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1.
There is increasing evidence that the growth of human tumours is driven by a small proportion of tumour stem cells with self-renewal properties. Multiplication of these cells leads to loss of self-renewal and after division for a finite number of times the cells undergo programmed cell death. Cell cycle times of human cancers have been measured in vivo and shown to vary in the range from two days to several weeks, depending on the individual. Cells cultured directly from tumours removed at surgery initially grow at a rate comparable to the in vivo rate but continued culture leads to the generation of cell lines that have shorter cycle times (1–3 days). It has been postulated that the more rapidly growing sub-population exhibits some of the properties of tumour stem cells and are the precursors of a slower growing sub-population that comprise the bulk of the tumour. We have previously developed a mathematical model to describe the behaviour of cell lines and we extend this model here to describe the behaviour of a system with two cell populations with different kinetic characteristics and a precursor–product relationship. The aim is to provide a framework for understanding the behaviour of cancer tissue that is sustained by a minor population of proliferating stem cells.  相似文献   

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A mathematical model of cell population growth introduced by J. L. Lebowitz and S. I. Rubinow is analyzed. Individual cells are distinguished by age and cell cycle length. The cell cycle length is viewed as an inherited property determined at birth. The density of the population satisfies a first order linear partial differential equation with initial and boundary conditions. The boundary condition models the process of cell division of mother cells and the inheritance of cycle length by daughter cells. The mathematical analysis of the model employs the theory of operator semigroups and the spectral theory of linear operators. It is proved that the solutions exhibit the property of asynchronous exponential growth.  相似文献   

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A model of the cell cycle, incorporating a deterministic cell-size monitor and a probabilistic component, is investigated. Steady-state distributions for cell size and generation time are calculated and shown to be globally asymptotically stable. These distributions are used to calculate various statistical quantities, which are then compared to known experimental data. Finally, the results are compared to distributions calculated from a Monte-Carlo simulation of the model.  相似文献   

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Closed form solutions are obtained for a Fokker-Planck model for cell growth as a function of maturation velocity and degree of maturation. For reproduction rules where daughter cells inherit their parent's maturation velocity the complete solution is derived in terms of Airy functions. For more complicated reproduction rules partial results are obtained. Emphasis is given to the relationship of these problems to time dependent linear transport theory.  相似文献   

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The dynamics of in situ 2D HeLa cell quasi-linear and quasi-radial colony fronts in a standard culture medium is investigated. For quasi-radial colonies, as the cell population increased, a kinetic transition from an exponential to a constant front average velocity regime was observed. Special attention was paid to individual cell motility evolution under constant average colony front velocity looking for its impact on the dynamics of the 2D colony front roughness. From the directionalities and velocity components of cell trajectories in colonies with different cell populations, the influence of both local cell density and cell crowding effects on individual cell motility was determined. The average dynamic behaviour of individual cells in the colony and its dependence on both local spatio-temporal heterogeneities and growth geometry suggested that cell motion undergoes under a concerted cell migration mechanism, in which both a limiting random walk-like and a limiting ballistic-like contribution were involved. These results were interesting to infer how biased cell trajectories influenced both the 2D colony spreading dynamics and the front roughness characteristics by local biased contributions to individual cell motion. These data are consistent with previous experimental and theoretical cell colony spreading data and provide additional evidence of the validity of the Kardar-Parisi-Zhang equation, within a certain range of time and colony front size, for describing the dynamics of 2D colony front roughness.  相似文献   

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In this paper we present an overview of the work undertaken to model a population of cells and the effects of cancer therapy. We began with a theoretical one compartment size structured cell population model and investigated its asymptotic steady size distributions (SSDs) (On a cell growth model for plankton, MMB JIMA 21 (2004) 49). However these size distributions are not similar to the DNA (size) distributions obtained experimentally via the flow cytometric analysis of human tumour cell lines (data obtained from the Auckland Cancer Society Research Centre, New Zealand). In our one compartment model, size was a generic term, but in order to obtain realistic steady size distributions we chose size to be DNA content and devised a multi-compartment mathematical model for the cell division cycle where each compartment corresponds to a distinct phase of the cell cycle (J. Math. Biol. 47 (2003) 295). We then incorporated another compartment describing the possible induction of apoptosis (cell death) from mitosis phase (Modelling cell death in human tumour cell lines exposed to anticancer drug paclitaxel, J. Math. Biol. 2004, in press). This enabled us to compare our model to flow cytometric data of a melanoma cell line where the anticancer drug, paclitaxel, had been added. The model gives a dynamic picture of the effects of paclitaxel on the cell cycle. We hope to use the model to describe the effects of other cancer therapies on a number of different cell lines.  相似文献   

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Probabilistic models of the cell cycle maintain that cell generation time is a random variable given by some distribution function, and that the probability of cell division per unit time is a function only of cell age (and not, for instance, of cell size). Given the probability density, f(t), for time spent in the random compartment of the cell cycle, we derive a recursion relation for n(x), the probability density for cell size at birth in a sample of cells in generation n. For the case of exponential growth of cells, the recursion relation has no steady-state solution. For the case of linear cell growth, we show that there exists a unique, globally asymptotically stable, steady-state birth size distribution, *(x). For the special case of the transition probability model, we display *(x) explicitly.This work was supported by the National Science Foundation under grants MCS8301104 (to J.J.T.) and MCS8300559 (to K.B.H.), and by the National Institutes of Health under grant GM27629 (to J.J.T.).  相似文献   

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基于地统计学的退化草地狼毒种群土壤种子库空间异质性   总被引:1,自引:0,他引:1  
土壤种子库作为植被天然更新的物质基础,其空间异质性对于认识种群繁殖更新机制具有重要意义。利用野外调查和地统计学方法,设置4个草地退化梯度,研究了祁连山北坡狼毒种群土壤种子库空间异质性及其与地上植被的关系。结果表明:4个退化梯度草地土壤种子库的半变异函数模型均为非线性模型,表现为聚集分布;随着天然草地退化程度加剧,狼毒种群土壤种子库的密度与变程不断增大、基台值与结构比呈"U"型变化趋势,其中76.88%~93.75%的空间异质性是由空间自相关引起;在未退化和重度退化草地地上植被密度与土壤种子库密度呈正相关,在轻度和中度退化草地中地上植被密度与土壤种子库密度之间未呈现相关性。在草地退化演替过程中,土壤种子库空间分布主要受地上植被等结构性因素影响,而放牧等干扰因素也在一定程度上降低了空间自相关性。  相似文献   

12.
This paper presents a general model for the cell division cycle in a population of cells. Three hypotheses are used: (1) There is a substance (mitogen) produced by cells which is necessary for mitosis; (2) The probability of mitosis is a function of mitogen levels; and (3) At mitosis each daughter cell receives exactly one-half of the mitogen present in the mother cell. With these hypotheses we derive expressions for the and curves, the distributions of mitogen and cell cycle times, and the correlation coefficients between mother-daughter (md) and sister-sister (ss) cell cycle times.The distribution of mitogen levels is shown to be given by the solution to an integral equation, and under very mild assumptions we prove that this distribution is globally asymptotically stable. We further show that the limiting logarithmic slopes of (t) and (t) are equal and constant, and that md0 while ss0. These results are in accord with the experimental results in many different cell lines. Further, the transition probability model of the cell cycle is shown to be a simple special case of the model presented here.  相似文献   

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Summary Analysis of the cell cycle by three methods has revealed unusual kinetics of proliferation in tumour derived suspensions ofCrepis capillaris. The different methods of analysis yield different estimates of cycle phase durations, and such discrepancies have been explained in terms of low growth fractions with rapid total cycle traverse. Specifically, confidence in the estimation of G2 duration by the fraction of labelled mitosis analysis, and comparison with shorter G2 estimates obtained by the two other methods, suggests that cells drop out in G1. However, cells which do not drop out of the proliferative compartment traverse G1 extremely rapidly. Extremely short cell cycle durations in which the G1 phase is virtually non-existent are uncharacteristic of plant cell suspension cultures, in which the G1 phase has previously been shown to be extended as compared with meristematic root tip cells. A model has been proposed in which a central core of rapidly dividing cells continuously loses cells into a subpopulation of resting or G0 cells with the G1 DNA content. Similarities between plant and animal tumours with respect to cell growth and division are discussed.  相似文献   

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Increasing evidence of intratumor heterogeneity and its augmentation due to selective pressure of microenvironment and recent achievements in cancer therapeutics lead to the need to investigate and track the tumor subclonal structure. Cell sorting of heterogeneous subpopulations of tumor and tumor-associated cells has been a long established strategy in cancer research. Advancement in lasers, computer technology and optics has led to a new generation of flow cytometers and cell sorters capable of high-speed processing of single cell suspensions. Over the last several years cell sorting was used in combination with molecular biological methods, imaging and proteomics to characterize primary and metastatic cancer cell populations, minimal residual disease and single tumor cells. It was the principal method for identification and characterization of cancer stem cells. Analysis of single cancer cells may improve early detection of tumors, monitoring of circulating tumor cells, evaluation of intratumor heterogeneity and chemotherapeutic treatments. The aim of this review is to provide an overview of major cell sorting applications and approaches with new prospective developments such as microfluidics and microchip technologies.  相似文献   

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Cell differentiation often appears to be a stochastic process particularly in the hemopoietic system. One of the earliest stochastic models for the growth of stem cell populations was proposed by Till et al. in 1964. In this model there are just two cell types: stem cells and specialized cells. At each time step there is a fixed probability that a stem cell differentiates into a specialized cell and a fixed probability that it undergoes mitosis to produce two stem cells. Even though this model is conceptually simple the myriad of possible outcomes has made it difficult to analyse. We present original closed-form expressions for the probability functions and a fast algorithm for computing them. Renewed interest in stem cells has raised questions about the effect de-differentiation has on stem cell populations. We have extended the stochastic model to include de-differentiation and show that even a small amount of de-differentiation can have a large effect on stem cell population growth.  相似文献   

16.
A cell population in which cells are allowed to enter a quiescent (nonproliferating) phase is analyzed using a stochastic approach. A general branching process is used to model the population which, under very mild conditions, exhibits balanced exponential growth. A formula is given for the asymptotic fraction of quiescent cells, and a numerical example illustrates how convergence toward the asymptotic fraction exhibits a typical oscillatory pattern. The model is compared with deterministic models based on semigroup analysis of systems of differential equations.  相似文献   

17.
Hemiclonal/hybridogenetic hybrids combine demographic superiority of asexuals and genetic diversity of sexuals, but their need for backcrossing with a parental species tightly couples them with this sexual host. How can systems like this persist in ecological and evolutionary time? Two discrete‐time mathematical models describing the complex life cycle and mating system of hybridogenetic waterfrogs (Rana esculenta) identified four factors and their interactions as important. Although female mating preferences, in combination with differences in fecundity, determine species coexistence, differences in larval competitiveness seem to be more important for the hybrid‘s actual frequency. However, coexistence is possible even when host and hybrid are equally fecund and competitive. Dispersal and competition interact in their influence on species composition, but ecological and reproductive dispersal has opposing effects. In ecological terms our results explain the remarkable stability of observed species ratios over time within natural hybridogenetic populations, and indicate why the species composition can vary so widely between localities. In evolutionary terms they explain the old age of these and other hybridogenetic systems. They also suggest interesting consequences for other tightly coupled systems.  相似文献   

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This paper considers a model for the dynamics of an age structured population subject to a density dependent factor which regulates the recruitment. Certain properties of biological interest are obtained and the stability of the equilibrium age distributions is investigated. Finally some applications to known fishery models are considered.Work done under the contract 80.02333.01 of C.N.R.  相似文献   

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红豆杉细胞悬浮培养结构化数学模型的探讨   总被引:2,自引:0,他引:2  
用10L机械搅拌式生物反应器悬浮培养红豆杉细胞,得到细胞生长、基质消耗和紫杉醇合成动力学曲线。经过代谢动力学分析建立了结构化数学模型。并将模型值与实验值进行比较,结果表明模型预测值与实验值较吻合。  相似文献   

20.
An experiment was conducted to determine if spatial nutrient heterogeneity affects mean plant size or size hierarchies in experimental populations of the weedy annual Abutilon theophrasti Medic. (Malvaceae). Heterogeneity was imposed by alternating 8 × 8 × 10 cm blocks of low and high nutrient soil in a checkerboard design, while a homogeneous soil treatment consisted of a spatially uniform mixture of the two soil types (mixed soil). Populations were planted at three densities. The effect of soil type on the growth of individuals was determined through a bioassay experiment using potted plants. The high nutrient, low nutrient, and mixed soil differed in their ability to support plant growth as indicated by differences in growth rates and final aboveground biomass. Concentrations of N, K, P, and Mg, measured at the end of the growing season in the experimental plots, also differed among all three soil types. Nevertheless, nutrient heterogeneity had little effect at the population level. Mean maximum leaf width measured at midseason was greater for populations on heterogeneous soil, but soil treatment did not affect midseason measurements of plant height, total number of leaves per plant, or canopy width. Population density affected all these parameters except plant height. When aboveground biomass was harvested at the end of the growing season, soil treatment was found to have no main effect on mean plant biomass, total population biomass, the coefficient of variation in plant biomass, or the combined biomass of the five largest plants in the population, but mean plant biomass was greater for populations on heterogeneous soils at the intermediate planting density. Mean plant biomass, total population biomass, and the coefficient of variation in plant biomass all varied with planting density. Mortality was low overall but significantly higher on homogeneous soil across all three densities. Soil heterogeneity had its strongest effect on individuals. In heterogeneous treatments plant size depended on the location of the plant stem with respect to high and low nutrient patches. Thus, soil nutrient heterogeneity influenced whether particular individuals were destined to be dominant or subordinate within the population but had little effect on overall population structure.  相似文献   

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