A Multi-Scale Agent Based Model of Colon Carcinogenesis

Colorectal cancer (CRC) is a major cause of cancer mortality and there remain aspects of its formation which are not understood. The colon contains an epithelium punctuated by flask shaped invaginations called the crypts of Lieberkühn. These crypts are monoclonal in nature while adenomas are thought to be polyclonal, suggesting that multiple crypts are involved in carcinogenesis. It has been reported that fields of mutated tissue surround adenomas but the causes and growth of these fields are not well understood. There are two competing hypotheses regarding growth, the first being that mutated cells from one crypt invade neighbouring crypts, and the second that mutated crypts replicate themselves more often than wild-type crypts. To investigate these processes two agent based models were developed. The first model represents cells as agents and is similar to previous models in the field, but is novel in including the geometry of the crypt mouth. This is necessary to model multiple interacting crypts. This model is the first in the literature to be used to represent multiple crypts and is used to investigate invasion of neighbour crypts by mutated cells. The second model represents whole crypts as agents, which allows the entire colon to be simulated for multiple decades of biological time, as far as we are aware this is the first such model. The cell scale model predicts that crypt invasion does not occur, but that mutated cells can invade the flat mucosa above neighbouring crypts. Analysis of in-vivo data is consistent with this prediction. The crypt as agent model predicts fields of ~41,000 crypts, in agreement with data in the literature, this corresponds to a field ~23mm in diameter. This project models pre-cancerous fields for the first time over a variety of scales, making specific novel predictions which are in agreement with in-vivo data where such data exist. Two agent based models were created to study the development of precancerous fields, one a model with cells as agents to study cell scale phenomena and the other with crypts as agents to allow processes to be studied on larger spatial and temporal scales. These models could potentially be used to refine clinic practice by predicting the required frequency of post-intervention monitoring of patients or the necessity of further intervention

An agent-based model of anoikis in the colon crypt displays novel emergent behaviour consistent with biological observations

Colorectal cancer (CRC) is a major cause of cancer mortality. Colon crypts are multi-cellular flask-shaped invaginations of the colonic epithelium, with stem cells at their base which support the continual turnover of the epithelium with loss of cells by anoikis from the flat mucosa. Mutations in these stem cells can become embedded in the crypts, a process that is strongly implicated in CRC initiation. We describe a computational model which includes novel features, including an accurate representation of the geometry of the crypt mouth. Model simulations yield previously unseen emergent phenomena, such as localization of cell death to a small region of the crypt mouth which corresponds with that observed in vivo. A mechanism emerges in the model for regulation of crypt cellularity in response to changes in either cell proliferation rates or membrane adhesion strengths. We show that cell shape assumptions influence this behaviour, with cylinders recapitulating biology better than spheres. Potential applications of the model include determination of roles of mutations in neoplasia and exploring factors for altered crypt morphodynamics

A cellular based model of the colon crypt suggests novel effects forApc phenotype in colorectal carcinogenesis

Colorectal cancer (CRC) is a major cause of cancer mortality; loss of the Apc gene is an early step in the formation of CRC. A new computational model of the colonic crypt has been developed to simulate the effects of Apc loss. The model includes a region of flat mucosa, which has not previously been considered in the context of Apc loss. The model suggests that Apc loss confers a survival advantage at the crypt mouth which may be a previously unknown method of mutation fixation

From cell to multi-crypt: Agent-based models of the human colon suggests novel processes of field cancerisation

Colorectal cancer (CRC) is a major cause of cancer mortality. It is known that loss of APC gene function through mutation is followed by the expansion of a field of mutated tissue, but the mechanisms behind this expansion are poorly understood. This study aimed to examine the processes involved in field expansion using two agent-based computational models: a cell-scale model allowing mapping of Apc-mutated cell expansion in small multcrypt arrays, and a tissue-scale model allowing simulation of the entire colon over oncologically relevant timescales. The cell scale model predicts that mutated cells spread through the flat mucosa of the simulated tissue without invading neighbouring crypts - a process not previously hypothesised in the literature. The crypt-scale model’s predictions of field sizes correspond to those estimated in the literature from in vivo studies. Our dual-scale modelling approach renders the spatial and temporal scales at which field cancerisation processes occur in vivo accessible to exploration by simulation for the first time

Cross-talk between Hippo and Wnt signalling pathways in intestinal crypts : insights from an agent-based model

Intestinal crypts are responsible for the total cell renewal of the lining of the intestines; this turnover is governed by the interplay between signalling pathways and the cell cycle. The role of Wnt signalling in cell proliferation and differentiation in the intestinal crypt has been extensively studied, with increased signalling found towards the lower regions of the crypt. Recent studies have shown that the Wnt signalling gradient found within the crypt may arise as a result of division-based spreading from a Wnt ‘reservoir’ at the crypt base. The discovery of the Hippo pathway’s involvement in maintaining crypt homeostasis is more recent; a mechanistic understanding of Hippo pathway dynamics, and its possible cross-talk with the Wnt pathway, remains lacking. To explore how the interplay between these pathways may control crypt homeostasis, we extended an ordinary differential equation model of the Wnt signalling pathway to include a phenomenological description of Hippo signalling in single cells, and then coupled it to a cell-based description of cell movement, proliferation and contact inhibition in agent-based simulations. Furthermore, we compared an imposed Wnt gradient with a division-based Wnt gradient model. Our results suggest that Hippo signalling affects the Wnt pathway by reducing the presence of free cytoplasmic β-catenin, causing cell cycle arrest. We also show that a division-based spreading of Wnt can form a Wnt gradient, resulting in proliferative dynamics comparable to imposed-gradient models. Finally, a simulated APC double mutant, with misregulated Wnt and Hippo signalling activity, is predicted to cause monoclonal conversion of the crypt

Cell Centre Crypt Simulation

Code for simulations presented in the pape