Colorectal Cancer Through Simulation and Experiment

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 modelling approach towards Epidermal homoeostasis control

In order to grasp the features arising from cellular discreteness and individuality, in large parts of cell tissue modelling agent-based models are favoured. The subclass of off-lattice models allows for a physical motivation of the intercellular interaction rules. We apply an improved version of a previously introduced off-lattice agent-based model to the steady-state flow equilibrium of skin. The dynamics of cells is determined by conservative and drag forces,supplemented with delta-correlated random forces. Cellular adjacency is detected by a weighted Delaunay triangulation. The cell cycle time of keratinocytes is controlled by a diffusible substance provided by the dermis. Its concentration is calculated from a diffusion equation with time-dependent boundary conditions and varying diffusion coefficients. The dynamics of a nutrient is also taken into account by a reaction-diffusion equation. It turns out that the analysed control mechanism suffices to explain several characteristics of epidermal homoeostasis formation. In addition, we examine the question of how {\em in silico} melanoma with decreased basal adhesion manage to persist within the steady-state flow-equilibrium of the skin.Interestingly, even for melanocyte cell cycle times being substantially shorter than for keratinocytes, tiny stochastic effects can lead to completely different outcomes. The results demonstrate that the understanding of initial states of tumour growth can profit significantly from the application of off-lattice agent-based models in computer simulations.Comment: 23 pages, 7 figures, 1 table; version that is to appear in Journal of Theoretical Biolog

Study of Eukaryotic Cellular Process by Mathematical Modeling: Chemotaxis and Mitosis

Chemotaxis, the directed cell movement in response to external chemical gradients, is a vital biological process. Single cell organisms, such as bacteria and amoebae, rely on chemotaxis for feeding. In multicellular organisms, it plays an important role during embryogenesis, directing cells of the immune system to sites of infection and disease, wound healing, and in cancer metastasis. In eukaryotic cells, a complex signaling system involving over one hundred biochemical components and numerous redundant pathways mediates chemotaxis. Because of the complexity of this system, it has proved to be advantageous to study chemotaxis by isolating the chemotactic response into a set of simpler processes: motility, gradient sensing, and polarization. Research into chemotaxis has also benefited from numerous theoretical and computational treatments that complement experimental studies. Here, we developed a computational framework using a modular view of the chemotactic behavior in Dictyostelium cells. The starting point is a proposed model that suggests that cells rely on firings of an excitable network to generate pseudopods. In the absence of chemoattractant stimuli, these firings can be triggered by stochastic perturbations in the signaling system. However, chemottractants bias the location of the firings by altering the level of the threshold. Here, we carry out tests of this local-excitation, global-inhibition biased excitable network (LEGI-BEN) hypothesis. In particular, we couple the model to a viscoelastic description of the cell and test through simulation how well the model can recreate observed behaviors of chemotactic cells. Based on these simulations and on new experimental findings, we propose several modifications to the existing models. One additional component incorporates a polarity module that endows cell movement with persistence. A second addition is an oscillatory cytoskeletal network that recreates fast oscillations observed in cells. In addition to the research in chemotaxis, this dissertation also reports on the development of a mathematical model describing mitotic matrix formation after nuclear envelope breakdown. Recent reports show that lamin B, a component of the nuclear lamina in interphase, localizes around the spindle and reassembles to form a mitotic matrix. How this process occurs, however, and what effect it has on the mitotic spindle is unclear. Here, we develop a computational model based on a continuum description to represent the abundance and location of the various molecular species involved during mitosis. We use this model to examine the role for the matrix during spindle formation and to test between several hypotheses regarding the formation of the mitotic matrix

Modeling and simulation of multi-cellular systems using hybrid FEM/Agent-based approaches

Muchas de las propiedades biomecánicas de los organismos multicelulares surgen directamente de las interacciones entre células. Las células de los órganos y tejidos interactúan entre sí y con su entorno de diferentes formas. Debido a este hecho, es fundamental analizar cómo estas interacciones se traducen como propiedades mecánicas a nivel del tejido. Por ejemplo, las adhesiones entre células determinan la rigidez aparente de una capa epitelial. Las interacciones célula-matriz pueden además determinar la formación de muchas estructuras biológicas y su morfología. Estos sistemas multicelulares no se pueden considerar como estructuras estáticas ya que sufren constantes cambios causados por la proliferación, la reorganización o la migración celular. Por lo tanto, es necesario estudiar la dinámica de la célula y las interacciones individuales para comprender plenamente cómo funcionan los fenómenos a escalas superiores, desde el desarrollo de tejidos hasta el crecimiento de tumores.Recientemente, el uso de enfoques basados en agentes se ha vuelto muy popular para modelar sistemas multicelulares. Los modelos basados en agentes representan células como entidades individuales. Estos modelos son especialmente adecuados para estudiar fenómenos biofísicos que ocurren a nivel celular. Aquí las interacciones célula-célula se pueden simular directamente de forma mecanicista. Además, estos modelos capturan realmente bien las heterogeneidades presentes en las estructuras biológicas. Por otra parte, los modelos continuos se utilizan comúnmente en problemas de escalas mayores. A diferencia de los modelos basados en agentes, en estos no representan células como entidades individuales, sino que se definen leyes constitutivas para modelar procesos biológicos, físicos y químicos. Por lo tanto, las propiedades celulares se promedian usando parámetros macroscópicos, y estos modelos a menudo trabajan con la densidad celular en lugar de entidades celulares separadas. En cualquier caso, los modelos continuos presentan una buena escalabilidad y una excelente representación de fenómenos físicos particulares como el transporte masivo y las transmisiones de fuerza en medios continuos.En esta tesis, se exploran las posibilidades que los enfoques híbridos pueden ofrecer para desarrollar nuevos modelos de sistemas multicelulares. Se presentan dos modelos híbridos diferentes que combinan un modelo basado en agentes y un modelo continuo. Ambos enfoques tienen en común que el modelo continuo se resuelve utilizando el método de los elementos finitos. También se muestra, siguiendo este patrón de diseño, cómo resolver varias de las limitaciones intrínsecas de cada tipo individual de modelo.En primer lugar, se presenta un modelo híbrido para simular la mecánica epitelial monocapa. Este modelo se centra en el modelado de las interacciones mecánicas célula-célula y célula-sustrato, pero también en la topología y morfología de los tejidos. Con este enfoque se reproducen tejidos epiteliales proliferativos, movimientos celular colectivo y procesos de migración. El segundo modelo presentado en esta tesis se ha diseñado para simular agregados celulares en entornos tridimensionales. Se estudian las interacciones mecánicas entre células, pero este modelo se centra especialmente en analizar cómo afecta el transporte de oxígeno a las células en un proceso de agrupamiento en 3D.Finalmente, se comparan los resultados de ambos modelos con datos experimentales de otros autores y se discuten los beneficios de combinar diferentes tipos de modelos. Se demuestra que los enfoques híbridos que se proponen en este trabajo son capaces de simular una amplia variedad de sistemas multicelulares. De hecho, son particularmente útiles para estudiar cómo algunos fenómenos emergen de las interacciones celulares individuales a escalas biológicas más grandes.<br /

An integrative computational model for intestinal tissue renewal

Objectives\ud \ud The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoretical models are powerful tools that can be used to test hypotheses concerning the regulation of this renewal process, to investigate how its dysfunction can lead to loss of homeostasis and neoplasia, and to identify potential therapeutic interventions. Here we propose a new multiscale model for crypt dynamics that links phenomena occurring at the subcellular, cellular and tissue levels of organisation.\ud \ud Methods\ud \ud At the subcellular level, deterministic models characterise molecular networks, such as cell-cycle control and Wnt signalling. The output of these models determines the behaviour of each epithelial cell in response to intra-, inter- and extracellular cues. The modular nature of the model enables us to easily modify individual assumptions and analyse their effects on the system as a whole.\ud \ud Results\ud \ud We perform virtual microdissection and labelling-index experiments, evaluate the impact of various model extensions, obtain new insight into clonal expansion in the crypt, and compare our predictions with recent mitochondrial DNA mutation data. \ud \ud Conclusions\ud \ud We demonstrate that relaxing the assumption that stem-cell positions are fixed enables clonal expansion and niche succession to occur. We also predict that the presence of extracellular factors near the base of the crypt alone suffices to explain the observed spatial variation in nuclear beta-catenin levels along the crypt axis

A multiple scale model for tumor growth

We present a physiologically structured lattice model for vascular tumor growth which accounts for blood flow and structural adaptation of the vasculature, transport of oxygen, interaction between cancerous and normal tissue, cell division, apoptosis, vascular endothelial growth factor release, and the coupling between these processes. Simulations of the model are used to investigate the effects of nutrient heterogeneity, growth and invasion of cancerous tissue, and emergent growth laws