A comprehensive model of Drosophila epithelium reveals the role of embryo geometry and cell topology in mechanical responses.

In order to understand morphogenesis, it is necessary to know the material properties or forces shaping the living tissue. In spite of this need, very few in vivo measurements are currently available. Here, using the early Drosophila embryo as a model, we describe a novel cantilever-based technique which allows for the simultaneous quantification of applied force and tissue displacement in a living embryo. By analyzing data from a series of experiments in which embryonic epithelium is subjected to developmentally relevant perturbations, we conclude that the response to applied force is adiabatic and is dominated by elastic forces and geometric constraints, or system size effects. Crucially, computational modeling of the experimental data indicated that the apical surface of the epithelium must be softer than the basal surface, a result which we confirmed experimentally. Further, we used the combination of experimental data and comprehensive computational model to estimate the elastic modulus of the apical surface and set a lower bound on the elastic modulus of the basal surface. More generally, our investigations revealed important general features that we believe should be more widely addressed when quantitatively modeling tissue mechanics in any system. Specifically, different compartments of the same cell can have very different mechanical properties; when they do, they can contribute differently to different mechanical stimuli and cannot be merely averaged together. Additionally, tissue geometry can play a substantial role in mechanical response, and cannot be neglected.

Evidence that tissue recoil in the early Drosophila embryo is a passive not active process.

Understanding tissue morphogenesis is impossible without knowing the mechanical properties of the tissue being shaped. Although techniques for measuring tissue material properties are continually being developed, methods for determining how individual proteins contribute to mechanical properties are very limited. Here, we developed two complementary techniques for the acute inactivation of spaghetti squash (the Drosophila myosin regulatory light chain), one based on the recently introduced (auxin-inducible degron 2 (AID2) system, and the other based on a novel method for conditional protein aggregation that results in nearly instantaneous protein inactivation. Combining these techniques with rheological measurements, we show that passive material properties of the cellularization-stage Drosophila embryo are essentially unaffected by myosin activity. These results suggest that this tissue is elastic, not predominantly viscous, on the developmentally relevant timescale.

Feedback in the ß-catenin destruction complex imparts bistability and cellular memory.

Wnt ligands are considered classical morphogens, for which the strength of the cellular response is proportional to the concentration of the ligand. Herein, we show an emergent property of bistability arising from feedback among the Wnt destruction complex proteins that target the key transcriptional co-activator ß-catenin for degradation. Using biochemical reconstitution, we identified positive feedback between the scaffold protein Axin and the kinase glycogen synthase kinase 3 (GSK3). Theoretical modeling of this feedback between Axin and GSK3 suggested that the activity of the destruction complex exhibits bistable behavior. We experimentally confirmed these predictions by demonstrating that cellular cytoplasmic ß-catenin concentrations exhibit an "all-or-none" response with sustained memory (hysteresis) of the signaling input. This bistable behavior was transformed into a graded response and memory was lost through inhibition of GSK3. These findings provide a mechanism for establishing decisive, switch-like cellular response and memory upon Wnt pathway stimulation.

A versatile oblique plane microscope for large-scale and high-resolution imaging of subcellular dynamics.

We present an oblique plane microscope (OPM) that uses a bespoke glass-tipped tertiary objective to improve the resolution, field of view, and usability over previous variants. Owing to its high numerical aperture optics, this microscope achieves lateral and axial resolutions that are comparable to the square illumination mode of lattice light-sheet microscopy, but in a user friendly and versatile format. Given this performance, we demonstrate high-resolution imaging of clathrin-mediated endocytosis, vimentin, the endoplasmic reticulum, membrane dynamics, and Natural Killer-mediated cytotoxicity. Furthermore, we image biological phenomena that would be otherwise challenging or impossible to perform in a traditional light-sheet microscope geometry, including cell migration through confined spaces within a microfluidic device, subcellular photoactivation of Rac1, diffusion of cytoplasmic rheological tracers at a volumetric rate of 14 Hz, and large field of view imaging of neurons, developing embryos, and centimeter-scale tissue sections.

Wnt/ß-catenin Signaling in Tissue Self-Organization.

Across metazoans, animal body structures and tissues exist in robust patterns that arise seemingly out of stochasticity of a few early cells in the embryo. These patterns ensure proper tissue form and function during early embryogenesis, development, homeostasis, and regeneration. Fundamental questions are how these patterns are generated and maintained during tissue homeostasis and regeneration. Though fascinating scientists for generations, these ideas remain poorly understood. Today, it is apparent that the Wnt/ß-catenin pathway plays a central role in tissue patterning. Wnt proteins are small diffusible morphogens which are essential for cell type specification and patterning of tissues. In this review, we highlight several mechanisms described where the spatial properties of Wnt/ß-catenin signaling are controlled, allowing them to work in combination with other diffusible molecules to control tissue patterning. We discuss examples of this self-patterning behavior during development and adult tissues' maintenance. The combination of new physiological culture systems, mathematical approaches, and synthetic biology will continue to fuel discoveries about how tissues are patterned. These insights are critical for understanding the intricate interplay of core patterning signals and how they become disrupted in disease.

A simplified mechanism for anisotropic constriction in Drosophila mesoderm.

Understanding how forces and material properties give rise to tissue shapes is a fundamental issue in developmental biology. Although Drosophila gastrulation is a well-used system for investigating tissue morphogenesis, a consensus mechanical model that explains all the key features of this process does not exist. One key feature of Drosophila gastrulation is its anisotropy: the mesoderm constricts much more along one axis than along the other. Previous explanations have involved graded stress, anisotropic stresses or material properties, or mechanosensitive feedback. Here, we show that these mechanisms are not required to explain the anisotropy of constriction. Instead, constriction can be anisotropic if only two conditions are met: the tissue is elastic, as was demonstrated in our recent study; and the contractile domain is asymmetric. This conclusion is general and does not depend on the values of model parameters. Our model can explain results from classical tissue-grafting experiments and from more-recent laser ablation studies. Furthermore, our model may provide alternative explanations for experiments in other developmental systems, including C. elegans and zebrafish.

Measurement of cortical elasticity in Drosophila melanogaster embryos using ferrofluids.

Many models of morphogenesis are forced to assume specific mechanical properties of cells, because the actual mechanical properties of living tissues are largely unknown. Here, we measure the rheology of epithelial cells in the cellularizing Drosophila embryo by injecting magnetic particles and studying their response to external actuation. We establish that, on timescales relevant to epithelial morphogenesis, the cytoplasm is predominantly viscous, whereas the cellular cortex is elastic. The timescale of elastic stress relaxation has a lower bound of 4 min, which is comparable to the time required for internalization of the ventral furrow during gastrulation. The cytoplasm was measured to be ∼103-fold as viscous as water. We show that elasticity depends on the actin cytoskeleton and conclude by discussing how these results relate to existing mechanical models of morphogenesis.

Apical constriction drives tissue-scale hydrodynamic flow to mediate cell elongation.

Epithelial folding mediated by apical constriction converts flat epithelial sheets into multilayered, complex tissue structures and is used throughout development in most animals. Little is known, however, about how forces produced near the apical surface of the tissue are transmitted within individual cells to generate the global changes in cell shape that characterize tissue deformation. Here we apply particle tracking velocimetry in gastrulating Drosophila embryos to measure the movement of cytoplasm and plasma membrane during ventral furrow formation. We find that cytoplasmic redistribution during the lengthening phase of ventral furrow formation can be precisely described by viscous flows that quantitatively match the predictions of hydrodynamics. Cell membranes move with the ambient cytoplasm, with little resistance to, or driving force on, the flow. Strikingly, apical constriction produces similar flow patterns in mutant embryos that fail to form cells before gastrulation ('acellular' embryos), such that the global redistribution of cytoplasm mirrors the summed redistribution occurring in individual cells of wild-type embryos. Our results indicate that during the lengthening phase of ventral furrow formation, hydrodynamic behaviour of the cytoplasm provides the predominant mechanism transmitting apically generated forces deep into the tissue and that cell individualization is dispensable.

Self-organized cell motility from motor-filament interactions.

Cell motility is driven primarily by the dynamics of the cell cytoskeleton, a system of filamentous proteins and molecular motors. It has been proposed that cell motility is a self-organized process, that is, local short-range interactions determine much of the dynamics that are required for the whole-cell organization that leads to polarization and directional motion. Here we present a mesoscopic mean-field description of filaments, motors, and cell boundaries. This description gives rise to a dynamical system that exhibits multiple self-organized states. We discuss several qualitative aspects of the asymptotic states and compare them with those of living cells.

Stability of localized patterns in neural fields.

We investigate two-dimensional neural fields as a model of the dynamics of macroscopic activations in a cortex-like neural system. While the one-dimensional case was treated comprehensively by Amari 30 years ago, two-dimensional neural fields are much less understood. We derive conditions for the stability for the main classes of localized solutions of the neural field equation and study their behavior beyond parameter-controlled destabilization. We show that a slight modification of the original model yields an equation whose stationary states are guaranteed to satisfy the original problem and numerically demonstrate that it admits localized noncircular solutions. Typically, however, only periodic spatial tessellations emerge on destabilization of rotationally invariant solutions.

Stochastic model for Soj relocation dynamics in Bacillus subtilis.

The Bacillus subtilis Spo0J/Soj proteins, implicated in chromosome segregation and transcriptional regulation, show striking dynamics: Soj undergoes irregular relocations from pole to pole or nucleoid to nucleoid. Here, we report on a mathematical model of the Soj dynamics. Our model, which is closely based on the available experimental data, readily generates dynamic Soj relocations. We show that the irregularity of the relocations may be due to the stochastic nature of the underlying Spo0J/Soj interactions and diffusion. We propose explanations for the behavior of several Spo0J/Soj mutants, including the "freezing" of the Soj dynamics observed in filamentous cells. Our approach underlines the importance of incorporating stochastic effects when modeling spatiotemporal protein dynamics inside cells.