A Preferred Curvature-Based Continuum Mechanics Framework for Modeling Embryogenesis

Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

4D reconstruction of murine developmental trajectories using spherical harmonics

Normal organogenesis cannot be recapitulated in vitro for mammalian organs, unlike in species including Drosophila and zebrafish. Available 3D data in the form of ex vivo images only provide discrete snapshots of the development of an organ morphology. Here, we propose a computer-based approach to recreate its continuous evolution in time and space from a set of 3D volumetric images. Our method is based on the remapping of shape data into the space of the coefficients of a spherical harmonics expansion where a smooth interpolation over time is simpler. We tested our approach on mouse limb buds and embryonic hearts. A key advantage of this method is that the resulting 4D trajectory can take advantage of all the available data while also being able to interpolate well through time intervals for which there are little or no data. This allows for a quantitative, data-driven 4D description of mouse limb morphogenesis.

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Computer-based method recreating a 3D plus time evolution of a set of volumetric images

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Technique based on the interpolation of the coefficients of spherical harmonics

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Data-driven quantitative 4D description of limb and heart morphogenesis

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Quantitatively reliable baseline description of organ development

Embryo-scale epithelial buckling forms a propagating furrow that initiates gastrulation

Cell apical constriction driven by actomyosin contraction forces is a conserved mechanism during tissue folding in embryo development. While much is now understood of the molecular mechanism responsible for apical constriction and of the tissue-scale integration of the ensuing in-plane deformations, it is still not clear if apical actomyosin contraction forces are necessary or sufficient per se to drive tissue folding. To tackle this question, we use the Drosophila embryo model system that forms a furrow on the ventral side, initiating mesoderm internalization. Past computational models support the idea that cell apical contraction forces may not be sufficient and that active or passive cell apico-basal forces may be necessary to drive cell wedging leading to tissue furrowing. By using 3D computational modelling and in toto embryo image analysis and manipulation, we now challenge this idea and show that embryo-scale force balance at the tissue surface, rather than cell-autonomous shape changes, is necessary and sufficient to drive a buckling of the epithelial surface forming a furrow which propagates and initiates embryo gastrulation.

Drosophila mesoderm invagination begins with the formation of a furrow. Here they show that a long-range mechanism, powered by actomyosin contraction between the embryo polar caps, works like a ‘cheese-cutter wire’ indenting the tissue surface and folding it into a propagating furrow.

Deconstructing gastrulation at single-cell resolution

Gastrulation movements in all animal embryos start with regulated deformations of patterned epithelial sheets, which are driven by cell divisions, cell shape changes, and cell intercalations. Each of these behaviors has been associated with distinct aspects of gastrulation1-4 and has been a subject of intense research using genetic, cell biological, and more recently, biophysical approaches.5-14 Most of these studies, however, focus either on cellular processes driving gastrulation or on large-scale tissue deformations.15-23 Recent advances in microscopy and image processing create a unique opportunity for integrating these complementary viewpoints.24-28 Here, we take a step toward bridging these complementary strategies and deconstruct the early stages of gastrulation in the entire Drosophila embryo. Our approach relies on an integrated computational framework for cell segmentation and tracking and on efficient algorithms for event detection. The detected events are then mapped back onto the blastoderm shell, providing an intuitive visual means to examine complex cellular activity patterns within the context of their initial anatomic domains. By analyzing these maps, we identified that the loss of nearly half of surface cells to invaginations is compensated primarily by transient mitotic rounding. In addition, by analyzing mapped cell intercalation events, we derived direct quantitative relations between intercalation frequency and the rate of axis elongation. This work is setting the stage for systems-level dissection of a pivotal step in animal development.

Predicting pattern formation in embryonic stem cells using a minimalist, agent-based probabilistic model

The mechanisms of pattern formation during embryonic development remain poorly understood. Embryonic stem cells in culture self-organise to form spatial patterns of gene expression upon geometrical confinement indicating that patterning is an emergent phenomenon that results from the many interactions between the cells. Here, we applied an agent-based modelling approach in order to identify plausible biological rules acting at the meso-scale within stem cell collectives that may explain spontaneous patterning. We tested different models involving differential motile behaviours with or without biases due to neighbour interactions. We introduced a new metric, termed stem cell aggregate pattern distance (SCAPD) to probabilistically assess the fitness of our models with empirical data. The best of our models improves fitness by 70% and 77% over the random models for a discoidal or an ellipsoidal stem cell confinement respectively. Collectively, our findings show that a parsimonious mechanism that involves differential motility is sufficient to explain the spontaneous patterning of the cells upon confinement. Our work also defines a region of the parameter space that is compatible with patterning. We hope that our approach will be applicable to many biological systems and will contribute towards facilitating progress by reducing the need for extensive and costly experiments.

Light-Sheet Microscopy and Its Potential for Understanding Developmental Processes

The ability to visualize and quantitatively measure dynamic biological processes in vivo and at high spatiotemporal resolution is of fundamental importance to experimental investigations in developmental biology. Light-sheet microscopy is particularly well suited to providing such data, since it offers exceptionally high imaging speed and good spatial resolution while minimizing light-induced damage to the specimen. We review core principles and recent advances in light-sheet microscopy, with a focus on concepts and implementations relevant for applications in developmental biology. We discuss how light-sheet microcopy has helped advance our understanding of developmental processes from single-molecule to whole-organism studies, assess the potential for synergies with other state-of-the-art technologies, and introduce methods for computational image and data analysis. Finally, we explore the future trajectory of light-sheet microscopy, discuss key efforts to disseminate new light-sheet technology, and identify exciting opportunities for further advances.

A practical guide to adaptive light-sheet microscopy

We describe the implementation and use of an adaptive imaging framework for optimizing spatial resolution and signal strength in a light-sheet microscope. The framework, termed AutoPilot, comprises hardware and software modules for automatically measuring and compensating for mismatches between light-sheet and detection focal planes in living specimens. Our protocol enables researchers to introduce adaptive imaging capabilities in an existing light-sheet microscope or use our SiMView microscope blueprint to set up a new adaptive multiview light-sheet microscope. The protocol describes (i) the mechano-optical implementation of the adaptive imaging hardware, including technical drawings for all custom microscope components; (ii) the algorithms and software library for automated adaptive imaging, including the pseudocode and annotated source code for all software modules; and (iii) the execution of adaptive imaging experiments, as well as the configuration and practical use of the AutoPilot framework. Setup of the adaptive imaging hardware and software takes 1-2 weeks each. Previous experience with light-sheet microscopy and some familiarity with software engineering and building of optical instruments are recommended. Successful implementation of the protocol recovers near diffraction-limited performance in many parts of typical multicellular organisms studied with light-sheet microscopy, such as fruit fly and zebrafish embryos, for which resolution and signal strength are improved two- to fivefold.

A Label-free Multicolor Optical Surface Tomography (ALMOST) imaging method for nontransparent 3D samples

Background

Current mesoscale 3D imaging techniques are limited to transparent or cleared samples or require the use of X-rays. This is a severe limitation for many research areas, as the 3D color surface morphology of opaque samples—for example, intact adult Drosophila, Xenopus embryos, and other non-transparent samples—cannot be assessed. We have developed “ALMOST,” a novel optical method for 3D surface imaging of reflective opaque objects utilizing an optical projection tomography device in combination with oblique illumination and optical filters.

Results

As well as demonstrating image formation, we provide background information and explain the reconstruction—and consequent rendering—using a standard filtered back projection algorithm and 3D software. We expanded our approach to fluorescence and multi-channel spectral imaging, validating our results with micro-computed tomography. Different biological and inorganic test samples were used to highlight the versatility of our approach. To further demonstrate the applicability of ALMOST, we explored the muscle-induced form change of the Drosophila larva, imaged adult Drosophila, dynamically visualized the closure of neural folds during neurulation of live Xenopus embryos, and showed the complementarity of our approach by comparison with transmitted light and fluorescence OPT imaging of a Xenopus tadpole.

Conclusion

Thus, our new modality for spectral/color, macro/mesoscopic 3D imaging can be applied to a variety of model organisms and enables the longitudinal surface dynamics during development to be revealed.

Electronic supplementary material

The online version of this article (10.1186/s12915-018-0614-4) contains supplementary material, which is available to authorized users.