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Towards a Colonic Crypt Model with Realistic, Deformable Geometry

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Colorectal cancer (CRC) is one of the leading causes of cancer-related death worldwide, demanding a response from scientists and clinicians to understand its aetiology and develop effective treatments. CRC is thought to originate via genetic alterations that cause disruption to the cellular dynamics of the crypts of Lieberk¨uhn, test tube shaped glands lined with a monolayer of epithelial cells, which responsible for renewing the intestinal surface through a coordinated sequence of cell division, migration and death. It is believed that in the first step of colorectal carcinogenesis, crypts acquire genetic mutations that disrupt the normal patterns of cell proliferation and migration, which can lead to crypt buckling and fission, and the formation of a benign tumour. Over time and via accumulated mutations, these growths progress to a malignant lesion that can break through to the underlying tissue stroma, and so aid metastasis. The dynamic cell properties that are required to initiate crypt buckling are poorly understood, as it is difficult for biologists to experimentally observe, either in vivo or in vitro, the initial changes in this sequence of events. Performing in silico experiments using an accurate, predictive computational model of the crypt can identify the key changes and responsible mechanisms. Such a model must account for the tissue structure, incorporating the elements that provide stability, without imposing a fixed shape. In particular, the role of the basement membrane is vital in maintaining the integrity and structure of the epithelial monolayer, acting as both a mechanical support and forming the physical interface between epithelial cells and the surrounding connective tissue.

A model is proposed here to directly address these criteria. An off-lattice cell-centre modelling approach is adopted, with cell-cell connectivity defined by a Delaunay triangulation, and polygonal cell shapes realistically prescribed by the dual Voronoi tessellation. A novel method for modelling the role of the basement membrane beneath a growing epithelium is presented, which subsequently allows the desired crypt geometry to develop. Further to this, the model takes into account the continuous meshwork of actin that forms a basket below each crypt base, and which provides stability to this region. Results from in silico simulations show that homeostasis of the growing epithelial monolayer can be achieved and sustained within this modelling framework, and the necessary balance of interactive cell forces, cell migration and cell death are presented.

The computational framework for this model is based within the Chaste environment (, an open source software library written in object-oriented C++. Chaste is a general purpose simulation package aimed at multi-scale, computationally demanding problems arising in biology and physiology, developed using agile programming techniques and following software engineering practices. The modular nature of the Chaste framework enhances model versatility – it is possible to apply and compare alternative cell interaction models, cell cycle models and tissue geometry. As a key component of the proposed crypt model, this computational modelling framework will be introduced.

This model is proposed as the foundation of a realistic representation of growth of an epithelial sheet in a deformable environment, and forms the basis for investigation of the deformation of the crypt structure that can occur due to proliferation of cells exhibiting abberant, mutant phenotypes. Whilst it is applied here specifically to the colonic crypt, the basic principles extend to other biological epithelia, such as the interfollicular epidermis, or the olfactory mucous membrane. Thus, this work and the results presented, hold potential for future research in other biological contexts.

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