlation between cells of distinct generations and between cells in distinct family trees.As this finding contrasts with one of the assumptions of the Cyton Model, in this paper we introduce three variants of the Cyton Model with increasing levels of collaterally consanguineous correlation Ken Duffy and Vijay Subramanian, Hamilton Institute, National University of Ireland, Maynooth, Ireland E-mail: {ken.duffy, vijay.subramanian}@nuim.ie 2 structure to incorporate these new found dependencies. We investigate their impact on the predicted expected variability of cell population size. Mathematically we conclude that while the introduction of correlation structure leaves the mean population size unchanged from the Cyton Model, the variance of the population size distribution is typically larger. Biologically, through comparison of model predictions for Cyton Model parameterizations determined by in vitro and in vivo experiments, we deduce that if collaterally consanguineous correlation extends beyond cousins, then the immune response is less predictable than would be concluded from the original Cyton Model. That is, some of the variability seen in data that we previously attributed to experimental error could be due to intrinsic variability in the cell population size dynamics.

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Transient Processes in Cell Proliferation Kinetics

Cited by 46 publications

References 8 publications

Quantitative insight into proliferation and differentiation of oligodendrocyte type 2 astrocyte progenitor cells in vitro

Quantitative insight into proliferation and differentiation of oligodendrocyte type 2 astrocyte progenitor cells in vitro

On Classes of Equivalence and Identifiability of Age-Dependent Branching Processes

On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics

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