Stem cell niche structure as an inherent cause of undulating epithelial morphologies

The role of interface geometry and appendages on the mesoscale mechanics of the skin

The skin is the largest organ in the human body and serves various functions, including mechanical protection and mechanosensation. Yet, even though skin's biomechanics are attributed to two main layers-epidermis and dermis-computational models have often treated this tissue as a thin homogeneous material or, when considering multiple layers, have ignored the most prominent heterogeneities of skin seen at the mesoscale. Here, we create finite element models of representative volume elements (RVEs) of skin, including the three-dimensional variation of the interface between the epidermis and dermis as well as considering the presence of hair follicles. The sinusoidal interface, which approximates the anatomical features known as Rete ridges, does not affect the homogenized mechanical response of the RVE but contributes to stress concentration, particularly at the valleys of the Rete ridges. The stress profile is three-dimensional due to the skin's anisotropy, leading to high-stress bands connecting the valleys of the Rete ridges through one type of saddle point. The peaks of the Rete ridges and the other class of saddle points of the sinusoidal surface form a second set of low-stress bands under equi-biaxial loading. Another prominent feature of the heterogeneous stress pattern is a switch in the stress jump across the interface, which becomes lower with respect to the flat interface at increasing deformations. These features are seen in both tension and shear loading. The RVE with the hair follicle showed strains concentrating at the epidermis adjacent to the hair follicle, the epithelial tissue surrounding the hair right below the epidermis, and the bulb or base region of the hair follicle. The regions of strain concentration near the hair follicle in equi-biaxial and shear loading align with the presence of distinct mechanoreceptors in the skin, except for the bulb or base region. This study highlights the importance of skin heterogeneities, particularly its potential mechanophysiological role in the sense of touch and the prevention of skin delamination.

The Role of Interface Geometry and Appendages on the Mesoscale Mechanics of the Skin

The skin is the largest organ in the human body and serves various functions, including mechanical protection and mechanosensation. Yet, even though skin's biomechanics are attributed to two main layers - epidermis and dermis-computational models have often treated this tissue as a thin homogeneous material or, when considering multiple layers, have ignored the most prominent heterogeneities of skin seen at the mesoscale. Here we create finite element models of representative volume elements (RVEs) of skin, including the three-dimensional variation of the interface between the epidermis and dermis as well as considering the presence of hair follicles. The sinusoidal interface, which approximates the anatomical features known as Rete ridges, does not affect the homogenized mechanical response of the RVE but contributes to stress concentration, particularly at the valleys of the Rete ridges. The stress profile is three-dimensional due to the skin's anisotropy, leading to high-stress bands connecting the valleys of the Rete ridges through one type of saddle point. The peaks of the Rete ridges and the other class of saddle points of the sinusoidal surface form a second set of low-stress bands under equi-biaxial loading. Another prominent feature of the heterogeneous stress pattern is a switch in the stress jump across the interface, which becomes lower with respect to the flat interface at increasing deformations. These features are seen in both tension and shear loading. The RVE with the hair follicle showed strains concentrating at the epidermis adjacent to the hair follicle, the epithelial tissue surrounding the hair right below the epidermis, and the bulb or base region of the hair follicle. The regions of strain concentration near the hair follicle in equi-biaxial and shear loading align with the presence of distinct mechanoreceptors in the skin, except for the bulb or base region. This study highlights the importance of skin heterogeneities, particularly its potential mechanophysiological role in the sense of touch and the prevention of skin delamination.

A multiscale chemical-mechanical model predicts impact of morphogen spreading on tissue growth

The exact mechanism controlling cell growth remains a grand challenge in developmental biology and regenerative medicine. The Drosophila wing disc tissue serves as an ideal biological model to study mechanisms involved in growth regulation. Most existing computational models for studying tissue growth focus specifically on either chemical signals or mechanical forces. Here we developed a multiscale chemical-mechanical model to investigate the growth regulation mechanism based on the dynamics of a morphogen gradient. By comparing the spatial distribution of dividing cells and the overall tissue shape obtained in model simulations with experimental data of the wing disc, it is shown that the size of the domain of the Dpp morphogen is critical in determining tissue size and shape. A larger tissue size with a faster growth rate and more symmetric shape can be achieved if the Dpp gradient spreads in a larger domain. Together with Dpp absorbance at the peripheral zone, the feedback regulation that downregulates Dpp receptors on the cell membrane allows for further spreading of the morphogen away from its source region, resulting in prolonged tissue growth at a more spatially homogeneous growth rate.

A Novel Technique of Amniotic Membrane Preparation Mimicking Limbal Epithelial Crypts Enhances the Number of Progenitor Cells upon Expansion

We aimed to investigate whether a novel technique of human amniotic membrane (HAM) preparation that mimics the crypts in the limbus enhances the number of progenitor cells cultured ex vivo. The HAMs were sutured on polyester membrane (1) standardly, to obtain a flat HAM surface, or (2) loosely, achieving the radial folding to mimic crypts in the limbus. Immunohistochemistry was used to demonstrate a higher number of cells positive for progenitor markers p63α (37.56 ± 3.34% vs. 62.53 ± 3.32%, p = 0.01) and SOX9 (35.53 ± 0.96% vs. 43.23 ± 2.32%, p = 0.04), proliferation marker Ki-67 (8.43 ± 0.38 % vs. 22.38 ± 1.95 %, p = 0.002) in the crypt-like HAMs vs. flat HAMs, while no difference was found for the quiescence marker CEBPD (22.99 ± 2.96% vs. 30.49 ± 3.33 %, p = 0.17). Most of the cells stained negative for the corneal epithelial differentiation marker KRT3/12, and some were positive for N-cadherin in the crypt-like structures, but there was no difference in staining for E-cadherin and CX43 in crypt-like HAMs vs. flat HAMs. This novel HAM preparation method enhanced the number of progenitor cells expanded in the crypt-like HAM compared to cultures on the conventional flat HAM.

The Importance of Mimicking Dermal-Epidermal Junction for Skin Tissue Engineering: A Review

There is a distinct boundary between the dermis and epidermis in the human skin called the basement membrane, a dense collagen network that creates undulations of the dermal-epidermal junction (DEJ). The DEJ plays multiple roles in skin homeostasis and function, namely, enhancing the adhesion and physical interlock of the layers, creating niches for epidermal stem cells, regulating the cellular microenvironment, and providing a physical boundary layer between fibroblasts and keratinocytes. However, the primary role of the DEJ has been determined as skin integrity; there are still aspects of it that are poorly investigated. Tissue engineering (TE) has evolved promising skin regeneration strategies and already developed TE scaffolds for clinical use. However, the currently available skin TE equivalents neglect to replicate the DEJ anatomical structures. The emergent ability to produce increasingly complex scaffolds for skin TE will enable the development of closer physical and physiological mimics to natural skin; it also allows researchers to study the DEJ effect on cell function. Few studies have created patterned substrates that could mimic the human DEJ to explore their significance. Here, we first review the DEJ roles and then critically discuss the TE strategies to create the DEJ undulating structure and their effects. New approaches in this field could be instrumental for improving bioengineered skin substitutes, creating 3D engineered skin, identifying pathological mechanisms, and producing and screening drugs.

Calcium-sensing receptor deletion in the mouse esophagus alters barrier function

Calcium-sensing receptor (CaSR) is the molecular sensor by which cells respond to small changes in extracellular Ca²⁺ concentrations. CaSR has been reported to play a role in glandular and fluid secretion in the gastrointestinal tract and to regulate differentiation and proliferation of skin keratinocytes. CaSR is present in the esophageal epithelium, but its role in this tissue has not been defined. We deleted CaSR in the mouse esophagus by generating keratin 5 CreER;CaSR^Flox+/+compound mutants, in which loxP sites flank exon 7 of CaSR gene. Recombination was initiated with multiple tamoxifen injections, and we demonstrated exon 7 deletion by PCR analysis of genomic DNA. Quantitative real-time PCR and Western blot analyses showed a significant reduction in CaSR mRNA and protein expression in the knockout mice (^EsoCaSR^-/-) as compared with control mice. Microscopic examination of ^EsoCaSR^-/- esophageal tissues showed morphological changes including elongation of the rete pegs, abnormal keratinization and stratification, and bacterial buildup on the luminal epithelial surface. Western analysis revealed a significant reduction in levels of adherens junction proteins E-cadherin and β catenin and tight junction protein claudin-1, 4, and 5. Levels of small GTPase proteins Rac/Cdc42, involved in actin remodeling, were also reduced. Ussing chamber experiments showed a significantly lower transepithelial resistance in knockout (KO) tissues. In addition, luminal-to-serosal-fluorescein dextran (4 kDa) flux was higher in KO tissues. Our data indicate that CaSR plays a role in regulating keratinization and cell-cell junctional complexes and is therefore important for the maintenance of the barrier function of the esophagus.NEW & NOTEWORTHY The esophageal stratified squamous epithelium maintains its integrity by continuous proliferation and differentiation of the basal cells. Here, we demonstrate that deletion of the calcium-sensing receptor, a G protein-coupled receptor, from the basal cells disrupts the structure and barrier properties of the epithelium.

STOCHASTIC DYNAMICS OF CELL LINEAGE IN TISSUE HOMEOSTASIS

During epithelium tissue maintenance, lineages of cells differentiate and proliferate in a coordinated way to provide the desirable size and spatial organization of different types of cells. While mathematical models through deterministic description have been used to dissect role of feedback regulations on tissue layer size and stratification, how the stochastic effects influence tissue maintenance remains largely unknown. Here we present a stochastic continuum model for cell lineages to investigate how both layer thickness and layer stratification are affected by noise. We find that the cell-intrinsic noise often causes reduction and oscillation of layer size whereas the cell-extrinsic noise increases the thickness, and sometimes, leads to uncontrollable growth of the tissue layer. The layer stratification usually deteriorates as the noise level increases in the cell lineage systems. Interestingly, the morphogen noise, which mixes both cell-intrinsic noise and cell-extrinsic noise, can lead to larger size of layer with little impact on the layer stratification. By investigating different combinations of the three types of noise, we find the layer thickness variability is reduced when cell-extrinsic noise level is high or morphogen noise level is low. Interestingly, there exists a tradeoff between low thickness variability and strong layer stratification due to competition among the three types of noise, suggesting robust layer homeostasis requires balanced levels of different types of noise in the cell lineage systems.

Modeling of Interactions between Cancer Stem Cells and their Microenvironment: Predicting Clinical Response

Mathematical models of cancer stem cells are useful in translational cancer research for facilitating the understanding of tumor growth dynamics and for predicting treatment response and resistance to combined targeted therapies. In this chapter, we describe appealing aspects of different methods used in mathematical oncology and discuss compelling questions in oncology that can be addressed with these modeling techniques. We describe a simplified version of a model of the breast cancer stem cell niche, illustrate the visualization of the model, and apply stochastic simulation to generate full distributions and average trajectories of cell type populations over time. We further discuss the advent of single-cell data in studying cancer stem cell heterogeneity and how these data can be integrated with modeling to advance understanding of the dynamics of invasive and proliferative populations during cancer progression and response to therapy.

Current and Future Perspectives of Stem Cell Therapy in Dermatology

Stem cells are undifferentiated cells capable of generating, sustaining, and replacing terminally differentiated cells and tissues. They can be isolated from embryonic as well as almost all adult tissues including skin, but are also generated through genetic reprogramming of differentiated cells. Preclinical and clinical research has recently tremendously improved stem cell therapy, being a promising treatment option for various diseases in which current medical therapies fail to cure, prevent progression or relieve symptoms. With the main goal of regeneration or sustained genetic correction of damaged tissue, advanced tissue-engineering techniques are especially applicable for many dermatological diseases including wound healing, genodermatoses (like the severe blistering disorder epidermolysis bullosa) and chronic (auto-)inflammatory diseases. This review summarizes general aspects as well as current and future perspectives of stem cell therapy in dermatology.

Supra-organization and optical anisotropies of the extracellular matrix in the amniotic membrane and limbal stroma before and after explant culture

In this research we evaluated the supramolecular organizations and the optical anisotropical properties of the de-epithelialized human amniotic membrane and rabbit limbal stroma, before and after explant culture. Birefringence, monochromatic light spectral absorption and linear dichroism of the main extracellular matrix biopolymers, that is, the fibrillar collagens and proteoglycans, were investigated by polarized light microscopy combined with image analysis. Our results demonstrated that the culture procedure-induced stimuli altered the supra-organizational characteristics (in terms of collagens/proteoglycans spatial orientation and ordered-aggregational state) of the amniotic and limbal extracellular matrix, which led to changes in optical anisotropical properties.

Emergence of Form from Function - Mechanical Engineering Approaches to Probe the Role of Stem Cell Mechanoadaptation in Sealing Cell Fate

Stem cell "mechanomics" refers to the effect of mechanical cues on stem cell and matrix biology, where cell shape and fate are intrinsic manifestations of form and function. Before specialization, the stem cell itself serves as a sensor and actuator; its structure emerges from its local mechanical milieu as the cell adapts over time. Coupling of novel spatiotemporal imaging and computational methods allows for linking of the energy of adaptation to the structure, biology and mechanical function of the cell. Cutting edge imaging methods enable probing of mechanisms by which stem cells' emergent anisotropic architecture and fate commitment occurs. A novel cell-scale model provides a mechanistic framework to describe stem cell growth and remodeling through mechanical feedback; making use of a generalized virtual power principle, the model accounts for the rate of doing work or the rate of using energy to effect the work. This coupled approach provides a basis to elucidate mechanisms underlying the stem cell's innate capacity to adapt to mechanical stimuli as well as the role of mechanoadaptation in lineage commitment. An understanding of stem cell mechanoadaptation is key to deciphering lineage commitment, during prenatal development, postnatal wound healing, and engineering of tissues.

Cellular adaptation to biomechanical stress across length scales in tissue homeostasis and disease

Human tissues are remarkably adaptable and robust, harboring the collective ability to detect and respond to external stresses while maintaining tissue integrity. Following injury, many tissues have the capacity to repair the damage - and restore form and function - by deploying cellular and molecular mechanisms reminiscent of developmental programs. Indeed, it is increasingly clear that cancer and chronic conditions that develop with age arise as a result of cells and tissues re-implementing and deregulating a selection of developmental programs. Therefore, understanding the fundamental molecular mechanisms that drive cell and tissue responses is a necessity when designing therapies to treat human conditions. Extracellular matrix stiffness synergizes with chemical cues to drive single cell and collective cell behavior in culture and acts to establish and maintain tissue homeostasis in the body. This review will highlight recent advances that elucidate the impact of matrix mechanics on cell behavior and fate across these length scales during times of homeostasis and in disease states.

Hydrodynamics of stratified epithelium: Steady state and linearized dynamics

A theoretical model for stratified epithelium is presented. The viscoelastic properties of the tissue are assumed to be dependent on the spatial distribution of proliferative and differentiated cells. Based on this assumption, a hydrodynamic description of tissue dynamics at the long-wavelength, long-time limit is developed, and the analysis reveals important insights into the dynamics of an epithelium close to its steady state. When the proliferative cells occupy a thin region close to the basal membrane, the relaxation rate towards the steady state is enhanced by cell division and cell apoptosis. On the other hand, when the region where proliferative cells reside becomes sufficiently thick, a flow induced by cell apoptosis close to the apical surface enhances small perturbations. This destabilizing mechanism is general for continuous self-renewal multilayered tissues; it could be related to the origin of certain tissue morphology, tumor growth, and the development pattern.

Regulatory effects on the population dynamics and wave propagation in a cell lineage model

We consider the interplay of cell proliferation, cell differentiation (and de-differentiation), cell movement, and the effect of feedback regulations on the population and propagation dynamics of different cell types in a cell lineage model. Cells are assumed to secrete and respond to negative feedback molecules which act as a control on the cell lineage. The cell densities are described by coupled reaction-diffusion partial differential equations, and the propagating wave front solutions in one dimension are investigated analytically and by numerical solutions. In particular, wavefront propagation speeds are obtained analytically and verified by numerical solutions of the equations. The emphasis is on the effects of the feedback regulations on different stages in the cell lineage. It is found that when the progenitor cell is negatively regulated, the populations of the cell lineage are strongly down-regulated with the steady growth rate of the progenitor cell being driven to zero beyond a critical regulatory strength. An analytic expression for the critical regulation strength in terms of the model parameters is derived and verified by numerical solutions. On the other hand, if the inhibition is acting on the differentiated cells, the change in the population dynamics and wave propagation speed is small. In addition, it is found that only the propagating speed of the progenitor cells is affected by the regulation when the diffusion of the differentiated cells is large. In the presence of de-differentiation, the effect on down-regulating the progenitor population is weakened and there is no effect on the propagation speed due to regulation, suggesting that the effect of regulatory control is diminished by de-differentiation pathways.

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.

Deciphering principles of morphogenesis from temporal and spatial patterns on the integument

BACKGROUND

How tissue patterns form in development and regeneration is a fundamental issue remaining to be fully understood. The integument often forms repetitive units in space (periodic patterning) and time (cyclic renewal), such as feathers and hairs. Integument patterns are visible and experimentally manipulatable, helping us reveal pattern formative processes. Variability is seen in regional phenotypic specificities and temporal cycling at different physiological stages.

RESULTS

Here we show some cellular/molecular bases revealed by analyzing integument patterns. (1) Localized cellular activity (proliferation, rearrangement, apoptosis, differentiation) transforms prototypic organ primordia into specific shapes. Combinatorial positioning of different localized activity zones generates diverse and complex organ forms. (2) Competitive equilibrium between activators and inhibitors regulates stem cells through cyclic quiescence and activation.

CONCLUSIONS

Dynamic interactions between stem cells and their adjacent niche regulate regenerative behavior, modulated by multi-layers of macro-environmental factors (dermis, body hormone status, and external environment). Genomics studies may reveal how positional information of localized cellular activity is stored. In vivo skin imaging and lineage tracing unveils new insights into stem cell plasticity. Principles of self-assembly obtained from the integumentary organ model can be applied to help restore damaged patterns during regenerative wound healing and for tissue engineering to rebuild tissues. Developmental Dynamics 244:905-920, 2015. © 2015 Wiley Periodicals, Inc.

Interactions and tradeoffs between cell recruitment, proliferation, and differentiation affect CNS regeneration

Regeneration of central nervous system (CNS) lesions requires movement of progenitor cells and production of their differentiated progeny. Although damage to the CNS clearly promotes these two processes, the interplay between these complex events and how it affects a response remains elusive. Here, we use spatial stochastic modeling to show that tradeoffs arise between production and recruitment during regeneration. Proper spatial control of cell cycle timing can mitigate these tradeoffs, maximizing recruitment, improving infiltration into the lesion, and reducing wasteful production outside of it. Feedback regulation of cell lineage dynamics alone however leads to spatial defects in cell recruitment, suggesting a novel, to our knowledge, hypothesis for the aggregation of cells to the periphery of a lesion in multiple sclerosis. Interestingly, stronger chemotaxis does not correct this aggregation and instead, substantial random cell motions near the site of the lesion are required to improve CNS regeneration.

A mathematical-biological joint effort to investigate the tumor-initiating ability of Cancer Stem Cells

The involvement of Cancer Stem Cells (CSCs) in tumor progression and tumor recurrence is one of the most studied subjects in current cancer research. The CSC hypothesis states that cancer cell populations are characterized by a hierarchical structure that affects cancer progression. Due to the complex dynamics involving CSCs and the other cancer cell subpopulations, a robust theory explaining their action has not been established yet. Some indications can be obtained by combining mathematical modeling and experimental data to understand tumor dynamics and to generate new experimental hypotheses. Here, we present a model describing the initial phase of ErbB2⁺ mammary cancer progression, which arises from a joint effort combing mathematical modeling and cancer biology. The proposed model represents a new approach to investigate the CSC-driven tumorigenesis and to analyze the relations among crucial events involving cancer cell subpopulations. Using in vivo and in vitro data we tuned the model to reproduce the initial dynamics of cancer growth, and we used its solution to characterize observed cancer progression with respect to mutual CSC and progenitor cell variation. The model was also used to investigate which association occurs among cell phenotypes when specific cell markers are considered. Finally, we found various correlations among model parameters which cannot be directly inferred from the available biological data and these dependencies were used to characterize the dynamics of cancer subpopulations during the initial phase of ErbB2⁺ mammary cancer progression.

Mathematical model of adult stem cell regeneration with cross-talk between genetic and epigenetic regulation

Adult stem cells, which exist throughout the body, multiply by cell division to replenish dying cells or to promote regeneration to repair damaged tissues. To perform these functions during the lifetime of organs or tissues, stem cells need to maintain their populations in a faithful distribution of their epigenetic states, which are susceptible to stochastic fluctuations during each cell division, unexpected injury, and potential genetic mutations that occur during many cell divisions. However, it remains unclear how the three processes of differentiation, proliferation, and apoptosis in regulating stem cells collectively manage these challenging tasks. Here, without considering molecular details, we propose a genetic optimal control model for adult stem cell regeneration that includes the three fundamental processes, along with cell division and adaptation based on differential fitnesses of phenotypes. In the model, stem cells with a distribution of epigenetic states are required to maximize expected performance after each cell division. We show that heterogeneous proliferation that depends on the epigenetic states of stem cells can improve the maintenance of stem cell distributions to create balanced populations. A control strategy during each cell division leads to a feedback mechanism involving heterogeneous proliferation that can accelerate regeneration with less fluctuation in the stem cell population. When mutation is allowed, apoptosis evolves to maximize the performance during homeostasis after multiple cell divisions. The overall results highlight the importance of cross-talk between genetic and epigenetic regulation and the performance objectives during homeostasis in shaping a desirable heterogeneous distribution of stem cells in epigenetic states.

Numerical Methods for Two-Dimensional Stem Cell Tissue Growth

Growth of developing and regenerative biological tissues of different cell types is usually driven by stem cells and their local environment. Here, we present a computational framework for continuum tissue growth models consisting of stem cells, cell lineages, and diffusive molecules that regulate proliferation and differentiation through feedback. To deal with the moving boundaries of the models in both open geometries and closed geometries (through polar coordinates) in two dimensions, we transform the dynamic domains and governing equations to fixed domains, followed by solving for the transformation functions to track the interface explicitly. Clustering grid points in local regions for better efficiency and accuracy can be achieved by appropriate choices of the transformation. The equations resulting from the incompressibility of the tissue is approximated by high-order finite difference schemes and is solved using the multigrid algorithms. The numerical tests demonstrate an overall spatiotemporal second-order accuracy of the methods and their capability in capturing large deformations of the tissue boundaries. The methods are applied to two biological systems: stratified epithelia for studying the effects of two different types of stem cell niches and the scaling of a morphogen gradient with the size of the Drosophila imaginal wing disc during growth. Direct simulations of both systems suggest that that the computational framework is robust and accurate, and it can incorporate various biological processes critical to stem cell dynamics and tissue growth.