An integrated vertex model of the mesoderm invagination during the embryonic development of Drosophila.

The mesoderm invagination of the Drosophila embryo is known as an archetypal morphogenic process. To explore the roles of the active cellular forces and the regulation of these forces, we developed an integrated vertex model that combines the regulation of morphogen expression with cell movements and tissue mechanics. Our results suggest that a successful furrow formation requires an apical tension gradient, decreased basal tension, and increased lateral tension, which corresponds to apical constriction, basal expansion, and apicobasal shortening respectively. Our model also considers the mechanical feedback which leads to an ectopic twist expression with external compression as observed in experiments. Our model predicts that ectopic invagination could happen if an external compressive gradient is applied.

Force measurements of Myosin II waves at the yolk surface during Drosophila dorsal closure.

The mechanical properties and the forces involved during tissue morphogenesis have been the focus of much research in the last years. Absolute values of forces during tissue closure events have not yet been measured. This is also true for a common force-producing mechanism involving Myosin II waves that results in pulsed cell surface contractions. Our patented magnetic tweezer, CAARMA, integrated into a spinning disk confocal microscope, provides a powerful explorative tool for quantitatively measuring forces during tissue morphogenesis. Here, we used this tool to quantify the in vivo force production of Myosin II waves that we observed at the dorsal surface of the yolk cell in stage 13 Drosophila melanogaster embryos. In addition to providing for the first time to our knowledge quantitative values on an active Myosin-driven force, we elucidated the dynamics of the Myosin II waves by measuring their periodicity in both absence and presence of external perturbations, and we characterized the mechanical properties of the dorsal yolk cell surface.

Hydrodynamic stress and phenotypic plasticity of the zebrafish regenerating fin.

Understanding how extrinsic factors modulate genetically encoded information to produce a specific phenotype is of prime scientific interest. In particular, the feedback mechanism between abiotic forces and locomotory organs during morphogenesis to achieve efficient movement is a highly relevant example of such modulation. The study of this developmental process can provide unique insights on the transduction of cues at the interface between physics and biology. Here, we take advantage of the natural ability of adult zebrafish to regenerate their amputated fins to assess its morphogenic plasticity upon external modulations. Using a variety of surgical and chemical treatments, we could induce phenotypic responses to the structure of the fin. Through the ablation of specific rays in regenerating caudal fins, we generated artificially narrowed appendages in which the fin cleft depth and the positioning of rays bifurcations were perturbed compared with normal regenerates. To dissect the role of mechanotransduction in this process, we investigated the patterns of hydrodynamic forces acting on the surface of a zebrafish fin during regeneration by using particle tracking velocimetry on a range of biomimetic hydrofoils. This experimental approach enabled us to quantitatively compare hydrodynamic stress distributions over flapping fins of varying sizes and shapes. As a result, viscous shear stress acting on the distal margin of regenerating fins and the resulting internal tension are proposed as suitable signals for guiding the regulation of ray growth dynamics and branching pattern. Our findings suggest that mechanical forces are involved in the fine-tuning of the locomotory organ during fin morphogenesis.

Disentangling geometrical, viscoelastic and hyperelastic effects in force-displacement relationships of folded biological tissues.

Drosophila wing discs show a remarkable variability when subject to mechanical perturbation. We developed a stretching bench that allows accurate measurements of instantaneous and time-dependent material behaviour of the disc as a whole, while determining the exact three-dimensional structure of the disc during stretching. Our experiments reveal force relaxation dynamics on timescales that are significant for development, along with a surprisingly nonlinear force-displacement relationship. Concurrently our imaging indicates that the disc is a highly heterogeneous tissue with a complex geometry. Using image-based 3D finite element modelling we are able to identify the contributions of size, shape and materials parameters to the measured force-displacement relations. In particular, we find that simulating the stretching of a disc with stiffness patterns in the extra-cellular matrix (ECM) recapitulates the experimentally found stretched geometries. In our simulations, linear hyperelasticity explains the measured nonlinearity to a surprising extent. To fully match the experimental force-displacement curves, we use an exponentially elastic material, which, when coupled to material relaxation also explains time-dependent experiments. Our simulations predict that as the disc develops, two counteracting effects, namely the discs foldedness and the hardening of the ECM lead to force-relative displacement curves that are nearly conserved during development.

In vivo quantification of mechanical properties of caudal fins in adult zebrafish.

The caudal fins of adult zebrafish are supported by multiple bony rays that are laterally interconnected by soft interray tissue. Little is known about the fin's mechanical properties that influence bending in response to hydrodynamic forces during swimming. Here, we developed an experimental setup to measure the elastic properties of caudal fins in vivo by applying micro-Newton forces to obtain bending stiffness and a tensional modulus. We detected overall bending moments of 1.5×10-9-4×10-9 N m2 along the proximal-distal axis of the appendage showing a non-monotonous pattern that was not due to the geometry of the fin itself. Surgical disruption of the interray tissues along the proximal-distal axis revealed no significant changes to the overall bending stiffness, which we confirmed by determining a tensional modulus of the interray tissue. Thus, the biophysical values suggest that the flexibility of the fin during its hydrodynamic performance predominantly relies on the mechanical properties of the rays.

Integrating force-sensing and signaling pathways in a model for the regulation of wing imaginal disc size.

The regulation of organ size constitutes a major unsolved question in developmental biology. The wing imaginal disc of Drosophila serves as a widely used model system to study this question. Several mechanisms have been proposed to have an impact on final size, but they are either contradicted by experimental data or they cannot explain a number of key experimental observations and may thus be missing crucial elements. We have modeled a regulatory network that integrates the experimentally confirmed molecular interactions underlying other available models. Furthermore, the network includes hypothetical interactions between mechanical forces and specific growth regulators, leading to a size regulation mechanism that conceptually combines elements of existing models, and can be understood in terms of a compression gradient model. According to this model, compression increases in the center of the disc during growth. Growth stops once compression levels in the disc center reach a certain threshold and the compression gradient drops below a certain level in the rest of the disc. Our model can account for growth termination as well as for the paradoxical observation that growth occurs uniformly in the presence of a growth factor gradient and non-uniformly in the presence of a uniform growth factor distribution. Furthermore, it can account for other experimental observations that argue either in favor or against other models. The model also makes specific predictions about the distribution of cell shape and size in the developing disc, which we were able to confirm experimentally.

Direct imaging of fluorescent structures behind turbid layers.

We present a method to directly image fluorescent structures inside turbid media. This is based on wave-front shaping to optimize the scattered light onto a single fluorescent particle, as the optical memory effect for a scanning image of the surroundings of this particle. We show that iterating the optimization leads to the focusing on a single particle whose surroundings are subsequently scanned. In combination with a parabolic phase pattern, this method can be extended to a three dimensional imaging method inside turbid media.

Exploring the effects of mechanical feedback on epithelial topology.

Apical cell surfaces in metazoan epithelia, such as the wing disc of Drosophila, resemble polygons with different numbers of neighboring cells. The distribution of these polygon numbers has been shown to be conserved. Revealing the mechanisms that lead to this topology might yield insights into how the structural integrity of epithelial tissues is maintained. It has previously been proposed that cell division alone, or cell division in combination with cell rearrangements, is sufficient to explain the observed epithelial topology. Here, we extend this work by including an analysis of the clustering and the polygon distribution of mitotic cells. In addition, we study possible effects of cellular growth regulation by mechanical forces, as such regulation has been proposed to be involved in wing disc size regulation. We formulated several theoretical scenarios that differ with respect to whether cell rearrangements are allowed and whether cellular growth rates are dependent on mechanical stress. We then compared these scenarios with experimental data on the polygon distribution of the entire cell population, that of mitotic cells, as well as with data on mitotic clustering. Surprisingly, we observed considerably less clustering in our experiments than has been reported previously. Only scenarios that include mechanical-stress-dependent growth rates are in agreement with the experimental data. Interestingly, simulations of these scenarios showed a large decrease in rearrangements and elimination of cells. Thus, a possible growth regulation by mechanical force could have a function in releasing the mechanical stress that evolves when all cells have similar growth rates.

Scattered light fluorescence microscopy in three dimensions.

Recently, we have proposed a method to image fluorescent structures behind turbid layers at diffraction limited resolution using wave-front shaping and the memory effect. However, this was limited to a raster scanning of the wave-front shaped focus to a two dimensional plane. In applications, it can however be of great importance to be able to scan a three dimensional volume. Here we show that this can be implemented in the same setup. This is achieved by the addition of a parabolic phase shift to the shaped wave-front. Via the memory effect, this phase shift leads to a shift of the interference based focus in the z-direction, thus opening the possibility of three dimensional imaging using scattered light fluorescence microscopy. Here, we show an example of such a three dimensional image of fluorescent nano-beads taken behind a turbid layer more than 10 mean free paths thick. Finally, we discuss the differences of the scanning in the z-direction with that in the x-y plane and the corresponding possibilities and limitations of the technique.

Hydrodynamic stress maps on the surface of a flexible fin-like foil.

We determine the time dependence of pressure and shear stress distributions on the surface of a pitching and deforming hydrofoil from measurements of the three dimensional flow field. Period-averaged stress maps are obtained both in the presence and absence of steady flow around the foil. The velocity vector field is determined via volumetric three-component particle tracking velocimetry and subsequently inserted into the Navier-Stokes equation to calculate the total hydrodynamic stress tensor. In addition, we also present a careful error analysis of such measurements, showing that local evaluations of stress distributions are possible. The consistency of the force time-dependence is verified using a control volume analysis. The flapping foil used in the experiments is designed to allow comparison with a small trapezoidal fish fin, in terms of the scaling laws that govern the oscillatory flow regime. As a complementary approach, unsteady Euler-Bernoulli beam theory is employed to derive instantaneous transversal force distributions on the flexible hydrofoil from its deflection and the results are compared to the spatial distributions of hydrodynamic stresses obtained from the fluid velocity field.

Scattered light fluorescence microscopy: imaging through turbid layers.

A major limitation of any type of microscope is the penetration depth in turbid tissue. Here, we demonstrate a fundamentally novel kind of fluorescence microscope that images through optically thick turbid layers. The microscope uses scattered light, rather than light propagating along a straight path, for imaging with subwavelength resolution. Our method uses constructive interference to focus scattered laser light through the turbid layer. Microscopic fluorescent structures behind the layer were imaged by raster scanning the focus.

Distribution and Restoration of Serotonin-Immunoreactive Paraneuronal Cells During Caudal Fin Regeneration in Zebrafish.

Aquatic vertebrates possess diverse types of sensory cells in their skin to detect stimuli in the water. In the adult zebrafish, a common model organism, the presence of such cells in fins has only rarely been studied. Here, we identified scattered serotonin (5-HT)-positive cells in the epidermis of the caudal fin. These cells were distinct from keratinocytes as revealed by their low immunoreactivity for cytokeratin and desmosome markers. Instead, they were detected by Calretinin (Calbindin-2) and Synaptic vesicle glycoprotein 2 (SV2) antibodies, indicating a calcium-regulated neurosecretory activity. Consistently, electron microscopy revealed abundant secretory organelles in desmosome-negative cells in the fin epidermis. Based on the markers, 5-HT, Calretinin and SV2, we referred to these cells as HCS-cells. We found that HCS-cells were spread throughout the entire caudal fin at an average density of 140 cells per mm2 on each fin surface. These cells were strongly enriched at ray bifurcations in wild type fins, as well as in elongated fins of another longfin mutant fish. To determine whether hydrodynamics play a role in the distribution of HCS-cells, we used an interdisciplinary approach and performed kinematic analysis. Measurements of particle velocity with a fin model revealed differences in fluid velocities between bifurcated rods and adjacent non-bifurcated regions. Therefore the accumulation of HCS-cells near bone bifurcations may be a biological adaptation for sensing of water parameters. The significance of this HCS-cell pattern is reinforced by the fact, that it is reestablished in the regenerated fin after amputation. Regeneration of HCS-cells was not impaired by the chemical inhibition of serotonin synthesis, suggesting that this neurotransmitter is not essential for the restorative process. In conclusion, our study identified a specific population of solitary paraneurons in the zebrafish fin, whose distribution correlates with fluid dynamics.

Model for the regulation of size in the wing imaginal disc of Drosophila.

For animal development it is necessary that organs stop growing after they reach a certain size. However, it is still largely unknown how this termination of growth is regulated. The wing imaginal disc of Drosophila serves as a commonly used model system to study the regulation of growth. Paradoxically, it has been observed that growth occurs uniformly throughout the disc, even though Decapentaplegic (Dpp), a key inducer of growth, forms a gradient. Here, we present a model for the control of growth in the wing imaginal disc, which can account for the uniform occurrence and termination of growth. A central feature of the model is that net growth is not only regulated by growth factors, but by mechanical forces as well. According to the model, growth factors like Dpp induce growth in the center of the disc, which subsequently causes a tangential stretching of surrounding peripheral regions. Above a certain threshold, this stretching stimulates growth in these peripheral regions. Since the stretching is not completely compensated for by the induced growth, the peripheral regions will compress the center of the disc, leading to an inhibition of growth in the center. The larger the disc, the stronger this compression becomes and hence the stronger the inhibiting effect. Growth ceases when the growth factors can no longer overcome this inhibition. With numerical simulations we show that the model indeed yields uniform growth. Furthermore, the model can also account for other experimental data on growth in the wing disc.

Dynamic light sheet generation and fluorescence imaging behind turbid media.

BACKGROUND: Light sheet microscopy became a popular tool allowing fast imaging with reduced out of focus light. However, when light penetrates turbid media such as biological tissues, multiple scattering scrambles the illumination into a speckle pattern and severely challenges conventional fluorescence imaging with focused light or with a light sheet. In this article, we present generation of light sheet type illumination patterns despite scattering. METHODS: We optimize the wave-front of the incoming light to transform the speckle pattern behind the scattering layer into a light sheet within the region of interest. We utilize a fast spatial light modulator for phase modulation and a genetic optimization algorithm. The light pattern behind the scattering layer is detected via a clear detection path and acts as a feedback signal for the algorithm. RESULTS: We enabled homogenous light sheet illumination behind turbid media and enhanced the signal of fluorescent beads selectively at the desired focal plane up to eight times on average. The technique is capable to compensate the dynamic changes of the speckle pattern as well, as shown on samples consisting of living drosophila pupae. CONCLUSION: Our technique shows that not only single foci, but also a homogenous light sheet illumination can directly be created and maintained behind static and dynamic scattering media. To make the technique suitable for common biological settings, where the detection path is turbid as well, a fluorescent probe can be used to provide the feedback signal.

Challenging FRET-based E-Cadherin force measurements in Drosophila.

Mechanical forces play a critical role during embryonic development. Cellular and tissue wide forces direct cell migration, drive tissue morphogenesis and regulate organ growth. Despite the relevance of mechanics for these processes, our knowledge of the dynamics of mechanical forces in living tissues remains scarce. Recent studies have tried to address this problem with the development of tension sensors based on Förster resonance energy transfer (FRET). These sensors are integrated into force bearing proteins and allow the measurement of mechanical tensions on subcellular structures. Here, we developed such a FRET-based sensor to measure E-Cadherin tensions in different Drosophila tissues in and ex vivo. Similar to previous studies, we integrated the sensor module into E-cadherin. We assessed the sensitivity of the sensor by measuring dynamic, developmental processes and mechanical modifications in three Drosophila tissues: the wing imaginal disc, the amnioserosa cells and the migrating border cells. However, these assays revealed that the sensor is not functional to measure the magnitude of tensions occurring in any of the three tissues. Moreover, we encountered technical problems with the measurement of FRET, which might represent more general pitfalls with FRET sensors in living tissues. These insights will help future studies to better design and control mechano-sensing experiments.

Comment on "Precise domain specification in the developing Drosophila embryo".

In a recent paper, Houchmandzadeh [Phys. Rev. E 72, 061920 (2005)] introduce a correlated bigradient model in order to explain the robust scaling of the boundary of hunchback (hb) expression in the early Drosophila embryo. In particular, they stress that recent experiments by Lucchetta [Nature (London) 434, 1134 (2005)], where embryos whose anterior and posterior halves develop at different temperatures still show excellent precision in the hb boundary, are in good agreement with such a model. We would like to show here that this conclusion is unwarranted. This is because the experiments of Lucchetta were done at different temperatures from those studied in the model. Since in other temperature combinations the model does not produce precise boundaries and there are no systematic trends in these deviations, a comparison to the experiment is not possible. Furthermore, we would like to point out that any correlated bigradient model should also take into account the fluctuations of the bicoid profile within an embryo. When forming correlated bigradients of experimental profiles from an online library, we observe that these intraembryo variations destroy robustness of the hb boundary even in the wild-type situation.

Reduced transport velocity of multiply scattered light due to resonant scattering.

The transport properties of photons traveling through random media are of great fundamental and applied importance. For instance the dwell time due to resonant Mie scattering can lead to a significant reduction in transport velocity. Here, we have measured directly the energy-transport velocity of photons in strongly scattering media using a combination of time resolved transmission, measuring the diffusion coefficient, and angular resolved backscattering, yielding the transport mean free path. We find that the transport velocity is strongly reduced when the effective diameter of the scattering particles is a multiple of half the wavelength. This is consistent with the occurrence of resonant Mie scattering in the samples. We compare our data to previous theoretical calculations of the transport velocity as a function of scatterer size.

Mechanical control of organ size in the development of the Drosophila wing disc.

Control of cessation of growth in developing organs has recently been proposed to be influenced by mechanical forces acting on the tissue due to its growth. In particular, it was proposed that stretching of the tissue leads to an increase in cell proliferation. Using the model system of the Drosophila wing imaginal disc, we directly stretch the tissue finding a significant increase in cell proliferation, thus confirming this hypothesis. In addition, we characterize the growth over the entire growth period of the wing disc finding a correlation between the apical cell area and cell proliferation rate. PACS NUMBERS: 87.19.lx, 87.18.Nq, 87.80.Ek, 87.17.Ee, 87.85.Xd.

In-vivo imaging of the Drosophila wing imaginal disc over time: novel insights on growth and boundary formation.

In developmental biology, the sequence of gene induction and pattern formation is best studied over time as an organism develops. However, in the model system of Drosophila larvae this oftentimes proves difficult due to limitations in imaging capabilities. Using the larval wing imaginal disc, we show that both overall growth, as well as the creation of patterns such as the distinction between the anterior(A) and posterior(P) compartments and the dorsal(D) and ventral(V) compartments can be studied directly by imaging the wing disc as it develops inside a larva. Imaged larvae develop normally, as can be seen by the overall growth curve of the wing disc. Yet, the fact that we can follow the development of individual discs through time provides the opportunity to simultaneously assess individual variability. We for instance find that growth rates can vary greatly over time. In addition, we observe that mechanical forces act on the wing disc within the larva at times when there is an increase in growth rates. Moreover, we observe that A/P boundary formation follows the established sequence and a smooth boundary is present from the first larval instar on. The division of the wing disc into a dorsal and a ventral compartment, on the other hand, develops quite differently. Contrary to expectation, the specification of the dorsal compartment starts with only one or two cells in the second larval instar and a smooth boundary is not formed until the third larval instar.

Determination of mechanical stress distribution in Drosophila wing discs using photoelasticity.

Morphogenesis, the process by which all complex biological structures are formed, is driven by an intricate interplay between genes, growth, as well as intra- and intercellular forces. While the expression of different genes changes the mechanical properties and shapes of cells, growth exerts forces in response to which tissues, organs and more complex structures are shaped. This is exemplified by a number of recent findings for instance in meristem formation in Arabidopsis and tracheal tube formation in Drosophila. However, growth not only generates forces, mechanical forces can also have an effect on growth rates, as is seen in mammalian tissues or bone growth. In fact, mechanical forces can influence the expression levels of patterning genes, allowing control of morphogenesis via mechanical feedback. In order to study the connections between mechanical stress, growth control and morphogenesis, information about the distribution of stress in a tissue is invaluable. Here, we applied stress-birefringence to the wing imaginal disc of Drosophila melanogaster, a commonly used model system for organ growth and patterning, in order to assess the stress distribution present in this tissue. For this purpose, stress-related differences in retardance are measured using a custom-built optical set-up. Applying this method, we found that the stresses are inhomogeneously distributed in the wing disc, with maximum compression in the centre of the wing pouch. This compression increases with wing disc size, showing that mechanical forces vary with the age of the tissue. These results are discussed in light of recent models proposing mechanical regulation of wing disc growth.