Morphoelastic models discriminate between different mechanisms of left-right asymmetric stomach morphogenesis.

The mechanisms by which the vertebrate stomach undergoes its evolutionarily conserved leftward bending remain incompletely understood. Although the left and right sides of the organ are known to possess different gene expression patterns and undergo distinct morphogenetic events, the physical mechanisms by which these differences generate morphological asymmetry remain unclear. Here, we develop a continuum model of asymmetric stomach morphogenesis. Using a morphoelastic framework, we investigate the morphogenetic implications of a variety of hypothetical, tissue-level growth differences between the left and right sides of a simplified tubular organ. Simulations reveal that, of the various differential growth mechanisms tested, only one category is consistent with the leftward stomach curvature observed in wild-type embryos: equal left and right volumetric growth rates, coupled with transversely isotropic tissue thinning on the left side. Simulating this mechanism in a defined region of the model over a longer period of growth leads to mature stomach-like curvatures.

Flexural rigidity of pressurized model notochords in regular packing patterns.

The biomechanics of embryonic notochords are studied using an elastic membrane model. An initial study varying internal pressure and stiffness ratio determines tension and geometric ratios as a function of internal pressure, membrane stiffness ratio, and cell packing pattern. A subsequent three-point bending study determines flexural rigidity as a function of internal pressure, configuration, and orientation. Flexural rigidity is found to be independent of membrane stiffness ratio. Controlling for number and volume of cells and their internal pressure, the eccentric staircase pattern of cell packing has more than double the flexural rigidity of the radially symmetric bamboo pattern. Moreover, the eccentric staircase pattern is found to be more than twice as stiff in lateral bending than in dorsoventral bending. This suggests a mechanical advantage to the eccentric WT staircase pattern of the embryonic notochord, over patterns with round cross-section.

Physical models of notochord cell packing reveal how tension ratios determine morphometry.

The physical and geometric aspects of notochords are investigated using a model of finite-length notochords, with interior vacuolated cells arranged in two common packing configurations, and sheath modeled as homogeneous and thin. The key ratios governing packing patterns and eccentricity are number of cells per unit length λ and cell tension ratio Γ. By analyzing simulations that vary Γ and total number of cells N, we find that eccentricity, λ, and internal pressure approach consistent asymptotic values away from the tapering ends, as N increases. The length of the tapering ends is quantified as a function of Γ and pattern. Formulas are derived for geometric ratios, pressure, and energy as functions of Γ and pattern. These observations on the relationship between mechanics, geometry, and pattern provide a framework for further work which may provide insight into the roles of mechanosensing and pressure-volume regulation in the notochord.

Bubble packing, eccentricity, and notochord development.

This paper develops a theoretical basis for the observed relationship between cell arrangements in notochords and analog physical models, and the eccentricity of their cross sections. Three models are developed and analyzed, of the mechanics of cell packing in sheaths. The key ratios governing the packing patterns and eccentricity are cells per unit length λ, tension ratio Γ, and eccentricity e. For flexible and semi-flexible sheaths, the optimal packing pattern shifts from "bamboo", with a symmetric cross section, to "staircase", with an eccentric cross section, at a critical value λ = 1.13. In rigid tubes, this threshold is lowered as imposed eccentricity is increased. Patterns can be observed which are not optimal; pattern transitions may occur below or above the critical λ values. The eccentricity of staircase patterns in flexible and semi-flexible tubes is found to be dependent on the tension ratio Γ, increasing as sheath tension decreases relative to interior cell tension. A novel "serpentine" packing pattern appears for low Γ near the critical λ. The developmental utility of enforcing notochord eccentricity is discussed, as well as potential mechanisms for such control.

Does viral load alter behavior of the bee parasite Varroa destructor?

The invasive mite Varroa destructor has negatively impacted global apiculture, by being a vector for many viruses of the honey bee (Apis mellifera). Until now, most studies have been limited to varroa-honey bee or virus-honey bee interactions. The aim of this study is to bridge the important research gap of varroa-virus interactions by correlating varroa behavior with viral load. Ten-minute video recordings of 200 varroa mites were analyzed, and average speeds of the mites were compared to individual qPCR viral loads for deformed wing virus (DWV) and sacbrood virus (SBV). Statistically significant models reveal that colony, DWV, and SBV all might play a role in mite behavior, suggesting that the varroa-virus interaction needs to be an integral part of future studies on honey bee pathogens.

Tissue self-organization underlies morphogenesis of the notochord.

The notochord is a conserved axial structure that in vertebrates serves as a hydrostatic scaffold for embryonic axis elongation and, later on, for proper spine assembly. It consists of a core of large fluid-filled vacuolated cells surrounded by an epithelial sheath that is encased in extracellular matrix. During morphogenesis, the vacuolated cells inflate their vacuole and arrange in a stereotypical staircase pattern. We investigated the origin of this pattern and found that it can be achieved purely by simple physical principles. We are able to model the arrangement of vacuolated cells within the zebrafish notochord using a physical model composed of silicone tubes and water-absorbing polymer beads. The biological structure and the physical model can be accurately described by the theory developed for the packing of spheres and foams in cylinders. Our experiments with physical models and numerical simulations generated several predictions on key features of notochord organization that we documented and tested experimentally in zebrafish. Altogether, our data reveal that the organization of the vertebrate notochord is governed by the density of the osmotically swelling vacuolated cells and the aspect ratio of the notochord rod. We therefore conclude that self-organization underlies morphogenesis of the vertebrate notochord.This article is part of the Theo Murphy meeting issue on 'Mechanics of development'.

Tissue geometry may govern lung branching mode selection.

Lung branching morphogenesis proceeds in three stereotyped modes (domain, planar, and orthogonal branching). Much is known about the molecular players, including growth factors such as fibroblast growth factor 10 but it is unknown how these signals could actuate the different branching patterns. With the aim of identifying mechanisms that may determine the different branching modes, we developed a computational model of the epithelial lung bud and its surrounding mesenchyme. We studied transport of morphogens and localization of morphogen flux at lobe surfaces and lobe edges. We find that a single simple mechanism is theoretically capable of directing an epithelial tubule to elongate, bend, flatten, or bifurcate, depending solely on geometric ratios of the tissues in the vicinity of a growing tubule tip. Furthermore, the same simple mechanism is capable of generating orthogonal or planar branching, depending only on the same geometric ratios.

Quantifying cellular and subcellular stretches in embryonic lung epithelia under peristalsis: where to look for mechanosensing.

Peristalsis begins in the lung as soon as the smooth muscle (SM) forms, and persists until birth. As the prenatal lung is filled with liquid, SM action can, through lumen pressure, deform tissues far from the immediately adjacent tissues. Stretching of embryonic tissues has been shown to have potent morphogenetic effects. We hypothesize that these effects are at work in lung morphogenesis. In order to refine that broad hypothesis in a quantitative framework, we geometrically analyse cell shapes in an epithelial tissue, and individual cell deformations resulting from peristaltic waves that completely occlude the airway. Typical distortions can be very large, with opposite orientations in the stalk and tip regions. Apical distortions are always greater than basal distortions. We give a quantitative estimate of the relationship between length of occluded airway and the resulting tissue stretch in the distal tip. We refine our analysis of cell stresses and strains from peristalsis with a simple mechanical model of deformation of cells within an epithelium, which accounts for basic subcellular geometry and material properties. The model identifies likely stress concentrations near the nucleus and at the apical cell-cell junction. The surprisingly large strains of airway peristalsis may serve to rearrange cells and stimulate other mechanosensitive processes by repeatedly aligning cytoskeletal components and/or breaking and reforming lateral cell-cell adhesions. Stress concentrations between nuclei of adjacent cells may serve as a mechanical control mechanism guiding the alignment of nuclei as an epithelium matures.

Morphogenetic Implications of Peristalsis-Driven Fluid Flow in the Embryonic Lung.

Epithelial organs are almost universally secretory. The lung secretes mucus of extremely variable consistency. In the early prenatal period, the secretions are of largely unknown composition, consistency, and flow rates. In addition to net outflow from secretion, the embryonic lung exhibits transient reversing flows from peristalsis. Airway peristalsis (AP) begins as soon as the smooth muscle forms, and persists until birth. Since the prenatal lung is liquid-filled, smooth muscle action can transport fluid far from the immediately adjacent tissues. The sensation of internal fluid flows has been shown to have potent morphogenetic effects, as has the transport of morphogens. We hypothesize that these effects play an important role in lung morphogenesis. To test these hypotheses in a quantitative framework, we analyzed the fluid-structure interactions between embryonic tissues and lumen fluid resulting from peristaltic waves that partially occlude the airway. We found that if the airway is closed, fluid transport is minimal; by contrast, if the trachea is open, shear rates can be very high, particularly at the stenosis. We performed a parametric analysis of flow characteristics' dependence on tissue stiffnesses, smooth muscle force, geometry, and fluid viscosity, and found that most of these relationships are governed by simple ratios. We measured the viscosity of prenatal lung fluid with passive bead microrheology. This paper reports the first measurements of the viscosity of embryonic lung lumen fluid. In the range tested, lumen fluid can be considered Newtonian, with a viscosity of 0.016 ± 0.008 Pa-s. We analyzed the interaction between the internal flows and diffusion and conclude that AP has a strong effect on flow sensing away from the tip and on transport of morphogens. These effects may be the intermediate mechanisms for the enhancement of branching seen in occluded embryonic lungs.

Morphogenetic implications of peristaltic fluid-tissue dynamics in the embryonic lung.

Peristalsis begins in the lung as soon as the smooth muscle forms, and persists until birth. Since the prenatal lung is liquid-filled, smooth muscle action can deform tissues and transport fluid far from the immediately adjacent tissues. Stretching of embryonic tissues and sensation of internal fluid flows have been shown to have potent morphogenetic effects. We hypothesize that these effects are at work in lung morphogenesis. To place that hypothesis in a quantitative framework, we analyze a model of the fluid-structure interactions between embryonic tissues and lumen fluid resulting from peristaltic waves that partially occlude the airway. We find that if the airway is closed, deformations are synchronized; by contrast, if the trachea is open, maximal occlusion precedes maximal pressure. We perform a parametric analysis of how occlusion, stretch, and flow depend on tissue stiffnesses, smooth muscle force, tissue shape and size, and fluid viscosity. We find that most of these relationships are governed by simple ratios.

Quantifying stretch and secretion in the embryonic lung: Implications for morphogenesis.

Branching in the embryonic lung is controlled by a variety of morphogens. Mechanics is also believed to play a significant role in lung branching. The relative roles and interactions of these two broad factors are challenging to determine. We considered three hypotheses for explaining why tracheal occlusion triples branching with no overall increase in size. Both hypotheses are based on tracheal occlusion blocking the exit of secretions. (H1) Increased lumen pressure stretches tissues; stretch receptors at shoulders of growing tips increase local rate of branching. (H2) Blocking exit of secretions blocks advective transport of morphogens, leading to (H2a) increased overall concentration of morphogens or (H2b) increased flux of morphogens at specific locations. We constructed and analyzed computational models of tissue stretch and solute transport in a 3D lung geometry. Observed tissue stresses and stretches were predominantly in locations unrelated to subsequent branch locations, suggesting that tissue stretch (H1) is not the mechanism of enhancement of branching. Morphogen concentration in the mesenchyme (H2a) increased with tracheal occlusion, consistent with previously reported results. Morphogen flux at the epithelial surface (H2b) completely changed its distribution pattern when the trachea was occluded, tripling the number of locations at which it was elevated. Our results are consistent with the hypothesis that tracheal occlusion blocks outflow of secretions, leading to a higher number of high-flux locations at branching tips, in turn leading to a large increase in number of branching locations.

AN AUGMENTED IMMERSED INTERFACE METHOD FOR MOVING STRUCTURES WITH MASS.

We present an augmented immersed interface method for simulating the dynamics of a deformable structure with mass in an incompressible fluid. The fluid is modeled by the Navier-Stokes equations in two dimensions. The acceleration of the structure due to mass is coupled with the flow velocity and the pressure. The surface tension of the structure is assumed to be a constant for simplicity. In our method, we treat the unknown acceleration as the only augmented variable so that the augmented immersed interface method can be applied. We use a modified projection method that can enforce the pressure jump conditions corresponding to the unknown acceleration. The acceleration must match the flow acceleration along the interface. The proposed augmented method is tested against an exact solution with a stationary interface. It shows that the augmented method has a second order of convergence in space. The dynamics of a deformable circular structure with mass is also investigated. It shows that the fluid-structure system has bi-stability: a stationary state for a smaller Reynolds number and an oscillatory state for a larger Reynolds number. The observation agrees with those in the literature.

Mechanical control of spheroid growth: distinct morphogenetic regimes.

We develop a model of transport and growth in epithelio-mesenchymal interactions. Analysis of the growth of an avascular solid spheroid inside a passive mesenchyme or gel shows that sustained volumetric growth requires four generic mechanisms: (1) growth factor, (2) protease, (3) control of cellularity, and (4) swelling. The model reveals a bifurcation delineating two distinct morphogenetic regimes: (A) steady growth, (B) growth arrested by capsule formation in the mesenchyme. In both morphogenetic regimes, growth velocity is constant unless and until a complete capsule forms. Comprehensive exploration of the large parameter space reveals that the bifurcation is determined by just two ratios representing the relative strengths of growth and proteolytic activity. Growth velocity is determined only by the ratio governing growth, independent of proteolytic activity. There is a continuum of interior versus surface growth, with fastest growth at the surface. The model provides a theoretical basis for explaining observations of growth arrest despite proteolysis of surrounding tissue, and gives a quantitative framework for the design and interpretation of experiments involving spheroids, and tissues which are locally equivalent to spheroids.

Regulation of hepatic stem/progenitor phenotype by microenvironment stiffness in hydrogel models of the human liver stem cell niche.

Human livers have maturational lineages of cells within liver acini, beginning periportally in stem cell niches, the canals of Hering, and ending in polyploid hepatocytes pericentrally and cholangiocytes in bile ducts. Hepatic stem cells (hHpSCs) in vivo are partnered with mesenchymal precursors to endothelia (angioblasts) and stellate cells, and reside in regulated microenvironments, stem cell niches, containing hyaluronans (HA). The in vivo hHpSC niche is modeled in vitro by growing hHpSC in two-dimensional (2D) cultures on plastic. We investigated effects of 3D microenvironments, mimicking the liver's stem cell niche, on these hHpSCs by embedding them in HA-based hydrogels prepared with Kubota's Medium (KM), a serum-free medium tailored for endodermal stem/progenitors. The KM-HA hydrogels mimicked the niches, matched diffusivity of culture medium, exhibited shear thinning and perfect elasticity under mechanical loading, and had predictable stiffness depending on their chemistry. KM-HA hydrogels, which supported cell attachment, survival and expansion of hHpSC colonies, induced transition of hHpSC colonies towards stable heterogeneous populations of hepatic progenitors depending on KM-HA hydrogel stiffness, as shown by both their gene and protein expression profile. These acquired phenotypes did not show morphological evidence of fibrotic responses. In conclusion, this study shows that the mechanical properties of the microenvironment can regulate differentiation in endodermal stem cell populations.

Lung organogenesis.

Developmental lung biology is a field that has the potential for significant human impact: lung disease at the extremes of age continues to cause major morbidity and mortality worldwide. Understanding how the lung develops holds the promise that investigators can use this knowledge to aid lung repair and regeneration. In the decade since the "molecular embryology" of the lung was first comprehensively reviewed, new challenges have emerged-and it is on these that we focus the current review. Firstly, there is a critical need to understand the progenitor cell biology of the lung in order to exploit the potential of stem cells for the treatment of lung disease. Secondly, the current familiar descriptions of lung morphogenesis governed by growth and transcription factors need to be elaborated upon with the reinclusion and reconsideration of other factors, such as mechanics, in lung growth. Thirdly, efforts to parse the finer detail of lung bud signaling may need to be combined with broader consideration of overarching mechanisms that may be therapeutically easier to target: in this arena, we advance the proposal that looking at the lung in general (and branching in particular) in terms of clocks may yield unexpected benefits.

Convergent extension by intercalation without mediolaterally fixed cell motion.

We construct and implement a stochastic model of convergent extension, using a minimal set of assumptions on cell behavior. In addition to the basic assumptions of volume conservation, random cell motion, and cell-cell and cell-ECM adhesion, and a non-standard assumption that cytoskeletal polymerization generates an internal pressure tending to keep cells convex, we find that we need only two conditions for convergent extension. (1) Each cell type has a particular aspect ratio towards which it regulates its geometry. We do not require that cells align in a specific orientation, e.g. to be oriented mediolaterally. (2) The elongating tissue is composed of cells that prefer to be elongated, and these cells must be accompanied by cells which prefer to be round. The latter effectively provide a boundary to capture. In simulations, our model tissue extends and converges to a stacked arrangement of elongated cells one cell wide, an arrangement which is seen in ascidian notochords, but which has not been observed in other models. This arrangement is achieved without any direct mediolateral bias other than that which is provided by the physical edge of the adjacent tissue.

Mechanics of mesenchymal contribution to clefting force in branching morphogenesis.

Branching morphogenesis is ubiquitous and may involve several different mechanisms. Glandular morphogenesis is affected by growth, cell rearrangements, changes in the basal lamina, changes in the stromal ECM, changes in cell-cell and cell-ECM adhesions, mesenchymal contractility, and possibly other mechanisms. We have developed a 3D model of the mechanics of clefting, focusing in this paper solely on the potential role of mesenchyme-generated traction forces. The tissue mechanics are assumed to be those of fluids, and the hypothesized traction forces are modeled as advected by the deformations which they generate. We find that mesenchymal traction forces are sufficient to generate a cleft of the correct size and morphology, in the correct time frame. We find that viscosity of the tissues affects the time course of morphogenesis, and also affects the resulting form of the organ. Morphology is also strongly dependent on the initial distribution of contractility. We suggest an in vitro method of examining the role of mesenchyme in branching morphogenesis.

Branched organs: mechanics of morphogenesis by multiple mechanisms.

Branching morphogenesis is ubiquitous and important in creating bulk transport systems. Branched ducts can be generated by several different mechanisms including growth, cell rearrangements, contractility, adhesion changes, and other mechanisms. We have developed several models of the mechanics of cleft formation, which we review. We discuss the implications of several candidate mechanisms and review what has been found in models and in experiments.

Semi-mechanistic partial buffer approach to modeling pH, the buffer properties, and the distribution of ionic species in complex solutions.

In many biological science and food processing applications, it is very important to control or modify pH. However, the complex, unknown composition of biological media and foods often limits the utility of purely theoretical approaches to modeling pH and calculating the distributions of ionizable species. This paper provides general formulas and efficient algorithms for predicting the pH, titration, ionic species concentrations, buffer capacity, and ionic strength of buffer solutions containing both defined and undefined components. A flexible, semi-mechanistic, partial buffering (SMPB) approach is presented that uses local polynomial regression to model the buffering influence of complex or undefined components in a solution, while identified components of known concentration are modeled using expressions based on extensions of the standard acid-base theory. The SMPB method is implemented in a freeware package, (pH)Tools, for use with Matlab. We validated the predictive accuracy of these methods by using strong acid titrations of cucumber slurries to predict the amount of a weak acid required to adjust pH to selected target values.

Enhanced growth of tumors in SPARC null mice is associated with changes in the ECM.

SPARC, a 32-kDa glycoprotein, participates in the regulation of morphogenesis and cellular differentiation through its modulation of cell-matrix interactions. Major functions defined for SPARC in vitro are de-adhesion and antiproliferation. In vivo, SPARC is restricted in its expression to remodeling tissues, including pathologies such as cancer. However, the function of endogenous SPARC in tumor growth and progression is not known. Here, we report that implanted tumors grew more rapidly in mice lacking SPARC. We observed that tumors grown in SPARC null mice showed alterations in the production and organization of ECM components and a decrease in the infiltration of macrophages. However, there was no change in the levels of angiogenic growth factors in comparison to tumors grown in wild-type mice, although there was a statistically significant difference in total vascular area. Whereas SPARC did inhibit the growth of tumor cells in vitro, it did not have a demonstrable effect on the proliferation or apoptosis of tumor cells in vivo. These data indicate that host-derived SPARC is important for the appropriate organization of the ECM in response to implanted tumors and highlight the importance of the ECM in regulating tumor growth.