Crypt dynamics and colorectal cancer: advances in mathematical modelling.

Mathematical modelling forms a key component of systems biology, offering insights that complement and stimulate experimental studies. In this review, we illustrate the role of theoretical models in elucidating the mechanisms involved in normal intestinal crypt dynamics and colorectal cancer. We discuss a range of modelling approaches, including models that describe cell proliferation, migration, differentiation, crypt fission, genetic instability, APC inactivation and tumour heterogeneity. We focus on the model assumptions, limitations and applications, rather than on the technical details. We also present a new stochastic model for stem-cell dynamics, which predicts that, on average, APC inactivation occurs more quickly in the stem-cell pool in the absence of symmetric cell division. This suggests that natural niche succession may protect stem cells against malignant transformation in the gut. Finally, we explain how we aim to gain further understanding of the crypt system and of colorectal carcinogenesis with the aid of multiscale models that cover all levels of organization from the molecular to the whole organ.

From exposure to effect: a comparison of modeling approaches to chemical carcinogenesis.

Standardized long-term carcinogenicity tests aim to reveal the relationship between exposure to a chemical and occurrence of a carcinogenic response. The analysis of such tests may be facilitated by the use of mathematical models. To what extent current models actually achieve this purpose is difficult to evaluate. Various aspects of chemically induced carcinogenesis are treated by different modeling approaches, which proceed very much in isolation of each other. With this paper we aim to provide for the non-mathematician a comprehensive and critical overview of models dealing with processes involved in chemical carcinogenesis. We cover the entire process of carcinogenesis, from exposure to effect. We succinctly summarize the biology underlying the models and emphasize the relationship between model assumptions and model formulations. The use of mathematics is restricted as far as possible with some additional information relegated to boxes.

An integrative computational model for intestinal tissue renewal.

OBJECTIVES: 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. METHODS: 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. RESULTS: 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. CONCLUSIONS: 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 mathematical model that accounts for the effects of caloric restriction on body weight and longevity.

Several aspects of energy dynamics, such as energy expenditure and caloric intake, are known to affect the aging process. In this article we therefore model the aging process within a mathematical framework describing the energy dynamics of an organism. The resulting model comprises food intake, body growth and survival. The equation for the mortality rate accounts for food consumption and is suited to describe caloric restriction data. For non-growing animals, the expression for the mortality rate reduces to the well-known Gompertz equation. We successfully applied our model to growth and survival data on mice exposed to different food levels.

The embedded tumour: host physiology is important for the evaluation of tumour growth.

The growth potential of a tumour can significantly depend on host features such as age, cell proliferation rates and caloric intake. Although this is widely known, existing mathematical models for tumour growth do not account for it. We therefore developed a new model for tumour growth, starting from a mathematical framework that describes the host's physiology. The resulting tumour-in-host model allowed us to study the implications of various specific interactions between the energetics of tumour and host. The model accounts for the influence of both age and feeding regimen of the host organism on the behaviour of a tumour. Concerning the effects of a tumour on its host, it explains why tumour-mediated body-weight loss is often more dramatic than expected from the energy demands of the tumour. We also show how the model can be applied to study enhanced body-weight loss in presence of cachectic factors. Our tumour-in-host model thus appears a proper tool to unite a wide range of phenomena in tumour-host interactions.