Continental Scale Modelling of Water Quality in Rivers

Global and continental scale modelling has been confined to water quantity (e.g. WaterGAP - Water Global Assessment and Prognosis (Alcamo et al. 2003), GWAVA - Global Water AVailability Assessment (Meigh et al, 1999)). Here we describe an approach to include water quality at these scales within the WaterGAP model. The application is to the pan-European area and is being carried out within the EU-funded SCENES Project which has the principal goal of developing new scenarios of the future of freshwater resources in Europe. The model operates on 5x5 arc-minute grid squares. Water flows in and between grid cells are provided by WaterGAP. The water quality loadings into the river system comprise point sources (domestic effluent, manufacturing discharges and urban runoff) and diffuse sources (runoff from land and scattered settlements not connected to the public sewerage system). Point source loadings are calculated for each country using easily available datasets. For example, the domestic load is a per capita emission factor times by country population multiplied by the percentage of the population connected to the sewage system, which is then reduced by the amount removed in each of three types of sewage treatment (primary, secondary and tertiary). Data on the amount treated in different types of sewage works is set for each country, while the amount removed by treatment types will vary with the water quality variable being modelled. Country level data is converted to grid square data required by the model, according to the population in each grid square. Diffuse sources from land are calculated by regression models based on runoff and land use (e.g. numbers of livestock) for each model grid square. The modelling system has currently been set up to simulate biochemical oxygen demand (BOD) and total dissolved solids. The model was tested against measured longitudinal profiles and time series data for BOD on contrasting rivers e.g. the River Thames (UK) driven by domestic loading and the River Ebro (Spain) with a high share of discharges from livestock farming. Further developments will see the inclusion of total nitrogen (TN), total phosphorus (TP) and dissolved oxygen. Within the SCENES project a set of future scenarios reflecting different outlooks on Europe has been developed, called “Economy First”, “Fortress Europe”, “Sustainability Eventually” and “Policy Rules”. An Expert Panel was used to suggest what these futures would mean for drivers of water quantity and water quality across pan-Europe. We have projected how changes in percentage population connected to sewers, the level of sewage treatment and population would change loadings from domestic effluent for TN, TP and BOD. In time, these will be used to predict future water quality in European rivers

A Dynamically Diluted Alignment Model Reveals the Impact of Cell Turnover on the Plasticity of Tissue Polarity Patterns

The polarisation of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern reorganisation in response to an opposing instructive cue, which we here consider by example of experimentally inducible body axis inversions in planarian flatworms. Our dynamically diluted alignment model represents three processes: entrainment of cell polarity by a global signal, local cell-cell coupling aligning polarity among neighbours and cell turnover inserting initially unpolarised cells. We show that a persistent global orienting signal determines the final mean polarity orientation in this stochastic model. Combining numerical and analytical approaches, we find that neighbour coupling retards polarity pattern reorganisation, whereas cell turnover accelerates it. We derive a formula for an effective neighbour coupling strength integrating both effects and find that the time of polarity reorganisation depends linearly on this effective parameter and no abrupt transitions are observed. This allows to determine neighbour coupling strengths from experimental observations. Our model is related to a dynamic $8$-Potts model with annealed site-dilution and makes testable predictions regarding the polarisation of dynamic systems, such as the planarian epithelium.Comment: Preprint as prior to first submission to Journal of the Royal Society Interface. 25 pages, 6 figures, plus supplement (18 pages, contains 1 table and 7 figures). A supplementary movie is available from https://dx.doi.org/10.6084/m9.figshare.c388781

Geschäftsmodelle im deutschen Viehhandel: Konzeptionelle Grundlagen und empirische Ergebnisse

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Modeling age-specific incidence of colon cancer via niche competition

Cancer development is a multistep process often starting with a single cell in which a number of epigenetic and genetic alterations have accumulated thus transforming it into a tumor cell. The progeny of such a single benign tumor cell expands in the tissue and can at some point progress to malignant tumor cells until a detectable tumor is formed. The dynamics from the early phase of a single cell to a detectable tumor with billions of tumor cells are complex and still not fully resolved, not even for the well-known prototype of multistage carcinogenesis, the adenoma-adenocarcinoma sequence of colorectal cancer. Mathematical models of such carcinogenesis are frequently tested and calibrated based on reported age-specific incidence rates of cancer, but they usually require calibration of four or more parameters due to the wide range of processes these models aim to reflect. We present a cell-based model, which focuses on the competition between wild-type and tumor cells in colonic crypts, with which we are able reproduce epidemiological incidence rates of colon cancer. Additionally, the fraction of cancerous tumors with precancerous lesions predicted by the model agree with clinical estimates. The correspondence between model and reported data suggests that the fate of tumor development is majorly determined by the early phase of tumor growth and progression long before a tumor becomes detectable. Due to the focus on the early phase of tumor development, the model has only a single fit parameter, the time scale set by an effective replacement rate of stem cells in the crypt. We find this effective rate to be considerable smaller than the actual replacement rate, which implies that the time scale is limited by the processes succeeding clonal conversion of crypts.Comment: 28 pages, 13 figure

Der Viehhandel in den Wertschöpfungsketten der Fleischwirtschaft: Entwicklungstendenzen und Perspektiven

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Is cell segregation like oil and water: asymptotic versus transitory regime

Segregation of different cell types is a crucial process for the pattern formation in tissues, in particular during embryogenesis. Since the involved cell interactions are complex and difficult to measure individually in experiments, mathematical modelling plays an increasingly important role to unravel the mechanisms governing segregation. The analysis of these theoretical models focuses mainly on the asymptotic behavior at large times, in a steady regime and for large numbers of cells. Most famously, cell-segregation models based on the minimization of the total surface energy, a mechanism also driving the demixing of immiscible fluids, are known to exhibit asymptotically a particular algebraic scaling behavior. However, it is not clear, whether the asymptotic regime of the numerical models is relevant at the spatio-temporal scales of actual biological processes and in-vitro experiments. By developing a mapping between cell-based models and experimental settings, we are able to directly compare previous experimental data to numerical simulations of cell segregation quantitatively. We demonstrate that the experiments are reproduced by the transitory regime of the models rather than the asymptotic one. Our work puts a new perspective on previous model-driven conclusions on cell segregation mechanisms.Comment: 24 pages, 7+4 figure

Patterns of Tumor Progression Predict Small and Tissue-Specific Tumor-Originating Niches

The development of cancer is a multistep process in which cells increase in malignancy through progressive alterations. Such altered cells compete with wild-type cells and have to establish within a tissue in order to induce tumor formation. The range of this competition and the tumor-originating cell type which acquires the first alteration is unknown for most human tissues, mainly because the involved processes are hardly observable, aggravating an understanding of early tumor development. On the tissue scale, one observes different progression types, namely with and without detectable benign precursor stages. Human epidemiological data on the ratios of the two progression types exhibit large differences between cancers. The idea of this study is to utilize data of the ratios of progression types in human cancers to estimate the homeostatic range of competition in human tissues. This homeostatic competition range can be interpreted as necessary numbers of altered cells to induce tumor formation on the tissue scale. For this purpose, we develop a cell-based stochastic model which is calibrated with newly-interpreted human epidemiological data. We find that the number of tumor cells which inevitably leads to later tumor formation is surprisingly small compared to the overall tumor and largely depends on the human tissue type. This result points toward the existence of a tissue-specific tumor-originating niche in which the fate of tumor development is decided early and long before a tumor becomes detectable. Moreover, our results suggest that the fixation of tumor cells in the tumor-originating niche triggers new processes which accelerate tumor growth after normal tissue homeostasis is voided. Our estimate for the human colon agrees well with the size of the stem cell niche in colonic crypts. For other tissues, our results might aid to identify the tumor-originating cell type. For instance, data on primary and secondary glioblastoma suggest that the tumors originate from a cell type competing in a range of 300 – 1,900 cells