An integrative computational model for intestinal tissue renewal

An adaptive numerical method for multi-cellular simulations of tissue development and maintenance

In recent years, multi-cellular models, where cells are represented as individual interacting entities, are becoming ever popular. This has led to a proliferation of novel methods and simulation tools. The first aim of this paper is to review the numerical methods utilised by multi-cellular modelling tools and to demonstrate which numerical methods are appropriate for simulations of tissue and organ development, maintenance, and disease. The second aim is to introduce an adaptive time-stepping algorithm and to demonstrate it's efficiency and accuracy. We focus on off-lattice, mechanics based, models where cell movement is defined by a series of first order ordinary differential equations, derived by assuming over-damped motion and balancing forces. We see that many numerical methods have been used, ranging from simple Forward Euler approaches through to higher order single-step methods like Runge-Kutta 4 and multi-step methods like Adams-Bashforth 2. Through a series of exemplar multi-cellular simulations, we see that if: care is taken to have events (births deaths and re-meshing/re-arrangements) occur on common time-steps; and boundaries are imposed on all sub-steps of numerical methods or implemented using forces, then all numerical methods can converge with the correct order. We introduce an adaptive time-stepping method and demonstrate that the best compromise between L∞ error and run-time is to use Runge-Kutta 4 with an increased time-step and moderate adaptivity. We see that a judicious choice of numerical method can speed the simulation up by a factor of 10-60 from the Forward Euler methods seen in Osborne et al. (2017), and a further speed up by a factor of 4 can be achieved by using an adaptive time-step.

Using picoliter droplet deposition to track clonal competition in adherent and organoid cancer cell cultures

Clonal growth and competition underlie processes of key relevance in etiology, progression and therapy response across all cancers. Here, we demonstrate a novel experimental approach, based on multi-color, fluorescent tagging of cell nuclei, in combination with picoliter droplet deposition, to study the clonal dynamics in two- and three-dimensional cell cultures. The method allows for the simultaneous visualization and analysis of multiple clones in individual multi-clonal colonies, providing a powerful tool for studying clonal dynamics and identifying clonal populations with distinct characteristics. Results of our experiments validate the utility of the method in studying clonal dynamics in vitro, and reveal differences in key aspects of clonal behavior of different cancer cell lines in monoculture conditions, as well as in co-cultures with stromal fibroblasts.

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.

Free and Interfacial Boundaries in Individual-Based Models of Multicellular Biological systems

Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages.

Nanoparticle-mediated cancer cell therapy: basic science to clinical applications

Every sixth person in the world dies due to cancer, making it the second leading severe cause of death after cardiovascular diseases. According to WHO, cancer claimed nearly 10 million deaths in 2020. The most common types of cancers reported have been breast (lung, colon and rectum, prostate cases), skin (non-melanoma) and stomach. In addition to surgery, the most widely used traditional types of anti-cancer treatment are radio- and chemotherapy. However, these do not distinguish between normal and malignant cells. Additional treatment methods have evolved over time for early detection and targeted therapy of cancer. However, each method has its limitations and the associated treatment costs are quite high with adverse effects on the quality of life of patients. Use of individual atoms or a cluster of atoms (nanoparticles) can cause a paradigm shift by virtue of providing point of sight sensing and diagnosis of cancer. Nanoparticles (1-100 nm in size) are 1000 times smaller in size than the human cell and endowed with safer relocation capability to attack mechanically and chemically at a precise location which is one avenue that can be used to destroy cancer cells precisely. This review summarises the extant understanding and the work done in this area to pave the way for physicians to accelerate the use of hybrid mode of treatments by leveraging the use of various nanoparticles.

In-silico and in-vitro morphometric analysis of intestinal organoids

Organoids offer a powerful model to study cellular self-organisation, the growth of specific tissue morphologies in-vitro, and to assess potential medical therapies. However, the intrinsic mechanisms of these systems are not entirely understood yet, which can result in variability of organoids due to differences in culture conditions and basement membrane extracts used. Improving the standardisation of organoid cultures is essential for their implementation in clinical protocols. Developing tools to assess and predict the behaviour of these systems may produce a more robust and standardised biological model to perform accurate clinical studies. Here, we developed an algorithm to automate crypt-like structure counting on intestinal organoids in both in-vitro and in-silico images. In addition, we modified an existing two-dimensional agent-based mathematical model of intestinal organoids to better describe the system physiology, and evaluated its ability to replicate budding structures compared to new experimental data we generated. The crypt-counting algorithm proved useful in approximating the average number of budding structures found in our in-vitro intestinal organoid culture images on days 3 and 7 after seeding. Our changes to the in-silico model maintain the potential to produce simulations that replicate the number of budding structures found on days 5 and 7 of in-vitro data. The present study aims to aid in quantifying key morphological structures and provide a method to compare both in-vitro and in-silico experiments. Our results could be extended later to 3D in-silico models.

Seven challenges in the multiscale modeling of multicellular tissues

The growth and dynamics of multicellular tissues involve tightly regulated and coordinated morphogenetic cell behaviors, such as shape changes, movement, and division, which are governed by subcellular machinery and involve coupling through short- and long-range signals. A key challenge in the fields of developmental biology, tissue engineering and regenerative medicine is to understand how relationships between scales produce emergent tissue-scale behaviors. Recent advances in molecular biology, live-imaging and ex vivo techniques have revolutionized our ability to study these processes experimentally. To fully leverage these techniques and obtain a more comprehensive understanding of the causal relationships underlying tissue dynamics, computational modeling approaches are increasingly spanning multiple spatial and temporal scales, and are coupling cell shape, growth, mechanics, and signaling. Yet such models remain challenging: modeling at each scale requires different areas of technical skills, while integration across scales necessitates the solution to novel mathematical and computational problems. This review aims to summarize recent progress in multiscale modeling of multicellular tissues and to highlight ongoing challenges associated with the construction, implementation, interrogation, and validation of such models. This article is categorized under: Reproductive System Diseases > Computational Models Metabolic Diseases > Computational Models Cancer > Computational Models.

A rigid body framework for multicellular modeling

Off-lattice models are a well-established approach in multicellular modeling, where cells are represented as points that are free to move in space. The representation of cells as point objects is useful in a wide range of settings, particularly when large populations are involved; however, a purely point-based representation is not naturally equipped to deal with objects that have length, such as cell boundaries or external membranes. Here we introduce an off-lattice modeling framework that exploits rigid body mechanics to represent objects using a collection of conjoined one-dimensional edges in a viscosity-dominated system. This framework can be used to represent cells as free moving polygons, to allow epithelial layers to smoothly interact with themselves, to model rod-shaped cells such as bacteria and to robustly represent membranes. We demonstrate that this approach offers solutions to the problems that limit the scope of current off-lattice multicellular models.

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.

Cooperative success in epithelial public goods games

Cancer cells obtain mutations which rely on the production of diffusible growth factors to confer a fitness benefit. These mutations can be considered cooperative, and studied as public goods games within the framework of evolutionary game theory. The population structure, benefit function and update rule all influence the evolutionary success of cooperators. We model the evolution of cooperation in epithelial cells using the Voronoi tessellation model. Unlike traditional evolutionary graph theory, this allows us to implement global updating, for which birth and death events are spatially decoupled. We compare, for a sigmoid benefit function, the conditions for cooperation to be favoured and/or beneficial for well-mixed and structured populations. We find that when population structure is combined with global updating, cooperation is more successful than if there were local updating or the population were well-mixed. Interestingly, the qualitative behaviour for the well-mixed population and the Voronoi tessellation model is remarkably similar, but the latter case requires significantly lower incentives to ensure cooperation.

Maintaining the proliferative cell niche in multicellular models of epithelia

The maintenance of the proliferative cell niche is critical to epithelial tissue morphology and function. In this paper we investigate how current modelling methods can result in the erroneous loss of proliferative cells from the proliferative cell niche. Using an established model of the inter-follicular epidermis we find there is a limit to the proliferative cell densities that can be maintained in the basal layer (the niche) if we do not include additional mechanisms to stop the loss of proliferative cells from the niche. We suggest a new methodology that enables maintenance of a desired homeostatic population of proliferative cells in the niche: a rotational force is applied to the two daughter cells during the mitotic phase of division to enforce a particular division direction. We demonstrate that this new methodology achieves this goal. This methodology reflects the regulation of the orientation of cell division.

Regenerative medicine meets mathematical modelling: developing symbiotic relationships

Successful progression from bench to bedside for regenerative medicine products is challenging and requires a multidisciplinary approach. What has not yet been fully recognised is the potential for quantitative data analysis and mathematical modelling approaches to support this process. In this review, we highlight the wealth of opportunities for embedding mathematical and computational approaches within all stages of the regenerative medicine pipeline. We explore how exploiting quantitative mathematical and computational approaches, alongside state-of-the-art regenerative medicine research, can lead to therapies that potentially can be more rapidly translated into the clinic.

Intestinal villus structure contributes to even shedding of epithelial cells

In the intestinal epithelium, proliferated epithelial cells ascend the crypts and villi and shed at the villus tips into the gut lumen. In this study, we theoretically investigate the roles of the villi on cell turnover. We present a stochastic model that focuses on the duration over which cells migrate the shortest paths between the crypt orifices and the villus tips, where shedding cells are randomly chosen from among those older than the shortest-path cell migration times. By extending the length of the shortest path to delay cell shedding, the finger-like shape of the villus would tightly regulate shedding-cell ages compared with flat surfaces and shorter projections; the villus allows epithelial cells to shed at around the same age, which limits them from shedding early or staying in the epithelium for long periods. Computational simulations of cell dynamics agreed well with the predictions. We also examine various mechanical conditions of cells and confirm that coordinated collective cell migration supports the predictions. These results suggest the important roles of the villi in homeostatic maintenance of the small intestine, and we discuss the applicability of our approach to other tissues with collective cell movement.

A mathematical model of cell fate selection on a dynamic tissue

Multicellular tissues are the building blocks of many biological systems and organs. These tissues are not static, but dynamically change over time. Even if the overall structure remains the same there is a turnover of cells within the tissue. This dynamic homeostasis is maintaned by numerous governing mechanisms which are finely tuned in such a way that the tissue remains in a homeostatic state, even across large timescales. Some of these governing mechanisms include cell motion, and cell fate selection through inter cellular signalling. However, it is not yet clear how to link these two processes, or how they may affect one another across the tissue. In this paper, we present a multicellular, multiscale model, which brings together the two phenomena of cell motility, and inter cellular signalling, to describe cell fate selection on a dynamic tissue. We find that the affinity for cellular signalling to occur greatly influences a cells ability to differentiate. We also find that our results support claims that cell differentiation is a finely tuned process within dynamic tissues at homeostasis, with excessive cell turnover rates leading to unhealthy (undifferentiated and unpatterned) tissues.

Evolution of cooperation in an epithelium

Cooperation is prevalent in nature, not only in the context of social interactions within the animal kingdom but also on the cellular level. In cancer, for example, tumour cells can cooperate by producing growth factors. The evolution of cooperation has traditionally been studied for well-mixed populations under the framework of evolutionary game theory, and more recently for structured populations using evolutionary graph theory (EGT). The population structures arising due to cellular arrangement in tissues, however, are dynamic and thus cannot be accurately represented by either of these frameworks. In this work, we compare the conditions for cooperative success in an epithelium modelled using EGT, to those in a mechanical model of an epithelium—the Voronoi tessellation (VT) model. Crucially, in this latter model, cells are able to move, and birth and death are not spatially coupled. We calculate fixation probabilities in the VT model through simulation and an approximate analytic technique and show that this leads to stronger promotion of cooperation in comparison with the EGT model.

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.

A system-level mechanistic explanation for asymmetric stem cell fates: Arabidopsis thaliana root niche as a study system

Asymmetric divisions maintain long-term stem cell populations while producing new cells that proliferate and then differentiate. Recent reports in animal systems show that divisions of stem cells can be uncoupled from their progeny differentiation, and the outcome of a division could be influenced by microenvironmental signals. But the underlying system-level mechanisms, and whether this dynamics also occur in plant stem cell niches (SCN), remain elusive. This article presents a cell fate regulatory network model that contributes to understanding such mechanism and identify critical cues for cell fate transitions in the root SCN. Novel computational and experimental results show that the transcriptional regulator SHR is critical for the most frequent asymmetric division previously described for quiescent centre stem cells. A multi-scale model of the root tip that simulated each cell's intracellular regulatory network, and the dynamics of SHR intercellular transport as a cell-cell coupling mechanism, was developed. It revealed that quiescent centre cell divisions produce two identical cells, that may acquire different fates depending on the feedback between SHR's availability and the state of the regulatory network. Novel experimental data presented here validates our model, which in turn, constitutes the first proposed systemic mechanism for uncoupled SCN cell division and differentiation.

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.

Chronic TNFα-driven injury delays cell migration to villi in the intestinal epithelium

The intestinal epithelium is a single layer of cells which provides the first line of defence of the intestinal mucosa to bacterial infection. Cohesion of this physical barrier is supported by renewal of epithelial stem cells, residing in invaginations called crypts, and by crypt cell migration onto protrusions called villi; dysregulation of such mechanisms may render the gut susceptible to chronic inflammation. The impact that excessive or misplaced epithelial cell death may have on villus cell migration is currently unknown. We integrated cell-tracking methods with computational models to determine how epithelial homeostasis is affected by acute and chronic TNFα-driven epithelial cell death. Parameter inference reveals that acute inflammatory cell death has a transient effect on epithelial cell dynamics, whereas cell death caused by chronic elevated TNFα causes a delay in the accumulation of labelled cells onto the villus compared to the control. Such a delay may be reproduced by using a cell-based model to simulate the dynamics of each cell in a crypt-villus geometry, showing that a prolonged increase in cell death slows the migration of cells from the crypt to the villus. This investigation highlights which injuries (acute or chronic) may be regenerated and which cause disruption of healthy epithelial homeostasis.

A multiscale mathematical model of cell dynamics during neurogenesis in the mouse cerebral cortex

Background

Neurogenesis in the murine cerebral cortex involves the coordinated divisions of two main types of progenitor cells, whose numbers, division modes and cell cycle durations set up the final neuronal output. To understand the respective roles of these factors in the neurogenesis process, we combine experimental in vivo studies with mathematical modeling and numerical simulations of the dynamics of neural progenitor cells. A special focus is put on the population of intermediate progenitors (IPs), a transit amplifying progenitor type critically involved in the size of the final neuron pool.

Results

A multiscale formalism describing IP dynamics allows one to track the progression of cells along the subsequent phases of the cell cycle, as well as the temporal evolution of the different cell numbers. Our model takes into account the dividing apical progenitors (AP) engaged into neurogenesis, both neurogenic and proliferative IPs, and the newborn neurons. The transfer rates from one population to another are subject to the mode of division (proliferative, or neurogenic) and may be time-varying. The model outputs are successfully fitted to experimental cell numbers from mouse embryos at different stages of cortical development, taking into account IPs and neurons, in order to adjust the numerical parameters. We provide additional information on cell kinetics, such as the mitotic and S phase indexes, and neurogenic fraction.

Conclusions

Applying the model to a mouse mutant for Ftm/Rpgrip1l, a gene involved in human ciliopathies with severe brain abnormalities, reveals a shortening of the neurogenic period associated with an increased influx of newborn IPs from apical progenitors at mid-neurogenesis. Our model can be used to study other mouse mutants with cortical neurogenesis defects and can be adapted to study the importance of progenitor dynamics in cortical evolution and human diseases.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-3018-8) contains supplementary material, which is available to authorized users.

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.

Antrodin C, an NADPH Dependent Metabolism, Encourages Crosstalk between Autophagy and Apoptosis in Lung Carcinoma Cells by Use of an AMPK Inhibition-Independent Blockade of the Akt/mTOR Pathway

The current study aims to explore the possible anti-lung carcinoma activity of ADC as well as the underlying mechanisms by which ADC exerts its actions in NSCLC. Findings showed that ADC potently inhibited the viability of SPCA-1, induced apoptosis triggered by ROS, and arrested the cell cycle at the G2/M phase via a P53 signaling pathway. Interestingly, phenomena such as autophagosomes accumulation, conversion of the LC3-I to LC3-II, etc., indicated that autophagy could be activated by ADC. The blockage of autophagy-augmented ADC induced inhibition of cell proliferation, while autophagy activation restored cell death, indicating that autophagy had a protective effect against cell death which was induced by ADC treatment. Meanwhile, ADC treatment suppressed both the Akt/mTOR and AMPK signaling pathways. The joint action of both ADC and the autophagy inhibitor significantly increased the death of SPCA-1. An in vitro phase I metabolic stability assay showed that ADC was highly metabolized in SD rat liver microsomes and moderately metabolized in human liver microsomes, which will assist in predicting the outcomes of clinical pharmacokinetics and toxicity studies. These findings imply that blocking the Akt/mTOR signaling pathway, which was independent of AMPK inhibition, could activate ADC-induced protective autophagy in non-small-cell lung cancer cells.

Three-Dimensional Spatiotemporal Modeling of Colon Cancer Organoids Reveals that Multimodal Control of Stem Cell Self-Renewal is a Critical Determinant of Size and Shape in Early Stages of Tumor Growth

We develop a three-dimensional multispecies mathematical model to simulate the growth of colon cancer organoids containing stem, progenitor and terminally differentiated cells, as a model of early (prevascular) tumor growth. Stem cells (SCs) secrete short-range self-renewal promoters (e.g., Wnt) and their long-range inhibitors (e.g., Dkk) and proliferate slowly. Committed progenitor (CP) cells proliferate more rapidly and differentiate to produce post-mitotic terminally differentiated cells that release differentiation promoters, forming negative feedback loops on SC and CP self-renewal. We demonstrate that SCs play a central role in normal and cancer colon organoids. Spatial patterning of the SC self-renewal promoter gives rise to SC clusters, which mimic stem cell niches, around the organoid surface, and drive the development of invasive fingers. We also study the effects of externally applied signaling factors. Applying bone morphogenic proteins, which inhibit SC and CP self-renewal, reduces invasiveness and organoid size. Applying hepatocyte growth factor, which enhances SC self-renewal, produces larger sizes and enhances finger development at low concentrations but suppresses fingers at high concentrations. These results are consistent with recent experiments on colon organoids. Because many cancers are hierarchically organized and are subject to feedback regulation similar to that in normal tissues, our results suggest that in cancer, control of cancer stem cell self-renewal should influence the size and shape in similar ways, thereby opening the door to novel therapies.

Quantitative translational modeling to facilitate preclinical to clinical efficacy & toxicity translation in oncology

Significant scientific advances in biomedical research have expanded our knowledge of the molecular basis of carcinogenesis, mechanisms of cancer growth, and the importance of the cancer immunity cycle. However, despite scientific advances in the understanding of cancer biology, the success rate of oncology drug development remains the lowest among all therapeutic areas. In this review, some of the key translational drug development objectives in oncology will be outlined. The literature evidence of how mathematical modeling could be used to build a unifying framework to answer these questions will be summarized with recommendations on the strategies for building such a mathematical framework to facilitate the prediction of clinical efficacy and toxicity of investigational antineoplastic agents. Together, the literature evidence suggests that a rigorous and unifying preclinical to clinical translational framework based on mathematical models is extremely valuable for making go/no-go decisions in preclinical development, and for planning early clinical studies.

Multi-scale modeling of APC and [Formula: see text]-catenin regulation in the human colonic crypt

Stem cell renewal and differentiation in the human colonic crypt are linked to the [Formula: see text]-catenin pathway. The spatial balance of Wnt factors in proliferative cells within the crypt maintain an appropriate level of cellular reproduction needed for normal crypt homeostasis. Mutational events at the gene level are responsible for deregulating the balance of Wnt factors along the crypt, causing an overpopulation of proliferative cells, a loss of structure of the crypt domain, and the initiation of colorectal carcinomas. We formulate a PDE model describing cell movement and reproduction in a static crypt domain. We consider a single cell population whose proliferative capabilities are determined by stemness, a quantity defined by intracellular levels of adenomatous polyposis coli (APC) scaffold protein and [Formula: see text]-catenin. We fit APC regulation parameters to biological data that describe normal protein gradients in the crypt. We also fit cell movement and protein flux parameters to normal crypt characteristics such as renewal time, total cell count, and proportion of proliferating cells. The model is used to investigate abnormal crypt dynamics when subjected to a diminished APC gradient, a scenario synonymous to mutations in the APC gene. We find that a 25% decrease in APC synthesis leads to a fraction of 0.88 proliferative, which is reflective of normal-appearing FAP crypts. A 50% drop in APC activity yields a fully proliferative crypt showing a doubling of the level of stemness, which characterizes the initial stages of colorectal cancer development. A sensitivity analysis of APC regulation parameters shows the perturbation of factors that is required to restore crypt dynamics to normal in the case of APC mutations.

On the utility of a compartmental population kinetics model of intestinal epithelial stem cell proliferation and differentiation

Background

The small intestinal epithelium is a dynamic system with specialized cell types. The various cell populations of this tissue are continually renewed and replenished from stem cells that reside in the small intestinal crypt. The cell types and their locations in the crypt and villus are well known, but the details of the kinetics of stem cell division, and precursor cell proliferation and differentiation into mature enterocytes and secretory cells are still being studied. These proliferation and differentiation events have been extensively modeled with a variety of computational approaches in the past.

Methods

A compartmental population kinetics model, incorporating experimentally measured proliferation rates for various intestinal epithelial cell types, is implemented for a previously reported scheme for the intestinal cell dynamics. A sensitivity analysis is performed to determine the effect that varying the model parameters has upon the model outputs, the steady-state cell populations.

Results

The model is unable to reproduce the experimentally known timescale of renewal of the intestinal epithelium if literature values for the proliferation rates of stem cells and transit amplifying cells are employed. Unphysically large rates of proliferation result when these parameters are allowed to vary to reproduce this timescale and the steady-state populations of terminally differentiated intestinal epithelial cells. Sensitivity analysis reveals that the strongest contributor to the steady-state populations is the transit amplifying cell proliferation rate when literature values are used, but that the differentiation rate of transit amplifying cells to secretory progenitor cells dominates when all parameters are allowed to vary.

Conclusions

A compartmental population kinetics model of proliferation and differentiation of cells of the intestinal epithelium can provide a simplifying means of understanding a complicated multistep process. However, when literature values for proliferation rates of the crypt based columnar and transit amplifying cell populations are employed in the model, it cannot reproduce the experimentally known timescale of intestinal epithelial renewal. Nevertheless, it remains a valuable conceptual tool, and its sensitivity analysis provides important clues for which events in the process are the most important in controlling the steady-state populations of specialized intestinal epithelial cells.

Electronic supplementary material

The online version of this article (10.1186/s12976-017-0071-8) contains supplementary material, which is available to authorized users.

Systems Pharmacology Model of Gastrointestinal Damage Predicts Species Differences and Optimizes Clinical Dosing Schedules

Gastrointestinal (GI) adverse events (AEs) are frequently dose limiting for oncology agents, requiring extensive clinical testing of alternative schedules to identify optimal dosing regimens. Here, we develop a translational mathematical model to predict these clinical AEs starting from preclinical GI toxicity data. The model structure incorporates known biology and includes stem cells, daughter cells, and enterocytes. Published data, including cellular numbers and division times, informed the system parameters for humans and rats. The drug‐specific parameters were informed with preclinical histopathology data from rats treated with irinotecan. The model fit the rodent irinotecan‐induced pathology changes well. The predicted time course of enterocyte loss in patients treated with weekly doses matched observed AE profiles. The model also correctly predicts a lower level of AEs for every 3 weeks (Q3W), as compared to the weekly schedule.

Stem cell competition in the gut: insights from multi-scale computational modelling

Three-dimensional (3D) computational tissue models can provide a comprehensive description of tissue dynamics at the molecular, cellular and tissue level. Moreover, they can support the development of hypotheses about cellular interactions and about synergies between major signalling pathways. We exemplify these capabilities by simulation of a 3D single-cell-based model of mouse small intestinal crypts. We analyse the impact of lineage specification, distribution and cellular lifespan on clonal competition and study effects of Notch- and Wnt activation on fixation of mutations within the tissue. Based on these results, we predict that experimentally observed synergistic effects between autonomous Notch- and Wnt signalling in triggering intestinal tumourigenesis originate in the suppression of Wnt-dependent secretory lineage specification by Notch, giving rise to an increased fixation probability of Wnt-activating mutations. Our study demonstrates that 3D computational tissue models can support a mechanistic understanding of long-term tissue dynamics under homeostasis and during transformation.

A Model for Adult Organ Resizing Demonstrates Stem Cell Scaling through a Tunable Commitment Rate

Many adult organs grow or shrink to accommodate different physiological demands. Often, as total cell number changes, stem cell number changes proportionally in a phenomenon called "stem cell scaling". The cellular behaviors that give rise to scaling are unknown. Here we study two complementary theoretical models of the adult Drosophila midgut, a stem cell-based organ with known resizing dynamics. First, we derive a differential equations model of midgut resizing and show that the in vivo kinetics of growth can be recapitulated if the rate of fate commitment depends on the tissue's stem cell proportion. Second, we develop a 2D simulation of the midgut and find that proportion-dependent commitment rate and stem cell scaling can arise phenomenologically from the stem cells' exploration of physical tissue space during its lifetime. Together, these models provide a biophysical understanding of how stem cell scaling is maintained during organ growth and shrinkage.

A kinetic model to study the regulation of β-catenin, APC, and Axin in the human colonic crypt

The Wnt/[Formula: see text]-catenin pathway plays a crucial role in stem cell renewal and differentiation in the normal human colonic crypt. The balance between [Formula: see text]-catenin and APC along the crypt axis determines its normal functionality. The mechanism that deregulates this balance may give insight into the initiation of colorectal cancer. This is significant because the spatial dysregulation of [Formula: see text]-catenin by the mutated tumor suppressor gene/protein APC in human colonic crypts is responsible for the initiation and growth of colorectal cancer. We consider a regulatory function that promotes APC synthesis within the cell and its effect on the accumulation of the Wnt target protein, [Formula: see text]-catenin. It is evident that an APC gradient exists along the crypt axis; however, the mechanism by which APC expression is regulated within the cell is not well known. We investigate the dynamics of an APC regulatory mechanism with an increased level of Axin at the subcellular level. Model output shows an increase of APC for a diminished Wnt signal, which explains the APC gradient along the crypt. We find that the dynamic interplay between [Formula: see text]-catenin, APC, and Axin produces oscillatory behavior, which is controlled by the Wnt stimulus. In the presence of reduced functional APC, the oscillations are amplified, which suggests that the cell remains in a more proliferative state for longer periods of time. Increased Axin levels (typical of mammalian cells) reduce oscillatory behavior and minimize the levels of [Formula: see text]-catenin within the cell while raising the levels of APC.

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.

Comparing individual-based approaches to modelling the self-organization of multicellular tissues

The coordinated behaviour of populations of cells plays a central role in tissue growth and renewal. Cells react to their microenvironment by modulating processes such as movement, growth and proliferation, and signalling. Alongside experimental studies, computational models offer a useful means by which to investigate these processes. To this end a variety of cell-based modelling approaches have been developed, ranging from lattice-based cellular automata to lattice-free models that treat cells as point-like particles or extended shapes. However, it remains unclear how these approaches compare when applied to the same biological problem, and what differences in behaviour are due to different model assumptions and abstractions. Here, we exploit the availability of an implementation of five popular cell-based modelling approaches within a consistent computational framework, Chaste (http://www.cs.ox.ac.uk/chaste). This framework allows one to easily change constitutive assumptions within these models. In each case we provide full details of all technical aspects of our model implementations. We compare model implementations using four case studies, chosen to reflect the key cellular processes of proliferation, adhesion, and short- and long-range signalling. These case studies demonstrate the applicability of each model and provide a guide for model usage.

Cell proliferation within small intestinal crypts is the principal driving force for cell migration on villi

The functional integrity of the intestinal epithelial barrier relies on tight coordination of cell proliferation and migration, with failure to regulate these processes resulting in disease. It is not known whether cell proliferation is sufficient to drive epithelial cell migration during homoeostatic turnover of the epithelium. Nor is it known precisely how villus cell migration is affected when proliferation is perturbed. Some reports suggest that proliferation and migration may not be related while other studies support a direct relationship. We used established cell-tracking methods based on thymine analog cell labeling and developed tailored mathematical models to quantify cell proliferation and migration under normal conditions and when proliferation is reduced and when it is temporarily halted. We found that epithelial cell migration velocities along the villi are coupled to cell proliferation rates within the crypts in all conditions. Furthermore, halting and resuming proliferation results in the synchronized response of cell migration on the villi. We conclude that cell proliferation within the crypt is the primary force that drives cell migration along the villus. This methodology can be applied to interrogate intestinal epithelial dynamics and characterize situations in which processes involved in cell turnover become uncoupled, including pharmacological treatments and disease models.—Parker, A., Maclaren, O. J., Fletcher, A. G., Muraro, D., Kreuzaler, P. A., Byrne, H. M., Maini, P. K., Watson, A. J. M., Pin, C. Cell proliferation within small intestinal crypts is the principal driving force for cell migration on villi.

A Geometrically-Constrained Mathematical Model of Mammary Gland Ductal Elongation Reveals Novel Cellular Dynamics within the Terminal End Bud

Mathematics is often used to model biological systems. In mammary gland development, mathematical modeling has been limited to acinar and branching morphogenesis and breast cancer, without reference to normal duct formation. We present a model of ductal elongation that exploits the geometrically-constrained shape of the terminal end bud (TEB), the growing tip of the duct, and incorporates morphometrics, region-specific proliferation and apoptosis rates. Iterative model refinement and behavior analysis, compared with biological data, indicated that the traditional metric of nipple to the ductal front distance, or percent fat pad filled to evaluate ductal elongation rate can be misleading, as it disregards branching events that can reduce its magnitude. Further, model driven investigations of the fates of specific TEB cell types confirmed migration of cap cells into the body cell layer, but showed their subsequent preferential elimination by apoptosis, thus minimizing their contribution to the luminal lineage and the mature duct.

Our paper describes a mathematical model of mammary ductal elongation during pubertal development. We make several conclusions that will be of interest to scientists studying mammary gland biology, epithelial tube formation, and branching morphogenesis. First, our model indicates that a common measurement of developmental outgrowth (‘percent fat pad filled’) underestimates the total growth and leads to mischaracterization of mutant phenotypes. Second, we show that cap cells, a population enriched with putative mammary stem cells, do not contribute to the luminal lineage as previously hypothesized. Further, we find that a high percentage of proliferation in these cells is not used productively to actually form the mammary duct. We believe our model has future application to other branching organs and also for the modeling of disease states in the breast.

Combined changes in Wnt signaling response and contact inhibition induce altered proliferation in radiation-treated intestinal crypts

Wnt concentration gradients operate in many tissues. Modeling of proliferation in control and irradiated intestinal crypts shows that the Wnt concentrations that cells experience when they are born set their proliferative fate and cell cycle duration. The simulations also predict the initial proportion of cells damaged by tumor-promoting radiation.

Curative intervention is possible if colorectal cancer is identified early, underscoring the need to detect the earliest stages of malignant transformation. A candidate biomarker is the expanded proliferative zone observed in crypts before adenoma formation, also found in irradiated crypts. However, the underlying driving mechanism for this is not known. Wnt signaling is a key regulator of proliferation, and elevated Wnt signaling is implicated in cancer. Nonetheless, how cells differentiate Wnt signals of varying strengths is not understood. We use computational modeling to compare alternative hypotheses about how Wnt signaling and contact inhibition affect proliferation. Direct comparison of simulations with published experimental data revealed that the model that best reproduces proliferation patterns in normal crypts stipulates that proliferative fate and cell cycle duration are set by the Wnt stimulus experienced at birth. The model also showed that the broadened proliferation zone induced by tumorigenic radiation can be attributed to cells responding to lower Wnt concentrations and dividing at smaller volumes. Application of the model to data from irradiated crypts after an extended recovery period permitted deductions about the extent of the initial insult. Application of computational modeling to experimental data revealed how mechanisms that control cell dynamics are altered at the earliest stages of carcinogenesis.

A cell-centered, agent-based framework that enables flexible environment granularities

BACKGROUND

Mechanistic explanations of cell-level phenomena typically adopt an observer perspective. Explanations developed from a cell's perspective may offer new insights. Agent-based models lend themselves to model from an individual perspective, and existing agent-based models generally utilize a regular lattice-based environment. A framework which utilizes a cell's perspective in an off-lattice environment could improve the overall understanding of biological phenomena.

RESULTS

We present an agent-based, discrete event framework, with a demonstrative focus on biomimetic agents. The framework was first developed in 2-dimensions and then extended, with a subset of behaviors, to 3-dimensions. The framework is expected to facilitate studies of more complex biological phenomena through exploitation of a dynamic Delaunay and Voronoi off-lattice environment. We used the framework to model biological cells and to specifically demonstrate basic biological cell behaviors in two- and three-dimensional space. Potential use cases are highlighted, suggesting the utility of the framework in various scenarios.

CONCLUSIONS

The framework presented in this manuscript expands on existing cell- and agent-centered methods by offering a new perspective in an off-lattice environment. As the demand for biomimetic models grows, the demand for new methods, such as the presented Delaunay and Voronoi framework, is expected to increase.

Adult Stem Cell Therapies for Wound Healing: Biomaterials and Computational Models

The increased incidence of diabetes and tumors, associated with global demographic issues (aging and life styles), has pointed out the importance to develop new strategies for the effective management of skin wounds. Individuals affected by these diseases are in fact highly exposed to the risk of delayed healing of the injured tissue that typically leads to a pathological inflammatory state and consequently to chronic wounds. Therapies based on stem cells (SCs) have been proposed for the treatment of these wounds, thanks to the ability of SCs to self-renew and specifically differentiate in response to the target bimolecular environment. Here, we discuss how advanced biomedical devices can be developed by combining SCs with properly engineered biomaterials and computational models. Examples include composite skin substitutes and bioactive dressings with controlled porosity and surface topography for controlling the infiltration and differentiation of the cells. In this scenario, mathematical frameworks for the simulation of cell population growth can provide support for the design of bioconstructs, reducing the need of expensive, time-consuming, and ethically controversial animal experimentation.

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.

Models, measurement and inference in epithelial tissue dynamics

The majority of solid tumours arise in epithelia and therefore much research effort has gone into investigating the growth, renewal and regulation of these tissues. Here we review different mathematical and computational approaches that have been used to model epithelia. We compare different models and describe future challenges that need to be overcome in order to fully exploit new data which present, for the first time, the real possibility for detailed model validation and comparison.

Discrete Element Framework for Modelling Extracellular Matrix, Deformable Cells and Subcellular Components

This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus) and extracellular matrix (e.g. collagen) are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties). Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings). Each particle is in effect an ‘agent’, meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.

Modelling is an important tool in understanding the behaviour of biological tissues. In this paper we advocate a new modelling framework in which cells and tissues are represented by a collection of particles with associated properties. The particles interact with each other and can change their behaviour in response to changes in their environment. We demonstrate how the propose framework can be used to represent the mechanical behaviour of different tissues with much greater flexibility as compared to traditional continuum based methods.

Multiscale Model of Colorectal Cancer Using the Cellular Potts Framework

Colorectal cancer (CRC) is one of the major causes of death in the developed world and forms a canonical example of tumorigenesis. CRC arises from a string of mutations of individual cells in the colorectal crypt, making it particularly suited for multiscale multicellular modeling, where mutations of individual cells can be clearly represented and their effects readily tracked. In this paper, we present a multicellular model of the onset of colorectal cancer, utilizing the cellular Potts model (CPM). We use the model to investigate how, through the modification of their mechanical properties, mutant cells colonize the crypt. Moreover, we study the influence of mutations on the shape of cells in the crypt, suggesting possible cell- and tissue-level indicators for identifying early-stage cancerous crypts. Crucially, we discuss the effect that the motility parameters of the model (key factors in the behavior of the CPM) have on the distribution of cells within a homeostatic crypt, resulting in an optimal parameter regime that accurately reflects biological assumptions. In summary, the key results of this paper are 1) how to couple the CPM with processes occurring on other spatial scales, using the example of the crypt to motivate suitable motility parameters; 2) modeling mutant cells with the CPM; 3) and investigating how mutations influence the shape of cells in the crypt.

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.

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.

Meta-analysis of the turnover of intestinal epithelia in preclinical animal species and humans

Due to the rapid turnover of the small intestinal epithelia, the rate at which enterocyte renewal occurs plays an important role in determining the level of drug-metabolizing enzymes in the gut wall. Current physiologically based pharmacokinetic (PBPK) models consider enzyme and enterocyte recovery as a lumped first-order rate. An assessment of enterocyte turnover would enable enzyme and enterocyte renewal to be modeled more mechanistically. A literature review together with statistical analysis was employed to establish enterocyte turnover in human and preclinical species. A total of 85 studies was identified reporting enterocyte turnover in 1602 subjects in six species. In mice, the geometric weighted combined mean (WX) enterocyte turnover was 2.81 ± 1.14 days (n = 169). In rats, the weighted arithmetic mean enterocyte turnover was determined to be 2.37 days (n = 501). Humans exhibited a geometric WX enterocyte turnover of 3.48 ± 1.55 days for the gastrointestinal epithelia (n = 265), displaying comparable turnover to that of cytochrome P450 enzymes in vitro (0.96-4.33 days). Statistical analysis indicated humans to display longer enterocyte turnover as compared with preclinical species. Extracted data were too sparse to support regional differences in small intestinal enterocyte turnover in humans despite being indicated in mice. The utilization of enterocyte turnover data, together with in vitro enzyme turnover in PBPK modeling, may improve the predictions of metabolic drug-drug interactions dependent on enzyme turnover (e.g., mechanism-based inhibition and enzyme induction) as well as absorption of nanoparticle delivery systems and intestinal metabolism in special populations exhibiting altered enterocyte turnover.

Quantification of crypt and stem cell evolution in the normal and neoplastic human colon

Human intestinal stem cell and crypt dynamics remain poorly characterized because transgenic lineage-tracing methods are impractical in humans. Here, we have circumvented this problem by quantitatively using somatic mtDNA mutations to trace clonal lineages. By analyzing clonal imprints on the walls of colonic crypts, we show that human intestinal stem cells conform to one-dimensional neutral drift dynamics with a "functional" stem cell number of five to six in both normal patients and individuals with familial adenomatous polyposis (germline APC(-/+)). Furthermore, we show that, in adenomatous crypts (APC(-/-)), there is a proportionate increase in both functional stem cell number and the loss/replacement rate. Finally, by analyzing fields of mtDNA mutant crypts, we show that a normal colon crypt divides around once every 30-40 years, and the division rate is increased in adenomas by at least an order of magnitude. These data provide in vivo quantification of human intestinal stem cell and crypt dynamics.