Control of epidermal stem cell clusters by Notch-mediated lateral induction

Emergent order in epithelial sheets by interplay of cell divisions and cell fate regulation

The fate choices of stem cells between self-renewal and differentiation are often tightly regulated by juxtacrine (cell-cell contact) signalling. Here, we assess how the interplay between cell division, cell fate choices, and juxtacrine signalling can affect the macroscopic ordering of cell types in self-renewing epithelial sheets, by studying a simple spatial cell fate model with cells being arranged on a 2D lattice. We show in this model that if cells commit to their fate directly upon cell division, macroscopic patches of cells of the same type emerge, if at least a small proportion of divisions are symmetric, except if signalling interactions are laterally inhibiting. In contrast, if cells are first 'licensed' to differentiate, yet retaining the possibility to return to their naive state, macroscopic order only emerges if the signalling strength exceeds a critical threshold: if then the signalling interactions are laterally inducing, macroscopic patches emerge as well. Lateral inhibition, on the other hand, can in that case generate periodic patterns of alternating cell types (checkerboard pattern), yet only if the proportion of symmetric divisions is sufficiently low. These results can be understood theoretically by an analogy to phase transitions in spin systems known from statistical physics.

Discrete Manhattan and Chebyshev pair correlation functions in k dimensions

Pair correlation functions provide a summary statistic which quantifies the amount of spatial correlation between objects in a spatial domain. While pair correlation functions are commonly used to quantify continuous-space point processes, the on-lattice discrete case is less studied. Recent work has brought attention to the discrete case, wherein on-lattice pair correlation functions are formed by normalizing empirical pair distances against the probability distribution of random pair distances in a lattice with Manhattan and Chebyshev metrics. These distance distributions are typically derived on an ad hoc basis as required for specific applications. Here we present a generalized approach to deriving the probability distributions of pair distances in a lattice with discrete Manhattan and Chebyshev metrics, extending the Manhattan and Chebyshev pair correlation functions to lattices in k dimensions. We also quantify the variability of the Manhattan and Chebyshev pair correlation functions, which is important to understanding the reliability and confidence of the statistic.

An agent-based model of the Notch signaling pathway elucidates three levels of complexity in the determination of developmental patterning

BACKGROUND

The Notch signaling pathway is involved in cell fate decision and developmental patterning in diverse organisms. A receptor molecule, Notch (N), and a ligand molecule (in this case Delta or Dl) are the central molecules in this pathway. In early Drosophila embryos, these molecules determine neural vs. skin fates in a reproducible rosette pattern.

RESULTS

We have created an agent-based model (ABM) that simulates the molecular components for this signaling pathway as agents acting within a spatial representation of a cell. The model captures the changing levels of these components, their transition from one state to another, and their movement from the nucleus to the cell membrane and back to the nucleus again. The model introduces stochastic variation into the system using a random generator within the Netlogo programming environment. The model uses these representations to understand the biological systems at three levels: individual cell fate, the interactions between cells, and the formation of pattern across the system. Using a set of assessment tools, we show that the current model accurately reproduces the rosette pattern of neurons and skin cells in the system over a wide set of parameters. Oscillations in the level of the N agent eventually stabilize cell fate into this pattern. We found that the dynamic timing and the availability of the N and Dl agents in neighboring cells are central to the formation of a correct and stable pattern. A feedback loop to the production of both components is necessary for a correct and stable pattern.

CONCLUSIONS

The signaling pathways within and between cells in our model interact in real time to create a spatially correct field of neurons and skin cells. This model predicts that cells with high N and low Dl drive the formation of the pattern. This model also be used to elucidate general rules of biological self-patterning and decision-making.

Comparison of Human Dermal Fibroblasts and HaCat Cells Cultured in Medium with or without Serum via a Generic Tissue Engineering Research Platform

A generic research platform with 2-dimensional (2D) cell culture technology, a 3-dimensional (3D) in vitro tissue model, and a scaled-down cell culture and imaging system in between, was utilized to address the problematic issues associated with the use of serum in skin tissue engineering. Human dermal fibroblasts (HDFs) and immortalized keratinocytes (HaCat cells) mono- or co-cultured in serum or serum-free medium were compared and analyzed via the platform. It was demonstrated that serum depletion had significant influence on the attachment of HaCat cells onto tissue culture plastic (TCP), porous substrates and cellulosic scaffolds, which was further enhanced by the pre-seeded HDFs. The complex structures formed by the HDFs colonized within the porous substrates and scaffolds not only prevented the seeded HaCat cells from filtering through the open pores, but also acted as cellular substrates for HaCat cells to attach onto. When mono-cultured on TCP, both HDFs and HaCat cells were less proliferative in medium without serum than with serum. However, both cell types were successfully co-cultured in 2D using serum-free medium if the initial cell seeding density was higher than 80,000 cells/cm² (with 1:1 ratio). Based on the results from 2D cultures, co-culture of both cell types on modular substrates with small open pores (125 μm) and cellulosic scaffolds with open pores of varying sizes (50–300 µm) were then conducted successfully in serum-free medium. This study demonstrated that the generic research platform had great potential for in-depth understanding of HDFs and HaCat cells cultivated in serum-free medium, which could inform the processes for manufacturing skin cells or tissues for clinical applications.

Notch-Jagged signalling can give rise to clusters of cells exhibiting a hybrid epithelial/mesenchymal phenotype

Metastasis can involve repeated cycles of epithelial-to-mesenchymal transition (EMT) and its reverse mesenchymal-to-epithelial transition. Cells can also undergo partial transitions to attain a hybrid epithelial/mesenchymal (E/M) phenotype that allows the migration of adhering cells to form a cluster of circulating tumour cells. These clusters can be apoptosis-resistant and possess an increased metastatic propensity as compared to the cells that undergo a complete EMT (mesenchymal cells). Hence, identifying the key players that can regulate the formation and maintenance of such clusters may inform anti-metastasis strategies. Here, we devise a mechanism-based theoretical model that links cell–cell communication via Notch-Delta-Jagged signalling with the regulation of EMT. We demonstrate that while both Notch-Delta and Notch-Jagged signalling can induce EMT in a population of cells, only Jagged-dominated Notch signalling, but not Delta-dominated signalling, can lead to the formation of clusters containing hybrid E/M cells. Our results offer possible mechanistic insights into the role of Jagged in tumour progression, and offer a framework to investigate the effects of other microenvironmental signals during metastasis.

Virtual cardiac monolayers for electrical wave propagation

The complex structure of cardiac tissue is considered to be one of the main determinants of an arrhythmogenic substrate. This study is aimed at developing the first mathematical model to describe the formation of cardiac tissue, using a joint in silico-in vitro approach. First, we performed experiments under various conditions to carefully characterise the morphology of cardiac tissue in a culture of neonatal rat ventricular cells. We considered two cell types, namely, cardiomyocytes and fibroblasts. Next, we proposed a mathematical model, based on the Glazier-Graner-Hogeweg model, which is widely used in tissue growth studies. The resultant tissue morphology was coupled to the detailed electrophysiological Korhonen-Majumder model for neonatal rat ventricular cardiomyocytes, in order to study wave propagation. The simulated waves had the same anisotropy ratio and wavefront complexity as those in the experiment. Thus, we conclude that our approach allows us to reproduce the morphological and physiological properties of cardiac tissue.

Phenomenological modelling and simulation of cell clusters in 3D cultures

Cell clustering and aggregation are fundamental processes in the development of several tissues and the progression of many diseases. The formation of these aggregates also has a direct impact on the oxygen concentration in their surroundings due to cellular respiration and poor oxygen diffusion through clusters. In this work, we propose a mathematical model that is capable of simulating cell cluster formation in 3D cultures through combining a particle-based and a finite element approach to recreate complex experimental conditions. Cells are modelled considering cell proliferation, cell death and cell-cell mechanical interactions. Additionally, the oxygen concentration profile is calculated through finite element analysis using a reaction-diffusion model that considers cell oxygen consumption and diffusion through the extracellular matrix and the cell clusters. In our model, the local oxygen concentration in the medium determines both cell proliferation and cell death. Numerical predictions are also compared with experimental data from the literature. The simulation results indicate that our model can predict cell clustering, cluster growth and oxygen distribution in 3D cultures. We conclude that the initial cell distribution, cell death and cell proliferation dynamics determine the size and density of clusters. Moreover, these phenomena are directly affected by the oxygen transport in the 3D culture.

A Cellular Potts Model of single cell migration in presence of durotaxis

Cell migration is a fundamental biological phenomenon during which cells sense their surroundings and respond to different types of signals. In presence of durotaxis, cells preferentially crawl from soft to stiff substrates by reorganizing their cytoskeleton from an isotropic to an anisotropic distribution of actin filaments. In the present paper, we propose a Cellular Potts Model to simulate single cell migration over flat substrates with variable stiffness. We have tested five configurations: (i) a substrate including a soft and a stiff region, (ii) a soft substrate including two parallel stiff stripes, (iii) a substrate made of successive stripes with increasing stiffness to create a gradient and (iv) a stiff substrate with four embedded soft squares. For each simulation, we have evaluated the morphology of the cell, the distance covered, the spreading area and the migration speed. We have then compared the numerical results to specific experimental observations showing a consistent agreement.

Jagged-Delta asymmetry in Notch signaling can give rise to a Sender/Receiver hybrid phenotype

Notch signaling pathway mediates cell-fate determination during embryonic development, wound healing, and tumorigenesis. This pathway is activated when the ligand Delta or the ligand Jagged of one cell interacts with the Notch receptor of its neighboring cell, releasing the Notch Intracellular Domain (NICD) that activates many downstream target genes. NICD affects ligand production asymmetrically--it represses Delta, but activates Jagged. Although the dynamical role of Notch-Jagged signaling remains elusive, it is widely recognized that Notch-Delta signaling behaves as an intercellular toggle switch, giving rise to two distinct fates that neighboring cells adopt--Sender (high ligand, low receptor) and Receiver (low ligand, high receptor). Here, we devise a specific theoretical framework that incorporates both Delta and Jagged in Notch signaling circuit to explore the functional role of Jagged in cell-fate determination. We find that the asymmetric effect of NICD renders the circuit to behave as a three-way switch, giving rise to an additional state--a hybrid Sender/Receiver (medium ligand, medium receptor). This phenotype allows neighboring cells to both send and receive signals, thereby attaining similar fates. We also show that due to the asymmetric effect of the glycosyltransferase Fringe, different outcomes are generated depending on which ligand is dominant: Delta-mediated signaling drives neighboring cells to have an opposite fate; Jagged-mediated signaling drives the cell to maintain a similar fate to that of its neighbor. We elucidate the role of Jagged in cell-fate determination and discuss its possible implications in understanding tumor-stroma cross-talk, which frequently entails Notch-Jagged communication.

Computational modeling reveals that a combination of chemotaxis and differential adhesion leads to robust cell sorting during tissue patterning

Robust tissue patterning is crucial to many processes during development. The "French Flag" model of patterning, whereby naïve cells in a gradient of diffusible morphogen signal adopt different fates due to exposure to different amounts of morphogen concentration, has been the most widely proposed model for tissue patterning. However, recently, using time-lapse experiments, cell sorting has been found to be an alternative model for tissue patterning in the zebrafish neural tube. But it remains unclear what the sorting mechanism is. In this article, we used computational modeling to show that two mechanisms, chemotaxis and differential adhesion, are needed for robust cell sorting. We assessed the performance of each of the two mechanisms by quantifying the fraction of correct sorting, the fraction of stable clusters formed after correct sorting, the time needed to achieve correct sorting, and the size variations of the cells having different fates. We found that chemotaxis and differential adhesion confer different advantages to the sorting process. Chemotaxis leads to high fraction of correct sorting as individual cells will either migrate towards or away from the source depending on its cell type. However after the cells have sorted correctly, there is no interaction among cells of the same type to stabilize the sorted boundaries, leading to cell clusters that are unstable. On the other hand, differential adhesion results in low fraction of correct clusters that are more stable. In the absence of morphogen gradient noise, a combination of both chemotaxis and differential adhesion yields cell sorting that is both accurate and robust. However, in the presence of gradient noise, the simple combination of chemotaxis and differential adhesion is insufficient for cell sorting; instead, chemotaxis coupled with delayed differential adhesion is required to yield optimal sorting.

Ligand-dependent Notch signaling strength orchestrates lateral induction and lateral inhibition in the developing inner ear

During inner ear development, Notch exhibits two modes of operation: lateral induction, which is associated with prosensory specification, and lateral inhibition, which is involved in hair cell determination. These mechanisms depend respectively on two different ligands, jagged 1 (Jag1) and delta 1 (Dl1), that rely on a common signaling cascade initiated after Notch activation. In the chicken otocyst, expression of Jag1 and the Notch target Hey1 correlates well with lateral induction, whereas both Jag1 and Dl1 are expressed during lateral inhibition, as are Notch targets Hey1 and Hes5. Here, we show that Jag1 drives lower levels of Notch activity than Dl1, which results in the differential expression of Hey1 and Hes5. In addition, Jag1 interferes with the ability of Dl1 to elicit high levels of Notch activity. Modeling the sensory epithelium when the two ligands are expressed together shows that ligand regulation, differential signaling strength and ligand competition are crucial to allow the two modes of operation and for establishing the alternate pattern of hair cells and supporting cells. Jag1, while driving lateral induction on its own, facilitates patterning by lateral inhibition in the presence of Dl1. This novel behavior emerges from Jag1 acting as a competitive inhibitor of Dl1 for Notch signaling. Both modeling and experiments show that hair cell patterning is very robust. The model suggests that autoactivation of proneural factor Atoh1, upstream of Dl1, is a fundamental component for robustness. The results stress the importance of the levels of Notch signaling and ligand competition for Notch function.

Distinguishing between mechanisms of cell aggregation using pair-correlation functions

Many cell types form clumps or aggregates when cultured in vitro through a variety of mechanisms including rapid cell proliferation, chemotaxis, or direct cell-to-cell contact. In this paper we develop an agent-based model to explore the formation of aggregates in cultures where cells are initially distributed uniformly, at random, on a two-dimensional substrate. Our model includes unbiased random cell motion, together with two mechanisms which can produce cell aggregates: (i) rapid cell proliferation and (ii) a biased cell motility mechanism where cells can sense other cells within a finite range, and will tend to move towards areas with higher numbers of cells. We then introduce a pair-correlation function which allows us to quantify aspects of the spatial patterns produced by our agent-based model. In particular, these pair-correlation functions are able to detect differences between domains populated uniformly at random (i.e. at the exclusion complete spatial randomness (ECSR) state) and those where the proliferation and biased motion rules have been employed - even when such differences are not obvious to the naked eye. The pair-correlation function can also detect the emergence of a characteristic inter-aggregate distance which occurs when the biased motion mechanism is dominant, and is not observed when cell proliferation is the main mechanism of aggregate formation. This suggests that applying the pair-correlation function to experimental images of cell aggregates may provide information about the mechanism associated with observed aggregates. As a proof of concept, we perform such analysis for images of cancer cell aggregates, which are known to be associated with rapid proliferation. The results of our analysis are consistent with the predictions of the proliferation-based simulations, which supports the potential usefulness of pair correlation functions for providing insight into the mechanisms of aggregate formation.

Multi-scale modeling in morphogenesis: a critical analysis of the cellular Potts model

Cellular Potts models (CPMs) are used as a modeling framework to elucidate mechanisms of biological development. They allow a spatial resolution below the cellular scale and are applied particularly when problems are studied where multiple spatial and temporal scales are involved. Despite the increasing usage of CPMs in theoretical biology, this model class has received little attention from mathematical theory. To narrow this gap, the CPMs are subjected to a theoretical study here. It is asked to which extent the updating rules establish an appropriate dynamical model of intercellular interactions and what the principal behavior at different time scales characterizes. It is shown that the longtime behavior of a CPM is degenerate in the sense that the cells consecutively die out, independent of the specific interdependence structure that characterizes the model. While CPMs are naturally defined on finite, spatially bounded lattices, possible extensions to spatially unbounded systems are explored to assess to which extent spatio-temporal limit procedures can be applied to describe the emergent behavior at the tissue scale. To elucidate the mechanistic structure of CPMs, the model class is integrated into a general multiscale framework. It is shown that the central role of the surface fluctuations, which subsume several cellular and intercellular factors, entails substantial limitations for a CPM's exploitation both as a mechanistic and as a phenomenological model.

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.

Multi-scale modeling of tissues using CompuCell3D

The study of how cells interact to produce tissue development, homeostasis, or diseases was, until recently, almost purely experimental. Now, multi-cell computer simulation methods, ranging from relatively simple cellular automata to complex immersed-boundary and finite-element mechanistic models, allow in silico study of multi-cell phenomena at the tissue scale based on biologically observed cell behaviors and interactions such as movement, adhesion, growth, death, mitosis, secretion of chemicals, chemotaxis, etc. This tutorial introduces the lattice-based Glazier-Graner-Hogeweg (GGH) Monte Carlo multi-cell modeling and the open-source GGH-based CompuCell3D simulation environment that allows rapid and intuitive modeling and simulation of cellular and multi-cellular behaviors in the context of tissue formation and subsequent dynamics. We also present a walkthrough of four biological models and their associated simulations that demonstrate the capabilities of the GGH and CompuCell3D.

Patterning as a signature of human epidermal stem cell regulation

Understanding how stem cells are regulated in adult tissues is a major challenge in cell biology. In the basal layer of human epidermis, clusters of almost quiescent stem cells are interspersed with proliferating and differentiating cells. Previous studies have shown that the proliferating cells follow a pattern of balanced stochastic cell fate. This behaviour enables them to maintain homeostasis, while stem cells remain confined to their quiescent clusters. Intriguingly, these clusters reappear spontaneously in culture, suggesting that they may play a functional role in stem cell auto-regulation. We propose a model of pattern formation that explains how clustering could regulate stem cell activity in homeostatic tissue through contact inhibition and stem cell aggregation.

Models at the single cell level

Many cellular behaviors cannot be completely captured or appropriately described at the cell population level. Noise induced by stochastic chemical reactions, spatially polarized signaling networks, and heterogeneous cell-cell communication are among the many phenomena that require fine-grained analysis. Accordingly, the mathematical models used to describe such systems must be capable of single cell or subcellular resolution. Here, we review techniques for modeling single cells, including models of stochastic chemical kinetics, spatially heterogeneous intracellular signaling, and spatial stochastic systems. We also briefly discuss applications of each type of model.

Targeting ADAM-17/notch signaling abrogates the development of systemic sclerosis in a murine model

OBJECTIVE

Systemic sclerosis (SSc) is characterized by the fibrosis of various organs, vascular hyperreactivity, and immunologic dysregulation. Since Notch signaling is known to affect fibroblast homeostasis, angiogenesis, and lymphocyte development, we undertook this study to investigate the role of the Notch pathway in human and murine SSc.

METHODS

SSc was induced in BALB/c mice by subcutaneous injections of HOCl every day for 6 weeks. Notch activation was analyzed in tissues from mice with SSc and from patients with scleroderma. Mice with SSc were either treated or not treated with the γ-secretase inhibitor DAPT, a specific inhibitor of the Notch pathway, and the severity of the disease was evaluated.

RESULTS

As previously described, mice exposed to HOCl developed a diffuse cutaneous SSc with pulmonary fibrosis and anti-DNA topoisomerase I antibodies. The Notch pathway was hyperactivated in the skin, lung, fibroblasts, and splenocytes of diseased mice and in skin biopsy samples from patients with scleroderma. ADAM-17, a proteinase involved in Notch activation, was overexpressed in the skin of mice and patients in response to the local production of reactive oxygen species. In HOCl-injected mice, DAPT significantly reduced the development of skin and lung fibrosis, decreased skin fibroblast proliferation and ex vivo serum-induced endothelial H(2)O(2) production, and abrogated the production of anti-DNA topoisomerase I antibodies.

CONCLUSION

Our results show the pivotal role of the ADAM-17/Notch pathway in SSc following activation by reactive oxygen species. The inhibition of this pathway may represent a new treatment of this life-threatening disease.

Integrative multicellular biological modeling: a case study of 3D epidermal development using GPU algorithms

BACKGROUND

Simulation of sophisticated biological models requires considerable computational power. These models typically integrate together numerous biological phenomena such as spatially-explicit heterogeneous cells, cell-cell interactions, cell-environment interactions and intracellular gene networks. The recent advent of programming for graphical processing units (GPU) opens up the possibility of developing more integrative, detailed and predictive biological models while at the same time decreasing the computational cost to simulate those models.

RESULTS

We construct a 3D model of epidermal development and provide a set of GPU algorithms that executes significantly faster than sequential central processing unit (CPU) code. We provide a parallel implementation of the subcellular element method for individual cells residing in a lattice-free spatial environment. Each cell in our epidermal model includes an internal gene network, which integrates cellular interaction of Notch signaling together with environmental interaction of basement membrane adhesion, to specify cellular state and behaviors such as growth and division. We take a pedagogical approach to describing how modeling methods are efficiently implemented on the GPU including memory layout of data structures and functional decomposition. We discuss various programmatic issues and provide a set of design guidelines for GPU programming that are instructive to avoid common pitfalls as well as to extract performance from the GPU architecture.

CONCLUSIONS

We demonstrate that GPU algorithms represent a significant technological advance for the simulation of complex biological models. We further demonstrate with our epidermal model that the integration of multiple complex modeling methods for heterogeneous multicellular biological processes is both feasible and computationally tractable using this new technology. We hope that the provided algorithms and source code will be a starting point for modelers to develop their own GPU implementations, and encourage others to implement their modeling methods on the GPU and to make that code available to the wider community.

Computational model of cell positioning: directed and collective migration in the intestinal crypt epithelium

The epithelium of the intestinal crypt is a dynamic tissue undergoing constant regeneration through cell growth, cell division, cell differentiation and apoptosis. How the epithelial cells maintain correct positioning and how they migrate in a directed and collective fashion are still not well understood. In this paper, we developed a computational model to elucidate these processes. We show that differential adhesion between epithelial cells, caused by the differential activation of EphB receptors and ephrinB ligands along the crypt axis, is necessary to regulate cell positioning. Differential cell adhesion has been proposed previously to guide cell movement and cause cell sorting in biological tissues. The proliferative cells and the differentiated post-mitotic cells do not intermingle as long as differential adhesion is maintained. We also show that, without differential adhesion, Paneth cells are randomly distributed throughout the intestinal crypt. In addition, our model suggests that, with differential adhesion, cells migrate more rapidly as they approach the top of the intestinal crypt. Finally, by calculating the spatial correlation function of the cell velocities, we observe that differential adhesion results in the differentiated epithelial cells moving in a coordinated manner, where correlated velocities are maintained at large distances, suggesting that differential adhesion regulates coordinated migration of cells in tissues.

In situ analysis of cell populations: long-term label-retaining cells

The mammary gland consists of an epithelial ductal tree embedded in a fat pad. Adult mammary epithelium has been demonstrated to have outstanding regenerative potential, consistent with the presence of resident, adult stem cells. However, there are currently no bona fide markers to identify these cells within their tissue context. Here, we introduce long-term label retention as a method to investigate the location of quiescent cells (a property attributed to adult stem cells) in situ. Long-term label retaining cells divide actively during tissue development and remain quiescent at homeostasis. These two properties have been attributed to adult stem cells. Therefore, label-retaining cells can be used to identify populations that contain stem cells. We describe the materials and methods necessary to identify and image mammary label-retaining cells, to carry out morphometric analysis on these cells and to map their distribution of the mammary epithelium. The morphometric and spatial analyses described here are generally applicable to any mammary cell populations, and will therefore be useful to characterize mammary stem cells once bona fide mammary stem cell markers become available.

Development of a mini 3D cell culture system using well defined nickel grids for the investigation of cell scaffold interactions

A bioreactor system was developed using a series of fine mesh nickel grids as free standing scaffolds to investigate the behaviours of fibroblasts and keratinocytes in tissue culture. It was found that the mesh size of the suspended grids, but not of the grids that attached to tissue culture surface, had significant influences on cell behaviour and there was a maximum size for fibroblast to span within the defined culture period. Time lapse video microscopy demonstrated fibroblasts cultured on these grids initially migrated onto the struts but then worked together to fill in the voids between struts with a membranous sheet of tissue. In contrast keratinocytes barely migrated from the initial site of cell deposition and when they moved (to a modest extent) it was as an integrated sheet of cells. Similar results were observed when both types of cells were co-cultured in the system.

Notch signalling in cancer stem cells

A new theory about the development of solid tumours is emerging from the idea that solid tumours, like normal adult tissues, contain stem cells (called cancer stem cells) and arise from them. Genetic mutations encoding for proteins involved in critical signalling pathways for stem cells such as BMP, Notch, Hedgehog and Wnt would allow stem cells to undergo uncontrolled proliferation and form tumours. Taking into account that cancer stem cells (CSCs) would represent the real driving force behind tumour growth and that they may be drug resistant, new agents that target the above signalling pathways could be more effective than current anti-solid tumour therapies. In the present paper we will review the molecular basis of the Notch signalling pathway. Additionally, we will pay attention to their role in adult stem cell self-renewal, and cell fate specification and differentiation, and we will also review evidence that supports their implication in cancer.

hnRNP I inhibits Notch signaling and regulates intestinal epithelial homeostasis in the zebrafish

Regulated intestinal stem cell proliferation and differentiation are required for normal intestinal homeostasis and repair after injury. The Notch signaling pathway plays fundamental roles in the intestinal epithelium. Despite the fact that Notch signaling maintains intestinal stem cells in a proliferative state and promotes absorptive cell differentiation in most species, it remains largely unclear how Notch signaling itself is precisely controlled during intestinal homeostasis. We characterized the intestinal phenotypes of brom bones, a zebrafish mutant carrying a nonsense mutation in hnRNP I. We found that the brom bones mutant displays a number of intestinal defects, including compromised secretory goblet cell differentiation, hyperproliferation, and enhanced apoptosis. These phenotypes are accompanied by a markedly elevated Notch signaling activity in the intestinal epithelium. When overexpressed, hnRNP I destabilizes the Notch intracellular domain (NICD) and inhibits Notch signaling. This activity of hnRNP I is conserved from zebrafish to human. In addition, our biochemistry experiments demonstrate that the effect of hnRNP I on NICD turnover requires the C-terminal portion of the RAM domain of NICD. Our results demonstrate that hnRNP I is an evolutionarily conserved Notch inhibitor and plays an essential role in intestinal homeostasis.

Mapping mammary gland architecture using multi-scale in situ analysis

We have built a novel computational microscopy platform that integrates image acquisition, storage, processing and analysis to study cell populations in situ. This platform allows high-content studies where multiple features are measured and linked at multiple scales. We used this approach to study the cellular composition and architecture of the mouse mammary gland by quantitatively tracking the distribution and type, position, proliferative state, and hormone receptor status of epithelial cells that incorporated bromodeoxyuridine while undergoing DNA synthesis during puberty and retained this label in the adult gland as a function of tissue structure. Immunofluorescence was used to identify label-retaining cells, as well as epithelial cells expressing the proteins progesterone receptor and P63. Only 3.6% of luminal cells were label-retaining cells, the majority of which did not express the progesterone receptor. Multi-scale in situ analysis revealed that luminal label-retaining cells have a distinct nuclear morphology, are enriched 3.4-fold in large ducts, and are distributed asymmetrically across the tissue. We postulated that LRC enriched in the ventral mammary gland represent progenitor cells. Epithelial cells isolated from the ventral versus the dorsal portion of the gland were enriched for the putative stem cell markers CD24 and CD49f as measured by fluorescence activated cell sorting. Thus, quantitative analysis of the cellular composition of the mammary epithelium across spatial scales identified a previously unrecognized architecture in which the ventral-most, large ducts contain a reservoir of undifferentiated, putative stem cells.

Multicell simulations of development and disease using the CompuCell3D simulation environment

Mathematical modeling and computer simulation have become crucial to biological fields from genomics to ecology. However, multicell, tissue-level simulations of development and disease have lagged behind other areas because they are mathematically more complex and lack easy-to-use software tools that allow building and running in silico experiments without requiring in-depth knowledge of programming. This tutorial introduces Glazier-Graner-Hogeweg (GGH) multicell simulations and CompuCell3D, a simulation framework that allows users to build, test, and run GGH simulations.

Gamma-secretase activation of notch signaling regulates the balance of proximal and distal fates in progenitor cells of the developing lung

Little is known about the mechanisms by which the lung epithelial progenitors are initially patterned and how proximal-distal boundaries are established and maintained when the lung primordium forms and starts to branch. Here we identified a number of Notch pathway components in respiratory progenitors of the early lung, and we investigated the role of Notch in lung pattern formation. By preventing gamma-secretase cleavage of Notch receptors, we have disrupted global Notch signaling in the foregut and in the lung during the initial stages of murine lung morphogenesis. We demonstrate that Notch signaling is not necessary for lung bud initiation; however, Notch is required to maintain a balance of proximal-distal cell fates at these early stages. Disruption of Notch signaling dramatically expands the population of distal progenitors, altering morphogenetic boundaries and preventing formation of proximal structures. Our data suggest a novel mechanism in which Notch and fibroblast growth factor signaling interact to control the proximal-distal pattern of forming airways in the mammalian lung.

Growth based morphogenesis of vertebrate limb bud

Many genes and their regulatory relationships are involved in developmental phenomena. However, by chemical information alone, we cannot fully understand changing organ morphologies through tissue growth because deformation and growth of the organ are essentially mechanical processes. Here, we develop a mathematical model to describe the change of organ morphologies through cell proliferation. Our basic idea is that the proper specification of localized volume source (e.g., cell proliferation) is able to guide organ morphogenesis, and that the specification is given by chemical gradients. We call this idea "growth-based morphogenesis." We find that this morphogenetic mechanism works if the tissue is elastic for small deformation and plastic for large deformation. To illustrate our concept, we study the development of vertebrate limb buds, in which a limb bud protrudes from a flat lateral plate and extends distally in a self-organized manner. We show how the proportion of limb bud shape depends on different parameters and also show the conditions needed for normal morphogenesis, which can explain abnormal morphology of some mutants. We believe that the ideas shown in the present paper are useful for the morphogenesis of other organs.

An integrated systems biology approach to understanding the rules of keratinocyte colony formation

Closely coupled in vitro and in virtuo models have been used to explore the self-organization of normal human keratinocytes (NHK). Although it can be observed experimentally, we lack the tools to explore many biological rules that govern NHK self-organization. An agent-based computational model was developed, based on rules derived from literature, which predicts the dynamic multicellular morphogenesis of NHK and of a keratinocyte cell line (HaCat cells) under varying extracellular Ca++ concentrations. The model enables in virtuo exploration of the relative importance of biological rules and was used to test hypotheses in virtuo which were subsequently examined in vitro. Results indicated that cell-cell and cell-substrate adhesions were critically important to NHK self-organization. In contrast, cell cycle length and the number of divisions that transit-amplifying cells could undergo proved non-critical to the final organization. Two further hypotheses, to explain the growth behaviour of HaCat cells, were explored in virtuo-an inability to differentiate and a differing sensitivity to extracellular calcium. In vitro experimentation provided some support for both hypotheses. For NHKs, the prediction was made that the position of stem cells would influence the pattern of cell migration post-wounding. This was then confirmed experimentally using a scratch wound model.

Involvement of notch signaling in wound healing

The Notch signaling pathway is critically involved in cell fate decisions during development of many tissues and organs. In the present study we employed in vivo and cell culture models to elucidate the role of Notch signaling in wound healing. The healing of full-thickness dermal wounds was significantly delayed in Notch antisense transgenic mice and in normal mice treated with γ-secretase inhibitors that block proteolytic cleavage and activation of Notch. In contrast, mice treated with a Notch ligand Jagged peptide showed significantly enhanced wound healing compared to controls. Activation or inhibition of Notch signaling altered the behaviors of cultured vascular endothelial cells, keratinocytes and fibroblasts in a scratch wound healing model in ways consistent with roles for Notch signaling in wound healing functions all three cell types. These results suggest that Notch signaling plays important roles in wound healing and tissue repair, and that targeting the Notch pathway might provide a novel strategy for treatment of wounds and for modulation of angiogenesis in other pathological conditions.

Simulating invasion with cellular automata: connecting cell-scale and population-scale properties

Interpretive and predictive tools are needed to assist in the understanding of cell invasion processes. Cell invasion involves cell motility and proliferation, and is central to many biological processes including developmental morphogenesis and tumor invasion. Experimental data can be collected across a wide range of scales, from the population scale to the individual cell scale. Standard continuum or discrete models used in isolation are insufficient to capture this wide range of data. We develop a discrete cellular automata model of invasion with experimentally motivated rules. The cellular automata algorithm is applied to a narrow two-dimensional lattice and simulations reveal the formation of invasion waves moving with constant speed. The simulation results are averaged in one dimension-these data are used to identify the time history of the leading edge to characterize the population-scale wave speed. This allows the relationship between the population-scale wave speed and the cell-scale parameters to be determined. This relationship is analogous to well-known continuum results for Fisher's equation. The cellular automata algorithm also produces individual cell trajectories within the invasion wave that are analogous to cell trajectories obtained with new experimental techniques. Our approach allows both the cell-scale and population-scale properties of invasion to be predicted in a way that is consistent with multiscale experimental data. Furthermore we suggest that the cellular automata algorithm can be used in conjunction with individual data to overcome limitations associated with identifying cell motility mechanisms using continuum models alone.

Modeling epithelial cell behavior and organization

We propose an individual cell based model for epithelial cell interactions. The model includes biological processes such as cell division, differentiation, adhesion, and death. Cell types include stem, transit amplifying, intermediate, mature, and dead. Stem and transit amplifying cells are allowed to divide provided they are on the basement membrane. In particular, the roles of differential adhesion and cell division during the development are discussed. The typical ordered structure of a healthy epithelium is shown to arise provided differential adhesion and cell division are modeled appropriately.

A modelling approach towards epidermal homoeostasis control

In order to grasp the features arising from cellular discreteness and individuality, in large parts of cell tissue modelling agent-based models are favoured. The subclass of off-lattice models allows for a physical motivation of the intercellular interaction rules. We apply an improved version of a previously introduced off-lattice agent-based model to the steady-state flow equilibrium of skin. The dynamics of cells is determined by conservative and drag forces, supplemented with delta-correlated random forces. Cellular adjacency is detected by a weighted Delaunay triangulation. The cell cycle time of keratinocytes is controlled by a diffusible substance provided by the dermis. Its concentration is calculated from a diffusion equation with time-dependent boundary conditions and varying diffusion coefficients. The dynamics of a nutrient is also taken into account by a reaction-diffusion equation. It turns out that the analysed control mechanism suffices to explain several characteristics of epidermal homoeostasis formation. In addition, we examine the question of how in silico melanoma with decreased basal adhesion manage to persist within the steady-state flow equilibrium of the skin. Interestingly, even for melanocyte cell cycle times being substantially shorter than for keratinocytes, tiny stochastic effects can lead to completely different outcomes. The results demonstrate that the understanding of initial states of tumour growth can profit significantly from the application of off-lattice agent-based models in computer simulations.

Lunatic fringe causes expansion and increased neurogenesis of trunk neural tube and neural crest populations

Both neurons and glia of the PNS are derived from the neural crest. In this study, we have examined the potential function of lunatic fringe in neural tube and trunk neural crest development by gain-of-function analysis during early stages of nervous system formation. Normally lunatic fringe is expressed in three broad bands within the neural tube, and is most prominent in the dorsal neural tube containing neural crest precursors. Using retrovirally-mediated gene transfer, we find that excess lunatic fringe in the neural tube increases the numbers of neural crest cells in the migratory stream via an apparent increase in cell proliferation. In addition, lunatic fringe augments the numbers of neurons and upregulates Delta-1 expression. The results indicate that, by modulating Notch/Delta signaling, lunatic fringe not only increases cell division of neural crest precursors, but also increases the numbers of neurons in the trunk neural crest.

Cell proliferation drives neural crest cell invasion of the intestine

A general mathematical model of cell invasion is developed and validated with an experimental system. The model incorporates two basic cell functions: non-directed (diffusive) motility and proliferation to a carrying capacity limit. The model is used here to investigate cell proliferation and motility differences along the axis of an invasion wave. Mathematical simulations yield surprising and counterintuitive predictions. In this general scenario, cells at the invasive front are proliferative and migrate into previously unoccupied tissues while those behind the front are essentially nonproliferative and do not directly migrate into unoccupied tissues. These differences are not innate to the cells, but are a function of proximity to uninvaded tissue. Therefore, proliferation at the invading front is the critical mechanism driving apparently directed invasion. An appropriate system to experimentally validate these predictions is the directional invasion and colonization of the gut by vagal neural crest cells that establish the enteric nervous system. An assay using gut organ culture with chick-quail grafting is used for this purpose. The experimental results are entirely concordant with the mathematical predictions. We conclude that proliferation at the wavefront is a key mechanism driving the invasive process. This has important implications not just for the neural crest, but for other invasion systems such as epidermal wound healing, carcinoma invasion and other developmental cell migrations.

Human mesenchymal stem cells favour healing of the cutaneous radiation syndrome in a xenogenic transplant model

It has been suggested that human mesenchymal stem cells (hMSC) could be used to repair numerous injured tissues. We have studied the potential use of hMSC to limit radiation-induced skin lesions. Immunodeficient NOD/SCID mice were locally irradiated to the leg (30 Gy, dose rate 2.7 Gy/min) using a (60)Co source to induce a severe skin lesion. Cultured bone marrow hMSC were delivered intravenously to the mice. The irradiated skin samples were studied for the presence of the human cells, the severity of the lesions and the healing process. Macroscopic analysis and histology results showed that the lesions were evolving to a less severe degree of radiation dermatitis after hMSC transplant when compared to irradiated non-transplanted controls. Clinical scores for the studied skin parameters of treated mice were significantly improved. A faster healing was observed when compared to untreated mouse. Immunohistology and polymerase chain reaction analysis provided evidence that the human cells were found in the irradiated area. These results suggest a possible use of hMSC for the treatment of the early phase of the cutaneous radiation syndrome. A successful transplant of stem cells and subsequent reduction in radiation-induced complication may open the road to completely new strategies in cutaneous radiation syndrome therapy.

Individual cell-based models of the spatial-temporal organization of multicellular systems--achievements and limitations

Computational approaches of multicellular assemblies have reached a stage where they may contribute to unveil the processes that underlie the organization of tissues and multicellular aggregates. In this article, we briefly review and present some new results on a number of 3D lattice free individual cell-based mathematical models of epithelial cell populations. The models we consider here are parameterized by bio-physical and cell-biological quantities on the level of an individual cell. Eventually, they aim at predicting the dynamics of the biological processes on the tissue level. We focus on a number of systems, the growth of cell populations in vitro, and the spatial-temporal organization of regenerative tissues. For selected examples we compare different model approaches and show that the qualitative results are robust with respect to many model details. Hence, for the qualitative features and largely for the quantitative features many model details do not matter as long as characteristic biological features and mechanisms are correctly represented. For a quantitative prediction, the control of the bio-physical and cell-biological parameters on the molecular scale has to be known. At this point, slide-based cytometry may contribute. It permits to track the fate of cells and other tissue subunits in time and validated the organization processes predicted by the mathematical models.

Modeling the Effect of Exogenous Calcium on Keratinocyte and HaCat Cell Proliferation and Differentiation Using an Agent-Based Computational Paradigm

In this study we sought to develop a computational modeling paradigm in order to describe the influence of calcium on normal and transformed keratinocyte proliferation and differentiation. Keratinocytes and HaCat cells were grown in monolayer cultures with low and physiologic calcium concentrations, and levels of proliferation and involucrin expression were assessed. Both types of cells grew as monolayers under a low-calcium environment, and stratified in media with physiologic levels of calcium. However, keratinocytes were more proliferative in low rather than physiologic levels of calcium, whereas the opposite was true for HaCat cells. Normal keratinocytes differentiated as calcium levels increased. HaCat cells showed little differentiation at any calcium concentration. However, while the computer simulation could be modified to describe the effect of calcium on the growth of normal keratinocytes, our findings did not support the hypothesis that simply "turning off" the ability of HaCat cells to differentiate would account for the growth characteristics of these transformed cells. This demonstrates the application of computational modeling to hypothesis testing in biological systems.

Kidney side population reveals multilineage potential and renal functional capacity but also cellular heterogeneity

Side population (SP) cells in the adult kidney are proposed to represent a progenitor population. However, the size, origin, phenotype, and potential of the kidney SP has been controversial. In this study, the SP fraction of embryonic and adult kidneys represented 0.1 to 0.2% of the total viable cell population. The immunophenotype and the expression profile of kidney SP cells was distinct from that of bone marrow SP cells, suggesting that they are a resident nonhematopoietic cell population. Affymetrix expression profiling implicated a role for Notch signaling in kidney SP cells and was used to identify markers of kidney SP. Localization by in situ hybridization confirmed a primarily proximal tubule location, supporting the existence of a tubular "niche," but also revealed considerable heterogeneity, including the presence of renal macrophages. Adult kidney SP cells demonstrated multilineage differentiation in vitro, whereas microinjection into mouse metanephroi showed that SP cells had a 3.5- to 13-fold greater potential to contribute to developing kidney than non-SP main population cells. However, although reintroduction of SP cells into an Adriamycin-nephropathy model reduced albuminuria:creatinine ratios, this was without significant tubular integration, suggesting a humoral role for SP cells in renal repair. The heterogeneity of the renal SP highlights the need for further fractionation to distinguish the cellular subpopulations that are responsible for the observed multilineage capacity and transdifferentiative and humoral activities.

Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling

Vasculogenesis, the de novo growth of the primary vascular network from initially dispersed endothelial cells, is the first step in the development of the circulatory system in vertebrates. In the first stages of vasculogenesis, endothelial cells elongate and form a network-like structure, called the primary capillary plexus, which subsequently remodels, with the size of the vacancies between ribbons of endothelial cells coarsening over time. To isolate such intrinsic morphogenetic ability of endothelial cells from its regulation by long-range guidance cues and additional cell types, we use an in vitro model of human umbilical vein endothelial cells (HUVEC) in Matrigel. This quasi-two-dimensional endothelial cell culture model would most closely correspond to vasculogenesis in flat areas of the embryo like the yolk sac. Several studies have used continuum mathematical models to explore in vitro vasculogenesis: such models describe cell ensembles but ignore the endothelial cells' shapes and active surface fluctuations. While these models initially reproduce vascular-like morphologies, they eventually stabilize into a disconnected pattern of vascular "islands." Also, they fail to reproduce temporally correct network coarsening. Using a cell-centered computational model, we show that the endothelial cells' elongated shape is key to correct spatiotemporal in silico replication of stable vascular network growth. We validate our simulation results against HUVEC cultures using time-resolved image analysis and find that our simulations quantitatively reproduce in vitro vasculogenesis and subsequent in vitro remodeling.

Multicellular tumor spheroid in an off-lattice Voronoi-Delaunay cell model

We study multicellular tumor spheroids by introducing a new three-dimensional agent-based Voronoi-Delaunay hybrid model. In this model, the cell shape varies from spherical in thin solution to convex polyhedral in dense tissues. The next neighbors of the cells are provided by a weighted Delaunay triangulation with on average linear computational complexity. The cellular interactions include direct elastic forces and cell-cell as well as cell-matrix adhesion. The spatiotemporal distribution of two nutrients--oxygen and glucose--is described by reaction-diffusion equations. Viable cells consume the nutrients, which are converted into biomass by increasing the cell size during the G1 phase. We test hypotheses on the functional dependence of the uptake rates and use computer simulations to find suitable mechanisms for the induction of necrosis. This is done by comparing the outcome with experimental growth curves, where the best fit leads to an unexpected ratio of oxygen and glucose uptake rates. The model relies on physical quantities and can easily be generalized towards tissues involving different cell types. In addition, it provides many features that can be directly compared with the experiment.

Bone marrow-derived cells contribute to epithelial engraftment during wound healing

Recent findings suggest that bone marrow-derived cells (BMDC) may contribute to tissue maintenance throughout the body. However, it is not yet known whether marrow-derived epithelial cells are capable of undergoing proliferation. Our laboratory has shown that BMDC engraft as keratinocytes in the skin at low levels (</= 1%) in the absence of injury. Here we show that skin damage affects the degree of engraftment of BMDC as keratinocytes and that the keratinocytes are actively cycling. Female mice reconstituted with sex-mismatched BM were wounded by punch biopsy and incision. At the wound site, engraftment of BMDC as epidermal cells increased within 1 day, and continued to increase to approximately 4% by 3 weeks after injury. Using a Cre-lox system, fusion of BMDC with epithelial cells was ruled out. BMDC-derived epithelial cells at the wound edges expressed Ki67, a marker for actively cycling cells, and this proliferation correlated with an increase in the number of donor-derived cells within the wound. Donor-derived cytokeratin 5-expressing cells were rare, suggesting that BMDC do not engraft as epidermal stem cells, and the level of engraftment peaked and then decreased over time, further suggesting that BMDC may assist in early wound healing by engrafting as transit-amplifying cells, which then differentiate into keratinocytes.