Clonal Growth Model Research Articles

An improved approximation to the exact solution of the two-stage clonal growth model of cancer.

Multistage clonal growth models are of interest for cancer risk assessment because they can explicitly incorporate data on cell replication. Both approximate and exact formulations of the two stage growth model have been described. The exact solution considers the conditional probability of tumors arising in previously tumor-free animals; the approximate solution estimates total probability of tumor formation. The exact solution is much more computationally intensive when time-dependent cell growth parameters are included. The approximate solution deviates from the exact solution at high incidences and probabilities of tumor. This report describes a computationally tractable, 'improved approximation' to the exact solution. Our improved approximation includes a correction term to adjust the unconditional expectation of intermediate cells based on the time history of formation of intermediate cells by mutation of normal cells (recruitment) or by cell division in the intermediate cell population (expansion). The improved approximation provided a much better match to the exact solution than the approximate solution for a wide range of parameter values. The correction term also appears to provide insight into the biological factors that contribute to the variance of the expectation for the number of intermediate cells over time.

Familial and sporadic human renal cell carcinoma: Evidence against a double-loss mechanism of carcinogenesis

It has been speculated that renal cell carcinoma (RCC) is an example of a double-loss mutation. We analyzed the age distribution of 71 cases of familial RCC and of 11 population-based cancer registries [German Democratic Republic, Denmark, Finland, Norway, Sweden, U.S.A. Whites, U.S.A. Blacks, Miyagi and Osaka Prefectures (Japan), Hong Kong, and Israeli Jews] according to the multi-hit and clonal growth models of carcinogenesis. The analysis rules out a double-loss mechanism for RCC. On both of the two models analyzed, carcinogenesis in the familial cases of RCC arises as a result of a three- to ten-fold increase in the average rate of mutation at the susceptible loci, as compared with the sporadic cases. In general, the clonal growth model provides a somewhat better fit to the age-distribution of RCC incidence than does the multi-hit model.

Stochastic simulation of clonal growth in the tall goldenrod, Solidago altissima.

As clonal plants grow they move through space. The movement patterns that result can be complex and difficult to interpret without the aid of models. We developed a stochastic simulation model of clonal growth in the tall goldenrod, Solidago altissima. Our model was calibrated with field data on the clonal expansion of both seedlings and established clones, and model assumptions were verified by statistical analyses.When simulations were based on empirical distributions with long rhizome lengths, there was greater dispersal, less leaf overlap, and less spatial aggregation than when simulations were based on distributions with comparatively short rhizome lengths. For the field data that we utilized, variation in rhizome lengths had a greater effect than variation for either branching angles or "rhizome initiation points" (see text). We also found that observed patterns of clonal growth in S. altissima did not cause the formation of "fairy rings". However, simulations with an artificial distribution of branching angles demonstrate that "fairy rings" can result solely from a plant's clonal morphology.Stochastic simulation models that incorporated variation in rhizome lengths, branching angles, and rhizome initiation points produced greater dispersal and less leaf overlap than deterministic models. Thus, variation for clonal growth parameters may increase the efficiency of substrate exploration by increasing the area covered and by decreasing the potential for intraclonal competition. We also demonstrated that ramet displacements were slightly, but consistently lower in stochastic simulation models than in random-walk models. This difference was due to the incorporation of details on rhizome bud initiation into stochastic simulation models, but not random-walk models. We discuss the advantages and disadvantages of deterministic, stochastic simulation, and random-walk models of clonal growth.

Long-term suppression of insect herbivores increases the production and growth of Solidago altissima rhizomes.

Although insect herbivores have many well documented effects on plant performance, there are few studies that assess the impact of above-ground herbivory on below-ground plant growth. For a seven year period in which no large-scale herbivore outbreaks occurred, a broad spectrum insecticide was utilized to suppress herbivorous insects in a natural community dominated by Solidago altissima. Ramet heights, rhizome lengths, rhizome biomass, and the number of daughter rhizomes all were lower in the control plots than in the insecticidetreated plots. These effects should lead to a decrease in the fitness of genets in the control plots relative to the fitness of genets in the insecticide-treated plots. We also found that ramets in the control plots appear to have compensated for herbivory: the ratio of rhizome length to rhizome biomass was greatest in the control plots, which indicates that clones moved farther per unit biomass in these plots than in the insecticide-treated plots. Clonal growth models show that this shift in allocation patterns greatly reduced the magnitude of treatment differences in long-term clonal displacements.Previous work has shown, and this study verified, that clonal growth in S. altissima is well represented by random-walk and diffusion models. Therefore, we used these models to examine possible treatment differences in rates of clonal expansion. Although rhizome lengths were greater in the insecticide-treated plots, results from the models suggest that our treatments had little impact on the short- and long-term displacement of S. altissima ramets from a point of origin. This occurred because S. altissima ramets backtrack often, and thus, treatment differences in net displacements are less pronounced than treatment differences in rhizome lengths.

Models of Clonal Growth in Solidago Altissima

In this paper, field data on the old-field perennial Solidago altissima were used to test a variety of clonal growth models, including random-walk models, a new way to analyse the vegetative spread of clonal plants.

Quantitative models for lung cancer induced by cigarette smoke.

This discussion paper gives a limited history of work done at this Institute on quantitative modeling relating to lung cancer and cigarette smoking, a health hazard whose study has been given much encouragement by Norton Nelson. It first starts with the proposal that life shortening be considered as a measure of the impact of lung cancer using log normal and Weibull types of distributions of time to occurrence; second, it continues with an examination of the fits of the log normal and Weibull distributions to the Doll and Hill data on smoking and lung cancer in British physicians and a systematic review and development of mathematical models of carcinogenesis; and third, it reports on the current work that points out inconsistencies in the Armitage-Doll multistage model with the Doll and Hill data and suggests a two-stage clonal growth model that assumes promotion of clonal growth is restricted to cells initiated by the smoke. This proposal and related work support a current trend in risk assessment to adopt a two-stage clonal growth model that incorporates birth and death rates of cells and the transitional probabilities of the stages.

Commentary: Quantitative Models for Lung Cancer Induced by Cigarette Smoke

This discussion paper gives a limited history of work done at this Institute on quantitative modeling relating to lung cancer and cigarette smoking, a health hazard whose study has been given much encouragement by Norton Nelson. It first starts with the proposal that life shortening be considered as a measure of the impact of lung cancer using log normal and Weibull types of distributions of time to occurrence; second, it continues with an examination of the fits of the log normal and Weibull distributions to the Doll and Hill data on smoking and lung cancer in British physicians and a systematic review and development of mathematical models of carcinogenesis; and third, it reports on the current work that points out inconsistencies in the Armitage-Doll multistage model with the Doll and Hill data and suggests a two-stage clonal growth model that assumes promotion of clonal growth is restricted to cells initiated by the smoke. This proposal and related work support a current trend in risk assessment to adopt a two-stage clonal growth model that incorporates birth and death rates of cells and the transitional probabilities of the stages.

Lithium stimulation of diffusion chamber colony growth is mediated by factors other than colony‐stimulating factor

Lithium is a recognized, potent stimulator of granulopoiesis. The present study used the model of clonal growth of granulopoietic precursors in diffusion chambers to investigate the relevance of certain colony-stimulating factors to lithium stimulation in vivo. In this system, lithium stimulation of granulopoiesis could not be attributed to changes in serum or chamber fluid colony-stimulating factor levels. Antibody to colony-stimulating factor-1 administered during culture markedly reduced morphologic expression of colonies in control and lithium-pretreated host mice, yet subculture of chamber contents revealed that lithium stimulation of a granulopoietic progenitor, perhaps of primitive potentiality, had nevertheless occurred. Therefore, we hypothesize that lithium acts in an indirect, hormonal fashion and that these colony-stimulating factors, while necessary for morphologic expression, play no role in the stimulatory effect. This hypothesis raises the possibility that lithium in combination with recombinant colony-stimulating factors may result in clinically effective synergistic stimulation of granulopoiesis.