Quantifying metastatic inefficiency:rare genotypes versus rare dynamics

abstract: We introduce and solve a ‘null model’ of stochastic metastatic colonization. The model is described by a single parameter θ: the ratio of the rate of cell division to the rate of cell death for a disseminated tumour cell in a given secondary tissue environment. We are primarily interested in the case in which colonizing cells are poorly adapted for proliferation in the local tissue environment, so that cell death is more likely than cell division, i.e. θ 1), i.e. the statistics show a duality mapping (1 − θ) → (θ − 1). We conclude our analysis with a study of heterogeneity in the fitness of colonising cells, and describe a phase diagram delineating parameter regions in which metastatic colonization is dominated either by low or high fitness cells, showing that both are plausible given our current knowledge of physiological conditions in human cancer

Modeling of Immunosenescence and Risk of Death from Respiratory Infections: Evaluation of the Role of Antigenic Load and Population Heterogeneity

It is well known that efficacy of immune functions declines with age. It results in an increase of severity and duration of respiratory infections and also in dramatic growth of risk of death due to these diseases after age 65. The goal of this work is to describe and investigate the mechanism underlying the age pattern of the mortality rate caused by infectious diseases and to determine the cause-specific hazard rate as a function of immune system characteristics. For these purposes we develop a three-compartment model explaining observed risk-of-death. The model incorporates up-to-date knowledge about cellular mechanisms of aging, disease dynamics, population heterogeneity in resistance to infections, and intrinsic aging rate. The results of modeling show that the age-trajectory of mortality caused by respiratory infections may be explained by the value of antigenic load, frequency of infections and the rate of aging of the stem cell population (i.e. the population of T-lymphocyte progenitor cells). The deceleration of infection-induced mortality at advanced age can be explained by selection of individuals with a slower rate of stem cell aging. Parameter estimates derived from fitting mortality data indicate that infection burden was monotonically decreasing during the twentieth century, and changes in total antigenic load were gender-specific: it experienced periodic fluctuations in males and increased approximately two-fold in females

Genetic composition of an exponentially growing cell population

We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values in bacteria and cancer cell populations, we take the mutation rate to zero and the final number of cells to infinity. We prove that almost every site (entry of the nucleotide sequence) is mutated in only a finite number of cells, and these numbers are independent across sites. However independence breaks down for the rare sites which are mutated in a positive fraction of the population. The model is free from the popular but disputed infinite sites assumption. Violations of the infinite sites assumption are widespread while their impact on mutation frequencies is negligible at the scale of population fractions. Some results are generalised to allow for cell death, selection, and site-specific mutation rates. For illustration we estimate mutation rates in a lung adenocarcinoma

Comfort Women in Indonesia: A Consideration of the Prewar Socio-legal context in Indonesia and Japan

14 páginas, 5 figuras, 10 tablas.A mechanistic lactation model, based on a theory of mammary cell proliferation and cell death, was studied and compared to the equation of Wood (1967). Lactation curves of British Holstein Friesian cows (176 curves), Spanish Churra sheep (40 curves) and Spanish Murciano-Granadina goats (30 curves) were used for model evaluation. Both models were fitted in their original form using non-linear least squares estimation. The parameters were compared among species and among parity groups within species. In general, both models provided highly significant fits to lactation data and described the data accurately. The mechanistic model performed well against Wood's 1967 equation (hereafter referred to as Wood's equation), resulting in smaller residual mean square values in more than two-thirds of the datasets investigated, and producing parameter estimates that allowed appropriate comparisons and noticeable trends attributed to shape. Using Akaike or Bayesian information criteria, goodness-of-fit with the mechanistic model was superior to that with Wood's equation for 1 Lie cow lactation curves, with no significant differences between models when fitted to goat or sheep lactation curves. The rate parameters of the mechanistic model, representing specific proliferation rate of mammary secretory cells at parturition, decay associated with reduction in cell proliferation capacity with time and specific death rate of mammary secretory cells, were smaller for primiparous than for multiparous cows. Greater lactation persistency of cows compared to goats and sheep, and decrease in persistency with parity, were shown to be represented by different values of the specific secretory cell death rate parameter in the mechanistic model. The plausible biological interpretation and fitting properties of the mechanistic model enable it to be used in complex models of whole-cow digestion and metabolism and as a tool in selection programmes and by dairy producers for management decisions.Canada Research Chairs ProgramPeer reviewe

Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model

Modeling viral dynamics in HIV/AIDS studies has resulted in a deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS290 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Yeast cell death caused by nutrient desequilibrium during alcoholic fermentation is impacted by nitrogen sources

Nutrients availability is a key factor for controlling wine alcoholic fermentation. Among them, nitrogen has been identified as an essential parameter, controlling both the fermentation rate and the durationof the fermentation. However, nitrogen is not sufficient to ensure a correct fermentation and other nutrients such as vitamins and lipids, present in lower quantities, are required. Furthermore, we showed in a previous study that an excess of nitrogen combined with a depletion in certain micronutrients can lead to cell death and sluggish or stuck fermentation. In this study, we provide evidence of the mechanism controlling cell death and we show that all the nitrogen sources are not equivalent in the initiation of this phenomenon.Fermentations limited in oleic acid, pantothenic acid and nicotinic acid showed yeast cell death linked to a high nitrogen content. In each case, lowering the nitrogen level restored yeast viability. We evidenced that yeast cell lack of a correct stress response to those micronutrient starvations in presence of high levels of nitrogen. A transcriptional analysis showed a correct stress response suggesting that the lack of resistance originates from a post-transcriptional control mechanism. We then provide evidence that the nitrogen Tor/Sch9 signaling pathway is involved in triggering cell death.Yeast cell viability was then monitored and compared during fermentation starting at different nitrogen levels, with the addition of different nitrogen sources (19 amino acids and NH4+) and two different timing of NH4+ addition. We observed that cell death was triggered with different intensities.Yeast cell death associated to disequilibrium between micronutrients and nitrogen has been evidenced and its implication on fermentations highlighted. We showed a strong impact of both the nature of the nitrogen source and time of addition on yeast cell death and fermentation outcome

Quantitative analysis of the potential role of basal cell hyperplasia in the relationship between clonal expansion and radon concentration

Applying the two-stage clonal expansion model to epidemiology of lung cancer among uranium miners, it has been revealed that radon acts as a promoting agent facilitating the clonal expansion of already mutated cells. Clonal expansion rate increases non-linearly by radon concentration showing a plateau above a given exposure rate. The underlying mechanisms remain unclear. Earlier we proposed that progenitor cell hyperplasia may be induced upon chronic radon exposure. The objective of the present study is to test whether the induction of hyperplasia may provide a quantitative explanation for the plateau in clonal expansion rate. For this purpose, numerical epithelium models were prepared with different number of basal cells. Cell nucleus hits were computed by an own-developed Monte-Carlo code. Surviving fractions were estimated based on the number of cell nucleus hits. Cell division rate was computed supposing equilibrium between cell death and cell division. It was also supposed that clonal expansion rate is proportional to cell division rate, and therefore the relative increase in cell division rate and clonal expansion rate are the same functions of exposure rate. While the simulation results highly depend on model parameters with high uncertainty, a parameter set has been found resulting in a cell division rate exposure rate relationship corresponding to the plateau in clonal expansion rate. Due to the high uncertainty of the applied parameters, however, further studies are required to decide whether the induction of hyperplasia is responsible for the non-linear increase in clonal expansion rate or not. Nevertheless the present study exemplifies how computational modelling can contribute to the integration of observational and experimental radiation protection research.Comment: paper presented in the 17th International Symposium on Microdosimetry (MICROS 2017 - Venice, Italy, 5-10 November, 2017), 5 pages, 1 table, 6 figure

Quantitative analysis of the potential role of basal cell hyperplasia in the relationship between clonal expansion and radon concentration

Applying the two-stage clonal expansion model to epidemiology of lung cancer among uranium miners, it has been revealed that radon acts as a promoting agent facilitating the clonal expansion of already mutated cells. Clonal expansion rate increases non-linearly by radon concentration showing a plateau above a given exposure rate. The underlying mechanisms remain unclear. Earlier we proposed that progenitor cell hyperplasia may be induced upon chronic radon exposure. The objective of the present study is to test whether the induction of hyperplasia may provide a quantitative explanation for the plateau in clonal expansion rate. For this purpose, numerical epithelium models were prepared with different number of basal cells. Cell nucleus hits were computed by an own-developed Monte-Carlo code. Surviving fractions were estimated based on the number of cell nucleus hits. Cell division rate was computed supposing equilibrium between cell death and cell division. It was also supposed that clonal expansion rate is proportional to cell division rate, and therefore the relative increase in cell division rate and clonal expansion rate are the same functions of exposure rate. While the simulation results highly depend on model parameters with high uncertainty, a parameter set has been found resulting in a cell division rate exposure rate relationship corresponding to the plateau in clonal expansion rate. Due to the high uncertainty of the applied parameters, however, further studies are required to decide whether the induction of hyperplasia is responsible for the non-linear increase in clonal expansion rate or not. Nevertheless the present study exemplifies how computational modelling can contribute to the integration of observational and experimental radiation protection research.Comment: paper presented in the 17th International Symposium on Microdosimetry (MICROS 2017 - Venice, Italy, 5-10 November, 2017), 5 pages, 1 table, 6 figure