A branching-process model for heterogeneous cell populations

A multitype branching-process model is introduced for the growth of heterogeneous cell populations. This model includes events representing mitosis, death, mutation, and conversion from one cell type to another. Formulas for conditioning on interim events, and generalizations allowing parameters to be functions of time or cell counts, are presented. The probability generating function (p.g.f.) is solved approximately in a way that is both accurate and efficient enough to solve important problems in tumor biology. The uses of the p.g.f. in the setting of clinical oncology are described.     

Algorithmic approaches to clonal reconstruction in heterogeneous cell populations

Background: The reconstruction of clonal haplotypes and their evolutionary history in evolving populations is a common problem in both microbial evolutionary biology and cancer biology. The clonal theory of evolution provides a theoretical framework for modeling the evolution of clones.Results: In this paper, we review the theoretical framework and assumptions over which the clonal reconstruction problem is formulated. We formally define the problem and then discuss the complexity and solution space of the problem. Various methods have been proposed to find the phylogeny that best explains the observed data. We categorize these methods based on the type of input data that they use (space-resolved or time-resolved), and also based on their computational formulation as either combinatorial or probabilistic. It is crucial to understand the different types of input data because each provides essential but distinct information for drastically reducing the solution space of the clonal reconstruction problem. Complementary information provided by single cell sequencing or from whole genome sequencing of randomly isolated clones can also improve the accuracy of clonal reconstruction. We briefly review the existing algorithms and their relationships. Finally we summarize the tools that are developed for either directly solving the clonal reconstruction problem or a related computational problem.Conclusions: In this review, we discuss the various formulations of the problem of inferring the clonal evolutionary history from allele frequeny data, review existing algorithms and catergorize them according to their problem formulation and solution approaches. We note that most of the available clonal inference algorithms were developed for elucidating tumor evolution whereas clonal reconstruction for unicellular genomes are less addressed. We conclude the review by discussing more open problems such as the lack of benchmark datasets and comparison of performance between available tools.     

Growth factors and growth control of heterogeneous cell populations

In an earlier work a model of the autocrine and paracrine pathways of tumor growth control was developed (Michelson and Leith. 1991. Autocrine and paracrine growth factors in tumor growth.Bull. math. Biol. 53, 639–656). The target population, a generic tumor, was modeled as a single, homogeneous population using the standard Verhulst equation of logistic growth. Mitogenic signals were represented by modifications to the Malthusian growth parameter and adaptational signals were represented by modifications to the carrying capacity. Three growth scenarios were described: (1) normal tissue wound healing, (2) unperturbed tumor growth, and (3) tumor growth in a radiation damaged environment, a phenomenon termed the Tumor Bed Effect (TBE). In this paper, we extend those results to include a “triad” of growth factor controls (autocrine, paracrine and endocrine) and heterogeneity of the target population. The heterogeneous factors in the model represent either intrinsic, epigenetic or environmental differences in both normally differentiating tissues and tumors. Three types of growth are modeled: (1) normal tissue differentiation or wound healing, assuming no communication between differentiated and undifferentiated cell compartments; (2) normal wound healing with feedback inhibition, due to signalling from the differentiated compartment; and (3) the development of hypoxia in a spherical tumor. The signal processing within the triad is discussed for each model and biologically reasonable constraints are defined for limits on growth control.     

Inheritance and regression toward the mean in heterogeneous cell populations

Traits such as birth size and lifetime can vary widely even among non-mutated progeny of the same cell proliferating in the same environment. On the other hand, population parameters of these traits may remain stable over many generations, and there may be a distinct inheritance of these traits from mother to daughters. We have reconsidered the implication of mother-daughter correlations in light of linear regression analysis. It is proposed that a non-mutant cell whose phenotype deviates from the population mean produces progeny whose rate of regression toward the mean is proportional to 1-r, where r is the mother-daughter correlation coefficient of the trait under study. Theoretical support for this proposition is derived from linear regression analysis. Empirical support is found in pedigree analysis of cell growth constants among NIH3T3 mouse fibroblast cells, where the presence of an activated human ras oncogene is associated with a decreased r and an increased rate at which the growth constants of progeny regress toward the population mean.     

A visual analytics approach for models of heterogeneous cell populations

In recent years, cell population models have become increasingly common. In contrast to classic single cell models, population models allow for the study of cell-to-cell variability, a crucial phenomenon in most populations of primary cells, cancer cells, and stem cells. Unfortunately, tools for in-depth analysis of population models are still missing. This problem originates from the complexity of population models. Particularly important are methods to determine the source of heterogeneity (e.g., genetics or epigenetic differences) and to select potential (bio-)markers. We propose an analysis based on visual analytics to tackle this problem. Our approach combines parallel-coordinates plots, used for a visual assessment of the high-dimensional dependencies, and nonlinear support vector machines, for the quantification of effects. The method can be employed to study qualitative and quantitative differences among cells. To illustrate the different components, we perform a case study using the proapoptotic signal transduction pathway involved in cellular apoptosis.     

Methods to analyze cell type-specific gene expression profiles from heterogeneous cell populations

Recent technical progress in DNA and protein identification has made genome-wide survey of gene expression at tissue and animal levels a routine approach, such as microarray and RNA sequencing technologies to measure mRNA abundance and mass spectrometry to measure protein abundance. A key limitation in applying these genome-wide gene expression profiling methods at tissue and animal levels is that the contribution of a specific cell type to the total amount of measured gene expression cannot be determined. Here, we review currently available approaches to resolve this and discuss future directions of study to solve questions not addressable by state-of-the-art techniques.     

Fluorescence activated cell sorting reveals heterogeneous and cell non-autonomous osteoprogenitor differentiation in fetal rat calvaria cell populations

Identification of osteoblast progenitors, with defined developmental capacity, would facilitate studies on a variety of parameters of bone development. We used expression of alkaline phosphatase (ALP) and the parathyroid hormone/parathyroid hormone-related protein receptor (PTH1R) as osteoblast markers in dual-color fluorescence activated cell sorting (FACS) to fractionate rat calvaria (RC) cells into ALP(-)PTH1R(-), ALP(+)PTH1R(-), ALP(-)PTH1R(+), and ALP(+)PTH1R(+) populations. These fractionated populations were seeded clonally (n = 96) or over a range of cell densities ( approximately 150-8,500 cell/cm(2); n = 3). Our results indicate that colony forming unit-osteoblast (CFU-O)/bone nodule-forming cells are found in all fractions, but the frequency of CFU-O and total mineralized area is different across fractions. Analysis of these differences suggests that ALP(-)PTH1R(-), ALP(-)PTH1R(+), ALP(+)PTH1R(-), and ALP(+)PTH1R(+) cell populations are separated in order of increasing bone formation capacity. Dexamethasone (dex) differentially increased the CFU-O number in the four fractions, with the largest stimulation in the ALP(-) cell populations. However, there was no significant difference in the number or size distribution of CFU-F (fibroblast) colonies that formed in vehicle versus dex. Finally, both cell autonomous and cell non-autonomous (i.e., inhibitory/stimulatory effects of cell neighbors) differentiation of osteoprogenitors was seen. Only the ALP(-)PTH1R(-) population was capable of forming nodules at the clonal level, at approximately 3- or 12-times the predicted frequency of unfractionated populations in dex or vehicle, respectively. These data suggest that osteoprogenitors can be significantly enriched by fractionation of RC populations, that assay conditions modify the osteoprogenitor frequencies observed and that fractionation of osteogenic populations is useful for interrogation of their developmental status and osteogenic capacity.     

The direction of selection of genetically heterogeneous cell populations ofDioscorea deltoidea Wall

The initial strain ofDioscorea cell culture is characterized by a double-peak curve of mitotic activity, by dominance in the population of meristematic cells, by a great variety in the number of chromosomes and also by polyploidization in the process of cultivation. After treatment with different doses of N-nitroso-N-methylurea (NMU) physiological parameters of the cell populations were found to change (dynamics of mitotic activity, ratio between types of cells). On passaging, physiological differences between the strains are levelled up. The studied strains are characterized by different directions of cell selections,i.e. the control strain — towards polyploidization, and in NMU treated strains are stabilized on di- and triploid levels.     

Dispersal distance of heterogeneous populations

 Heterogeneity among individuals in a population is one of the important factors that influence the rate of population spread. To incorporate the population heterogeneity into dispersal rate, we assume that the traveling duration varies following a gamma distribution with a shape parameter k, where (1/k) indicates the heterogeneity in the traveling duration. The resultant distribution of the traveling distance, which is called dispersal function, is then expressed by using a modified Bessel function of the second kind of order (k − 1). It is shown that the front of the distribution spreads with time in an accelerated manner during an early phase of expansion if the heterogeneity is sufficiently large, which is consistent with the results from previous studies of biological invasions. By using the data obtained from mark–recapture experiments using traps, we can obtain the maximum likelihood estimates of three parameters: heterogeneity in the traveling duration, which is defined by (1/k); the mean dispersal ability, which is defined by the product of the diffusion coefficient and the mean traveling duration; and the trap efficiency. The usefulness of this model is shown by using the data of mark–recapture experiments with the common cutworm, Spodoptera litura (Fabricius) (Lepidoptera: Noctuidae). Received: December 3, 2001 / Accepted: May 16, 2002     

Identifying subgroup markers in heterogeneous populations

Traditional methods that aim to identify biomarkers that distinguish between two groups, like Significance Analysis of Microarrays or the t-test, perform optimally when such biomarkers show homogeneous behavior within each group and differential behavior between the groups. However, in many applications, this is not the case. Instead, a subgroup of samples in one group shows differential behavior with respect to all other samples. To successfully detect markers showing such imbalanced patterns of differential signal, a different approach is required. We propose a novel method, specifically designed for the Detection of Imbalanced Differential Signal (DIDS). We use an artificial dataset and a human breast cancer dataset to measure its performance and compare it with three traditional methods and four approaches that take imbalanced signal into account. Supported by extensive experimental results, we show that DIDS outperforms all other approaches in terms of power and positive predictive value. In a mouse breast cancer dataset, DIDS is the only approach that detects a functionally validated marker of chemotherapy resistance. DIDS can be applied to any continuous value data, including gene expression data, and in any context where imbalanced differential signal is manifested.     

Consanguinity analysis in heterogeneous populations.

Consanguinity analysis can be performed in populations comprising collections of genetic isolates, and the resulting estimates can be valid and useful in phenotypes caused by numerous recessive genes, such as mental retardation and congenital nerve deafness. Maximum likelihood methods are presented for estimating gene frequency and proportions of homozygous cases of morbid phenotypes in such populations.     

Analytical cytometric approaches to heterogeneous cell populations in solid tumors: a review

The problems encountered in studying the heterogeneity of cells in solid tumors is reviewed with emphasis on the role of various analytical cytometric assays for studying both the biology and the dynamics and proliferating, quiescent and dead malignant cells in vitro and in vivo. Due to advances in cytometric technology, many interesting in vitro studies on tumor cells heterogeneity have been and will be conducted over the next several years. For example, the acidic acridine orange staining of HeLa cells in suspension culture does readily discriminate between proliferating and quiescent cells. Some of these assays have been and others will be extended to in vivo studies. However, it is obvious that either the current analytical cytometric techniques must be modified and refined to permit better resolution for the complex situation in vivo or other new analytical cytometric techniques will have to be developed before many interesting studies on tumor cell heterogeneity in vivo can be addressed with reasonable efficiency.     

On treatment of tuberculosis in heterogeneous populations

Global eradication of tuberculosis (TB) is an international agenda. Thus understanding effects of treatment of TB in different settings is crucial. In previous work, we introduced the framework for a mathematical model of epidemic TB in demographically distinct, heterogeneous populations. Simulations showed the importance of genetic susceptibility in determining endemic prevalence levels. In the work presented here, we include treatment and investigate different strategies for treatment of latent and active TB disease in heterogeneous populations. We illustrate how the presence of a genetically susceptible subpopulation dramatically alters effects of treatment in the same way a core population does in the setting of sexually transmitted diseases. In addition, we evaluate treatment strategies that focus specifically on this subpopulation, and our results indicate that genetically susceptible subpopulations should be accounted for when designing treatment strategies to achieve the greatest reduction in disease prevalence.     

Eradication of infectious diseases in heterogeneous populations

We present a model of infectious diseases in heterogeneous populations, which allows for variable intra- to intergroup contact ratios. We give necessary and sufficient conditions for disease eradication by means of vaccination. Smallpox is used as an illustrative example.     

Variability in cell yield for heterogeneous microbial populations of sewage origin grown on glucose

Values of cell yield collected over a period of eight years for heterogeneous populations of sewage origin acclimated to glucose in both batch and continuous culture were subjected to statistical analysis. The cell yield for this sole source of carbon (glucose) ranged from 36 to 88 per cent in batch culture, and 32 to 69 per cent in continuous culture. Because experimental conditions were known and well defined, the variability in cell yield is attributable to the ecological variation inherent in a heterogeneous population. The data presented demonstrate the futility of attempts to define Y for such populations as a precise theoretical constant dependent upon thermodynamic properties of the substrate.     

MTT方法评价微生物细胞活性的探讨

对MTT比色法用于评价微生物细胞活性进行了探讨。本文以大肠杆菌为模式菌株,研究了不同浓度MTT、不同用量、在不同时间对试验结果OD570值的影响,结果表明细菌数在4.9×107－4.9×108个/mL范围内测出的OD570值与细菌浓度呈良好的正相关,0.5 mg/mL MTT用量20 L,反应时间20 min时效果最佳,其相关回归方程为y = 0.1769x + 0.03,R2 = 0.9983。     

Flow cytometric analysis of live cell proliferation and phenotype in populations with low viability.

BACKGROUND: Combined analysis of DNA content and immunofluorescence on single cells by flow cytometry provides information on the proliferative response of subpopulations to stimuli in mixed cell preparations; however, in low-viability cell preparations, dead cells interfere with accurate flow cytometric data analysis because of nonspecific binding of antibodies and altered DNA-staining profiles. Light scatter differences between nonviable and viable cells are unreliable, particularly after the cell permeabilization step that is necessary for DNA staining. We developed a method for identification of nonviable cells by fluorescence in cell preparations that are stained simultaneously for cell surface or intracellular immunofluorescence and DNA content. MATERIALS AND METHODS: Nonviable cells that have lost membrane integrity are identified by uptake of 7-amino-actinomycin D (7-AAD). Transfer of 7-AAD from stained nonviable cells to unstained viable cells after permeabilization is prevented by blocking DNA binding with nonfluorescent actinomycin D (AD). Pyronin Y(G) (PY) is used for DNA staining because the orange spectral emission of PY can be separated from the green fluorescein isothiocyanate (FITC) emission and the red emission of 7-AAD, respectively. RESULTS: Application of the method to the analysis of the T-cell leukemia cell line Molt-4f and of cultured human peripheral blood mononuclear cells is presented. In both cell preparations, 7-AAD staining permitted reliable dead cell exclusion. Live, 7-AAD-negative Molt-4f cells showed higher expression levels of cell surface CD4 and of intracellular CD3, showed a higher proportion of cells in the G1 phase of the cell cycle, and showed a lower coefficient of variation of the G1 peak compared with data obtained from all the cells in the preparation. Live, CD8+ lymphocytes from OKT3-stimulated cultures of human peripheral blood mononuclear cells showed a specific proliferative response as measured by DNA content analysis. CONCLUSIONS: The results show that cells stained with FITC-labeled antibodies can be analyzed by single-laser flow cytometry for DNA content combined with dead cell discrimination. Furthermore, they emphasize the need for exclusion of dead cells from the analysis of cell preparations with low viability to obtain reliable data on immunofluorescence and cell-cycle distributions.     

Single-cell immuno-beta-galactosidase staining of heterogeneous populations. Practical application on limited cell numbers

Summary In this paper we describe a sensitive immunocytochemical staining method, particularly useful for the study of subpopulations of cells in complex mixtures such as bone marrow cell suspensions.E.coli -galactosidase is used as a label, which has the advantage that no endogenous activity is observed under the present experimental conditions. Direct sedimentation of cells on to poly-l-lysine-pretreated multi-well slides followed by gentle fixation prevents cell loss during preparation and subsequent incubation steps. Furthermore, analysis of only a few hundred cells per sample is possible.We examined the sensitivity of this method by comparing the percentages of positive cells in a spleen cell suspension after staining with a panel of monoclonal antibodies followed by analysis with the present immuno--galactosidase method or standard flow cytometry. For almost all antibodies used, the percentages of positive spleen cells obtained with the immuno--galactosidase method at least equalled those obtained with flow cytometry.Several fixatives, used to permanently adhere the cells to the slide's surface, were tested for the preservation of both morphological and antigenic structure. Glutaraldehyde and formol acetone proved to be the best choices in this respect.The present method combines high sensitivity with good morphology and is especially useful for immunophenotyping low cell numbers of heterogeneous populations.