Biomedical subjects

D E Axelrod

Publications and source records attributed to D E Axelrod.

At least 19 recordsLinked to original sources

PubMed2005

Logical analysis of diffuse large B-cell lymphomas.

OBJECTIVE: The goal of this study is to re-examine the oligonucleotide microarray dataset of Shipp et al., which contains the intensity levels of 6817 genes of 58 patients with diffuse large B-cell lymphoma (DLBCL) and 19 with follicular lymphoma (FL), by means of the combinatorics, optimisation, and logic-based methodology of logical analysis of data (LAD). The motivations for this new analysis included the previously demonstrated capabilities of LAD and its expected potential (1) to identify different informative genes than those discovered by conventional statistical methods, (2) to identify combinations of gene expression levels capable of characterizing different types of lymphoma, and (3) to assemble collections of such combinations that if considered jointly are capable of accurately distinguishing different types of lymphoma. METHODS AND MATERIALS: The central concept of LAD is a pattern or combinatorial biomarker, a concept that resembles a rule as used in decision tree methods. LAD is able to exhaustively generate the collection of all those patterns which satisfy certain quality constraints, through a systematic combinatorial process guided by clear optimization criteria. Then, based on a set covering approach, LAD aggregates the collection of patterns into classification models. In addition, LAD is able to use the information provided by large collections of patterns in order to extract subsets of variables, which collectively are able to distinguish between different types of disease. RESULTS: For the differential diagnosis of DLBCL versus FL, a model based on eight significant genes is constructed and shown to have a sensitivity of 94.7% and a specificity of 100% on the test set. For the prognosis of good versus poor outcome among the DLBCL patients, a model is constructed on another set consisting also of eight significant genes, and shown to have a sensitivity of 87.5% and a specificity of 90% on the test set. The genes selected by LAD also work well as a basis for other kinds of statistical analysis, indicating their robustness. CONCLUSION: These two models exhibit accuracies that compare favorably to those in the original study. In addition, the current study also provides a ranking by importance of the genes in the selected significant subsets as well as a library of dozens of combinatorial biomarkers (i.e. pairs or triplets of genes) that can serve as a source of mathematically generated, statistically significant research hypotheses in need of biological explanation.

Combinatorial Chemistry Techniques↗

PubMed2001

Progression of heterogeneous breast tumors.

Two possible pathways of breast tumor progression were investigated by searching for values of transition rates that could reproduce the clinically observed co-occurrence frequencies of grades of ductal carcinoma in situ and grades of invasive ductal carcinoma in heterogeneous tumors. Two different pathways were analysed, a linear pathway with seven parameters, and a nonlinear pathway with three parameters. In each pathway ductal carcinoma in situ (DCIS) is a progenitor of invasive carcinoma (IDC). In the linear pathway breast tumor progression is along increasing grades: DCIS 1-DCIS 2-DCIS 3-IDC 1-IDC 2-IDC 3. In the nonlinear pathway progression of DCIS and progression of IDC can proceed in parallel steps, and in addition, with transitions from each grade of DCIS to a corresponding grade of IDC. The biological pathways were interpreted mathematically as compartment models with transition rates between stages in an explicit series of coupled differential equations. Two methods were used to search for transition rates that could reproduce the observed co-occurrence frequencies, a limited empirical search and an extensive genetic algorithmic search. Neither search method, with either pathway, could find a combination of transition rates that would reproduce the set of observed co-occurrence frequencies. We conclude that neither the linear pathway, nor the nonlinear pathway considered here, is an adequate description of progression in heterogeneous breast tumors. This quantitative investigation lends support to previous evidence from histopathology and molecular biology that the grades of DCIS and IDC seen together in heterogeneous breast tumors may not be obligate steps in tumor progression.

Breast Neoplasms↗

PubMed2000

A monthly period of symptoms associated with benign prostatic hyperplasia.

The number of times that a man with benign prostatic hyperplasia awoke each night with the urge to urinate (nocturia) was analyzed for randomness by Bartlett's Kolmogorov-Smirnov white noise test and for a periodic component by Fourier analysis. The data series (n = 1549) was not white noise; it had a peak periodic component of 25 days, with a range of 21 to 37 days. The possibility that the monthly period of nocturia is a general phenomenon and is coupled to a monthly menstrual period, and the implications for more accurate diagnosis and new modes of therapy, are discussed.

Fourier Analysis↗

PubMed1998

Assessing genetic markers of tumour progression in the context of intratumour heterogeneity.

This is a report from the Kananaskis working group on quantitative methods in tumour heterogeneity. Tumour progression is currently believed to result from genetic instability and consequent acquisition of new genetic properties in some of the tumour cells. Cross-sectional assessment of genetic markers for human tumours requires quantifiable measures of intratumour heterogeneity for each parameter or characteristic observed; the relevance of heterogeneity to tumour progression can best be ascertained by repeated assessment along a tumour progressional time line. This paper outlines experimental and analytic considerations that, with repeated use, should lead to a better understanding of tumour heterogeneity, and hence, to improvements in patient diagnosis and therapy. Four general principles were agreed upon at the Symposium: (1) the concept of heterogeneity requires a quantifiable definition so that it can be assessed repeatably; (2) the quantification of heterogeneity is necessary so that testable hypotheses may be formulated and checked to determine the degree of support from observed data; (3) it is necessary to consider (a) what is being measured, (b) what is currently measurable, and (c) what should be measured; and (4) the proposal of working models is a useful step that will assist our understanding of the origins and significance of heterogeneity in tumours. The properties of these models should then be studied so that hypotheses may be refined and validated.

Disease Progression↗

PubMed1997

Computer simulation of expansions of DNA triplet repeats in the fragile X syndrome and Huntington's disease.

The expansion of DNA triplet repeats has been shown to be responsible for about a dozen hereditary diseases. In this paper we are concerned with a computer model of such expansion, applied to the fragile X syndrome and Huntington's disease, for which enough quantitative data have been collected. The nucleotide sequence associated with the fragile X consists of CGG repeats and is located inside the FMR1 gene. In normal individuals there is a variable number of triplet repeats less than 60; in asymptomatic carriers the number of repeats is 60-200 (premutation). From the premutation range, the number of triplet repeats can increase within one generation to more than 200 producing affected individuals. In Huntington's disease the CAG repeats are located inside the HD gene. In normal individuals the number of repeats varies from around 11, up to 34. In the intermediate range (34-37 repeats), the mutability is increased, frequently leading to alleles of more than 37 repeats, and the disease phenotype. The rapid increase of the number of triplet repeats in affected individuals has been proposed to be due to the formation of folded DNA structures (hairpins) and their repair or misrepair. In order to determine if this proposed mechanism is adequate to account for the rapid increase of repeats and the large number of repeats in affected individuals we developed a mathematical model that includes the known mechanisms of hairpin formation, and strand synthesis and repair. Simulations based on the model using realistic probabilities of hairpin formation produced results that corresponded with the observed range of repeats and transition probabilities from normal to affected individuals. Similar modelling has been published for the Huntington's disease data. However, in this paper we demonstrate that a uniform approach works for fragile X and Huntington's disease, although the detailed assumptions of the model have to be different. These difference provide insight into the mechanisms of expansion in both cases. Among these insights is that an apparent threshold in the number of repeats for rapid expansion, and the preference for expansion over contraction, may be accounted for by relative probabilities of hairpin formation, replication, slippage and repair.

Computer Simulation↗

PubMed1997

Estimating clonal heterogeneity and interexperiment variability with the bifurcating autoregressive model for cell lineage data.

We utilize an extension of the variance-components models for cell lineage data in Huggins and Staudte (R.M. Huggins and R.G. Staudte, Variance components models for dependent cell populations. J. Am. Stat. Assoc. 89:19-29 (1994) to analyze NIH3T3 cells grown in two different media. This modeling approach has the advantage of a simple built-in correlation structure between familial members and allows for estimating experimental effects, rather than treating them as random effects. In addition, this methodology gives robust estimates of model parameters together with standard errors required for statistical inference. The importance of clonal heterogeneity and interexperiment variability in modeling eukaryotic cell cycles was previously pointed out by Kuczek and Axelrod (T. Kuczek and D.E. Axelrod, The importance of clonal heterogeneity and interexperimental variability in modeling the eukaryotic cell cycle. Math. Biosci. 79:87-96 (1986). This analysis confirms significantly positive sister-sister correlation when cells are grown in rich or poor medium and negative mother-daughter correlation when cells are grown in poor medium. However, for cells grown in rich medium, Kuczek and Axelrod's analysis gives negative mother-daughter correlations, whereas this analysis gives significant positive mother-daughter correlations.

3T3 Cells↗

PubMed1997

Ras oncogene-transformed and nontransformed cell populations are each heterogeneous but respond differently to the chemotherapeutic drug cytosine arabinoside (Ara-C).

In order to determine whether the growth of ras oncogene-transformed cells and nontransformed cells was inhibited differently by the chemotherapuetic drug cytosine arabinoside (Ara-C) their growth was analyzed by a novel colony-based assay that is sensitive and appropriate for heterogeneous cell populations. Colonies of nontransformed NIH3T3 cells, or ras oncogene-transformed NIH(ras) cells, were grown in the absence of drug and then divided into subclones. Subclones were allowed to continue to grow in the absence or presence of drug. Growth inhibition was determined by comparing the growth of drug-treated subclones. Colonies of nontransformed cells grown in the absence of the drug displayed a large variation in growth, and when grown in the presence of the drug displayed a large variation in growth inhibition. Colonies of transformed cells also displayed a large variation in the absence and presence of the drug. For each cell line, related subclones were more similar to each other than to unrelated subclones, implying inheritance of growth rates and drug response. For NIH3T3 cells, the growth of subclones in the presence of drug was highly correlated with the growth of related subclones in the absence of drug. However, for NIH3T3(ras) cells the growth of subclones in the presence of drug was not correlated with the growth of related subclones in the absence of drug. Therefore, ras oncogene-transformed and nontransformed cell populations differ in their response to Ara-C.

3T3 Cells↗

PubMed1996

A discrete-time, multi-type generational inheritance branching process model of cell proliferation.

Mammalian cell populations, such as tumors, may contain subpopulations differing in parameters such as cell lifetimes, even if the populations are derived from single cells. The mode of inheritance of cell lifetimes has previously been the subject of experimental and mathematical investigation. To obtain data on cell lifetimes over more cell generations then previously available, Axelrod et al. [Cell Prolif. 26:235-249(1988)] measured the number of cells in primary colonies and secondary colonies derived form the primary colonies. The experimental results indicated large variance of cells per colony and highly significant correlations between the numbers of cells in primary and secondary colonies. To mathematically model these results we derive, for previously uninvestigated multi-type Galton-Watson branching process models, the covariance of the cell counts in the primary and secondary colonies. As a result, we are able to successfully model the data with two subpopulations having differing proliferation rates, in which the proliferation rate of a daughter cell is primarily determined by the proliferation rate of its mother. Interestingly, simulations display a trade-off between high values of variances and correlation coefficients. The values obtained from experiment are located on the boundary of the region attainable by simulation.

Animals↗

PubMed1994

Gene amplification by unequal sister chromatid exchange: probabilistic modeling and analysis of drug resistance data.

Unequal sister chromatid exchange has been proposed as one of several possible mechanisms for gene amplification resulting in tandemly repeated sequences on chromosomes. Two requirements for testing this hypothesis are analytical observations and a mathematical model. Recently observations were reported for the number of tandemly repeated sequences on chromosomes of cells growing in the presence of a toxic drug and the mechanism was proposed to be unequal sister chromatid exchange. We now develop a mathematical model of this process based on the following hypotheses, (i) the extent of slippage between paired sister chromatids is a random variable with geometric distribution, (ii) the number of crossover sites is a random variable with a Poisson distribution, and (iii) cells with less than a threshold number of copies of an essential gene are eliminated when grown in selective conditions. Iterating the model at successive cell divisions results in a Markov chain with a denumerable infinity of states. The resulting distributions of gene copy number per cell at a particular population size are compared to published data on the CAD gene in BHK cells growing in the presence of the drug PALA (Smith et al., 1990, Cell, 63, 1219). The mathematical model can reproduce the observed means and standard deviations of gene copy number per cell and allows construction of confidence region estimates of parameters describing the extent of slippage, density of crossover sites, and strength of selection. An important prediction of the model is that in non-selective conditions the cells with amplified sequences gradually disappear from the population even if they are not at a growth disadvantage, though rare cells with a very large number of amplified sequences might continue to exist. The success of modeling suggests that the proposed mechanism of gene amplification by unequal sister chromatid exchange is consistent with the number of tandemly repeated sequences on chromosomes observed in some circumstances.

Animals↗

PubMed1994

Fluctuation test for two-stage mutations: application to gene amplification.

The determination of mutation rates is an important experimental procedure for characterizing mutation processes. The accepted method of determining mutation rates, the fluctuation test, was introduced by Luria and Delbrück in 1943. Since then it has been applied to various microorganisms and cells. The Luria-Delbrück test is based on a restrictive hypothesis of mutations being due to single irreversible events. However, some inherited changes in phenotype, like gene amplification, may be due to two or more genetic changes, some of which may be reversible. The Luria-Delbrück model of mutation was compared to other models which included reversibility and more than one mutation stage. The Luria-Delbrück model has been confirmed to be consistent with the original bacteriophage resistance data. However, for gene amplification this model gives incompatible estimates of mutation rates by the P0 and r methods. Relaxing the hypotheses of the single-stage models did not improve the fit. In contrast, a two-stage reversible model provided a fit. Analysis of gene amplification data by the two-stage reversible model provides new information, including estimates of rates for each of the two forward stages and of the reverse step.

Animals↗

PubMed1993

Persistence of cell cycle times over many generations as determined by heritability of colony sizes of ras oncogene-transformed and non-transformed cells.

The persistence of cell lifetimes during about 10 successive cell generations was investigated by comparing the number of cells in primary colonies and in secondary colonies derived from primary colonies. Primary colonies were grown from single cells for 3 or 4 days (a time equivalent to an average of five cell generations) and the number of cells in each primary colony determined. Cells in each primary colony were dispersed to initiate secondary colonies, grown for the same time, and the number of cells in secondary colonies determined. Several criteria were used to compare primary and related secondary colonies, the most informative was found to be regression and correlation coefficients between number of cells in primary colonies and mean numbers of cells in related secondary colonies. For two non-transformed mouse fibroblast cell lines, NIH 3T3 and BALB 3T3, the regression and correlation coefficients of cell number in primary and secondary colonies were positive. This suggests inheritance of cell lifetimes over many cell generations. After the addition of an activated ras oncogene (human cellular Harvey ras, or viral Kirsten ras) some regression and correlation coefficients changed in magnitude but all remained positive. Comparison of experimental data and the results of computer simulations suggest that several models of inheritance of cell lifetimes are not adequate to explain the results, including a model of independence between lifetimes of mother and daughter cells and the common model that describes daughter cells as inheriting the lifetime of their mother with deviation. Simulations do suggest that cell lifetimes are inherited within clones as deviation from the lifetime of the initial cell, and that the ras oncogene does not destroy persistence within clones but does increase heterogeneity of cell lifetimes.

3T3 Cells↗

PubMed1992

A branching process model of gene amplification following chromosome breakage.

We have devised a mathematical model of gene amplification utilizing recent experimental observations concerning dihydrofolate reductase (DHFR) gene amplification in CHO cells. The mathematical model, based on a biological model which proposes that acentric elements are the initial intermediates in gene amplification, includes the following features: (1) initiation of amplification by chromosomal breakage to produce an acentric structure; (2) replication of acentric DNA, once per cell cycle; (3) dissociation of replicated acentric DNA; (4) unequal segregation of acentric DNA fragments to daughter cells at mitosis; (5) subsequent reintegration of acentric fragments into chromosomes. These processes are assumed to be independent for each element present in a cell at a given time. Thus, processes of unequal segregation and integration may occur in parallel, not necessarily in a unique sequence, and may be reiterated in one or multiple cell cycles. These events are described mathematically as a Galton-Watson branching process with denumerable infinity of object types. This mathematical model qualitatively and quantitatively reproduces the major elements of the dynamical behavior of DHFR genes observed experimentally. The agreement between the mathematical model and the experimental data lends credence to the biological model proposed by Windle et al. (1991), including the importance of chromosome breakage and subsequent gene deletion resulting from resection of the broken chromosome ends as initial events in gene amplification.

Animals↗

PubMed1991

Unequal cell division, growth regulation and colony size of mammalian cells: a mathematical model and analysis of experimental data.

This work describes mathematically the dynamics of expansion of cell populations from the initial division of single cells to colonies of several hundred cells. This stage of population growth is strongly influenced by stochastic (random) elements including, among others, cell death and quiescence. This results in a wide distribution of colony sizes. Experimental observations of the NIH3T3 cell line as well as for the NIH3T3 cell line transformed with the ras oncogene were obtained for this study. They include the number of cells in 4-day-old colonies initiated from single cells and measurements of sizes of sister cells after division, recorded in the 4-day-old colonies. The sister cell sizes were recorded in a way which enabled investigation of their interdependence. We developed a mathematical model which includes cell growth and unequal cell division, with three possible outcomes of each cell division: continued cell growth and division, quiescence, and cell death. The model is successful in reproducing experimental observations. It provides good fits to colony size distributions for both NIH3T3 mouse fibroblast cells and the same cells transformed with the rasEJ human cancer gene. The difference in colony size distributions could be fitted by assuming similar cell lifetimes (12-13 hr) and similar probabilities of cell death (q = 0.15), but using different probabilities of quiescence, r = 0 for the ras oncogene transformed cells and r = 0.1 for the non-transformed cells. The model also reproduces the evolution of distributions of sizes of cells in colonies, from a single founder cell of any specified size to the stable limit distribution after eight to ten cell divisions. Application of the model explains in what way both random events and deterministic control mechanisms strongly influence cell proliferation at early stages in the expansion of colonies.

Animals↗

PubMed1991

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.

Animals↗

PubMed1991

Altered post-translational processing of p21ras oncoprotein in a transformation-suppressed cell line.

We have isolated a transformation-suppressed cell line, R35, which is altered in the maturation of p21ras. It was obtained from the transformed cell line NIH3T3(rasEJ) as a revertant with flat morphology and anchorage dependent growth. Immunoprecipitation of steady state labeled ras proteins reveals that the revertant produces p21ras, and in addition, accumulates a protein that migrates as 23kD. Fusion of revertant cells with nontransformed rat2 cells yields cell hybrids which are retransformed and do not accumulate p23, suggesting that accumulation of p23 and suppression of transformation may be related. The accumulated p23 appears to be a precursor to p21 because (1) pulse labeling and cell fractionation of revertant cells shows that label chases from cytoplasmic p23 to membrane-associated p21, although at a slower rate, and (2) the p23 of revertant cells is indistinguishable from the p23 precursor of p21 in parent cells by partial V8 protease digestion and two dimensional electrophoresis. R35 cells are slower than their transformed parent in palmitylation and polyisoprenylation, but not in methylation of ras proteins. These results suggest that the transformation-suppressed cell line R35 is defective in the rate at which it posttranslationally processes ras proteins, possibly because it is slower in polyisoprenylation of the cytoplasmic p23 precursor protein.

Animals↗

PubMed1990

Mathematical models of gene amplification with applications to cellular drug resistance and tumorigenicity.

An increased number of copies of specific genes may offer an advantage to cells when they grow in restrictive conditions such as in the presence of toxic drugs, or in a tumor. Three mathematical models of gene amplification and deamplification are proposed to describe the kinetics of unstable phenotypes of cells with amplified genes. The models differ in details but all assume probabilistic mechanisms of increase and decrease in gene copy number per cell (gene amplification/deamplification). Analysis of the models indicates that a stable distribution of numbers of copies of genes per cell, observed experimentally, exists only if the probability of deamplification exceeds the probability of amplification. The models are fitted to published data on the loss of methotrexate resistance in cultured cell lines, due to the loss of amplified dihydrofolate reductase gene. For two mouse cell lines unstably resistant to methotrexate the probabilities of amplification and deamplification of the dihydrofolate reductase gene on double minute chromosomes are estimated to be approximately 2% and 10%, respectively. These probabilities are much higher than widely presumed. The models explain the gradual disappearance of the resistant phenotype when selective pressure is withdrawn, by postulating that the rate of deamplification exceeds the rate of amplification. Thus it is not necessary to invoke a growth advantage of nonresistant cells which has been the standard explanation. For another analogous process, the loss of double minute chromosomes containing the myc oncogene from SEWA tumor cells, the growth advantage model does seem to be superior to the amplification and deamplification model. In a more theoretical section of the paper, it is demonstrated that gene amplification/deamplification can result in reduction to homozygosity, such as is observed in some tumors. Other applications are discussed.

Animals↗

PubMed1987

Tumor cell heterogeneity: divided-colony assay for measuring drug response.

In vitro tests for predicting the response of tumors to chemotherapeutic agents might be improved if they were modified to take into account tumor-cell heterogeneity. We have studied the heterogeneity of cellular growth rate and drug response in mouse fibroblast NIH 3T3 cells and in NIH 3T3 cells transformed with the human HRAS gene (homologue of the Harvey sarcoma virus oncogene v-Ha-ras) from the EJ human bladder carcinoma cell line. Growth-rate heterogeneity was detected as a broad distribution of numbers of cells per colony. In spite of this heterogeneity, secondary colonies have numbers of cells per colony that resemble that of the primary colony from which they were derived. The variance between unrelated secondary colonies is increased by HRASEJ. Colony-size measurements are reliable because primary colonies divided in half formed two groups of secondary colonies (on two separate plates) that had indistinguishable mean colony sizes. Based on these observations, a divided-colony procedure was devised to detect the drug response of heterogeneous cell populations. Primary colonies are divided into two groups of cells, one of which is treated with a drug and the other is left untreated as a control. The size distribution of treated secondary colonies is then compared to that of the untreated control and to that of the primary colony from which it was derived. The divided-colony procedure is proposed as a modification of the human-tumor-cloning system to increase the sensitivity and reliability of in vitro procedures used to determine the drug response of heterogeneous tumor-cell populations.

Animals↗

PubMed1986

Distribution of interdivisional times in proliferating and differentiating Friend murine erythroleukaemia cells.

The interdivisional times of Friend murine erythroleukaemia cells which are growing continuously, or during terminal erythroid differentiation after exposure to dimethyl sulphoxide (DMSO), were determined by time lapse video photography. The median interdivisional times were found to increase from 11.75 hr before exposure to DMSO, to 24.0 hr at 72 hr after exposure. This increase in median interdivisional time was accompanied by an increase in heterogeneity of interdivisional times (%CV = 8.5----40.8), by an increase in the similarity of sister interdivisional times (ryy = 0.622----0.925), and by a decrease in the fraction of cells observed to divide (F = 1.0----0.807). Cells exposed to DMSO for 72 hr can be induced to divide at least once with nearly normal interdivisional times, if they are resuspended at a tenfold higher cell concentration. Computer simulations of cell cycle regulation, based on the opposing reactions model of Murphy, generate interdivisional time distributions which resemble the experimental data better than the single transition probability model of Smith and Martin.

Animals↗