Towards 3D in silico modeling of the sea urchin embryonic development
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Embryogenesis is a dynamic process with an intrinsic variability whose understanding requires the integration of molecular, genetic, and cellular dynamics. Biological circuits function over time at the level of single cells and require a precise analysis of the topology, temporality, and probability of events. Integrative developmental biology is currently looking for the appropriate strategies to capture the intrinsic properties of biological systems. The “–omic” approaches require disruption of the function of the biological circuit; they provide static information, with low temporal resolution and usually with population averaging that masks fast or variable features at the cellular scale and in a single individual. This data should be correlated with cell behavior as cells are the integrators of biological activity. Cellular dynamics are captured by the in vivo microscopy observation of live organisms. This can be used to reconstruct the 3D + time cell lineage tree to serve as the basis for modeling the organism's multiscale dynamics. We discuss here the progress that has been made in this direction, starting with the reconstruction over time of three-dimensional digital embryos from in toto time-lapse imaging. Digital specimens provide the means for a quantitative description of the development of model organisms that can be stored, shared, and compared. They open the way to in silico experimentation and to a more theoretical approach to biological processes. We show, with some unpublished results, how the proposed methodology can be applied to sea urchin species that have been model organisms in the field of classical embryology and modern developmental biology for over a century.
KeywordsMorphogenesis Sea urchin Cellular dynamics In vivo imaging Multiscale digital specimens In silico modeling
The phenomenological and theoretical reconstruction of multiscale dynamics in animal embryogenesis: a general perspective
Among all possible genetically and epigenetically encoded processes, cells divide, differentiate, and migrate in the context of their self-produced external environment [67, 102]. Cell features over time can be described with a set of parameters including the cell position, cell lineage, volume, surface, shape indexes, local convexity or concavity, nuclear/cytoplasmic ratio, cell neighborhood and surface of contact, cell polarization assessed by the asymmetric distribution of sub-cellular structures, intrinsic motility, and directionality. At the mesoscopic level, tissue patterning depends on cell displacements, cell–cell adhesion, and cell division characteristics. The emergence of the most macroscopic features shapes the whole embryo and provides global mechanical constraints. Changes in cell and tissue properties can be described by biomechanical models whose behavior depends on initial and boundary conditions given by the cellular environment . A number of recent publications on different model organisms have focused on the mechanical properties of cells and their emergence from the interaction of cells with their environment [41, 46, 65, 66] and the interplay between mechanical constraints and gene expression patterning [13, 74, 114]. The biomechanical approach readily leads to the integration of the genetic and molecular basis of cell activities into the macroscopic deformation of tissues that shape the embryo .
Building multiscale models, integrating the biomechanics, and the molecular and genetic dynamics of embryonic development requires the quantitative description of cell behaviors. We review here how the state of the art reflects this paradigm, focusing on the reconstruction of digital specimens from in vivo and in toto imaging.
From in vivo imaging to modeling to understand animal embryogenesis: the premises
A number of studies in different model organisms have more or less explicitly tackled the reconstruction of digital specimens from live observation. Pioneering work in the late 1970s [23, 128] led to the full reconstruction of the cell lineage tree of Caenorhabditis elegans . This was obtained from the manual annotation of different embryos observed through Nomarski optics and was made possible thanks to the lineage invariance in Caenorhabditis elegans. Then, in the late 1990s, advances in microscopy and computation to handle high-dimensional data brought the first computer-aided cell tracking . The authors used a new 3D multifocal time lapse system  to observe the early embryogenesis of Caenorhabditis elegans and the software Simi BioCell provided means for annotating and comparing the lineage trees of different embryos. The synergistic efforts of different disciplines brought further major advances. Developmental biology benefited from breakthroughs in fluorescent protein engineering [14, 16, 84, 85], microscopy imaging systems [34, 60, 107, 127, 130], image processing methods for cell segmentation and cell tracking [69, 90, 91, 92], the development of software for computer-aided data processing and visualization , and computer hardware for processing high dimensional datasets on computing grids .
From in vivo imaging to modeling to understand animal embryogenesis: reconstructing multiscale digital specimens
However, the reconstruction of animal embryogenesis from 3D + time imaging data remains a challenging approach, suffering from intrinsic limitations mainly related to the quality of the original data and the simultaneous requirement of automation and precision. The field of image processing has only recently turned to biological images, first dealing with 2D images, then 3D data, and then addressing one more level of complexity with 3D + time processing . But even the most sophisticated algorithms are currently unable to distinguish objects or track them where the human eye cannot provide an accurate benchmark. So, the next breakthroughs in the field will have to originate from the biological side. In vivo 3D + time imaging has to deal with the trade-off between conflicting requirements including spatial and temporal resolution, signal-to-noise ratio, and photo damage. High spatial resolution and signal-to-noise ratio are needed to capture cell position and shape, but high temporal resolution is necessary to achieve single cell tracking. Further constraints are imposed by photo bleaching and photo damage, which limit the acquisition rate and overall imaging duration. In addition, fluorescent staining of subcellular structures in live model organisms is often non-homogeneous and adds artifacts in data acquisition, limiting the quality of the reconstruction, despite the development of sophisticated pre-processing methods [72, 134].
We can expect further improvements in fluorescent staining with more stable and brighter protein variants. Revealing contrasts intrinsic to the tissues such as the generation of harmonics by multiphoton illumination, has also proved to be useful . When the cell density becomes too high, e.g., at late developmental stages, strategies to decrease the image complexity by providing color combinations and mosaic staining should be further developed. On the side of microscopy techniques, there is still room for improvement in depth imaging, spatial and temporal resolution, and signal-to-noise ratio. The recently developed single-plane illumination microscopy seems a valuable alternative to laser point-scanning microscopy, as it definitely improves the temporal resolution and the signal-to-noise ratio. But various imaging artifacts have not been solved yet and single-plane 2-photon excitation, which looks very promising, is still under development by physicists .
Model organisms with their digital representation
Manual lineage tree extraction and comparison of different embryos.
Semiautomatic tracking and annotations at the single cell resolution up to 350 cells
StarryNite and AceTree
Automated analysis of reporter gene expression in Caenorhabditis elegans with cellular resolution
StarryNite and AceTree
Digital nuclear atlas of first larval stage (L1) at single-cell resolution from confocal imaging of 15 individual worms
Analysis of cell fate from single-cell gene expression profiles
Tracking and analysis at the single cell resolution
C. intestinalis and H. roretzi
Quantitative reconstruction and analysis of digital data at the cellular scale
Imaris and Amira
Interactive developmental table
Manual segmentation of the tailbud embryo and analysis of its anatomy
3D reconstruction and analysis of gastrulation movement
Imaging and reconstruction of the first 24 h of development from DLSLM imaging 3D + time data
Imaging and reconstruction of the first 10 cleavages from multiharmonic microscopy imaging
The digital reconstruction of Nematoda
The reconstruction of the cell lineage tree of Caenorhabditis elegans led to the development of dedicated software applications. The first available tools were designed to perform manual tracking and annotations. Worth mentioning, as it was pioneering in the field, is the development of 3D-DIASemb  for performing manual tracking, nuclear and membrane segmentation, and cell motion analysis from Nomarski video microscopy imaging of Caenorhabditis elegans up to the 28-cell stage. Simi BioCell, first mentioned in 1997, was used for manual tracking and annotation in Nematoda [58, 59], for combining the lineage tree with gene expression , and even lately for investigating cell lineages in the early mouse embryo . Semiautomatic tracking with StarryNite  and AceTree  (available at http://waterston.gs.washington.edu/) provided the cell lineage tree of the Caenorhabditis elegans embryo up to 350 cells . A digital atlas of the first larval stage (L1) with single-cell resolution was obtained from confocal images of 15 individual worms . Gene expression and cell fate were then investigated  with the volume-object annotation system . More recently, NucleiTracker4D (available at http://sourceforge.net/projects/nucleitracker4d/) was used for the semiautomatic tracking of nuclei imaged by laser scanning confocal microscopy of Caenorhabditis elegans development . Further details concerning the cell clonal analysis in Caenorhabditis elegans can be found in [38, 44] and all the available data has been collected by the Nematode community on http://www.wormatlas.org/. It should be noted that the digital reconstruction performed so far on Nematoda has focused on displaying the gene regulatory network data according to cell position, but little integration has been achieved with cell behavior, and to our best knowledge, the assessment of cell shape through the segmentation of membrane images has not been addressed.
The digital reconstruction of Ascidiacea
As for the Nematodes, Ascidians exhibit a largely invariant cell lineage and digital embryos have been reconstructed from confocal images of fixed specimens at different stages of development. The most remarkable work has been collected in the Ascidian Network for In Situ Expression and Embryological Data (ANISEED) database  and the 3D Virtual Embryo software for visualization and interaction , both available through http://aniseed-ibdm.univ-mrs.fr/virtual_embryo.php. The 3D Virtual Embryo has been introduced as a tool for quantifying the geometry of cells and cell–cell contacts in an interactive three-dimensional environment and provides cell volumes, mathematical descriptors of cell shape, and cell–cell contacts. Initially used to describe the first developmental stages of Ciona intestinalis and a late 32-cell stage of Halocynthia roretzi, the concept has been extended to other Ascidian species. The ANISEED database integrating molecular, embryological, and anatomical data in the virtual embryo provides a new paradigm in the field of developmental biology. It should, however, be noted that so far, ANISEED has been based on the segmentation of fixed embryos. Further extending the concept will require the segmentation of live specimens. The Ascidian community has also contributed another interesting initiative. At first, dealing with raw data only, the Four-dimensional Ascidian Body Atlas, with interactive visualization of the development of Ciona intestinalis  is available online through http://chordate.bpni.bio.keio.ac.jp/faba/1.4/top.html. More recently, Hotta et al. achieved the manual segmentation of Ciona intestinalis tailbud embryos, and the interactive visualization of the data is available through 3D pdf files .
Reconstructing the multiscale dynamics of the sea urchin embryogenesis
The sea urchin as an animal model in experimental biology: historical perspective
The importance of the sea urchin as a model organism in biological investigations dates back to the nineteenth century and its characteristic features led to cornerstone discoveries in the history of embryology and cell biology. The transparency of the embryo allowed for the first time to observe the fusion between oocyte and sperm during the process of fertilization . In 1892, blastomeres isolated at the 2-cell stage were shown to produce complete sea urchin larvae . Such experimental possibilities made the sea urchin a very valuable model for investigating the components of individual variation. Pioneering studies on teratogenesis carried out by changing the chemical content of the sea urchin embryo helped to found the concept of embryonic induction . The manipulation of double fertilized eggs  inspired the chromosome theory of inheritance and opened the way to the understanding of cancer as a genetic disease (English translation in ). Further work opened the way to modern Developmental Biology with the exploration of early development including gastrulation , cell mechanics underlying morphogenetic movements , and the mechanical properties of the sea urchin embryo at early stages of development [53, 54]. During the same period, Gustafson and Kinnander developed a technique allowing the gastrulation of the sea urchin Psammechinus miliaris to be analyzed for the first time, through time-lapse cinematography . A few years later, the sea urchin was selected as a suitable animal model for large-scale analysis of gene expression regulation during early development . More recently (2001), the discovery of cyclin and its role in cell cycle progression in the sea urchin  resulted in the award of the Nobel Prize in Physiology and Medicine to Tim Hunt (jointly with Leland H. Hartwell and Paul M. Nurse). Further information about the contribution of the sea urchin animal model to the foundation of paradigms in embryology and developmental biology can be found in .
The sea urchin in modern developmental biology
Some online resources from the sea urchin community
Sea urchin embryology tutorial, the web site is designed to provide material for teaching developmental biology to undergraduates.
Interactive tutorial developed by the Stanford University with support from the National Science Foundation.
Protocols to study the sea urchin development from the Stanford University
Protocols from the Swarthmore College
The web site of E. Davidson's laboratory providing an updated version of the BioTapestry Interactive Network Viewer  for the GRN of the endomesoderm in Strongylocentrotus purpuratus
Reconstructing the digital sea urchin from 3D + time in toto imaging
The sea urchin has a number of desirable characteristics, making it a model of choice for in toto time-lapse microscopy imaging of the embryonic and larval stages. The embryo is easily accessible, relatively transparent and small, develops fast, grows to a fairly small number of cells and can be engineered to express fluorescent proteins. After overcoming the problem of the immobilization of the swimming blastula, the embryo can be imaged in toto for extended periods of time by two-photon laser scanning or selective plane illumination microscopy. The sea urchin is the ideal model for making a proof of concept for the reconstruction of the multiscale dynamics of a developing model organism from Deuterostomia, exploiting the unique data available in terms of the GRN architecture and dynamics.
We should, however, emphasize here that the task of long-term 3D + time imaging of the developing sea urchin and automated image processing to achieve cell tracking and shape segmentation is still subject to a number of limitations. These limitations are mainly on the biological side: highlighting structures without ectopic staining, e.g., staining membranes or nuclei without spurious cytoplasmic staining, immobilizing the specimen without mechanical deformation, compensating for light absorption and dispersion and thus loss of signal at depth, resolving individual nuclei throughout the entire volume including at late developmental stages, keeping a temporal resolution high enough to optimize the cell tracking outcome, e.g., ideally keeping the time step smaller than 2 min. Both 2-photon laser scanning and selective plane microscopy imaging are suitable, although they are based on quite different compromises, for the long-term 3D + time imaging of sea urchin embryos. It may soon be demonstrated that for specimens as small as sea urchin embryos, SPIM/DSLM offers the best conditions, provided that specimen mounting is improved compared with what is currently achieved .
Over the past few years, the BioEmergences platform (http://www.bioemergences.eu) and its interdisciplinary team have been exploring this paradigm, starting with the systematic reconstruction of the cell lineage tree of Paracentrotus lividus from in toto imaging and automated algorithmic processing. The reconstructed digital embryo consists of cell positions and shapes over time and cell clonal history. The corresponding data can be displayed and interactively explored, validated, and annotated with the visualization interface, Mov-IT,  (Figs. 2 and 3). The lineages of the different cell populations described in the early embryo according to  were highlighted from the 32-cell stage until blastula stages. These reconstructions provide precise measurements hitherto unavailable to model the dynamics at the microscopic scale and reconstruct the overall dynamics of the morphogenetic process at the macroscopic scale as well as possible. This is a most promising approach for the systematic identification of symmetry breaking or intra-individual and inter-individual variation. It would be a major paradigm change in the field of developmental biology, as it uses new theoretical frameworks to revisit classical embryology concepts.
When completed up to late developmental stages, the precise reconstruction of the cell's clonal history with associated shape, volume, and contact changes will contribute to our understanding of morphogenesis and differentiation processes [47, 48, 49] and answer a number of open questions. Digital specimens and the corresponding raw data should be made available to the entire community and scientists should all work to enrich a common database and contribute to the validation and correction of cell trajectories and cell shape. By sharing this 3D + time quantitative data for cohorts of individuals in defined genetic and environmental conditions, scientists will have the tools to bring a new perspective to classical questions of embryology.
First, a series of questions would be settled with the analysis of cell clonal history and cell fate such as for ectoderm/endoderm boundaries in the veg1 territory (reviewed by ) or the clonal origin of larval structures such as coelomic pouches. A second series of questions concerns the biomechanics of generic morphogenetic movements. The thickening of the vegetal plate during the ingression of the primary mesenchymal cells [28, 29] is described as a case of epithelial-mesenchymal transition, that should be compared to other similar processes . The elongation and narrowing of the archenteron and the flattening of the epithelial cells in the wall gut rudiment , described in terms of the convergent extension movements , can be related to processes described in other model organisms [66, 67]. The Drosophila germ band extension , and the gastrulation and axis elongation in Ascidians , zebrafish [40, 70], avians [76, 122, 125], and mice  should, at some point, be quantified and compared. Achieving such a goal in the sea urchin will be insightful for a comparative study of morphogenetic processes and their evolutionary relationship.
Modeling morphogenetic processes in sea urchin development
The long-term goal of integrated modeling of the multiscale dynamics of sea urchin development will take advantage of the partial models established at different scales. The tentative modeling strategies available so far are scarce and much remains to be done in terms of comparing the models with quantitative data. A careful bibliographic search has brought to light four papers, all addressing early developmental steps and dealing respectively with: the biomechanical modeling of the primary invagination , the mechanical modeling of division asymmetry , the molecular modeling of cell proliferation  and the Boolean modeling of GRN dynamics .
Finite element modeling was used to discriminate between the possible mechanisms accounting for the primary invagination leading to the formation of the archenteron . Hypothetical mechanisms driving invagination included at the time: apical constriction [7, 31], annular ring contraction [15, 31], cell tractoring , gel swelling , and apicobasal contraction . But each of these mechanisms required different properties of the composite epithelial sheet. Further studies on Strongylocentrotus purpuratus embryos at the mesenchyme blastula stage  revealed that the extracellular matrix of the blastula wall was considerably stiffer than the cell layer. The authors then suggested that neither apical constriction nor annular ring contraction could drive invagination while all other hypotheses remained plausible.
Akiyama et al. developed an ad hoc mathematical model to reproduce the first four cleavages of the sea urchin egg, including the asymmetric divisions giving rise to micromeres . The model established the planes of mitosis by assuming a chemotactic motion of centrosomes based on the diffusion of a chemical substance with repellent effects at the animal pole and attractive activity at the vegetal pole.
Ciliberto and Tyson  modified a previously developed mathematical model  based on molecular interactions underlying early embryonic cell-cycle control to investigate the hypothesis of a mitotic gradient along the animal-vegetal axis. Their results exhibited a good match with experimental data from  on Temnopleurus toreumaticus. They concluded that the mitotic wave was primarily attributable to differences in interdivision times in different parts of the embryo, although some subtle details of the wave were probably due to diffusive coupling between neighboring cells.
The transformation of the well-established GRN architecture into a predictive, dynamic Boolean computational model was a major recent breakthrough by the team led by Eric Davidson. This Boolean model computes spatial and temporal gene expression according to the GRN structure established for the embryonic development in the sea urchin. Direct comparison with experimental observations showed that the model predictively computed known gene expression patterns with remarkable spatial and temporal accuracy, thus validating the GRN architecture established so far.
All these models are intended to be both predictive and explanatory and to provide a formal basis to support or refute the intuition. They also tackle specific and limited scales and components of the system. Their integration in a multiscale modeling of morphogenesis will require a huge interdisciplinary and synergistic effort.
We have depicted an ideal scenario for a complex systems approach to morphogenetic processes underlying early animal development. The proposed strategy, based on the evidence that morphogenesis is a multiscale dynamic process, requires the integration of quantitative data across spatio-temporal scales into a yet-to-be-defined theoretical framework. A new interdisciplinary community coming from different perspectives and sharing the same goals is progressing fast. However, the overall conceptual and experimental landscape is still disparate, resembling a huge puzzle whose pieces do not yet fit together. Synergistic efforts by the scientific community are producing public databases of genome and GRN components for many model organisms. State-of-the-art microscopy imaging has made it possible to observe embryo development in small transparent organisms in toto, in vivo, with resolution at the cellular level. Software tools are being developed for visualizing, reconstructing and analyzing 3D + time image data. Computer hardware enables the processing of high-dimensional datasets on computing grids. Digital embryos can be directly manipulated and visualized in 3D to inspect and analyze cell clonal history and cell shape changes and cell–cell interactions over time. Much effort is being dedicated to the development of mathematical models of morphogenesis, based on either GRN architecture or the mechanical properties of tissue, for testing biological hypotheses and predicting the system's behavior. A new generation of digital resources anticipates the need to integrate multimodal and multiscale data and to provide tools for in silico experimentation. The availability of multimodal and multiscale quantitative data from the in vivo observation and reconstruction of cohorts of individuals should revolutionize practices in the field of developmental biology. Some major bottlenecks remain, related to the current limitations of long-term in vivo imaging and their consequences in terms of automated image processing. Imaging artifacts make 3D + time data from developing organisms difficult to process automatically. And the need for human supervision and time-consuming manual validation and correction is a major issue. The next breakthroughs may come from imaging techniques and may also rely on crowd sourcing for validating and correcting data. We also need new concepts in data analysis and theoretical modeling based on new representations of biological systems, faithful to biological observations but derived from formal descriptions to be shared by a new interdisciplinary community. In this context, the sea urchin is a model organism of choice for unprecedented achievements.
We thank Louise Duloquin for the time-lapse imaging of live sea urchin embryos and our collaborators at the BioEmergences platform for their contribution. This work was supported by the Centre National de la Recherche Scientifique, the Agence Nationale de la Recherche, the European Commission and the Region Ile de France. We thank Paul Bourgine for helpful discussions and Yannick Kergosien for critical reading of the manuscript. We apologize to the many authors whose work we were unable to cite owing to space constraints.
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