197 research outputs found

    A Comprehensive Model of the Spatio-Temporal Stem Cell and Tissue Organisation in the Intestinal Crypt

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    We introduce a novel dynamic model of stem cell and tissue organisation in murine intestinal crypts. Integrating the molecular, cellular and tissue level of description, this model links a broad spectrum of experimental observations encompassing spatially confined cell proliferation, directed cell migration, multiple cell lineage decisions and clonal competition

    A comprehensive Model of the Spatio-Temporal Stem Cell and Tissue Organisation in the Intestinal Crypt

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    We introduce a novel dynamic model of stem cell and tissue organisation in murine intestinal crypts. Integrating the molecular, cellular and tissue level of description, this model links a broad spectrum of experimental observations encompassing spatially confined cell proliferation, directed cell migration, multiple cell lineage decisions and clonal competition. Using computational simulations we demonstrate that the model is capable of quantitatively describing and predicting the dynamic behaviour of the intestinal tissue during steady state as well as after cell damage and following selective gain or loss of gene function manipulations affecting Wnt- and Notch-signalling. Our simulation results suggest that reversibility and flexibility of cellular decisions are key elements of robust tissue organisation of the intestine. We predict that the tissue should be able to fully recover after complete elimination of cellular subpopulations including subpopulations deemed to be functional stem cells. This challenges current views of tissue stem cell organisation

    Models, measurement and inference in epithelial tissue dynamics

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    The majority of solid tumours arise in epithelia and therefore much research effort has gone into investigating the growth, renewal and regulation of these tissues. Here we review different mathematical and computational approaches that have been used to model epithelia. We compare different models and describe future challenges that need to be overcome in order to fully exploit new data which present, for the first time, the real possibility for detailed model validation and comparison

    Modelling the Spatio-Temporal Cell Dynamics Reveals Novel Insights on Cell Differentiation and Proliferation in the Small Intestinal Crypt

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    We developed a slow structural relaxation model to describe cellular dynamics in the crypt of the mouse small intestine. Cells are arranged in a three dimensional spiral the size of which dynamically changes according to cell production demands of adjacent villi. Cell differentiation and proliferation is regulated through Wnt and Notch signals, the strength of which depends on the local cell composition. The highest level of Wnt activity is associated with maintaining equipotent stem cells (SC), Paneth cells and common goblet-Paneth cell progenitors (CGPCPs) intermingling at the crypt bottom. Low levels of Wnt signalling area are associated with stem cells giving rise to secretory cells (CGPCPs, enteroendocrine or Tuft cells) and proliferative absorptive progenitors. Deciding between these two fates, secretory and stem/absorptive cells, depends on Notch signalling. Our model predicts that Notch signalling inhibits secretory fate if more than 50% of cells they are in contact with belong to the secretory lineage. CGPCPs under high Wnt signalling will differentiate into Paneth cells while those migrating out from the crypt bottom differentiate into goblet cells. We have assumed that mature Paneth cells migrating upwards undergo anoikis. Structural relaxation explains the localisation of Paneth cells to the crypt bottom in the absence of active forces. The predicted crypt generation time from one SC is 4–5 days with 10–12 days needed to reach a structural steady state. Our predictions are consistent with experimental observations made under altered Wnt and Notch signalling. Mutations affecting stem cells located at the crypt floor have a 50% chance of being propagated throughout the crypt while mutations in cells above are rarely propagated. The predicted recovery time of an injured crypt losing half of its cells is approximately 2 days

    Multiscale modelling of intestinal crypt organization and carcinogenesis

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    Colorectal cancers are the third most common type of cancer. They originate from intestinal crypts, glands that descend from the intestinal lumen into the underlying connective tissue. Normal crypts are thought to exist in a dynamic equilibrium where the rate of cell production at the base of a crypt is matched by that of loss at the top. Understanding how genetic alterations accumulate and proceed to disrupt this dynamic equilibrium is fundamental to understanding the origins of colorectal cancer. Colorectal cancer emerges from the interaction of biological processes that span several spatial scales, from mutations that cause inappropriate intracellular responses to changes at the cell/tissue level, such as uncontrolled proliferation and altered motility and adhesion. Multiscale mathematical modelling can provide insight into the spatiotemporal organisation of such a complex, highly regulated and dynamic system. Moreover, the aforementioned challenges are inherent to the multiscale modelling of biological tissue more generally. In this review we describe the mathematical approaches that have been applied to investigate multiscale aspects of crypt behavior, highlighting a number of model predictions that have since been validated experimentally. We also discuss some of the key mathematical and computational challenges associated with the multiscale modelling approach. We conclude by discussing recent efforts to derive coarse-grained descriptions of such models, which may offer one way of reducing the computational cost of simulation by leveraging well-established tools of mathematical analysis to address key problems in multiscale modelling

    Colorectal Cancer Through Simulation and Experiment

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    Colorectal cancer has continued to generate a huge amount of research interest over several decades, forming a canonical example of tumourigenesis since its use in Fearon and Vogelstein’s linear model of genetic mutation. Over time, the field has witnessed a transition from solely experimental work to the inclusion of mathematical biology and computer-based modelling. The fusion of these disciplines has the potential to provide valuable insights into oncologic processes, but also presents the challenge of uniting many diverse perspectives. Furthermore, the cancer cell phenotype defined by the ‘Hallmarks of Cancer’ has been extended in recent times and provides an excellent basis for future research. We present a timely summary of the literature relating to colorectal cancer, addressing the traditional experimental findings, summarising the key mathematical and computational approaches, and emphasising the role of the Hallmarks in current and future developments. We conclude with a discussion of interdisciplinary work, outlining areas of experimental interest which would benefit from the insight that mathematical and computational modelling can provide

    A theoretical investigation of the effect of proliferation and\ud adhesion on monoclonal conversion in the colonic crypt

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    Colorectal cancers are initiated by the accumulation of mutations in the colonic epithelium. Using a spatially structured cell-based model of a colonic crypt, we investigate the likelihood that the progeny of a mutated cell will dominate, or be sloughed out of, a crypt. Our approach is to perform multiple simulations, varying the spatial location of the initial mutation, and its proliferative and adhesive properties, to obtain statistical distributions for the probability of domination. Our simulations lead us to make a number of predictions. The process of monoclonal conversion always occurs, and does not require that the cell which initially gave rise to the population remains in the crypt. Mutations occurring more than one to two cells from the base of the crypt are unlikely to become the dominant clone. The probability of a mutant clone persisting in the crypt is sensitive to dysregulation of adhesion, and comparison with a one-dimensional model suggests that this is caused by competition directly at the base of the crypt.\ud We also predict that increases in the extent of the spatial domain in which the mutant cells proliferate cause counter-intuitive non-linear changes to the probability of its fixation, due to effects that cannot be captured in simpler models

    A theoretical investigation of the effect of proliferation & adhesion on monoclonal conversion in the colonic crypt

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    The surface epithelium lining the intestinal tract renews itself rapidly by a coordinated programme of cell proliferation, migration and differentiation events that is initiated in the crypts of Lieberkühn. It is generally believed that colorectal cancer arises due to mutations that disrupt the normal cellular dynamics of the crypts. Using a spatially structured cell-based model of a colonic crypt, we investigate the likelihood that the progeny of a mutated cell will dominate, or be sloughed out of, a crypt. Our approach is to perform multiple simulations, varying the spatial location of the initial mutation, and the proliferative and adhesive properties of the mutant cells, to obtain statistical distributions for the probability of their domination. Our simulations lead us to make a number of predictions. The process of monoclonal conversion always occurs, and does not require that the cell which initially gave rise to the population remains in the crypt. Mutations occurring more than one to two cells from the base of the crypt are unlikely to become the dominant clone. The probability of a mutant clone persisting in the crypt is sensitive to dysregulation of adhesion. By comparing simulation results with those from a simple one-dimensional stochastic model of population dynamics at the base of the crypt, we infer that this sensitivity is due to direct competition between wild-type and mutant cells at the base of the crypt. We also predict that increases in the extent of the spatial domain in which the mutant cells proliferate can give rise to counter-intuitive, non-linear changes to the probability of their fixation, due to effects that cannot be captured in simpler models

    Cell organisation in the colonic crypt: A theoretical comparison of the pedigree and niche concepts

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    The intestinal mucosa is a monolayer of rapidly self-renewing epithelial cells which is not only responsible for absorption of water and nutrients into the bloodstream but also acts as a protective barrier against harmful microbes entering the body. New functional epithelial cells are produced from stem cells, and their proliferating progeny. These stem cells are found within millions of crypts (tubular pits) spaced along the intestinal tract. The entire intestinal epithelium is replaced every 2–3 days in mice (3–5 days in humans) and hence cell production, differentiation, migration and turnover need to be tightly regulated. Malfunctions in this regulation are strongly linked to inflammatory bowel diseases and to the formation of adenomas and ultimately cancerous tumours. Despite a great deal of biological experimentation and observation, precisely how colonic crypts are regulated to produce mature colonocytes remains unclear. To assist in understanding how cell organisation in crypts is achieved, two very different conceptual models of cell behaviour are developed here, referred to as the ‘pedigree’ and the ‘niche’ models. The pedigree model proposes that crypt cells are largely preprogrammed and receive minimal prompting from the environment as they move through a routine of cell differentiation and proliferation to become mature colonocytes. The niche model proposes that crypt cells are primarily influenced by the local microenvironments along the crypt, and that predetermined cell behaviour plays a negligible role in their development. In this paper we present a computational model of colonic crypts in the mouse, which enables a comparison of the quality and controllability of mature coloncyte production by crypts operating under these two contrasting conceptual models of crypt regulation
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