Physical Biology of Tissue Morphogenesis - Mechanics, Metabolism and Signaling

Concentration profiles of signaling molecules, also called morphogens, control patterning and growth of developing tissues. In this regard, the morphogen transport dynamics defines the shape of the morphogen profile, which has been highlighted as a key factor in control mechanisms. We propose a general framework and a novel approach for the study of effective transport dynamics in the formation of graded morphogen concentration profiles in cell monolayer tissues. In particular, we analyse the hydrodynamic modes of a transport model, where we allow molecules to be transported by free diffusion and transcytosis that is a trafficking process in which molecules travel long distances by subsequent rounds of internalization and externalization at different positions in cells. Our theory reveals different transport modes in the system with different effective dynamics. We discuss how seemingly contradictory interpretation of experiments that measure morphogen transport dynamics may capture different dynamical modes in the system. As a particular case of study, we apply our theory to describe the transport of the morphogen Dpp in the Drosophila wing disc.

The transition from an epithelial monolayer to a spheroidal cell aggregate, which is key to tumor formation, is analogous to a dewetting process. In an epithelial cancer cell monolayer in vitro, an increasing E-cadherin expression is paralleled by an increase in myosin-generated contractility, which induces tissue dewetting. We develop an active polar fluid model of the epithelium that predicts that the wetting transition depends on tissue size, which is verified in experiments. Specifically, the critical tissue contractility depends on tissue size, whereas the critical traction force depends only on substrate ligand density. Thus, the active wetting transition may give insight into tissue morphogenesis and tumor progression.

In the Drosophila testis, Hedgehog (Hh) is a key niche signal that operates alongside the previously recognized Jak/Stat pathway in maintaining the somatic stem cell pool. The two niche signalling pathways converge on Zfh-1, the fly homologue of the vertebrate Zeb1/2 transcriptional regulators, that is necessary for somatic stem cell maintenance and proliferation. We have performed a genome wide, in vivo damID screen to identify the relevant Zfh-1 target genes directly within the somatic stem cell pool. We have identified several pathways not previously implicated in niche activity, whose removal or overexpression affects somatic stem cell behaviour. Specifically, Zfh-1 regulates several components of the Hippo/Wts/Yki pathway, a signalling cascade generally associated with promoting cell growth, survival, and proliferation. Importantly, activation of this pathway exclusively impinges on stem cell proliferation without affecting their ability to differentiate. In addition, our list of Zfh-1 target genes also contained multiple enzymes and regulators of the glycolysis and TCA pathways, implying a direct role of the niche signals in establishing a Warburg type stem cell metabolism. Biasing individual cells towards oxidative phosphorylation induced stem cell loss from the niche by differentiation, placing metabolism upstream of stemness in the regulatory logic. At the same time, manipulation of other niche signals, e.g. the cytokine receptor - Jak/Stat or Notch pathways, impinges on different aspects of somatic stem cell behaviour, e.g. blocking differentiation and inducing niche like properties in the affected stem cells. Different aspects of stem cell behaviour can thus be genetically uncoupled at the level of niche signalling input. I will discuss these observations in the context of a modified model of niche function, whereby individual niche signals directly "micromanage" subsets of stem cell behaviour, rather than being integrated into a binary cell fate decision between stemness vs. differentiation.

Pathogenic bacteria have highly contaminated the different fruit. Present in contaminated tomatoes, they are responsible for their contamination. The distinction of these types is a very difficult challenge in the tomato’s industry. It has therefore become necessary to develop methods to inactivate these pathogens in order to ensure the quality of the tomato. Our work is based on that framework with the general objective to study the inactivation of Escherichia coli bacteria species by ultraviolet radiation type C. While studying the effect of different radiation doses on the inactivation of Escherichia coli bacteria, we noticed that the high radiation doses (the radiation source being very close to the bacteria), have an efficient effect on the inactivation. Furthermore, its effectiveness depends on the physical factors. Indeed, it increases proportionally to the increase of the duration of the exposure to these radiations. The presence of radiation in the environment improves the efficiency of the energetic treatment in inactivating pathogenic bacteria E.coli. This study demonstrates the potential of the use of radiation in combination with energy or with its distant source in order to inactivate the highly pathogenic E.coli bacteria.The apparatus used for this purpose has a UV lamp. In fact, the physical characterization of the UV lamp used in the tests demonstrated that the lamp’s output is 254 nm. Moreover, this method allows to remotely process samples for a controlled period of time. Finally, the colonies listing operation after exposure to ultraviolet (UV) radiation type C is performed. UV rays are responsible for the bactericidal action. The different results obtained in our experiment confirm the sensitivity or the effect of the different strains tested for UV radiation. We plan to apply this study to other types of bacteria in order to test the validity of the model used in this work.

Adhesion molecules join cell membranes but also mediate a contractile actomyosin network, which limits contact expansion. Despite their fundamental role in tissue morphogenesis and homeostasis, how adhesion molecules quantitatively control cell shapes and cell patterns in tissues remains unclear. Here we address this question in vivo by using the highly organized Drosophila eye. We show that cone cell shapes depend little on cadherin bonds and mostly on Myosin-II. However, N-cadherin has an indirect control of cone cell shape. At homotypic contacts, junctional N-cadherin bonds downregulate Myosin-II contractility. At heterotypic contacts with E-cadherin, non-junctional N-cadherin induces an asymmetric accumulation of Myosin-II at junctions, which leads to a highly contractile cell interface. Such differential regulation of contractility by N-cadherins is essential for morphogenesis as loss of N-cadherin disrupts cell rearrangements. Our results establish a quantitative link between adhesion and contractility during morphogenesis in vivo, and reveal an unprecedented role of N-cadherin on cell shapes and cell packing.

Dense monolayers of living cells migrate collectively, for example during wound healing and in cancer invasion. They are driven by active forces and invade when free space is available. Here we show that this motion occurs in bursts similar to the ones observed in other driven systems, such as the propagation of cracks, fluid fronts in porous media, and ferromagnetic domain walls [1]. In analogy with these systems, the distribution of activity bursts displays scaling laws that are universal in different cell types and for cells moving on different substrates. This main feature of the dynamics is captured by a model of interacting active particles moving through disordered landscape. Our results demonstrate that living systems display universal nonequilibrium critical fluctuations, that are usually associated with externally driven inanimate media. 1. O. Chepizhko, C. Giampietro, E. Mastrapasqua, M. Nourazar, M. Ascagni, M. Sugni, U. Fascio, L. Leggio, C. Malinverno, G. Scita, S. Santucci, M. J. Alava, S. Zapperi, and C. A. M. La Porta, PNAS 2016; published ahead of print September 28, 2016, doi:10.1073/pnas.1600503113

To date, much research has focused on how tissues build and repair themselves, as well as how their integrity is maintained. Yet, despite the large variety of stresses they experience along adult life and development, very little is known about how living tissues resist to cracking and what the mechanical and biological conditions leading to their rupture are. Here I will present an analysis of fracture tests performed on suspended epithelial monolayers. These monolayers are devoid of extra-cellular matrix and are a minimal model representative of many epithelia involved in early development. In our setup, monolayers are cultured between two flexible rods which allow the monolayer to be stretched in a controlled manner on the one hand, and stress in the material to be monitored on the other hand. Force-clamp experiments have been performed showing that the monolayer flows according to a power-law of time before cell-cell detachments occur. The transition time between those two phases is shown to be dependent on the applied stress. We also show that a chemically-induced increase in endogenous stress can lead to monolayer fracture through cell contraction. The stress at which monolayer failure occurs is found to be about twice the prestress internally generated in control conditions. Altogether it appears that the cell cytoskeleton can play a dual role in epithelium fracture : it can dissipate stress by allowing the tissue to flow under exogenous stress, but fragilize it by exerting high-level of tension within junctions.

Tissue spreading is fundamental to many developmental and disease-related processes, such as gastrulation and wound healing. Radial cell intercalations are commonly thought to mediate tissue spreading by simultaneously narrowing the tissue along its height (radial extend) and expanding it along its plane. Yet, whether radial cell intercalations drive tissue spreading or represent the response of the tissue to exogenous spreading forces remains unclear. In this talk, we use a combination of theory and experiments to dissect the fundamental force-generating processes underlying the initial spreading of the blastoderm over the yolk cell at early zebrafish gastrulation, an exemplary case of tissue spreading involving radial cell intercalations. Unexpectedly, we found that active radial cell intercalations are dispensable for blastoderm spreading per se and that, instead, this process is driven by epithelial surface cells autonomously reducing their surface tension and thus actively expanding. This work was done in tight collaboration with C.-P. Heisenberg's Lab at IST Austria. Most of the experiments here discussed were performed by Dr. Hitoshi Morita (IST Austria).

Coherent angular motion of cell collectives plays a vital role in many physiological processes including tissue morphogenesis and glandular formation. Various studies have established the inevitable role of confinement in setting up rotational mode of migration of cells. In the present study, we examine the implications of various confining conditions on built up of coherent motion of cells. As any perturbation of coherent rotation leads to the interruption of the related activities, we also investigate the effects of different perturbations on coherently rotating cells. A self-propelled particle based model is used, wherein each cell is assumed as motile particle and interacts with neighboring cells via harmonic forces. Using this model, we show that cells, when confined in circular geometry, exhibit coherent motion with cell density, cell-cell adhesion stiffness and size of the tissue dictating the pattern of the motion. Further we also show that even motile cells confined inside a passive tissue of non-motile cells are capable of exhibiting coherent rotation. In this case, depending upon the properties of external tissue cells, motile cells exhibit different migratory patterns, which suggest that it is not necessary to have a geometric confinement for built up of coherence. In the later part of the study, where the effect of various perturbations are examined, we show that synchronous division of cells can change the direction of coherent rotation of cells. Finally when the confinement is removed, cells are shown to migrate in different pattern depending up on the stiffness of cell- cell connection.

An outstanding challenge in biology is to understand how stem cells self-organize into the diverse organs that compose our body. We have yet to obtain a mechanistic explanation to how the interplay of cell proliferation, communication and differentiation result in an organ of correct size, cell type composition, and architecture. This has been, in part, due to the lack of an accessible model system, in which we can manipulate living cells at the genetic level and simultaneously tune the external environment to observe their effects at the tissue scale. The neural tube is a fundamental organ for neural development, giving rise to our entire nervous system including the brain and the spinal cord. We have recently established an in vitro organ reconstitution approach to study neural tube formation. Single mouse embryonic stem cells are encapsulated in a 3D hydrogel environment and directed to neural differentiation. Cells proliferate, interact with each other and form a pseudo-stratified neuroepithelium enclosing a fluid filled lumen. By Day 7, some cells start to differentiate into post-mitotic neurons. By fine-tuning the properties of synthetic hydrogels, we are studying how the elasticity of the 3D environment influences the size and patterns of neurogenesis in neural tube organoids.

During the development of the medulla, one of the ganglia in the fly visual system, neuroepithelial cells undergo a transition to neural stem cells (neuroblasts). This transition proceeds sequentially from one end of the tissue to the other—a process termed the proneural wave. This sequential transition is important to generate a population of cells of different developmental ages which is crucial for further differentiation. However, the mechanism behind the propagation of this wave is still unknown. Here, we investigate the biochemical basis of proneural wave progression and invoke a reaction-diffusion model describing the interplay of proneural genes, EGF signalling, and Delta-Notch signalling. We show that diffusion, self-activation and differentiation are sufficient to explain the emergence of a travelling transition zone through the tissue. Predictions of our model on perturbations of the proneural wave caused by mutant clones are currently being tested in experiments.

During embryonic development the embryo subdivides into various compartments that eventually grow into different tissues and organs. Each compartment is delimited by a boundary that prevents adjacent cell populations from intermixing. Further, cells at the boundaries act as an organizer by secreting essential factors necessary for proper patterning and growth of the tissue. The midbrain-hindbrain boundary (MHB) is such an organizer that prevents the intermingling of prospective midbrain and hindbrain cells and secretes factors like fibroblast growth factor 8 (Fgf8). However, the molecular mechanism(s) that regulate cell sorting at the MHB are poorly understood. Using a combination of biophysical tools such as atomic force microscopy and transgenic and/or mutant zebrafish to specifically identify and track cells involved in MHB formation, we aim to directly visualize and measure the mechanical forces involved in cell sorting at the MHB and use this data to model and better understand the process of boundary formation.

We plan to describe 3D deformations of epithelial sheets via mechanics-based mathematical (variational) models. This requires a good understanding of how forces in sheets interact with their geometry. To do this we follow a variationsl approach based on mechanical energies.

We model the wing disc tissue as a viscoelastic body using the cell-based simulation environment LBIBCell (Tanaka et al. 2015) to investigate the implications of mechanical stimuli and mechanical feedback on growth.

Cell metabolism has emerged as a major determinant of cell proliferation and cell fate choice, but the functional significance of metabolic regulation during tissue growth and differentiation as well as the signals regulating the metabolic state of stem cells during animal development are mostly unclear. Here, I present data showing how blood vessel formation in the developing cerebral cortex synchronizes metabolic regulation and neural stem cell differentiation to balance neural stem cell expansion and neuron formation to safeguard brain morphogenesis. We find that ingrowth of blood vessels reliefs the physiological hypoxia in the early developing cerebral cortex, induces degradation of the hypoxia-inducible transcription factor HIF-1alpha and downregulates glycolytic genes in close spatio-temporal correlation with the onset of neural stem cell differentiation. Using a mutant mouse model to prevent vessel formation in the cortex in a vessel-autonomous manner, we show that relief of hypoxia and HIF-1a degradation are required to allow the switch from neural stem cell expansion towards differentiation and neurogenesis. Conversely, we show that HIF-1α stabilization is sufficient to prevent neural stem cell differentiation and that maintaining a high glycolytic activity in neural stem cells is required for this effect. In summary, we identify a novel regulation of neural stem cells in the developing brain by blood vessels and exemplify how changing oxygenation as a chemical property of the stem cell niche can control cell fate by regulating cell metabolism.

Epithelial tissues are under constant mechanical stress. To adapt to applied forces, cells and tissues use a variety of mechanisms, such as cell fusion, cell intercalation or extrusion. A major process that is influenced by mechanical forces and by which tissues respond to the applied stress is oriented cell division. Precise orientation of division is crucial for high fidelity of chromosome segregation, cell fate, tissue organisation and morphogenesis. Therefore, understanding the mechanics of dividing cells and orientation of divisions remains an important problem in cell biology. Here, we use suspended epithelial monolayers to study mechanical changes that occur during mitosis and the conditions that determine cell division orientation in tissues under stress. Our aim is to identify molecular mechanisms involved in force transmission and orientation of the spindle by perturbing key molecular players: cortical regulators and astral microtubules.

Drosophila gastrulation involves large scaled constriction events driven by actomyosin dynamics. These constrictions occur in pulses synchronized with the pulsatile clustering and declustering of actin and myosin in the cortices of contracting cells. Through Brownian dynamics simulations, we determine the phase map of the mechanical state of cytoskeletal networks, which marks the transition between homogeneous and clustered actomyosin networks as a function of basic cytoskeletal components. Our results demonstrate that myosin motor activity and actin turnover kinetics are key drivers of this phase transition, and pulsing across phase transition enables large force generation over prolonged periods, required for the completion of tissue constriction during gastrulation. Disrupting myosin activity or actin turnover dynamics can inhibit pulsatile phase transition and diminish contractile forces over time, consistent with experimental data in vivo.

In epithelial tissues, the regulation of mitotic spindle orientation by cell shape and mechanical strain profoundly affects proliferation, morphogenesis and layering. Yet, the mechanisms ensuring shape and strain orientation sensing in tissue are largely unknown. We find that in Drosophila epithelia, microtubule pulling forces reside at the tricellular junctions (TCJ) where at least three cells meet. The TCJ distribution thereby produces a torque orienting the spindle. Moreover, as cells rounded up during mitosis, TCJ serve as landmarks encoding the information on interphase cell shape and tissue strain anisotropies needed for spindle orientation. While TCJ have been mainly viewed as core epithelial barrier structures, we propose that they also define a class of polarity cues participating in geometry and mechanical sensing in epithelial tissues.

In this work, we developed a 2D numerical vertex model (based on the work of Farhadifar et al, [1]) to simulate cell monolayers, in particular epithelium. The model takes into account the mechanical properties of cells, their proliferation and signaling, and the external mechanical constraints applied on the tissue. This model was used to study how the cell biophysics affects the mechanical response of tissues to stretching, and inversely how tissue stretching may affect the mechanical properties of cells [2]. We simulated tissue stretching and calibrated the parameter of our model using the experimental stress-strain results published by Harris et al. [3]. We observed that the model parameters must vary with the tissue strain to be in agreement with the experiments. In particular, it was found that, while the perimeter contractility

We derive the constitutive relations of an active polar gel from the nonequilibrium dynamics of its elastic linker molecules. The molecular kinetics drives a fluidization process that gives rise to Maxwell viscoelasticity and, provided that detailed balance is broken, to the generation of active stresses. We predict an active thinning phenomenon of kinetic origin, regardless of the extensile/contractile nature of the material, which could explain some experimental results.

Neisseria gonorrhoeae is the causative agent of gonorrhea, one of the most common sexually transmitted diseases worldwide. A fundamental step during the infection process is the pili-mediated formation of so called microcolonies, agglomerates of up to thousands of cells. Type IV pili are µm-long polymers that emerge out of the cell membrane and are able to create attractive cell-cell and cell-substrate forces by a mechanism reminiscent of a grappling hook. While the role of pili during the motility of single cells over a surface is well understood, a clear understanding of how they drive the formation of colonies is missing. I will present a simulation model of individual cells interacting via pili. This tool allows us to quantify pili mediated dynamics on different length scales: from the motion of single cells over a surface, the dynamics of individual cells inside of individual colonies, up to the self-organized assembly of thousands of cells.

The adult wing of the fruit fly Drosophila develops in the larvae from an imaginal disk which consists of two layers of epithelial tissue. During development, this wing imaginal disk is highly dynamic. It grows and changes its shape and the polygonal network of cell packings undergoes topological changes as cells undergo divisions, extrusions and neighbor exchenges. We are focussing on the wing pouch region of the imaginal disk from which the adult wing blade forms. Cells in the wing pouch show a radially symmetric pattern of cell elongation with a center located close to the intersection of the dorsal-ventral and the anterio-posterior compartment boundaries. Peripheral cells have larger apical area and are more elongated tangentally than central ones. How does this elongation pattern emerge and how is it related to mechanical forces acting in the wing pouch tissue? To answer these questions we observe third instar larval wing disks in culture where they grow for over 12 hours. Imaging the tissue at cellular resolution allows us to track individual cells in time and space and to identify different cellular processes. We calculate the contributions of divisions, extrusions and neighbor exchanges to overall tissue shape changes. Furthermore, we use a hydrodynamic theory that relates tissue stresses to tissue deformations and cell shape changes [Etournay et al. eLife e07090; Etournay et al. eLife e14334; Merkel et al., arXiv:1607.00357; Popovic et al., arXiv:1607.03304]. We find that cell neighbor exchanges contribute to shear in along an axis that is per- pendicular to local cell elongation and actively increase this cell elongation. We recently reported such active cell rearrangements during the pupal wing development but their role in morphogenesis remains unclear. To determine interplay between cell rearrangement, proliferation, and the mechanical stresses we solve hydrodynamic equations for a radially symmetric tissue.

In this work, a coupling scheme based on Nonlinear Open Loop Controllers, between two non-identical coupled Hindmarsh–Rose neuron models is investigated. In more details the case of bidirectional coupling is chosen, which are designed for achieving interesting types of synchronization, such as the complete synchronization and anti-synchronization. Even when the neurons are in different behavior (chaos, periodic behavior) it presents synchronization phenomena. The stability of the proposed method is ensured by using the Lyapunov function stability theory. Simulation results verified that the proposed coupling scheme drives the system either to complete synchronization or anti-synchronization depending on the choice of the signs of the error function’s parameters.

Self-organization is a fundamental strategy in nature. In {\it E. coli} bacteria, for example, self-organized pole-to-pole oscillations of the Min proteins have an important function within the cell division machinery. Such pole-to-pole oscillations in living cells behave like standing waves (SW) in very small (confined) systems. In extended in vitro experiments, Min oscillations develop into nonlinear traveling waves (TW). TW patterns are also known from many other nonequilibrium systems. But is the transition from traveling waves in extended to standing waves in strongly confined systems a specific property of the Min oscillation pattern? Or is it a generic and robust universal principle of all nonlinear traveling waves that just also applies to the Min oscillations in cells? We address this central question by imposing strong spatial confinement to a generic model for nonlinear traveling waves. Using simulations, analytical and symmetry considerations, we conclude that traveling waves inevitably change into standing waves in sufficiently small confined systems. This transition to standing waves, corresponding to pole-to-pole oscillations, is confirmed for a model for Min protein patterns and a model for a chemical reaction. Both examples underline the universality and robustness of the TW/SW transition in small systems and its independence from the specific details of a single system. Interestingly, experiments with growing E. coli bacteria show that a pole-to-pole oscillation with one or two nodes can adapt to a wide range of cell lengths. We show that this multistability and adabtability of a standing wave to different system lengths is part of the syntax of nonlinear standing waves in general. By exploiting their syntax further, we also predict a coexistence between standing waves with different numbers of nodes over a certain length regime. These examples highlight the importance of universal principles from pattern formation theory as a robust tool for (cellular) self-organization.

We study the dynamics of a thick permeating epithelial tissue which pumps interstitial fluid. We consider the average cell polarity inside the tissue to be normal to the tissue layer. The cells pump fluid against a pressure difference. Using a two-component hydrodynamic continuum theory, we study the dependence of tissue stress, cell velocity and fluid flow on the the external fluid pressure and the cell pumping activity. We find that the existence of steady states depend strongly on the external pressure difference, the pumping activity and the properties of the interface seperating the tissue from the surrounding fluid.

Tissue cells typically exhibit an anisotropic distribution of membrane proteins that characterizes a structural polarity of the cell. This cell polarity is linked to function, such as directed transport. In cellular monolayers and various epithelial tissues, cells are known to exhibit a vectorial cell polarity with distinct domains of apical and basal membrane proteins at opposite sides of the cell that face the two boundary surfaces of the flat tissue. Here, we analyze cell polarity in a bulk tissue, namely the mouse liver. We propose a concept of nematic cell polarity to describe the distinct cell polarity of hepatocyte liver cells. Analyzing high-resolution two-photon microscopy images of mouse liver, we find spatial patterns of aligned cell polarity axes at the tissue scale. These spatial patterns characterize liver tissue as a biological nematic liquid crystal. Spatial patterns are well-accounted for by a curvilinear reference system set by structural landmarks of large veins within the liver tissue. We discuss minimal mechanisms of cell-scale interactions that can account for the emergence of tissue-scale patterns.

Epithelial sheets consist of interconnected polarized cells. The epithelia serve as barriers to protect underlying tissues and undergo folding to form organ structures. While numerous molecular machineries have been identified for epithelial folding, the mechanical mechanisms underlying cell deformation and tissue bending still remain unclear. Based on a vertex model, we systematically analyze the change of cell shape and tissue morphology due to the modulation of each cell surfaces. In particular, we find that the differential basal and lateral mechanics within the sheets can initiate folding, producing morphology distinct from those induced by apical constriction. This suggests that besides the canonical mode of apical remodeling, the mechanical modulation at the basal and lateral surfaces also play crucial roles in epithelial morphogenesis.

Our research aims to reveal how body plan patterns scale with organism size during growth and regeneration using flatworms as a model system. By developing minimal theoretical models that capture the basic features of our system, we derive underlying guiding principles, which allow us to make testable predictions for experiments. Here, we present a framework for the scaling of self-organized patterns as observed in flatworms. Biological patterns and morphologies, generated during development and regeneration, often scale with organism size. Flatworms mastered the art of scaling, being able to reversibly change their size over a 40-fold range in length, depending on feeding conditions. Even more remarkable, a small amputation fragment can re-pattern itself into a miniature version of the original worm. This robust regeneration from almost arbitrary initial conditions and the ability to rescale its body plan requires self-organized patterning mechanisms, which must function reliably independent of worm size. Here, we report a minimal mathematical model implicating both self-organized and self-scaling pattern formation. The mechanism augments Turing's classical theory of self-organized, yet non-scaling patterns, to result in patterns that scale with system size. A feedback loop involving diffusing expander molecules regulates the reaction rates of the Turing system, thereby adjusting pattern length scales proportional to system size. Our theory makes specific experimental predictions and we are closely collaborating with the experimental lab of Jochen Rink at the MPI CBG (Dresden), to test the theoretical framework in flatworms. S. Werner et al. Phys. Rev. Lett. 114, 138101, 2015

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.