Crypt dynamics and colorectal cancer: advances in mathematical modelling

Stochastic model for cell population dynamics quantifies homeostasis in colonic crypts and its disruption in early tumorigenesis

The questions of how healthy colonic crypts maintain their size, and how homeostasis is disrupted by driver mutations, are central to understanding colorectal tumorigenesis. We propose a three-type stochastic branching process, which accounts for stem, transit-amplifying (TA) and fully differentiated (FD) cells, to model the dynamics of cell populations residing in colonic crypts. Our model is simple in its formulation, allowing us to estimate all but one of the model parameters from the literature. Fitting the single remaining parameter, we find that model results agree well with data from healthy human colonic crypts, capturing the considerable variance in population sizes observed experimentally. Importantly, our model predicts a steady-state population in healthy colonic crypts for relevant parameter values. We show that APC and KRAS mutations, the most significant early alterations leading to colorectal cancer, result in increased steady-state populations in mutated crypts, in agreement with experimental results. Finally, our model predicts a simple condition for unbounded growth of cells in a crypt, corresponding to colorectal malignancy. This is predicted to occur when the division rate of TA cells exceeds their differentiation rate, with implications for therapeutic cancer prevention strategies.

Beyond the Genetic Code: A Tissue Code?

The genetic code determines how the precise amino acid sequence of proteins is specified by genomic information in cells. But what specifies the precise histologic organization of cells in plant and animal tissues is unclear. We now hypothesize that another code, the tissue code , exists at an even higher level of complexity which determines how tissue organization is dynamically maintained. Accordingly, we modeled spatial and temporal asymmetries of cell division and established that five simple mathematical laws ("the tissue code") convey a set of biological rules that maintain the specific organization and continuous self-renewal dynamics of cells in tissues. These laws might even help us understand wound healing, and how tissue disorganization leads to birth defects and tissue pathology like cancer.

Mechanobiology of Colorectal Cancer

In this review, the mechanobiology of colorectal cancer (CRC) are discussed. Mechanotransduction of CRC is addressed considering the relationship of several biophysical cues and biochemical pathways. Mechanobiology is focused on considering how it may influence epithelial cells in terms of motility, morphometric changes, intravasation, circulation, extravasation, and metastization in CRC development. The roles of the tumor microenvironment, ECM, and stroma are also discussed, taking into account the influence of alterations and surface modifications on mechanical properties and their impact on epithelial cells and CRC progression. The role of cancer-associated fibroblasts and the impact of flow shear stress is addressed in terms of how it affects CRC metastization. Finally, some insights concerning how the knowledge of biophysical mechanisms may contribute to the development of new therapeutic strategies and targeting molecules and how mechanical changes of the microenvironment play a role in CRC disease are presented.

3D cyclorama for digital unrolling and visualisation of deformed tubes

Colonic crypts are tubular glands that multiply through a symmetric branching process called crypt fission. During the early stages of colorectal cancer, the normal fission process is disturbed, leading to asymmetrical branching or budding. The challenging shapes of the budding crypts make it difficult to prepare paraffin sections for conventional histology, resulting in colonic cross sections with crypts that are only partially visible. To study crypt budding in situ and in three dimensions (3D), we employ X-ray micro-computed tomography to image intact colons, and a new method we developed (3D cyclorama) to digitally unroll them. Here, we present, verify and validate our '3D cyclorama' method that digitally unrolls deformed tubes of non-uniform thickness. It employs principles from electrostatics to reform the tube into a series of onion-like surfaces, which are mapped onto planar panoramic views. This enables the study of features extending over several layers of the tube's depth, demonstrated here by two case studies: (i) microvilli in the human placenta and (ii) 3D-printed adhesive films for drug delivery. Our 3D cyclorama method can provide novel insights into a wide spectrum of applications where digital unrolling or flattening is necessary, including long bones, teeth roots and ancient scrolls.

Mathematical modeling of multiple pathways in colorectal carcinogenesis using dynamical systems with Kronecker structure

Like many other types of cancer, colorectal cancer (CRC) develops through multiple pathways of carcinogenesis. This is also true for colorectal carcinogenesis in Lynch syndrome (LS), the most common inherited CRC syndrome. However, a comprehensive understanding of the distribution of these pathways of carcinogenesis, which allows for tailored clinical treatment and even prevention, is still lacking. We suggest a linear dynamical system modeling the evolution of different pathways of colorectal carcinogenesis based on the involved driver mutations. The model consists of different components accounting for independent and dependent mutational processes. We define the driver gene mutation graphs and combine them using the Cartesian graph product. This leads to matrix components built by the Kronecker sum and product of the adjacency matrices of the gene mutation graphs enabling a thorough mathematical analysis and medical interpretation. Using the Kronecker structure, we developed a mathematical model which we applied exemplarily to the three pathways of colorectal carcinogenesis in LS. Beside a pathogenic germline variant in one of the DNA mismatch repair (MMR) genes, driver mutations in APC, CTNNB1, KRAS and TP53 are considered. We exemplarily incorporate mutational dependencies, such as increased point mutation rates after MMR deficiency, and based on recent experimental data, biallelic somatic CTNNB1 mutations as common drivers of LS-associated CRCs. With the model and parameter choice, we obtained simulation results that are in concordance with clinical observations. These include the evolution of MMR-deficient crypts as early precursors in LS carcinogenesis and the influence of variants in MMR genes thereon. The proportions of MMR-deficient and MMR-proficient APC-inactivated crypts as first measure for the distribution among the pathways in LS-associated colorectal carcinogenesis are compatible with clinical observations. The approach provides a modular framework for modeling multiple pathways of carcinogenesis yielding promising results in concordance with clinical observations in LS CRCs.

Mathematical model of colorectal cancer initiation

Quantifying evolutionary dynamics of cancer initiation and progression can provide insights into more effective strategies of early detection and treatment. Here we develop a mathematical model of colorectal cancer initiation through inactivation of two tumor suppressor genes and activation of one oncogene, accounting for the well-known path to colorectal cancer through loss of tumor suppressors APC and TP53 and gain of the KRAS oncogene. In the model, we allow mutations to occur in any order, leading to a complex network of premalignant mutational genotypes on the way to colorectal cancer. We parameterize the model using experimentally measured parameter values, many of them only recently available, and compare its predictions to epidemiological data on colorectal cancer incidence. We find that the reported lifetime risk of colorectal cancer can be recovered using a mathematical model of colorectal cancer initiation together with experimentally measured mutation rates in colorectal tissues and proliferation rates of premalignant lesions. We demonstrate that the order of driver events in colorectal cancer is determined primarily by the fitness effects that they provide, rather than their mutation rates. Our results imply that there may not be significant immune suppression of untreated benign and malignant colorectal lesions.

Personalizing Gastric Cancer Screening With Predictive Modeling of Disease Progression Biomarkers

Gastric cancer (GC) remains the third most common cause of cancer-related death worldwide. Infection with Helicobacter pylori is responsible for over 70% of GC incidence; colonization induces chronic inflammation, which can facilitate progression to intestinal metaplasia, dysplasia, and GC (Correa pathway). Although H. pylori eradication is a necessary first step in GC prevention, some patients continue to progress to advanced stage disease if substantial tissue damage has occurred or inflammation persists. This progression is often asymptomatic until cancer reaches stage IV, yet efficient, cost-effective screening protocols for patients who present with early stages of the Correa pathway do not exist. Given the high interpatient heterogeneity in progression time through this pathway, such screening protocols must necessarily be personalized. This requires the identification of reliable and longitudinally assessable biomarkers of patient-specific progression. Several gastric stem cell (GSC) markers including CD44, CD133, and Lgr5 are upregulated in GC. Here we show a significant stepwise increase in immunohistochemical staining for these markers in biopsies at different stages of the Correa pathway, suggesting GSC fraction to be a promising candidate biomarker for early detection of malignant transformation. We present a mathematical model capable of both simulating clinically observed increases in GSC fraction in longitudinal biopsy samples of individual patients, and forecasting patient-specific disease progression trajectories based only on characteristics identified from immunohistochemistry at initial presentation. From these forecasts, personalized screening schedules may be identified that would allow early stratification of high-risk patients, and potentially earlier detection of dysplasia or early-stage GC.

Stochastic cell renewal process and lengthening of cell cycle

Evolution of the stem cell population responsible for homeostatic cell renewal processes is analyzed. We assume that this regime is the product of a delicate balance between symmetric divisions that, after each cell cycle, originates a new stem cell or its disappearance (through cell differentiation). This dynamics leads to a monoclonal population, that is for an initial homogeneous set of stem cells, fixation of each clone is equiprobable. In this work we show that if there is an altered stem cell with a longer cell cycle than the rest, the fixation of this altered clone is more likely. We also study the consequeces of the appearance of successive alterations with these characteristics and their fixations. This effect is purely due to inherent characteristics of the cell renewal dynamics and as time goes by it leads to a quiescence state for stem cells owing to the recurrent fixation of such altered cells. Therefore it would contribute to the aging process.

Biomathematical model for simulating abnormal orifice patterns in colonic crypts

Colonic polyps, which are abnormal growths in the colon, are a major concern in colon cancer diagnosis and prevention. Medical studies evidence that there is a correlation between histopathology and the shapes of the orifices in colonic crypts. We propose a biomathematical model for simulating the appearance of anomalous shapes for the orifices of colonic crypts, associated to an abnormal cell proliferation. It couples a mechanical model that is a mixed elastic/viscoelastic quasi-static model describing the deformation of the crypt orifice, with a convection-diffusion model that simulates the crypt cell dynamics in space and time. The coupling resides in the variation of pressure generated by abnormal proliferative cells that induce a mechanical force and originate the change in shape of the crypt orifice. Furthermore the model is formulated in a two-dimensional setting, for emulating the top view of the colonic mucosa, observed in vivo in colonoscopy images. The primary focus of this study is on the modeling of this complex biological phenomenon, by defining an appropriate reduced biomathematical model. Additionally, a numerical procedure to determine its solution is also addressed. The overall numerical simulations indicate that an excess of cell proliferation, in different crypt locations, creates some of the anomalous patterns of the colonic crypt orifices, observed in vivo in medical images.

Optimization of Dose Schedules for Chemotherapy of Early Colon Cancer Determined by High-Performance Computer Simulations

Cancer chemotherapy dose schedules are conventionally applied intermittently, with dose duration of the order of hours, intervals between doses of days or weeks, and cycles repeated for weeks. The large number of possible combinations of values of duration, interval, and lethality has been an impediment to empirically determine the optimal set of treatment conditions. The purpose of this project was to determine the set of parameters for duration, interval, and lethality that would be most effective for treating early colon cancer. An agent-based computer model that simulated cell proliferation kinetics in normal human colon crypts was calibrated with measurements of human biopsy specimens. Mutant cells were simulated as proliferating and forming an adenoma, or dying if treated with cytotoxic chemotherapy. Using a high-performance computer, a total of 28 800 different parameter sets of duration, interval, and lethality were simulated. The effect of each parameter set on the stability of colon crypts, the time to cure a crypt of mutant cells, and the accumulated dose was determined. Of the 28 800 parameter sets, 434 parameter sets were effective in curing the crypts of mutant cells before they could form an adenoma and allowed the crypt normal cell dynamics to recover to pretreatment levels. A group of 14 similar parameter sets produced a minimal time to cure mutant cells. A different group of nine similar parameter sets produced the least accumulated dose. These parameter sets may be considered as candidate dose schedules to guide clinical trials for early colon cancer.

Neutral dynamics and cell renewal of colonic crypts in homeostatic regime

The self renewal process in colonic crypts is the object of several studies. We present here a new compartment model with the following characteristics: (a) we distinguish different classes of cells: stem cells, six generations of transit amplifying cells and the differentiated cells; (b) in order to take into account the monoclonal character of crypts in homeostatic regimes we include symmetric divisions of the stem cells. We first consider the dynamic differential equations that describe the evolution of the mean values of the populations, but the small observed value of the total number of cells involved plus the huge dispersion of experimental data found in the literature leads us to study the stochastic discrete process. This analysis allows us to study fluctuations, the neutral drift that leads to monoclonality, and the effects of the fixation of mutant clones.

Determining the control networks regulating stem cell lineages in colonic crypts

The question of stem cell control is at the center of our understanding of tissue functioning, both in healthy and cancerous conditions. It is well accepted that cellular fate decisions (such as divisions, differentiation, apoptosis) are orchestrated by a network of regulatory signals emitted by different cell populations in the lineage and the surrounding tissue. The exact regulatory network that governs stem cell lineages in a given tissue is usually unknown. Here we propose an algorithm to identify a set of candidate control networks that are compatible with (a) measured means and variances of cell populations in different compartments, (b) qualitative information on cell population dynamics, such as the existence of local controls and oscillatory reaction of the system to population size perturbations, and (c) statistics of correlations between cell numbers in different compartments. Using the example of human colon crypts, where lineages are comprised of stem cells, transit amplifying cells, and differentiated cells, we start with a theoretically known set of 32 smallest control networks compatible with tissue stability. Utilizing near-equilibrium stochastic calculus of stem cells developed earlier, we apply a series of tests, where we compare the networks' expected behavior with the observations. This allows us to exclude most of the networks, until only three, very similar, candidate networks remain, which are most compatible with the measurements. This work demonstrates how theoretical analysis of control networks combined with only static biological data can shed light onto the inner workings of stem cell lineages, in the absence of direct experimental assessment of regulatory signaling mechanisms. The resulting candidate networks are dominated by negative control loops and possess the following properties: (1) stem cell division decisions are negatively controlled by the stem cell population, (2) stem cell differentiation decisions are negatively controlled by the transit amplifying cell population.

Changes in cellular mechanical properties during onset or progression of colorectal cancer

Colorectal cancer (CRC) development represents a multistep process starting with specific mutations that affect proto-oncogenes and tumour suppressor genes. These mutations confer a selective growth advantage to colonic epithelial cells that form first dysplastic crypts, and then malignant tumours and metastases. All these steps are accompanied by deep mechanical changes at the cellular and the tissue level. A growing consensus is emerging that such modifications are not merely a by-product of the malignant progression, but they could play a relevant role in the cancer onset and accelerate its progression. In this review, we focus on recent studies investigating the role of the biomechanical signals in the initiation and the development of CRC. We show that mechanical cues might contribute to early phases of the tumour initiation by controlling the Wnt pathway, one of most important regulators of cell proliferation in various systems. We highlight how physical stimuli may be involved in the differentiation of non-invasive cells into metastatic variants and how metastatic cells modify their mechanical properties, both stiffness and adhesion, to survive the mechanical stress associated with intravasation, circulation and extravasation. A deep comprehension of these mechanical modifications may help scientist to define novel molecular targets for the cure of CRC.

Mathematical modeling of drug resistance due to KRAS mutation in colorectal cancer

The most challenging task in colorectal cancer research nowadays is to understand the development of acquired resistance to anti-EGFR drugs. The key reason for this problem is the KRAS mutations appearance after the treatment with monoclonal antibodies (moAb). Here we present a mathematical model for the analysis of KRAS mutations behavior in colorectal cancer with respect to moAb treatments. To evaluate the drug performance we have developed equations for two types of tumors cells, KRAS mutated and KRAS wild-type. Both tumor cell populations were treated with a combination of moAb and chemotherapy drugs. It was observed that even the minimal initial concentration of KRAS mutation before the treatment has the ability to make the tumor refractory to the treatment. Minor population of KRAS mutations has strong influence on large number of wild-type cells as well rendering them resistant to chemotherapy. Patient׳s immune responses are specifically taken into considerations and it is found that, in case of KRAS mutations, the immune strength does not affect medication efficacy. Finally, cetuximab (moAb) and irinotecan (chemotherapy) drugs are analyzed as first-line treatment of colorectal cancer with few KRAS mutated cells. Results show that this combined treatment could be only effective for patients with high immune strengths and it should not be recommended as first-line therapy for patients with moderate immune strengths or weak immune systems because of a potential risk of relapse, with KRAS mutant cells acquired resistance involved with them.

CoGNaC: A Chaste Plugin for the Multiscale Simulation of Gene Regulatory Networks Driving the Spatial Dynamics of Tissues and Cancer

We introduce a Chaste plugin for the generation and the simulation of Gene Regulatory Networks (GRNs) in multiscale models of multicellular systems. Chaste is a widely used and versatile computational framework for the multiscale modeling and simulation of multicellular biological systems. The plugin, named CoGNaC (Chaste and Gene Networks for Cancer), allows the linking of the regulatory dynamics to key properties of the cell cycle and of the differentiation process in populations of cells, which can subsequently be modeled using different spatial modeling scenarios. The approach of CoGNaC focuses on the emergent dynamical behavior of gene networks, in terms of gene activation patterns characterizing the different cellular phenotypes of real cells and, especially, on the overall robustness to perturbations and biological noise. The integration of this approach within Chaste’s modular simulation framework provides a powerful tool to model multicellular systems, possibly allowing for the formulation of novel hypotheses on gene regulation, cell differentiation, and, in particular, cancer emergence and development. In order to demonstrate the usefulness of CoGNaC over a range of modeling paradigms, two example applications are presented. The first of these concerns the characterization of the gene activation patterns of human T-helper cells. The second example is a multiscale simulation of a simplified intestinal crypt, in which, given certain conditions, tumor cells can emerge and colonize the tissue.

Evolution of pre-existing versus acquired resistance to platinum drugs and PARP inhibitors in BRCA-associated cancers

Platinum drugs and PARP inhibitors (“PARPis”) are considered to be effective in BRCA-associated cancers with impaired DNA repair. These agents cause stalled and collapsed replication forks and create double-strand breaks effectively in the absence of repair mechanisms, resulting in arrest of the cell cycle and induction of cell death. However, recent studies have shown failure of these chemotherapeutic agents due to emerging drug resistance. In this study, we developed a stochastic model of BRCA-associated cancer progression in which there are four cancer populations: those with (i) functional BRCA, (ii) dysfunctional BRCA, (iii) functional BRCA and a growth advantage, and (iv) dysfunctional BRCA and a growth advantage. These four cancer populations expand from one cancer cell with normal repair function until the total cell number reaches a detectable amount. We derived formulas for the probability and expected numbers of each population at the time of detection. Furthermore, we extended the model to consider the tumor dynamics during treatment. Results from the model were validated and showed good agreement with clinical and experimental evidence in BRCA-associated cancers. Based on the model, we investigated conditions in which drug resistance during the treatment course originated from either a pre-existing drug-resistant population or a de novo population, due to secondary mutations. Finally, we found that platinum drugs and PARPis were effective if (i) BRCA inactivation is present, (ii) the cancer was diagnosed early, and (iii) tumor growth is rapid. Our results indicate that different types of cancers have a preferential way of acquiring resistance to platinum drugs and PARPis according to their growth and mutational characteristics.

The protective role of symmetric stem cell division on the accumulation of heritable damage

Stem cell divisions are either asymmetric—in which one daughter cell remains a stem cell and one does not—or symmetric, in which both daughter cells adopt the same fate, either stem or non-stem. Recent studies show that in many tissues operating under homeostatic conditions stem cell division patterns are strongly biased toward the symmetric outcome, raising the question of whether symmetry confers some benefit. Here, we show that symmetry, via extinction of damaged stem-cell clones, reduces the lifetime risk of accumulating phenotypically silent heritable damage (mutations or aberrant epigenetic changes) in individual stem cells. This effect is greatest in rapidly cycling tissues subject to accelerating rates of damage accumulation over time, a scenario that describes the progression of many cancers. A decrease in the rate of cellular damage accumulation may be an important factor favoring symmetric patterns of stem cell division.

Recently, highly symmetric patterns of stem cell division have been observed in a variety of adult mammalian somatic tissues. Here we identify conditions under which this behavior serves as a strategy to protect the organism against mutation accumulation. First, we find that a sufficient number of lifetime stem cell divisions must occur, potentially explaining why stem cell pools with the most symmetric divisions are rapidly cycling. Second, we find that late-occurring mutations must occur rapidly, a scenario known in cancer biology as genetic instability. These findings provide a potential explanation for the observation that cancer risks among large, long-lived organisms fail to rise as expected with lifespan and body size.

Investigating the relation between stochastic differentiation, homeostasis and clonal expansion in intestinal crypts via multiscale modeling

Colorectal tumors originate and develop within intestinal crypts. Even though some of the essential phenomena that characterize crypt structure and dynamics have been effectively described in the past, the relation between the differentiation process and the overall crypt homeostasis is still only partially understood. We here investigate this relation and other important biological phenomena by introducing a novel multiscale model that combines a morphological description of the crypt with a gene regulation model: the emergent dynamical behavior of the underlying gene regulatory network drives cell growth and differentiation processes, linking the two distinct spatio-temporal levels. The model relies on a few a priori assumptions, yet accounting for several key processes related to crypt functioning, such as: dynamic gene activation patterns, stochastic differentiation, signaling pathways ruling cell adhesion properties, cell displacement, cell growth, mitosis, apoptosis and the presence of biological noise. We show that this modeling approach captures the major dynamical phenomena that characterize the regular physiology of crypts, such as cell sorting, coordinate migration, dynamic turnover, stem cell niche correct positioning and clonal expansion. All in all, the model suggests that the process of stochastic differentiation might be sufficient to drive the crypt to homeostasis, under certain crypt configurations. Besides, our approach allows to make precise quantitative inferences that, when possible, were matched to the current biological knowledge and it permits to investigate the role of gene-level perturbations, with reference to cancer development. We also remark the theoretical framework is general and may be applied to different tissues, organs or organisms.

A calibrated agent-based computer model of stochastic cell dynamics in normal human colon crypts useful for in silico experiments

BACKGROUND

Normal colon crypts consist of stem cells, proliferating cells, and differentiated cells. Abnormal rates of proliferation and differentiation can initiate colon cancer. We have measured the variation in the number of each of these cell types in multiple crypts in normal human biopsy specimens. This has provided the opportunity to produce a calibrated computational model that simulates cell dynamics in normal human crypts, and by changing model parameter values, to simulate the initiation and treatment of colon cancer.

RESULTS

An agent-based model of stochastic cell dynamics in human colon crypts was developed in the multi-platform open-source application NetLogo. It was assumed that each cell's probability of proliferation and probability of death is determined by its position in two gradients along the crypt axis, a divide gradient and in a die gradient. A cell's type is not intrinsic, but rather is determined by its position in the divide gradient. Cell types are dynamic, plastic, and inter-convertible. Parameter values were determined for the shape of each of the gradients, and for a cell's response to the gradients. This was done by parameter sweeps that indicated the values that reproduced the measured number and variation of each cell type, and produced quasi-stationary stochastic dynamics. The behavior of the model was verified by its ability to reproduce the experimentally observed monocolonal conversion by neutral drift, the formation of adenomas resulting from mutations either at the top or bottom of the crypt, and by the robust ability of crypts to recover from perturbation by cytotoxic agents. One use of the virtual crypt model was demonstrated by evaluating different cancer chemotherapy and radiation scheduling protocols.

CONCLUSIONS

A virtual crypt has been developed that simulates the quasi-stationary stochastic cell dynamics of normal human colon crypts. It is unique in that it has been calibrated with measurements of human biopsy specimens, and it can simulate the variation of cell types in addition to the average number of each cell type. The utility of the model was demonstrated with in silico experiments that evaluated cancer therapy protocols. The model is available for others to conduct additional experiments.

Colon cryptogenesis: asymmetric budding

The process of crypt formation and the roles of Wnt and cell-cell adhesion signaling in cryptogenesis are not well described; but are important to the understanding of both normal and cancer colon crypt biology. A quantitative 3D-microscopy and image analysis technique is used to study the frequency, morphology and molecular topography associated with crypt formation. Measurements along the colon reveal the details of crypt formation and some key underlying biochemical signals regulating normal colon biology. Our measurements revealed an asymmetrical crypt budding process, contrary to the previously reported symmetrical fission of crypts. 3D immunofluorescence analyses reveals heterogeneity in the subcellular distribution of E-cadherin and β-catenin in distinct crypt populations. This heterogeneity was also found in asymmetrical budding crypts. Singular crypt formation (i.e. no multiple new crypts forming from one parent crypt) were observed in crypts isolated from the normal colon mucosa, suggestive of a singular constraint mechanism to prevent aberrant crypt production. The technique presented improves our understanding of cryptogenesis and suggests that excess colon crypt formation occurs when Wnt signaling is perturbed (e.g. by truncation of adenomatous polyposis coli, APC protein) in most colon cancers.

Buckling of a growing tissue and the emergence of two-dimensional patterns

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We model the growth of gut epithelial cells cultured upon a deformable substrate.

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Growth generates buckling instabilities, contributing to crypt formation in vivo.

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Variations in mechanical properties have little effect on resulting configurations.

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Configurations are controlled by growth patterns & interactions with strata below.

The process of biological growth and the associated generation of residual stress has previously been considered as a driving mechanism for tissue buckling and pattern selection in numerous areas of biology. Here, we develop a two-dimensional thin plate theory to simulate the growth of cultured intestinal epithelial cells on a deformable substrate, with the goal of elucidating how a tissue engineer might best recreate the regular array of invaginations (crypts of Lieberkühn) found in the wall of the mammalian intestine. We extend the standard von Kármán equations to incorporate inhomogeneity in the plate’s mechanical properties and surface stresses applied to the substrate by cell proliferation. We determine numerically the configurations of a homogeneous plate under uniform cell growth, and show how tethering to an underlying elastic foundation can be used to promote higher-order buckled configurations. We then examine the independent effects of localised softening of the substrate and spatial patterning of cellular growth, demonstrating that (within a two-dimensional framework, and contrary to the predictions of one-dimensional models) growth patterning constitutes a more viable mechanism for control of crypt distribution than does material inhomogeneity.

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

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.

Risk factor-dependent dynamics of atopic dermatitis: modelling multi-scale regulation of epithelium homeostasis

Epithelial tissue provides the body with its first layer of protection against harmful environmental stimuli by enacting the regulatory interplay between a physical barrier preventing the influx of external stimuli and an inflammatory response to the infiltrating stimuli. Importantly, this interdependent regulation occurs on different time scales: the tissue-level barrier permeability is regulated over the course of hours, whereas the cellular-level enzymatic reactions leading to inflammation take place within minutes. This multi-scale regulation is key to the epithelium's function and its dysfunction leads to various diseases. This paper presents a mathematical model of regulatory mechanisms in the epidermal epithelium that includes processes on two different time scales at the cellular and tissue levels. We use this model to investigate the essential regulatory interactions between epidermal barrier integrity and skin inflammation and how their dysfunction leads to atopic dermatitis (AD). Our model exhibits a structure of dual (positive and negative) control at both cellular and tissue levels. We also determined how the variation induced by well-known risk factors for AD can break the balance of the dual control. Our model analysis based on time-scale separation suggests that each risk factor leads to qualitatively different dynamic behaviours of different severity for AD, and that the coincidence of multiple risk factors dramatically increases the fragility of the epithelium's function. The proposed mathematical framework should also be applicable to other inflammatory diseases that have similar time-scale separation and control architectures.

Stochastic Tunneling of Two Mutations in a Population of Cancer Cells

Cancer initiation, progression, and the emergence of drug resistance are driven by specific genetic and/or epigenetic alterations such as point mutations, structural alterations, DNA methylation and histone modification changes. These alterations may confer advantageous, deleterious or neutral effects to mutated cells. Previous studies showed that cells harboring two particular alterations may arise in a fixed-size population even in the absence of an intermediate state in which cells harboring only the first alteration take over the population; this phenomenon is called stochastic tunneling. Here, we investigated a stochastic Moran model in which two alterations emerge in a cell population of fixed size. We developed a novel approach to comprehensively describe the evolutionary dynamics of stochastic tunneling of two mutations. We considered the scenarios of large mutation rates and various fitness values and validated the accuracy of the mathematical predictions with exact stochastic computer simulations. Our theory is applicable to situations in which two alterations are accumulated in a fixed-size population of binary dividing cells.

Patterns of proliferative activity in the colonic crypt determine crypt stability and rates of somatic evolution

Epithelial cells in the colon are arranged in cylindrical structures called crypts in which cellular proliferation and migration are tightly regulated. We hypothesized that the proliferation patterns of cells may determine the stability of crypts as well as the rates of somatic evolution towards colorectal tumorigenesis. Here, we propose a linear process model of colonic epithelial cells that explicitly takes into account the proliferation kinetics of cells as a function of cell position within the crypt. Our results indicate that proliferation kinetics has significant influence on the speed of cell movement, kinetics of mutation propagation, and sensitivity of the system to selective effects of mutated cells. We found that, of all proliferation curves tested, those with mitotic activities concentrated near the stem cell, including the actual proliferation kinetics determined in in vivo labeling experiments, have a greater ability of delaying the rate of mutation accumulation in colonic stem cells compared to hypothetical proliferation curves with mitotic activities focused near the top of the crypt column. Our model can be used to investigate the dynamics of proliferation and mutation accumulation in spatially arranged tissues.

Mathematical and computational models have a long and rich history in enhancing our understanding of intestinal epithelial cells. A plethora of models have been proposed to describe different aspects of cellular behavior, including cell proliferation, migration, differentiation, and mutation accumulation. Here, we present a novel approach to examine the effects of proliferation kinetics on the rate of somatic evolution in a spatially arranged model of the colon. Based on our simulation results, we demonstrate that spatially determined proliferation kinetics has the ability to delay the rate of somatic evolution, and changes in proliferation patterns can significantly affect the speed of mutation accumulation. Our work highlights the importance of considering proliferation kinetics as well as the spatial organization of tissues when investigating the dynamics of cancer initiation.

Can cell mortality determine division of labor in tissue organization?

Tissue organization comes from the emergence of cell cooperation where cell homeostasis and function are performed as a trade-off of two excluding proliferative and differentiated cellular states. By introducing function in a population dynamics approach, I study the role of division of labor in tissue optimality when cell turn-over and limitation of space and resources are imposed as natural restrictions of a living tissue. The results indicate that although cell turn-over imposes a inevitable reduction in function abilities, the penalty is smaller when division of labor is at work, especially when a rapid cell-turnover and high cell density is a requirement for the tissue, as occurred in epithelia hierarchical tissues. Analytic results are in agreement with the experimental data available in literature. The study provides an explanation about why homogeneous tissues for which proliferative and functional tasks are performed by a same cell type are unlikely to be observed under high cell-renewal requirements.

What are the best routes to effectively model human colorectal cancer?

Colorectal cancer (CRC) is the third most common cancer in the UK, with over 37,500 people being diagnosed every year. Survival rates for CRC have doubled in the last 30 years and it is now curable if diagnosed early, but still over half of all sufferers do not survive for longer than 5 years after diagnosis. The major complication to treating this disease is that of metastasis, specifically to the liver, which is associated with a 5 year survival of less than 5%. These statistics highlight the importance of the development of earlier detection techniques and more targeted therapeutics. The future of treating this disease therefore lies in increasing understanding of the mutations which cause tumourigenesis, and insight into the development and progression of this complex disease. This can only be achieved through the use of functional models which recapitulate all aspects of the human disease. There is a wide range of models of CRC available to researchers, but all have their own strengths and weaknesses. Here we review how CRC can be modelled and discuss the future of modelling this complex disease, with a particular focus on how genetically engineered mouse models have revolutionised this area of research.

Mathematical model of colitis-associated colon cancer

As a result of chronic inflammation of their colon, patients with ulcerative colitis or Crohn's disease are at risk of developing colon cancer. In this paper, we consider the progression of colitis-associated colon cancer. Unlike normal colon mucosa, the inflammed colon mucosa undergoes genetic mutations, affecting, in particular, tumor suppressors TP53 and adenomatous polyposis coli (APC) gene. We develop a mathematical model that involves these genes, under chronic inflammation, as well as NF-κB, β-catenin, MUC1 and MUC2. The model demonstrates that increased level of cells with TP53 mutations results in abnormal growth and proliferation of the epithelium; further increase in the epithelium proliferation results from additional APC mutations. The model may serve as a conceptual framework for further data-based study of the early stage of colon cancer.

Multispecies model of cell lineages and feedback control in solid tumors

We develop a multispecies continuum model to simulate the spatiotemporal dynamics of cell lineages in solid tumors. The model accounts for protein signaling factors produced by cells in lineages, and nutrients supplied by the microenvironment. Together, these regulate the rates of proliferation, self-renewal and differentiation of cells within the lineages, and control cell population sizes and distributions. Terminally differentiated cells release proteins (e.g., from the TGFβ superfamily) that feedback upon less differentiated cells in the lineage both to promote differentiation and decrease rates of proliferation (and self-renewal). Stem cells release a short-range factor that promotes self-renewal (e.g., representative of Wnt signaling factors), as well as a long-range inhibitor of this factor (e.g., representative of Wnt inhibitors such as Dkk and SFRPs). We find that the progression of the tumors and their response to treatment is controlled by the spatiotemporal dynamics of the signaling processes. The model predicts the development of spatiotemporal heterogeneous distributions of the feedback factors (Wnt, Dkk and TGFβ) and tumor cell populations with clusters of stem cells appearing at the tumor boundary, consistent with recent experiments. The nonlinear coupling between the heterogeneous expressions of growth factors and the heterogeneous distributions of cell populations at different lineage stages tends to create asymmetry in tumor shape that may sufficiently alter otherwise homeostatic feedback so as to favor escape from growth control. This occurs in a setting of invasive fingering, and enhanced aggressiveness after standard therapeutic interventions. We find, however, that combination therapy involving differentiation promoters and radiotherapy is very effective in eradicating such a tumor.

A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development

Colon rectal cancers (CRC) are the result of sequences of mutations which lead the intestinal tissue to develop in a carcinoma following a "progression" of observable phenotypes. The actual modeling and simulation of the key biological structures involved in this process is of interest to biologists and physicians and, at the same time, it poses significant challenges from the mathematics and computer science viewpoints. In this report we give an overview of some mathematical models for cell sorting (a basic phenomenon that underlies several dynamical processes in an organism), intestinal crypt dynamics and related problems and open questions. In particular, major attention is devoted to the survey of so-called in-lattice (or grid) models and off-lattice (off-grid) models. The current work is the groundwork for future research on semi-automated hypotheses formation and testing about the behavior of the various actors taking part in the adenoma-carcinoma progression, from regulatory processes to cell-cell signaling pathways.

A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development

Colon rectal cancers (CRC) are the result of sequences of mutations which lead the intestinal tissue to develop in a carcinoma following a "progression" of observable phenotypes. The actual modeling and simulation of the key biological structures involved in this process is of interest to biologists and physicians and, at the same time, it poses significant challenges from the mathematics and computer science viewpoints. In this report we give an overview of some mathematical models for cell sorting (a basic phenomenon that underlies several dynamical processes in an organism), intestinal crypt dynamics and related problems and open questions. In particular, major attention is devoted to the survey of so-called in-lattice (or grid) models and off-lattice (off-grid) models. The current work is the groundwork for future research on semi-automated hypotheses formation and testing about the behavior of the various actors taking part in the adenoma-carcinoma progression, from regulatory processes to cell-cell signaling pathways.

Role of heterozygous APC mutation in niche succession and initiation of colorectal cancer--a computational study

Mutations in the adenomatous polyposis coli (APC) gene are found in most colorectal cancers. They cause constitutive activation of proliferative pathways when both alleles of the gene are mutated. However studies on individuals with familial adenomatous polyposis (FAP) have shown that a single mutated APC allele can also create changes in the precancerous colon crypt, like increased number of stem cells, increased crypt fission, greater variability of DNA methylation patterns, and higher somatic mutation rates. In this paper, using a computational model of colon crypt dynamics, we evolve and investigate a hypothesis on the effect of heterozygous APC mutation that explains these different observations. Based on previous reports and the results from the computational model we propose the hypothesis that heterozygous APC mutation has the effect of increasing the chances for a stem cell to divide symmetrically, producing two stem cell daughters. We incorporate this hypothesis into the model and perform simulation experiments to investigate the consequences of the hypothesis. Simulations show that this hypothesis links together the changes in FAP crypts observed in previous studies. The simulations also show that an APC(+/-) stem cell gets selective advantages for dominating the crypt and progressing to cancer. This explains why most colon cancers are initiated by APC mutation. The results could have implications for preventing or retarding the onset of colon cancer in people with inherited or acquired mutation of one APC allele. Experimental validation of the hypothesis as well as investigation into the molecular mechanisms of this effect may therefore be worth undertaking.

Comparing a discrete and continuum model of the intestinal crypt

The integration of processes at different scales is a key problem in the modelling of cell populations. Owing to increased computational resources and the accumulation of data at the cellular and subcellular scales, the use of discrete, cell-level models, which are typically solved using numerical simulations, has become prominent. One of the merits of this approach is that important biological factors, such as cell heterogeneity and noise, can be easily incorporated. However, it can be difficult to efficiently draw generalizations from the simulation results, as, often, many simulation runs are required to investigate model behaviour in typically large parameter spaces. In some cases, discrete cell-level models can be coarse-grained, yielding continuum models whose analysis can lead to the development of insight into the underlying simulations. In this paper we apply such an approach to the case of a discrete model of cell dynamics in the intestinal crypt. An analysis of the resulting continuum model demonstrates that there is a limited region of parameter space within which steady-state (and hence biologically realistic) solutions exist. Continuum model predictions show good agreement with corresponding results from the underlying simulations and experimental data taken from murine intestinal crypts.

Computational modeling of epithelial tissues

There is an extensive literature on the computational modeling of epithelial tissues at all levels from subcellular to whole tissue. This review concentrates on behavior at the individual cell to whole tissue level, and particularly on organizational aspects, and provides an indication of where information from other areas, such as the modeling of angiogenesis, is relevant. The skin, and the lining of all of the body cavities (lung, gut, cervix, bladder etc) are epithelial tissues, which in a topological sense are the boundary between inside and outside the body. They are thin sheets of cells (usually of the order of 0.5 mm thick) without extracellular matrix, have a relatively simple structure, and contain few types of cells. They have important barrier, secretory and transport functions, which are essential for the maintenance of life, so homeostasis and wound healing are important aspects of the behavior of epithelial tissues. Carcinomas originate in epithelial tissues.There are essentially two approaches to modeling tissues--to start at the level of the tissue (i.e., a length scale of the order of 1 mm) and develop generalized equations for behavior (a continuum approach); or to start at the level of the cell (i.e., a length scale of the order of 10 µm) and develop tissue behavior as an emergent property of cellular behavior (an individual-based approach). As will be seen, these are not mutually exclusive approaches, and they come in a variety of flavors.

Spindles losing their bearings: does disruption of orientation in stem cells predict the onset of cancer?

Recently, Quyn et al. demonstrated that cells within the stem cell zone of human and mouse intestinal crypts tend to align their mitotic spindles perpendicular to the basal membrane of the crypt. This is associated with asymmetric division, whereby particular proteins and individual chromatids are preferentially segregated to one daughter cell. In colonic mucosa containing a heterozygous adenomatous polyposis coli gene (APC) mutation the asymmetry is lost. Here, we discuss asymmetric stem cell division as an anti-tumourigenic mechanism. We describe how hierarchical tissue structures suppress somatic evolution, and discuss the relative merits of template strand retention to limit the accumulation of DNA replication errors. We suggest experiments to determine whether somatic mutations resulting in loss of spindle alignment confer an advantage within the stem cell niche. Finally, we discuss whether lack of spindle alignment constitutes an oncogenic event per se, with particular reference to studies in model organisms, and the timing of chromosomal instability in human cancers.

New models of neoplastic progression in Barrett's oesophagus

Research in Barrett's oesophagus, and neoplastic progression to OAC (oesophageal adenocarcinoma), is hobbled by the lack of good pre-clinical models that capture the evolutionary dynamics of Barrett's cell populations. Current models trade off tractability for realism. Computational models are perhaps the most tractable and can be used both to interpret data and to develop intuitions and hypotheses for neoplastic progression. Tissue culture models include squamous cell lines, Barrett's oesophagus cell lines and OAC cell lines, although it was recognized recently that BIC-1, SEG-1 and TE-7 are not true OAC cell lines. Some of the unrealistic aspects of the micro-environment in two-dimensional tissue culture may be overcome with the development of three-dimensional organotypic cultures of Barrett's oesophagus. The most realistic, but least tractable, model is a canine surgical model that generates reflux and leads to an intestinal metaplasia. Alternatively, rat surgical models have gained popularity and should be tested for the common genetic features of Barrett's oesophagus neoplastic progression in humans including loss of CDKN2A (cyclin-dependent kinase inhibitor 2A) and TP53 (tumour protein 53), generation of aneuploidy and realistic levels of genetic diversity. This last feature will be important for studying the effects of cancer-prevention interventions. In order to study the dynamics of progression and the effects of an experimental intervention, there is a need to follow animals longitudinally, with periodic endoscopic biopsies. This is now possible and represents an exciting opportunity for the future.

New models of neoplastic progression in Barrett's oesophagus

Research in Barrett's oesophagus, and neoplastic progression to OAC (oesophageal adenocarcinoma), is hobbled by the lack of good pre-clinical models that capture the evolutionary dynamics of Barrett's cell populations. Current models trade off tractability for realism. Computational models are perhaps the most tractable and can be used both to interpret data and to develop intuitions and hypotheses for neoplastic progression. Tissue culture models include squamous cell lines, Barrett's oesophagus cell lines and OAC cell lines, although it was recognized recently that BIC-1, SEG-1 and TE-7 are not true OAC cell lines. Some of the unrealistic aspects of the micro-environment in two-dimensional tissue culture may be overcome with the development of three-dimensional organotypic cultures of Barrett's oesophagus. The most realistic, but least tractable, model is a canine surgical model that generates reflux and leads to an intestinal metaplasia. Alternatively, rat surgical models have gained popularity and should be tested for the common genetic features of Barrett's oesophagus neoplastic progression in humans including loss of CDKN2A (cyclin-dependent kinase inhibitor 2A) and TP53 (tumour protein 53), generation of aneuploidy and realistic levels of genetic diversity. This last feature will be important for studying the effects of cancer-prevention interventions. In order to study the dynamics of progression and the effects of an experimental intervention, there is a need to follow animals longitudinally, with periodic endoscopic biopsies. This is now possible and represents an exciting opportunity for the future.

Variable renewal rate and growth properties of cell populations in colon crypts

A nonlinear mathematical model is used to investigate the time evolution of the cell populations in colon crypts (stem, semidifferentiated and fully differentiated cells). To mimic pathological alteration of the biochemical pathways leading to abnormal proliferative activity of the population of semidifferentiated cells their renewal rate is assumed to be dependent on the population size. Then, the effects of such perturbation on the population dynamics are investigated theoretically. Using both theoretical methods and numerical simulations it is shown that the increase in the renewal rate of semidifferentiated cells strongly impacts the dynamical behavior of the cell populations.

Current trends in mathematical modeling of tumor-microenvironment interactions: a survey of tools and applications

In its simplest description, a tumor is comprised of an expanding population of transformed cells supported by a surrounding microenvironment termed the tumor stroma. The tumor microenvironment has a very complex composition, including multiple types of stromal cells, a dense network of various extracellular matrix (ECM) fibers interpenetrated by the interstitial fluid and gradients of several chemical species that either are dissolved in the fluid or are bound to the ECM structure. In order to study experimentally such complex interactions between multiple players, cancer is dissected and considered at different scales of complexity, such as protein interactions, biochemical pathways, cellular functions or whole organism studies. However, the integration of information acquired from these studies into a common description is as difficult as the disease itself. Computational models of cancer can provide cancer researchers with invaluable tools that are capable of integrating the complexity into organizing principles as well as suggesting testable hypotheses. We will focus in this Minireview on mathematical models in which the whole cell is a main modeling unit. We will present a current stage of such cell-focused mathematical modeling incorporating different stromal components and their interactions with growing tumors, and discuss what modeling approaches can be undertaken to complement the in vivo and in vitro experimentation.

Variational image segmentation for endoscopic human colonic aberrant crypt foci

The aim of this paper is to introduce a variational image segmentation method for assessing the aberrant crypt foci (ACF) in the human colon captured in vivo by endoscopy. ACF are thought to be precursors for colorectal cancer, and therefore their early detection may play an important clinical role. We enhance the active contours without edges model of Chan and Vese to account for the ACF's particular structure. We employ level sets to represent the segmentation boundaries and discretize in space by finite elements and in (artificial) time by finite differences. The approach is able to identify the ACF, their boundaries, and some of the internal crypts' orifices.

Characterisation of human bone marrow stromal cell heterogeneity for skeletal regeneration strategies using a two-stage colony assay and computational modelling

Skeletal regeneration and tissue engineering strategies rely critically on the efficient expansion of progenitor cell populations whilst simultaneously preserving multipotentiality and the ability to induce differentiation towards bone and cartilage. Cell population heterogeneity has a significant impact on this process, but is currently poorly quantified, hampering the interpretation of experimental results and the design of optimised expansion protocols. The objective of this study was to characterise individual human bone marrow stromal cell heterogeneity in terms of colony expansion potential. For this purpose, a novel two-stage CFU-F assay was developed in which cells from primary single cell-derived colonies were detached and reseeded again at clonal density as single cells to form new secondary colonies. This clearly demonstrated how secondary colony growth potential varies markedly both between and within primary colonies. Depending on the primary colony, cells either generated small secondary colonies only, or else a wide range of colony sizes. Using computational modelling it was shown how such colony heterogeneity could arise from hierarchical progenitor cell populations and what the limits of such a population structure were in explaining the experimental data. In addition the model demonstrated the significant potential impact of cell mobility on expansion potential and its implications for inducing population heterogeneity. This combined experimental-computational approach will ascertain the impact of cell culture protocols on the expansion potential and functional composition of heterogeneous progenitor populations. Such insights are likely to be of crucial importance for the success of skeletal regeneration strategies.

Nonlinear modelling of cancer: bridging the gap between cells and tumours

Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis.

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.

Epigenetics, stem cells and epithelial cell fate

Establishment and maintenance of epigenetic profiles are essential steps of development during which stem cells, despite identical genetic information, will acquire different and selective gene expression patterns, specific for their fate. This highly complex programming process involves mechanisms that are not yet completely understood although it has been established over the past few years that chromatin modifier enzymes (i.e. DNA and histone methyltransferases, histone deacetylases, histone demethylases, histone acetyltransferases) play essential roles in the establishment of transcriptional programs accompanying cell differentiation. Investigators in this field have been studying a wide variety of cell types including neural, muscular, mesenchymal and blood cells. This review will focus on epithelial cells of the digestive tract, intestinal stem cell niches being a model of choice to understand how epigenetic changes can drive nuclear programming and specific cell differentiation. Moreover, deregulation of epigenetic programming is frequently observed in human tumours and therefore, decoding these molecular mechanisms is essential to better understand both developmental and cancerous processes.

Stem cells and solid cancers

Recently, there have been significant advances in our knowledge of stem cells found in tissues that can develop solid tumours. In particular, novel stem cell markers have been identified for the first time identifying multipotential cells: a required characteristic of a stem cell. The scarcity of cancer stem cells has been questioned. Current dogma states that they are rare, but novel research has suggested that this may not be the case. Here, we review the latest literature on stem cells, particularly cancer stem cells within solid tumours. We discuss current thinking on how stem cells develop into cancer stem cells and how they protect themselves from doing so and do they express unique markers that can be used to detect stem cells. We attempt to put into perspective these latest advances in stem cell biology and their potential for cancer therapy.