Elucidating the interactions between the adhesive and transcriptional functions of -catenin in normal and cancerous cells

Engineering Strategies to Move from Understanding to Steering Renal Tubulogenesis

Rebuilding the kidney in the context of tissue engineering offers a major challenge as the organ is structurally complex and has a high variety of specific functions. Recreation of kidney function is inherently connected to the formation of tubules since the functional subunit of the kidney, the nephron, is based on tubular structures. In vivo, tubulogenesis culminates in a perfectly shaped, patterned, and functional renal tubule via different morphogenic processes that depend on delicately orchestrated chemical, physical, and mechanical interactions between cells and between cells and their microenvironment. This review summarizes the current understanding of the role of the microenvironment in the morphogenic processes involved in in vivo renal tubulogenesis. We highlight the current state-of-the-art of renal tubular engineering and provide a view on the design elements that can be extracted from these studies. Next, we discuss how computational modeling can aid in specifying and identifying design parameters and provide directions on how these design parameters can be incorporated in biomaterials for the purpose of engineering renal tubulogenesis. Finally, we propose that a step-by-step reciprocal interaction between understanding and engineering is necessary to effectively guide renal tubulogenesis. Impact statement Tubular tissue engineering lies at the foundation of regenerating kidney tissue function, as the functional subunit of the kidney, the nephron, is based on tubular structures. Guiding renal tubulogenesis toward functional renal tubules requires in-depth knowledge of the developmental processes that lead to the formation of native tubules as well as engineering approaches to steer these processes. In this study, we review the role of the microenvironment in the developmental processes that lead to functional renal tubules and give directions how this knowledge can be harnessed for biomaterial-based tubular engineering using computational models.

Signalling dynamics in embryonic development

In multicellular organisms, cellular behaviour is tightly regulated to allow proper embryonic development and maintenance of adult tissue. A critical component in this control is the communication between cells via signalling pathways, as errors in intercellular communication can induce developmental defects or diseases such as cancer. It has become clear over the last years that signalling is not static but varies in activity over time. Feedback mechanisms present in every signalling pathway lead to diverse dynamic phenotypes, such as transient activation, signal ramping or oscillations, occurring in a cell type- and stage-dependent manner. In cells, such dynamics can exert various functions that allow organisms to develop in a robust and reproducible way. Here, we focus on Erk, Wnt and Notch signalling pathways, which are dynamic in several tissue types and organisms, including the periodic segmentation of vertebrate embryos, and are often dysregulated in cancer. We will discuss how biochemical processes influence their dynamics and how these impact on cellular behaviour within multicellular systems.

Relating simulation studies by provenance-Developing a family of Wnt signaling models

For many biological systems, a variety of simulation models exist. A new simulation model is rarely developed from scratch, but rather revises and extends an existing one. A key challenge, however, is to decide which model might be an appropriate starting point for a particular problem and why. To answer this question, we need to identify entities and activities that contributed to the development of a simulation model. Therefore, we exploit the provenance data model, PROV-DM, of the World Wide Web Consortium and, building on previous work, continue developing a PROV ontology for simulation studies. Based on a case study of 19 Wnt/β-catenin signaling models, we identify crucial entities and activities as well as useful metadata to both capture the provenance information from individual simulation studies and relate these forming a family of models. The approach is implemented in WebProv, a web application for inserting and querying provenance information. Our specialization of PROV-DM contains the entities Research Question, Assumption, Requirement, Qualitative Model, Simulation Model, Simulation Experiment, Simulation Data, and Wet-lab Data as well as activities referring to building, calibrating, validating, and analyzing a simulation model. We show that most Wnt simulation models are connected to other Wnt models by using (parts of) these models. However, the overlap, especially regarding the Wet-lab Data used for calibration or validation of the models is small. Making these aspects of developing a model explicit and queryable is an important step for assessing and reusing simulation models more effectively. Exposing this information helps to integrate a new simulation model within a family of existing ones and may lead to the development of more robust and valid simulation models. We hope that our approach becomes part of a standardization effort and that modelers adopt the benefits of provenance when considering or creating simulation models.

We revise a provenance ontology for simulation studies of cellular biochemical models. Provenance information is useful for understanding the creation of a simulation model because it not only contains information about the entities and activities that have led to a simulation model but also their relations, all of which can be visualized. It provides additional structure by explicitly recording research questions, assumptions, and requirements and relating them along with data, qualitative models, simulation models, and simulation experiments through a small set of predefined but extensible activities.

We have applied our concept to a family of 19 Wnt signaling models and implemented a web-based tool (WebProv) to store the provenance information from these studies. The resulting provenance graph visualizes the story line of simulation studies and demonstrates the creation and calibration of simulation models, the successive attempts of validation and extension, and shows, beyond an individual simulation study, how the Wnt models are related. Thereby, the steps and sources that contributed to a simulation model are made explicit.

Our approach complements other approaches aimed at facilitating the reuse and assessment of simulation products in systems biology such as model repositories as well as annotation and documentation guidelines.

Modelling the effect of subcellular mutations on the migration of cells in the colorectal crypt

Background

Many cancers arise from mutations in cells within epithelial tissues. Mutations manifesting at the subcellular level influence the structure and function of the tissue resulting in cancer. Previous work has proposed how cell level properties can lead to mutant cell invasion, but has not incorporated detailed subcellular modelling

Results

We present a framework that allows the straightforward integration and simulation of SBML representations of subcellular dynamics within multiscale models of epithelial tissues. This allows us to investigate the effect of mutations in subcellular pathways on the migration of cells within the colorectal crypt. Using multiple models we find that mutations in APC, a key component in the Wnt signalling pathway, can bias neutral drift and can also cause downward invasion of mutant cells in the crypt.

Conclusions

Our framework allows us to investigate how subcellular mutations, i.e. knockouts and knockdowns, affect cell-level properties and the resultant migration of cells within epithelial tissues. In the context of the colorectal crypt, we see that mutations in APC can lead directly to mutant cell invasion.

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.

Towards personalized computational oncology: from spatial models of tumour spheroids, to organoids, to tissues

A main goal of mathematical and computational oncology is to develop quantitative tools to determine the most effective therapies for each individual patient. This involves predicting the right drug to be administered at the right time and at the right dose. Such an approach is known as precision medicine. Mathematical modelling can play an invaluable role in the development of such therapeutic strategies, since it allows for relatively fast, efficient and inexpensive simulations of a large number of treatment schedules in order to find the most effective. This review is a survey of mathematical models that explicitly take into account the spatial architecture of three-dimensional tumours and address tumour development, progression and response to treatments. In particular, we discuss models of epithelial acini, multicellular spheroids, normal and tumour spheroids and organoids, and multi-component tissues. Our intent is to showcase how these in silico models can be applied to patient-specific data to assess which therapeutic strategies will be the most efficient. We also present the concept of virtual clinical trials that integrate standard-of-care patient data, medical imaging, organ-on-chip experiments and computational models to determine personalized medical treatment strategies.

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.

Src- and confinement-dependent FAK activation causes E-cadherin relaxation and β-catenin activity

β-Catenin is a transcription cofactor proposed to be released from E-cadherin upon mechanically induced phosphorylation. However, evidence for this mechanism is lacking. Gayrard et al. show instead that during epithelial-to-mesenchymal transition, Src- and multicellular confinement–dependent FAK-induced cytoskeleton remodeling causes E-cadherin tension relaxation and phosphorylation-independent β-catenin nuclear translocation from the membrane.

In epithelia, E-cadherin cytoplasmic tail is under cytoskeleton-generated tension via a link that contains β-catenin. A cotranscription factor, β-catenin, is also active in morphogenetic processes associated with epithelial-to-mesenchymal transition. β-Catenin signaling appears mechanically inducible and was proposed to follow phosphorylation-induced β-catenin release from E-cadherin. Evidence for this mechanism is lacking, and whether E-cadherin tension is involved is unknown. To test this, we combined quantitative fluorescence microscopies with genetic and pharmacological perturbations of epithelial-to-mesenchymal transition–induced cells in culture. We showed that β-catenin nuclear activity follows a substantial release from the membrane specific to migrating cells and requires multicellular deconfinement and Src activity. Selective nuclear translocation occurs downstream of focal adhesion kinase activation, which targets E-cadherin tension relaxation through actomyosin remodeling. In contrast, phosphorylations of the cadherin/catenin complex are not substantially required. These data demonstrate that E-cadherin acts as a sensor of intracellular mechanics in a crosstalk with cell-substrate adhesions that target β-catenin signaling.

Paracrine and autocrine regulation of gene expression by Wnt-inhibitor Dickkopf in wild-type and mutant hepatocytes

Background

Cells are able to communicate and coordinate their function within tissues via secreted factors. Aberrant secretion by cancer cells can modulate this intercellular communication, in particular in highly organised tissues such as the liver. Hepatocytes, the major cell type of the liver, secrete Dickkopf (Dkk), which inhibits Wnt/ β-catenin signalling in an autocrine and paracrine manner. Consequently, Dkk modulates the expression of Wnt/ β-catenin target genes. We present a mathematical model that describes the autocrine and paracrine regulation of hepatic gene expression by Dkk under wild-type conditions as well as in the presence of mutant cells.

Results

Our spatial model describes the competition of Dkk and Wnt at receptor level, intra-cellular Wnt/ β-catenin signalling, and the regulation of target gene expression for 21 individual hepatocytes. Autocrine and paracrine regulation is mediated through a feedback mechanism via Dkk and Dkk diffusion along the porto-central axis. Along this axis an APC concentration gradient is modelled as experimentally detected in liver. Simulations of mutant cells demonstrate that already a single mutant cell increases overall Dkk concentration. The influence of the mutant cell on gene expression of surrounding wild-type hepatocytes is limited in magnitude and restricted to hepatocytes in close proximity. To explore the underlying molecular mechanisms, we perform a comprehensive analysis of the model parameters such as diffusion coefficient, mutation strength and feedback strength.

Conclusions

Our simulations show that Dkk concentration is elevated in the presence of a mutant cell. However, the impact of these elevated Dkk levels on wild-type hepatocytes is confined in space and magnitude. The combination of inter- and intracellular processes, such as Dkk feedback, diffusion and Wnt/ β-catenin signal transduction, allow wild-type hepatocytes to largely maintain their gene expression.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0470-9) contains supplementary material, which is available to authorized users.

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.

The role of the Hes1 crosstalk hub in Notch-Wnt interactions of the intestinal crypt

The Notch pathway plays a vital role in determining whether cells in the intestinal epithelium adopt a secretory or an absorptive phenotype. Cell fate specification is coordinated via Notch's interaction with the canonical Wnt pathway. Here, we propose a new mathematical model of the Notch and Wnt pathways, in which the Hes1 promoter acts as a hub for pathway crosstalk. Computational simulations of the model can assist in understanding how healthy intestinal tissue is maintained, and predict the likely consequences of biochemical knockouts upon cell fate selection processes. Chemical reaction network theory (CRNT) is a powerful, generalised framework which assesses the capacity of our model for monostability or multistability, by analysing properties of the underlying network structure without recourse to specific parameter values or functional forms for reaction rates. CRNT highlights the role of β-catenin in stabilising the Notch pathway and damping oscillations, demonstrating that Wnt-mediated actions on the Hes1 promoter can induce dynamic transitions in the Notch system, from multistability to monostability. Time-dependent model simulations of cell pairs reveal the stabilising influence of Wnt upon the Notch pathway, in which β-catenin- and Dsh-mediated action on the Hes1 promoter are key in shaping the subcellular dynamics. Where Notch-mediated transcription of Hes1 dominates, there is Notch oscillation and maintenance of fate flexibility; Wnt-mediated transcription of Hes1 favours bistability akin to cell fate selection. Cells could therefore regulate the proportion of Wnt- and Notch-mediated control of the Hes1 promoter to coordinate the timing of cell fate selection as they migrate through the intestinal epithelium and are subject to reduced Wnt stimuli. Furthermore, mutant cells characterised by hyperstimulation of the Wnt pathway may, through coupling with Notch, invert cell fate in neighbouring healthy cells, enabling an aberrant cell to maintain its neighbours in mitotically active states.

The Integrated Role of Wnt/β-Catenin, N-Glycosylation, and E-Cadherin-Mediated Adhesion in Network Dynamics

The cellular network composed of the evolutionarily conserved metabolic pathways of protein N-glycosylation, Wnt/β-catenin signaling pathway, and E-cadherin-mediated cell-cell adhesion plays pivotal roles in determining the balance between cell proliferation and intercellular adhesion during development and in maintaining homeostasis in differentiated tissues. These pathways share a highly conserved regulatory molecule, β-catenin, which functions as both a structural component of E-cadherin junctions and as a co-transcriptional activator of the Wnt/β-catenin signaling pathway, whose target is the N-glycosylation-regulating gene, DPAGT1. Whereas these pathways have been studied independently, little is known about the dynamics of their interaction. Here we present the first numerical model of this network in MDCK cells. Since the network comprises a large number of molecules with varying cell context and time-dependent levels of expression, it can give rise to a wide range of plausible cellular states that are difficult to track. Using known kinetic parameters for individual reactions in the component pathways, we have developed a theoretical framework and gained new insights into cellular regulation of the network. Specifically, we developed a mathematical model to quantify the fold-change in concentration of any molecule included in the mathematical representation of the network in response to a simulated activation of the Wnt/ β-catenin pathway with Wnt3a under different conditions. We quantified the importance of protein N-glycosylation and synthesis of the DPAGT1 encoded enzyme, GPT, in determining the abundance of cytoplasmic β-catenin. We confirmed the role of axin in β-catenin degradation. Finally, our data suggest that cell-cell adhesion is insensitive to E-cadherin recycling in the cell. We validate the model by inhibiting β-catenin-mediated activation of DPAGT1 expression and predicting changes in cytoplasmic β-catenin concentration and stability of E-cadherin junctions in response to DPAGT1 inhibition. We show the impact of pathway dysregulation through measurements of cell migration in scratch-wound assays. Collectively, our results highlight the importance of numerical analyses of cellular networks dynamics to gain insights into physiological processes and potential design of therapeutic strategies to prevent epithelial cell invasion in cancer.

Construction and Experimental Validation of a Petri Net Model of Wnt/β-Catenin Signaling

The Wnt/β-catenin signaling pathway is important for multiple developmental processes and tissue maintenance in adults. Consequently, deregulated signaling is involved in a range of human diseases including cancer and developmental defects. A better understanding of the intricate regulatory mechanism and effect of physiological (active) and pathophysiological (hyperactive) WNT signaling is important for predicting treatment response and developing novel therapies. The constitutively expressed CTNNB1 (commonly and hereafter referred to as β-catenin) is degraded by a destruction complex, composed of amongst others AXIN1 and GSK3. The destruction complex is inhibited during active WNT signaling, leading to β-catenin stabilization and induction of β-catenin/TCF target genes. In this study we investigated the mechanism and effect of β-catenin stabilization during active and hyperactive WNT signaling in a combined in silico and in vitro approach. We constructed a Petri net model of Wnt/β-catenin signaling including main players from the plasma membrane (WNT ligands and receptors), cytoplasmic effectors and the downstream negative feedback target gene AXIN2. We validated that our model can be used to simulate both active (WNT stimulation) and hyperactive (GSK3 inhibition) signaling by comparing our simulation and experimental data. We used this experimentally validated model to get further insights into the effect of the negative feedback regulator AXIN2 upon WNT stimulation and observed an attenuated β-catenin stabilization. We furthermore simulated the effect of APC inactivating mutations, yielding a stabilization of β-catenin levels comparable to the Wnt-pathway activities observed in colorectal and breast cancer. Our model can be used for further investigation and viable predictions of the role of Wnt/β-catenin signaling in oncogenesis and development.

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non-exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.

Newly Constructed Network Models of Different WNT Signaling Cascades Applied to Breast Cancer Expression Data

INTRODUCTION

WNT signaling is a complex process comprising multiple pathways: the canonical β-catenin-dependent pathway and several alternative non-canonical pathways that act in a β-catenin-independent manner. Representing these intricate signaling mechanisms through bioinformatic approaches is challenging. Nevertheless, a simplified but reliable bioinformatic WNT pathway model is needed, which can be further utilized to decipher specific WNT activation states within e.g. high-throughput data.

RESULTS

In order to build such a model, we collected, parsed, and curated available WNT signaling knowledge from different pathway databases. The data were assembled to construct computationally suitable models of different WNT signaling cascades in the form of directed signaling graphs. This resulted in four networks representing canonical WNT signaling, non-canonical WNT signaling, the inhibition of canonical WNT signaling and the regulation of WNT signaling pathways, respectively. Furthermore, these networks were integrated with microarray and RNA sequencing data to gain deeper insight into the underlying biology of gene expression differences between MCF-7 and MDA-MB-231 breast cancer cell lines, representing weakly and highly invasive breast carcinomas, respectively. Differential genes up-regulated in the MDA-MB-231 compared to the MCF-7 cell line were found to display enrichment in the gene set originating from the non-canonical network. Moreover, we identified and validated differentially regulated modules representing canonical and non-canonical WNT pathway components specific for the aggressive basal-like breast cancer subtype.

CONCLUSIONS

In conclusion, we demonstrated that these newly constructed WNT networks reliably reflect distinct WNT signaling processes. Using transcriptomic data, we shaped these networks into comprehensive modules of the genes implicated in the aggressive basal-like breast cancer subtype and demonstrated that non-canonical WNT signaling is important in this context. The topology of these networks can be further refined in the future by integration with complementary data such as protein-protein interactions, in order to gain greater insight into signaling processes.

Interlocked positive and negative feedback network motifs regulate β-catenin activity in the adherens junction pathway

The integrity of epithelial tissue architecture is maintained through adherens junctions that are created through extracellular homotypic protein-protein interactions between cadherin molecules. Cadherins also provide an intracellular scaffold for the formation of a multiprotein complex that contains signaling proteins, including β-catenin. Environmental factors and controlled tissue reorganization disrupt adherens junctions by cleaving the extracellular binding domain and initiating a series of transcriptional events that aim to restore tissue homeostasis. However, it remains unclear how alterations in cell adhesion coordinate transcriptional events, including those mediated by β-catenin in this pathway. Here were used quantitative single-cell and population-level in vitro assays to quantify the endogenous pathway dynamics after the proteolytic disruption of the adherens junctions. Using prior knowledge of isolated elements of the overall network, we interpreted these data using in silico model-based inference to identify the topology of the regulatory network. Collectively the data suggest that the regulatory network contains interlocked network motifs consisting of a positive feedback loop, which is used to restore the integrity of adherens junctions, and a negative feedback loop, which is used to limit β-catenin-induced gene expression.

Parameter-free methods distinguish Wnt pathway models and guide design of experiments

The canonical Wnt signaling pathway, mediated by β-catenin, is crucially involved in development, adult stem cell tissue maintenance, and a host of diseases including cancer. We analyze existing mathematical models of Wnt and compare them to a new Wnt signaling model that targets spatial localization; our aim is to distinguish between the models and distill biological insight from them. Using Bayesian methods we infer parameters for each model from mammalian Wnt signaling data and find that all models can fit this time course. We appeal to algebraic methods (concepts from chemical reaction network theory and matroid theory) to analyze the models without recourse to specific parameter values. These approaches provide insight into aspects of Wnt regulation: the new model, via control of shuttling and degradation parameters, permits multiple stable steady states corresponding to stem-like vs. committed cell states in the differentiation hierarchy. Our analysis also identifies groups of variables that should be measured to fully characterize and discriminate between competing models, and thus serves as a guide for performing minimal experiments for model comparison.

Mathematical modelling suggests a differential impact of β-transducin repeat-containing protein paralogues on Wnt/β-catenin signalling dynamics

The Wnt/β-catenin signalling pathway is involved in the regulation of a multitude of cellular processes by controlling the concentration of the transcriptional regulator β-catenin. Proteasomal degradation of β-catenin is mediated by two β-transducin repeat-containing protein paralogues, homologous to Slimb protein (HOS) and F-box/WD repeat-containing protein 1A (FWD1), which are functionally interchangeable and thereby considered to function redundantly in the pathway. HOS and FWD1 are both regulated by Wnt/β-catenin signalling, albeit in opposite directions, thus establishing interlocked negative and positive feedback loops. The functional relevance of the opposite regulation of HOS and FWD1 by Wnt/β-catenin signalling in conjunction with their redundant activities in proteasomal degradation of β-catenin remains unresolved. Using a detailed ordinary differential equation model, we investigated the specific influence of each individual feedback mechanism and their combination on Wnt/β-catenin signal transduction under wild-type and cancerous conditions. We found that, under wild-type conditions, the signalling dynamics are predominantly affected by the HOS feedback as a result of a higher concentration of HOS than FWD1. Transcriptional up-regulation of FWD1 by other signalling pathways reduced the impact of the HOS feedback. The opposite regulation of HOS and FWD1 expression by Wnt/β-catenin signalling allows the FWD1 feedback to be employed as a compensation mechanism against aberrant pathway activation as a result of a reduced HOS concentration. By contrast, the FWD1 feedback provides no protection against aberrant activation in adenomatous polyposis coli protein mutant cancer cells.

Computational modeling of the interplay between cadherin-mediated cell adhesion and Wnt signaling pathway

Wnt signaling and cadherin-mediated adhesion have been implicated in both processes of embryonic development and the progression of carcinomas. Recent experimental studies revealed that Wnt signaling and cadherin-mediated cell adhesion have close crosstalk with each other. A comprehensive model that investigates the dynamic balance of β-catenins in Wnt signaling and cell adhesion will improve our understanding to embryonic development and carcinomas. We constructed a network model to evaluate the dynamic interplay between adhesion and Wnt signaling. The network is decomposed into three interdependent modules: the cell adhesion, the degradation circle and the transcriptional regulation. In the cell adhesion module, we consider the effect of cadherin’s lateral clustering. We found adhesion negatively contributes to Wnt signaling through competition for cytoplasmic β-catenins. In the network of degradation circle, we incorporated features from various existing models. Our simulations reproduced the most recent experimental phenomena with semi-quantitative accuracy. Finally, in the transcriptional regulation module, we developed a function selection strategy to analyze the outcomes of genetic feedback loops in modulating the gene expression of Wnt targets. The specific cellular phenomena such as cadherin switch and Axin oscillation were archived and their biological insights were discussed. Our model provides the theoretical basis of how spatial organization regulates the dynamics of cellular signaling pathways. We suggest that cell adhesion affects Wnt signaling in both negative and positive ways. Cadherins can inhibit Wnt signaling not only in a way as a stoichiometric binding partner of β-catenins that sequesters them from signaling, but also in a way through their clustering to impacts the rate at which β-catenins are involved in the destruction loop. Additionally, cadherin clustering increases the phosphorylation rate of β-catenins and promotes its signaling in nucleus.

Analysis of Wnt signaling β-catenin spatial dynamics in HEK293T cells

Background

Wnt/β-catenin signaling is involved in different stages of mammalian development and implicated in various cancers (e.g. colorectal cancer). Recent experimental and computational studies have revealed characteristics of the pathway, however a cell-specific spatial perspective is lacking. In this study, a novel 3D confocal quantitation protocol is developed to acquire spatial (two cellular compartments: nucleus and cytosol-membrane) and temporal quantitative data on target protein (e.g. β-catenin) concentrations in Human Epithelial Kidney cells (HEK293T) during perturbation (with either cycloheximide or Wnt3A). Computational models of the Wnt pathway are constructed and interrogated based on this data.

Results

A single compartment Wnt pathway model is compared with a simple β-catenin two compartment model to investigate Wnt3A signaling in HEK293T cells. When protein synthesis is inhibited, β-catenin decreases at the same rate in both cellular compartments, suggesting diffusional transport is fast compared to β-catenin degradation in the cytosol. With Wnt3A stimulation, the total amount of β-catenin rises throughout the cell, however the increase is initially (~first hour) faster in the nuclear compartment. While both models were able to reproduce the whole cell changes in β-catenin, only the compartment model reproduced the Wnt3A induced changes in β-catenin distribution and it was also the best fit for the data obtained when active transport was included alongside passive diffusion transport.

Conclusions

This integrated 3D quantitation imaging protocol and computational modeling approach allowed cell-specific compartment models of the signaling pathways to be constructed and analyzed. The Wnt models constructed in this study are the first for HEK293T and have suggested potential roles of inter-compartment transport to the dynamics of signaling.

Analysing the impact of nucleo-cytoplasmic shuttling of β-catenin and its antagonists APC, Axin and GSK3 on Wnt/β-catenin signalling

The canonical Wnt signalling pathway plays a critical role in development and disease. The key player of the pathway is β-catenin. Its activity is mainly regulated by the destruction complex consisting of APC, Axin and GSK3. In the nucleus, the complex formation of β-catenin and TCF initiates target gene expression. Our study provides a comprehensive analysis of the role of nucleo-cytoplasmic shuttling of APC, Axin, and GSK3 and the inactivation of β-catenin by the destruction complex in Wnt/β-catenin signalling. We address the following questions: Can nucleo-cytoplasmic shuttling of APC, Axin and GSK3 increase the [β-catenin/TCF] concentration? And, how is the [β-catenin/TCF] concentration influenced by phosphorylation and subsequent degradation of nuclear β-catenin? Based on experimental findings, we develop a compartmental model and conduct several simulation experiments. Our analysis reveals the following key findings: 1) nucleo-cytoplasmic shuttling of β-catenin and its antagonists can yield a spatial separation between the said proteins, which results in a breakdown of β-catenin degradation, followed by an accumulation of β-catenin and hence leads to an increase of the [β-catenin/TCF] concentration. Our results strongly suggest that Wnt signalling can benefit from nucleo-cytoplasmic shuttling of APC, Axin and GSK3, although they are in general β-catenin antagonising proteins. 2) The total robustness of the [β-catenin/TCF] output is closely linked to its absolute concentration levels. We demonstrate that the compartmental separation of β-catenin and the destruction complex does not only lead to a maximization, but additionally to an increased robustness of [β-catenin/TCF] signalling against perturbations in the cellular environment. 3) A nuclear accumulation of the destruction complex renders the pathway robust against fluctuations in Wnt signalling and against changes in the compartmental distribution of β-catenin. 4) Elucidating the impact of destruction complex inhibition, we show that the [β-catenin/TCF] concentration is more effectively enhanced by inhibition of the kinase GSK3 rather than the binding of β-catenin to the destruction complex.

Toward a quantitative understanding of the Wnt/β-catenin pathway through simulation and experiment

Wnt signaling regulates cell survival, proliferation, and differentiation throughout development and is aberrantly regulated in cancer. The pathway is activated when Wnt ligands bind to specific receptors on the cell surface, resulting in the stabilization and nuclear accumulation of the transcriptional co-activator β-catenin. Mathematical and computational models have been used to study the spatial and temporal regulation of the Wnt/β-catenin pathway and to investigate the functional impact of mutations in key components. Such models range in complexity, from time-dependent, ordinary differential equations that describe the biochemical interactions between key pathway components within a single cell, to complex, multiscale models that incorporate the role of the Wnt/β-catenin pathway target genes in tissue homeostasis and carcinogenesis. This review aims to summarize recent progress in mathematical modeling of the Wnt pathway and to highlight new biological results that could form the basis for future theoretical investigations designed to increase the utility of theoretical models of Wnt signaling in the biomedical arena.

Modeling Wnt/β-Catenin Target Gene Expression in APC and Wnt Gradients Under Wild Type and Mutant Conditions

The Wnt/β-catenin pathway is involved in the regulation of a multitude of physiological processes by controlling the differential expression of target genes. In certain tissues such as the adult liver, the Wnt/β-catenin pathway can attain different levels of activity due to gradients of Wnt ligands and/or intracellular pathway components like APC. How graded pathway activity is converted into regionally distinct patterns of Wnt/β-catenin target gene expression is largely unknown. Here, we apply a mathematical modeling approach to investigate the impact of different regulatory mechanisms on target gene expression within Wnt or APC concentration gradients. We develop a minimal model of Wnt/β-catenin signal transduction and combine it with various mechanisms of target gene regulation. In particular, the effects of activation, inhibition, and an incoherent feedforward loop (iFFL) are compared. To specify activation kinetics, we analyze experimental data that quantify the response of β-catenin/TCF reporter constructs to different Wnt concentrations, and demonstrate that the induction of these constructs occurs in a cooperative manner with Hill coefficients between 2 and 5. In summary, our study shows that the combination of specific gene regulatory mechanisms with a time-independent gradient of Wnt or APC is sufficient to generate distinct target gene expression patterns as have been experimentally observed in liver. We find that cooperative gene activation in combination with a TCF feedback can establish sharp borders of target gene expression in Wnt or APC gradients. In contrast, the iFFL renders gene expression independent of gradients of the upstream signaling components. Our subsequent analysis of carcinogenic pathway mutations reveals that their impact on gene expression is determined by the gene regulatory mechanism and the APC concentration of the cell in which the mutation occurs.

Elucidating the sources of β-catenin dynamics in human neural progenitor cells

Human neural progenitor cells (hNPCs) form a new prospect for replacement therapies in the context of neurodegenerative diseases. The Wnt/β-catenin signaling pathway is known to be involved in the differentiation process of hNPCs. RVM cells form a common cell model of hNPCs for in vitro investigation. Previous observations in RVM cells raise the question of whether observed kinetics of the Wnt/β-catenin pathway in later differentiation phases are subject to self-induced signaling. However, a concern when investigating RVM cells is that experimental results are possibly biased by the asynchrony of cells w.r.t. the cell cycle. In this paper, we present, based on experimental data, a computational modeling study on the Wnt/β-catenin signaling pathway in RVM cell populations asynchronously distributed w.r.t. to their cell cycle phases. Therefore, we derive a stochastic model of the pathway in single cells from the reference model in literature and extend it by means of cell populations and cell cycle asynchrony. Based on this, we show that the impact of the cell cycle asynchrony on wet-lab results that average over cell populations is negligible. We then further extend our model and the thus-obtained simulation results provide additional evidence that self-induced Wnt signaling occurs in RVM cells. We further report on significant stochastic effects that directly result from model parameters provided in literature and contradict experimental observations.

A theoretical investigation of the effect of proliferation and adhesion on monoclonal conversion in the colonic crypt

The surface epithelium lining the intestinal tract renews itself rapidly by a coordinated programme of cell proliferation, migration and differentiation events that is initiated in the crypts of Lieberkühn. It is generally believed that colorectal cancer arises due to mutations that disrupt the normal cellular dynamics of the crypts. Using a spatially structured cell-based model of a colonic crypt, we investigate the likelihood that the progeny of a mutated cell will dominate, or be sloughed out of, a crypt. Our approach is to perform multiple simulations, varying the spatial location of the initial mutation, and the proliferative and adhesive properties of the mutant cells, to obtain statistical distributions for the probability of their domination. Our simulations lead us to make a number of predictions. The process of monoclonal conversion always occurs, and does not require that the cell which initially gave rise to the population remains in the crypt. Mutations occurring more than one to two cells from the base of the crypt are unlikely to become the dominant clone. The probability of a mutant clone persisting in the crypt is sensitive to dysregulation of adhesion. By comparing simulation results with those from a simple one-dimensional stochastic model of population dynamics at the base of the crypt, we infer that this sensitivity is due to direct competition between wild-type and mutant cells at the base of the crypt. We also predict that increases in the extent of the spatial domain in which the mutant cells proliferate can give rise to counter-intuitive, non-linear changes to the probability of their fixation, due to effects that cannot be captured in simpler models.

A two-dimensional model of the colonic crypt accounting for the role of the basement membrane and pericryptal fibroblast sheath

The role of the basement membrane is vital in maintaining the integrity and structure of an epithelial layer, acting as both a mechanical support and forming the physical interface between epithelial cells and the surrounding connective tissue. The function of this membrane is explored here in the context of the epithelial monolayer that lines the colonic crypt, test-tube shaped invaginations that punctuate the lining of the intestine and coordinate a regular turnover of cells to replenish the epithelial layer every few days. To investigate the consequence of genetic mutations that perturb the system dynamics and can lead to colorectal cancer, it must be possible to track the emerging tissue level changes that arise in the crypt. To that end, a theoretical crypt model with a realistic, deformable geometry is required. A new discrete crypt model is presented, which focuses on the interaction between cell- and tissue-level behaviour, while incorporating key subcellular components. The model contains a novel description of the role of the surrounding tissue and musculature, based upon experimental observations of the tissue structure of the crypt, which are also reported. A two-dimensional (2D) cross-sectional geometry is considered, and the shape of the crypt is allowed to evolve and deform. Simulation results reveal how the shape of the crypt may contribute mechanically to the asymmetric division events typically associated with the stem cells at the base. The model predicts that epithelial cell migration may arise due to feedback between cell loss at the crypt collar and density-dependent cell division, an hypothesis which can be investigated in a wet lab. This work forms the basis for investigation of the deformation of the crypt structure that can occur due to proliferation of cells exhibiting mutant phenotypes, experiments that would not be possible in vivo or in vitro.

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.

Wnt signalling pathway parameters for mammalian cells

Wnt/β-catenin signalling regulates cell fate, survival, proliferation and differentiation at many stages of mammalian development and pathology. Mutations of two key proteins in the pathway, APC and β-catenin, have been implicated in a range of cancers, including colorectal cancer. Activation of Wnt signalling has been associated with the stabilization and nuclear accumulation of β-catenin and consequential up-regulation of β-catenin/TCF gene transcription. In 2003, Lee et al. constructed a computational model of Wnt signalling supported by experimental data from analysis of time-dependent concentration of Wnt signalling proteins in Xenopus egg extracts. Subsequent studies have used the Xenopus quantitative data to infer Wnt pathway dynamics in other systems. As a basis for understanding Wnt signalling in mammalian cells, a confocal live cell imaging measurement technique is developed to measure the cell and nuclear volumes of MDCK, HEK293T cells and 3 human colorectal cancer cell lines and the concentrations of Wnt signalling proteins β-catenin, Axin, APC, GSK3β and E-cadherin. These parameters provide the basis for formulating Wnt signalling models for kidney/intestinal epithelial mammalian cells. There are significant differences in concentrations of key proteins between Xenopus extracts and mammalian whole cell lysates. Higher concentrations of Axin and lower concentrations of APC are present in mammalian cells. Axin concentrations are greater than APC in kidney epithelial cells, whereas in intestinal epithelial cells the APC concentration is higher than Axin. Computational simulations based on Lee's model, with this new data, suggest a need for a recalibration of the model.A quantitative understanding of Wnt signalling in mammalian cells, in particular human colorectal cancers requires a detailed understanding of the concentrations of key protein complexes over time. Simulations of Wnt signalling in mammalian cells can be initiated with the parameters measured in this report.

Wnt signalling pathway parameters for mammalian cells

Wnt/β-catenin signalling regulates cell fate, survival, proliferation and differentiation at many stages of mammalian development and pathology. Mutations of two key proteins in the pathway, APC and β-catenin, have been implicated in a range of cancers, including colorectal cancer. Activation of Wnt signalling has been associated with the stabilization and nuclear accumulation of β-catenin and consequential up-regulation of β-catenin/TCF gene transcription. In 2003, Lee et al. constructed a computational model of Wnt signalling supported by experimental data from analysis of time-dependent concentration of Wnt signalling proteins in Xenopus egg extracts. Subsequent studies have used the Xenopus quantitative data to infer Wnt pathway dynamics in other systems. As a basis for understanding Wnt signalling in mammalian cells, a confocal live cell imaging measurement technique is developed to measure the cell and nuclear volumes of MDCK, HEK293T cells and 3 human colorectal cancer cell lines and the concentrations of Wnt signalling proteins β-catenin, Axin, APC, GSK3β and E-cadherin. These parameters provide the basis for formulating Wnt signalling models for kidney/intestinal epithelial mammalian cells. There are significant differences in concentrations of key proteins between Xenopus extracts and mammalian whole cell lysates. Higher concentrations of Axin and lower concentrations of APC are present in mammalian cells. Axin concentrations are greater than APC in kidney epithelial cells, whereas in intestinal epithelial cells the APC concentration is higher than Axin. Computational simulations based on Lee's model, with this new data, suggest a need for a recalibration of the model.A quantitative understanding of Wnt signalling in mammalian cells, in particular human colorectal cancers requires a detailed understanding of the concentrations of key protein complexes over time. Simulations of Wnt signalling in mammalian cells can be initiated with the parameters measured in this report.

Signaling from the adherens junction

The cadherin/catenin complex organizes to form a structural Velcro that joins the cytoskeletal networks of adjacent cells. Functional loss of this complex arrests the development of normal tissue organization, and years of research have gone into teasing out how the physical structure of adhesions conveys information to the cell interior. Evidence that most cadherin-binding partners also localize to the nucleus to regulate transcription supports the view that cadherins serve as simple stoichiometric inhibitors of nuclear signals. However, it is also clear that cadherin-based adhesion initiates a variety of molecular events that can ultimately impact nuclear signaling. This chapter discusses these two modes of cadherin signaling in the context of tissue growth and differentiation.

Novel common integration sites targeted by mouse mammary tumor virus insertion in mammary tumors have oncogenic activity

Non-acute transforming retroviruses like mouse mammary tumor virus (MMTV) cause cancer, at least in part, through integration near cellular genes involved in growth control, thereby de-regulating their expression. It is well-established that MMTV commonly integrates near and activates expression of members of the Wnt and Fgf pathways in mammary tumors. However, there are a significant number of tumors for which the proviral integration sites have not been identified. Here, we used high through-put screening to identify common integration sites (CISs) in MMTV-induced tumors from C3H/HeN and BALB/c mice. As expected, members of both the Wnt and Fgf families were identified in this screen. In addition, a number of novel CISs were found, including Tcf7l2, Antxr1/Tem8, and Arhgap18. We show here that expression of these three putative oncogenes in normal murine mammary gland cells altered their growth kinetics and caused their morphological transformation when grown in three dimensional cultures. Additionally, expression of Tcf7l2 and Antxr1/Tem8 sensitized cells to exogenous WNT ligand. As Tcf7l2, Antxr1/Tem8, and Arhgap18 have been associated with human breast and other cancers, these data demonstrate that MMTV-induced insertional mutation remains an important means for identifying genes involved in breast cancer.

Techniques for analysing pattern formation in populations of stem cells and their progeny

Background

To investigate how patterns of cell differentiation are related to underlying intra- and inter-cellular signalling pathways, we use a stochastic individual-based model to simulate pattern formation when stem cells and their progeny are cultured as a monolayer. We assume that the fate of an individual cell is regulated by the signals it receives from neighbouring cells via either diffusive or juxtacrine signalling. We analyse simulated patterns using two different spatial statistical measures that are suited to planar multicellular systems: pair correlation functions (PCFs) and quadrat histograms (QHs).

Results

With a diffusive signalling mechanism, pattern size (revealed by PCFs) is determined by both morphogen decay rate and a sensitivity parameter that determines the degree to which morphogen biases differentiation; high sensitivity and slow decay give rise to large-scale patterns. In contrast, with juxtacrine signalling, high sensitivity produces well-defined patterns over shorter lengthscales. QHs are simpler to compute than PCFs and allow us to distinguish between random differentiation at low sensitivities and patterned states generated at higher sensitivities.

Conclusions

PCFs and QHs together provide an effective means of characterising emergent patterns of differentiation in planar multicellular aggregates.

E-cadherin acts as a regulator of transcripts associated with a wide range of cellular processes in mouse embryonic stem cells

Background

We have recently shown that expression of the cell adhesion molecule E-cadherin is required for LIF-dependent pluripotency of mouse embryonic stem (ES) cells.

Methodology

In this study, we have assessed global transcript expression in E-cadherin null (Ecad-/-) ES cells cultured in either the presence or absence of LIF and compared these to the parental cell line wtD3.

Results

We show that LIF has little effect on the transcript profile of Ecad-/- ES cells, with statistically significant transcript alterations observed only for Sp8 and Stat3. Comparison of Ecad-/- and wtD3 ES cells cultured in LIF demonstrated significant alterations in the transcript profile, with effects not only confined to cell adhesion and motility but also affecting, for example, primary metabolic processes, catabolism and genes associated with apoptosis. Ecad-/- ES cells share similar, although not identical, gene expression profiles to epiblast-derived pluripotent stem cells, suggesting that E-cadherin expression may inhibit inner cell mass to epiblast transition. We further show that Ecad-/- ES cells maintain a functional β-catenin pool that is able to induce β-catenin/TCF-mediated transactivation but, contrary to previous findings, do not display endogenous β-catenin/TCF-mediated transactivation. We conclude that loss of E-cadherin in mouse ES cells leads to significant transcript alterations independently of β-catenin/TCF transactivation.

A hybrid approach to multi-scale modelling of cancer

In this paper, we review multi-scale models of solid tumour growth and discuss a middle-out framework that tracks individual cells. By focusing on the cellular dynamics of a healthy colorectal crypt and its invasion by mutant, cancerous cells, we compare a cell-centre, a cell-vertex and a continuum model of cell proliferation and movement. All models reproduce the basic features of a healthy crypt: cells proliferate near the crypt base, they migrate upwards and are sloughed off near the top. The models are used to establish conditions under which mutant cells are able to colonize the crypt either by top-down or by bottom-up invasion. While the continuum model is quicker and easier to implement, it can be difficult to relate system parameters to measurable biophysical quantities. Conversely, the greater detail inherent in the multi-scale models means that experimentally derived parameters can be incorporated and, therefore, these models offer greater scope for understanding normal and diseased crypts, for testing and identifying new therapeutic targets and for predicting their impacts.

Modelling spatially regulated beta-catenin dynamics and invasion in intestinal crypts

Experimental data (e.g., genetic lineage and cell population studies) on intestinal crypts reveal that regulatory features of crypt behavior, such as control via morphogen gradients, are remarkably well conserved among numerous organisms (e.g., from mouse and rat to human) and throughout the different regions of the small and large intestines. In this article, we construct a partial differential equation model of a single colonic crypt that describes the spatial distribution of Wnt pathway proteins along the crypt axis. The novelty of our continuum model is that it is based upon assumptions that can be directly related to processes at the cellular and subcellular scales. We use the model to predict how the distributions of Wnt pathway proteins are affected by mutations. The model is then extended to investigate how mutant cell populations can invade neighboring crypts. The model simulations suggest that cell crowding caused by increased proliferation and decreased cell loss may be sufficient for a mutant cell population to colonize a neighboring healthy crypt.

Mathematical modelling of Wnt/β-catenin signalling

The Wnt/β-catenin pathway plays an important role in development and disease. Theoretical approaches have been used to describe this pathway and have provided intriguing insights into its signalling characteristics. In the present paper, we review mathematical models of the pathway. We focus on a quantitative kinetic model for canonical Wnt/β-catenin signalling describing the reactions of the pathway's core compounds [Lee, Salic, Krüger, Heinrich and Kirschner (2003) PLoS Biol. 1, 116–132]. Numerous modifications and further analyses with respect to signalling characteristics, transcriptional feedback and cross-talk were performed. In addition, the role of β-catenin in gene expression and cell–cell adhesion as well as spatial aspects of signalling are investigated in various theoretical models.

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.

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.

From pathway to population--a multiscale model of juxtacrine EGFR-MAPK signalling

BACKGROUND

Most mathematical models of biochemical pathways consider either signalling events that take place within a single cell in isolation, or an 'average' cell which is considered to be representative of a cell population. Likewise, experimental measurements are often averaged over populations consisting of hundreds of thousands of cells. This approach ignores the fact that even within a genetically-homogeneous population, local conditions may influence cell signalling and result in phenotypic heterogeneity. We have developed a multi-scale computational model that accounts for emergent heterogeneity arising from the influences of intercellular signalling on individual cells within a population. Our approach was to develop an ODE model of juxtacrine EGFR-ligand activation of the MAPK intracellular pathway and to couple this to an agent-based representation of individual cells in an expanding epithelial cell culture population. This multi-scale, multi-paradigm approach has enabled us to simulate Extracellular signal-regulated kinase (Erk) activation in a population of cells and to examine the consequences of interpretation at a single cell or population-based level using virtual assays.

RESULTS

A model consisting of a single pair of interacting agents predicted very different Erk activation (phosphorylation) profiles, depending on the formation rate and stability of intercellular contacts, with the slow formation of stable contacts resulting in low but sustained activation of Erk, and transient contacts resulting in a transient Erk signal. Extension of this model to a population consisting of hundreds to thousands of interacting virtual cells revealed that the activated Erk profile measured across the entire cell population was very different and may appear to contradict individual cell findings, reflecting heterogeneity in population density across the culture. This prediction was supported by immunolabelling of an epithelial cell population grown in vitro, which confirmed heterogeneity of Erk activation.

CONCLUSION

These results illustrate that mean experimental data obtained from analysing entire cell populations is an oversimplification, and should not be extrapolated to deduce the signal:response paradigm of individual cells. This multi-scale, multi-paradigm approach to biological simulation provides an important conceptual tool in addressing how information may be integrated over multiple scales to predict the behaviour of a biological system.

Towards a multiscale model of colorectal cancer

Colorectal cancer (CRC) is one of the best characterised cancers, with extensive data documenting the sequential gene mutations that underlie its development. Complementary datasets are also being generated describing changes in protein and RNA expression, tumour biology and clinical outcome. Both the quantity and the variety of information are inexorably increasing and there is now an accompanying need to integrate these highly disparate datasets. In this article we aim to explain why we believe that mathematical modelling represents a natural tool or language with which to integrate these data and, in so doing, to provide insight into CRC.