Image-based Modeling and Simulation of Morphogenesis

Fluorescence microscopy is a powerful tool for studying cell and molecular behavior in living cells. However, due to photobleaching and phototoxicity it is rarely able to provide 3-dimensional movies of cell behavior with sufficient spatial and temporal resolution to enable analysis or modeling of a single cell or tissue throughout complex behaviors. Therefore, analysis of dynamic behaviors usually requires the ability to combine information from multiple images or movies of different samples to cover different spatial and/or temporal resolutions. This can be done by constructing a generative model, a model that can produce synthetic movies of the full behavior and that has the highest likelihood of having produced all available data. Tools developed by our group and incorporated in the open source CellOrganizer project can construct generative models for different aspects of cell organization and behavior.

Centrioles are crucial cellular organelles that form cores of centrosomes and cilia. Centrioles must replicate once every cell cycle producing exactly one daughter centriole. Both failure to replicate and production of supernumerary centrioles jeopardizes cellular life and can cause disease, such as microcephaly and cancer. Temporary regulation of centriole replication, which is provided by the cell cycle, has been largely elucidated. However, the numeric control that ensures that only one procentriole is produced by each pre-existing centriole remains an unsolved puzzle. In this talk I will present our theoretical model of the centriole initiation process. We postulate that a small module comprising a kinase PLK4 and its activator-substrate STIL/Ana2/SAS-5 is the core of the protein network responsible for the initiation of a procentriole. Our model recapitulates symmetry-breaking transition in the spatial localization of PLK4 from a symmetric ring surrounding mother centriole to a single spot marking the position of nascent procentriole. Importantly, our model predicts that induction of a single procentriole is not just an advantageous happenstance but the result of winner-takes-all competition between multiple centriolar loci for the PLK4-STIL complexes. Weakening of competition by overexpression of PLK4 and STIL causes progressive addition of supernumerary procentrioles, as has been observed experimentally.

Development and morphogenesis of tissues, organs, and embryos emerges from the collective self-organization of cells that communicate though chemical and mechanical signals. The resulting material can be described by the physical models of active matter. Mechanistically understanding and reprogramming this system is a grand challenge. Our vision is to develop a virtual laboratory for active tissue biophysics, incorporating the known chemistry and mechanics into a computational model in 3D-space and time, in order to understand morphogenesis on an algorithmic basis. We present a scalable and efficient parallel simulation platform, which has enabled direct numerical simulations of active flows and materials both in bulk and on moving and deforming surfaces. This has led to the characterization of active turbulence and suggests a novel mechanical regulation of cell division. We outline the computational methods and software tools and present ongoing work in image-derived geometries and in using 3D virtual-reality visualization to gain a better intuition about these systems.

Cells have complex mechanical properties and can undergo significant deformations in flows. Accurate state-of-the-art cell models are potent to give an insight into the cell mechanics in microcirculation as well as various microfluidic devices. In order to perform predictive simulations the development of new models, methods, and algorithms is required. We will present particle-based methods and models suitable for large-scale simulations of cells in complex flow domains.

Choanoflagellates are unicellular microswimmers that are ubiquitous in aquatic habitats. They have a single flagellum that creates a flow toward the collar, the filtration apparatus composed of closely spaced filter strands. Loricate choanoflagellates have evolved a basket-like “skeleton” around the cell, the lorica, the function of which remains unknown. Here, we use Computational Fluid Dynamics (CFD) to explore the possible hydrodynamic function of the lorica by studying the choanoflagellate Diaphaoneca grandis, with and without its lorica. We study the flow rate, the flow recirculation, and the resulting clearance rate for the capture of motile and non-motile prey by the freely swimming choanoflagellate. We find no support for several previous hypotheses regarding the effects of the lorica. Rather, our simulations suggest that the main function of the lorica is to enhance the capture efficiency, but this happens at the cost of lower encounter rate with motile prey. The talk will also include results from CFD simulations of the leucon pumping unit.

Genetically, epigenetically and phenotypically cancer cells are known to be heterogeneous. While a plethora of studies have focused on genetic heterogeneity, very few studies have probed phenotypic heterogeneity in these cells, how such heterogeneity emerges, and the consequences of such heterogeneity vis-à-vis cancer invasion. We hypothesize that the buildup of compressive forces during initial tumor formation leads to emergence of phenotypically distinct sub-populations. To test this, we have developed a computational model using Cellular Potts model (CPM), wherein we track the growth of a tumor within a confined region from a single cell incorporating cell division, cell migration and cell death within the confined region.Assuming a simple time and area-dependent cell division rule, we show that temporal reduction in space owing to cell division leads to generation of cells which are both smaller and softer than the starting cell. Ongoing studies are evaluating the implication of such heterogeneity on invasion patterns as well as experimentally testing the predictions of our model.

Miquel Marin-Riera, Philipp Germann and James Sharpe. The vertebrate limb is a complex organ that has been key to the evolution of this group. Its early development involves outgrowth of a bud from the embryo flank and patterning of mesenchymal condensations that will later differentiate into skeletal elements. Although the molecular basis of patterning has been extensively studied, less is known about the cell and tissue-level morphogenetic processes driving limb bud growth and elongation. It has been previously shown that normal limb bud morphology cannot be achieved through volumetric growth alone, suggesting that directional cell behaviours are required. In order to theoretically explore how these can lead to proper limb bud elongation, we have built a cell-based computational model of limb bud morphogenesis that includes cell proliferation, cell polarisation and intercalation. Known morphogen gradients originating from the limb bud ectoderm (WNT3a, WNT7a) and mesenchyme (SHH) and the apical ectodermal ridge (FGF8) were simulated in order to provide spatial cues for cells to become polarised. By systematically building different hypotheses based on how cells can orient relative to these gradients, we were able to rule out the ones that did not result in proximo-distal tissue elongation or did not result in a limb bud-like morphology, whilst keeping the ones that did produce limb-like shapes. We found out that a model in which most cells intercalate within the plane normal to the distal (FGF8) morphogen gradient results in distal elongation and a limb-like shape. To further refine our model, we performed a parameter optimisation scheme in which we fine-tuned cell intercalation, cell proliferation and morphogen gradient properties and fit to the time-sequence of OPT scanned limb bud morphologies. As a next step, and as a more stringent test of our hypothesis we will fit the internal tissue movements by comparing mesenchymal cell clones with in silico clones predicted by our model. This study brings us one step closer to understanding the cell and tissue-level principles of early limb bud elongation and sheds some light into a general theory of mesenchyme elongation in early morphogenesis.

Embryogenesis is the process by which a single fertilized cell is turned into a multi-cellular organism. It is a process involving coordinated dynamics at multiple scales, from single molecules, to cells, to tissues. Dynamical processes in biology are studied using an ever-increasing number of microscopy techniques, each of which brings out unique features of the system. What can we learn from partial measurements of a developing embryo? How can we detect reproducible behaviors in 1000s of cells? How accurately can we predict the behavior of individual cells? This requires developing acquisition tools, integrating heterogeneous measurements, developing pattern recognition algorithms and inventing predictive theories. The techniques that we are using stem from the fields of multi-dimensional statistics, machine learning, image processing, complex systems and data visualization. We will illustrate our approaches with specific examples using datasets from studies of development in the sea urchin, drosophila, and mouse embryos.

Breaking symmetry of cell and tissues through elongation can be done by different means in epithelial tissues of the developing embryos, for example by neighbour exchange in Drosophila or by cell elongation in C. elegans. Despite understanding the generic rules of interactions between cells, the mechanisms leading to distinct morphogenesis processes are poorly understood. This is, partly, because of the complexity of interactions within in vivo tissues and an unclear understanding of the boundary conditions. Here, we show that in vivo tissue elongation can be recapitulated via in vitro experiments and explained by numerical simulations of physical models with simple rules. Using microfabrication to prepare circular epithelial MDCK colonies, cell biology experiments and numerical simulations, we report that anisotropy in the nematic field correlates with the appearance of leader cells, which are at the tips of local protrusions An outer acto-myosin cable delineates a boundary to the colony. The axis of this global symmetry breaking can be imposed by an external time periodic stretch which leads to directional protrusion of a cell, mimicking muscle driven elongation in C. elegans. We show that in vitro tissue elongation can reach the same extent as in vivo experiments, but cellular reorganisations through cell elongation, neighbour exchange or oriented cell division can be distinct. These in vitro results thus suggest that new rules could be utilized to direct in vivo tissue elongation.

The predominant emphasis of genomics, bioinformatics and computational biology is at the molecular scale, however many of the things we wish to understand occur at the macroscopic scale of organs and organisms: the development of a phenotype, the spread of a cancer, the regeneration of an organ. At the molecular scale, regulation of genes and proteins creates complex networks which control cell activities (division, migration, cell fate decisions, differentiation, and many others), with both an intracellular part (circuits of transcription factors) and an extracellular part (secreted ligands which move between cells allowing cell-cell communication, such as FGFs, WNTs, etc). The coordination of thousands of cells by this extended molecular network, leads to large-scale morphogenesis at the scale of tissues and organs. However, these large-scale tissue movements also feedback to the molecular scale: the movement of tissue regions relative to each other causes cells to receive dynamically changing concentrations of signaling molecules, and this in turn changes the activation or repression of genes and proteins. A full understanding of this large-scale feedback between genes, cells and tissues will require multi-scale computer modeling, and we have chosen vertebrate limb development as a model system to explore this problem. Crucially, the data on gene expression and tissue movements should be both dynamic and spatial. Traditional high-throughput “omics” technologies do not preserve spatial information, and we therefore develop novel 3D imaging technologies (OPT and SPIM) to generate geometric and spatial data for the models. I will present results of this interdisciplinary modeling approach, which is gradually allowing us to tackle this complex problem.

Recent advances in automated identification of partial differential equations (PDEs) from time-series data hold the promise to routinely discover novel governing equations of an underlying (bio-)physical system from (high-throughput) experimental observations. A common framework for learning such equations comprises three steps: (i) numerical approximation of spatial and temporal derivatives of the measured quantities across the observed domain, (ii) formulation and solution of sparsity-promoting penalized regression problem for data fitting, and (iii) data-driven model selection from the set of regularized solutions. In this framework, non-zero coefficients in the regression problem indicate partial derivatives that may be present in the underlying PDE formulation. We here introduce and analyze stability-based model selection approaches for PDE inference. Stability selection relies on data subsampling in combination with high dimensional variable selection algorithms, such as the Lasso and its variants. Variables are considered important if they are frequently selected in the penalized regression problem across multiple subsampled data sets. We show that stability selection can identify the true underlying PDE even in the presence of limited and noisy simulated data in a fully data-driven fashion. We also characterize the achievability performance of stability-based schemes, i.e., the number of samples necessary to achieve exact PDE selection. We also show the behavior of our stability-based model selection framework on fluorescence microscopy data in the context of developmental biology where the true underlying PDE model is not known. This is joint work with Suryanarayana Maddu and Ivo F. Sbalzarini.

The motion of living cells is in large part due to the interaction of semi-flexible actin filaments (F-actin) and myosin molecular motors, which induce the relative sliding of F-actin. It is often assumed that this simple sliding is sufficient to account for all actomyosin-based motion. While this is correct in our highly organized striated muscle, we question the application of this dogma to less ordered actomyosin systems, thus reexamining a cornerstone of our understanding of cellular motion.

Recent progress in imaging and computer modelling have increased our understanding of morphogenetic processes at different scales - from organs up to entire organisms. However, in the case of complex animal models (e.g. mouse embryogenesis), it is not yet entirely possible to observe in real time the full growth of a developing embryo, because it beyond E10.5 mouse embryos cannot be correctly cultured in vitro. Consequently, the current 3D data availability in these cases, even if extensive and detailed, provides only a characterisation of development at discrete moments in time, through single snapshots. To fill this gap, we are creating a computer-based approach to describe the evolution in time and space of developmental stages from 3D volumetric images. Specifically, we (1) represent the scalar intensity of each voxel of the images using the Fourier transform, (2) expand the Fourier coefficients using spherical harmonics and then (3) interpolate the spherical harmonics coefficients in time (over the developmental stages). As a result, (4) the reconstruction describes a continuous and smooth changing shape over space and time. We tested this approach using ~100 3D images of mouse limb buds generated by optical projection tomography (OPT), which had previously been staged using the embryonic Mouse Ontogenetic Staging System (eMOSS). The result represents the 4D growth of an ideal limb which take into account the common characteristics and features of all the limbs in the data set. In particular, we recreate the growing process starting from E10 (i.e. 10 days after conception) when the limb bud is just a small bump of tissue and finishing at E12.5 when the limb bud already shows a distinctive “paddle” shape. This approach, able to combine the complexity of different arbitrary shapes over space and time, increases our understanding of morphogenetic processes from a purely geometrical point of view and provides a quantitative basis for validating predictive models (e.g. computational modelling of limb development). This method could be in principle applied to more complex shapes like a whole embryo.

Keisuke Ishihara1,2,3, Elena Gromberg4, Marta N. Shahbazi5, Magdalena Zernicka-Goetz5, Jan F. Brugués1,2,3, Frank Jülicher2,3, Elly M. Tanaka4 1 Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany 2 Max Planck Institute for the Physics of Complex Systems, Dresden, Germany 3 Center for Systems Biology Dresden, Dresden, Germany 4 Research Institute of Molecular Pathology, Vienna, Austria 5 University of Cambridge, Cambridge, UK Abstract: The epithelium is a fundamental tissue architecture that lines the outer surfaces of many organs and inner cavities within them. While past studies have demonstrated how local differences in cell mechanical properties induce epithelial folding, the topology of epithelial surfaces has not been addressed. What are the cell biological and physical conditions that determine whether an epithelium remains connected, or divides into multiple, topologically distinct epithelia? To address this issue, we study neuroepithelium formation by differentiating free-floating 3D aggregates of mouse embryonic stem cells. Within 4 days, a continuous apical membrane domain forms in the interior of the tissue as a result of collective cell polarization and epithelialization. Treatment with retinoic acid induces the apical membrane to split up into multiple spherical structures, or fluid-filled cysts. We hypothesize that apical surface area and its topology are controlled by retinoic acid-mediated down regulation of PODXL, an apical membrane protein with a negatively charged extracellular domain. Indeed, PODXL heterozygote cells show fragmented apical surfaces in the absence of retinoic acid, and PODXL overexpression show continuous epithelium overcoming the effect of retinoic acid. Neutralizing the negative charge in the system mimics the effect of PODXL reduction, underscoring the importance of electrostatic charge in apical membrane mechanics. We develop a biophysical framework based on vertex model of tissue mechanics that predicts cell shape and epithelial topology from the abundance of apically localized, charged membrane proteins. Thus, we elucidate the cell biological basis for retinoic acid-mediated morphogenesis, and propose that epithelial self-organization can be conceptually understood in analogy to the topological transitions of surfactant self-assembly.

During development, epithelia undergo drastic shape changes that drive the formation of organs with distinct structures and functions. Many epithelia attach to an extracellular matrix (ECM) called the basement membrane. The basement membrane has distinct physical and chemical properties that depend on its composition, arrangement and dynamics. While most studies so far focused on the contribution of different cell behaviors to tissue shape changes, the role of the ECM in tissue morphogenesis is not as well understood. Can the physical properties of the ECM affect epithelial shape changes? What kinds of forces are exerted by the ECM onto cells in a tissue during morphogenesis? How do the cells in turn rearrange and change the mechanical and chemical properties of the ECM to accommodate tissue shape changes? My project aims to answer these questions using novel tools developed in our lab that help visualize the ECM in vivo in real time, during zebrafish optic cup morphogenesis. The optic cup gives rise to the neural retina and its characteristic hemispherical shape is crucial for organ function. This shape is obtained early in development during a morphogenetic event that transforms a flat bilayer optic vesicle into a hemispherical cup. This tissue wide shape change is brought about by various coordinated cell behaviors like basal constriction and collective cell migration. Previous studies have shown the requirements for functional ECM and cell-ECM interactions in facilitating these different cell behaviors to drive overall tissue shape change. However, the mechanism by which the ECM influences optic cup development remains poorly understood. By visualizing the ECM directly, we can now document how its composition, structure and mechanical properties change as the tissue changes its shape. This characterization will then allow us to test how dynamic ECM properties might influence the different cell behaviors to ultimately facilitate optic cup morphogenesis.

A deep and functional understanding of regeneration requires, not only an account of single cell activities such as gene expression, but also of the regenerating organism as an intricate system exhibiting complex dynamics and coordination over multiple levels of scale. Elucidating the rules of body-wide morphogenesis is especially essential for transitioning signalling data at the cellular level into advances in regenerative medicine. Here we report on the construction and validation of a computational model elucidating self-assembly mechanisms of morphogen gradients required for planaria regeneration. Vector transport of morphogens was identified as a fundamental requirement to account for virtually scale-free self-assembly of the morphogen gradients observed in planarian homeostasis and regeneration. The model correctly describes heteromorphoses following many known experimental manipulations, and accurately predicts outcomes of novel cutting scenarios. Experimental validation further supports vector transport mediated by motor proteins in nerve axons distributed throughout the planarian tissue, and indicates that the head-tail axis is controlled by the net polarity of neurons in a regenerating fragment. This model provides a comprehensive framework for mechanistically understanding fundamental aspects of target morphology and regenerated morphology, and sheds new light on the role of the nervous system in directing growth and form.

Pattern formation and growth of developing tissues involve the graded distribution of morphogens. Scaling of the morphogen gradient ensures proportioned morphological patterning of tissues with different sizes. On the other hand, we showed that growth of the drosophila wing disc is mediated by a mechanism in which cells compute the relative time derivative of the concentration of a morphogen: Dpp. In this context, scaling drives a homogenous increase of the morphogen concentration throughout the tissue and thereby can fuel homogeneous growth. A key question is how does the morphogen gradient scale? Scaling of the gradient implicates changes in endocytic trafficking of the morphogen and the rates of its lysosomal degradation. Effective changes of endocytic rates is fine tuned by the trafficking of the morphogen through two pathways: clathrin-mediated endocytosis and clic/geec. The molecular machinery controlling these endocytic events involve two extracellular factors, Pentagone and the HSPG Dally. We propose a mechanism by which these molecules can control scaling. The key observation is that Pentagone scale itself. We show that Pentagone scaling can drive the scaling of Dpp. How is then Pentagone scaling? We consider a model in which Pentagone scales itself by Advection/Dilution without the necessity of a further scaling factor.

Computational modeling and simulation become increasingly important to analyze tissue morphogenesis. A number of corresponding software tools have been developed but require scientists to encode their models in an imperative programming language. Morpheus (1,2), on the other hand, is an extensible open-source software framework that is entirely based on declarative modeling. It uses the domain-specific language MorpheusML to define multicellular models through a user-friendly GUI and has since proven applicable by a much broader community, including experimentalists and trainees. We here present how MorpheusML (3) and the open-source framework (4) allow for advanced scientific work-flows. MorpheusML provides a bio-mathematical language in which symbolic identifiers in mathematical expressions describe the dynamics of and coupling between the various model components. It can represent the spatial aspects of interacting cells and follows the software design rule of separation of model from implementation, enabling model sharing, versioning and archiving (3). A numerical simulation is then composed by automatic scheduling of predefined components in the simulator. Moreover, Morpheus supports simulations based on experimental data, e.g. segmented cell configurations, and offers a broad set of analysis tools to extract features right during simulation. A rich c++ API allows to extend MorpheusML and the simulator with user-tailored plugins. Finally, we apply Morpheus and image-based modeling to study the regulatory mechanisms underlying liver tissue architecture and flatworm regeneration (5). (1) Starruß et al. Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology. Bioinformatics 30, 1331, 2014. (2) Homepage: https://morpheus.gitlab.io (3) Model repository: https://imc.zih.tu-dresden.de/wiki/morpheus/doku.php?id=examples:examples (4) Open source code: https://gitlab.com/morpheus.lab/morpheus (5) Vu et al. Multi-scale coordination of planar cell polarity in planarians. BioRxiv 324822, 2018. Co-Authors: Jörn Starruß(1), Walter de Back(2), Andreas Deutsch(1), Lutz Brusch(1) (1) Center for Information Services and High Performance Computing (ZIH), (2) Institute for Medical Informatics and Biometry (IMB), TU Dresden, Germany

The evolution of organ asymmetries is less explored than the field of organ morphology and coiling. The digestive tract of elasmobranchs provides a fascinating model for studying the evolution of morphological asymmetries. Unique to elasmobranchs and all basal fishes is the spiral intestine, which may represent an intermediate morphology in evolution from the straight gut of lamprey to the elongated coils of higher vertebrates. The short spiral allows for a large absorptive surface area that can fit into a restrictive abdominal space. Using histology and high resolution microCT, we provide the first 3D morphometric analysis of the spiral intestine during development in the little skate, Leucoraja erinacea. Spiral formation is initiated by asymmetric growth in the mesenchyme, causing a bulging fold that protrudes into the lumen of the gut. As development proceeds, the fold elongates and spirals into a right-handed helix. Spiraling progresses along the anterior-posterior axis and is likely the result of mechanical forces driven by the asymmetric growth of surrounding tissues. After initial asymmetric growth, radial constraints from within the gut tube create constrictive forces further propagating spiraling. We propose a model for potential molecular and biophysical mechanisms that direct the morphogenesis of the spiral intestine.

A key challenge for the future of computational modelling is how to easily share complex image-driven simulations between a diverse community of theoreticians and experimentalists. This is essential so that different researchers can test and compare each others’ hypotheses, and to allow their new results to build on the previous results of others. We present our new modelling platform LIMB-NET, an openly accessible online simulator for intuitive image-based computational modelling, simulation, and visualisation of gene expression patterns crucial to limb development. LIMB-NET will allow remote users to upload and share the spatiotemporally-varying expression patterns of genes relevant to limb development throughout different stages of morphogenesis, mapping them onto a previously published standarised computational description of limb growth. LIMB-NET will incorporate three key functionalities, permitting researchers in the field of limb development to: 1) browse a database of existing known 2D gene expression patterns across a range of time points during early limb development 2) upload their own gene expression patterns, e.g., from WMISH, immunostaining, or other images, align the images based on developmental stage, and map the patterns into the modelling framework 3) straightforwardly formulate, simulate and compare computational models of gene regulatory networks In LIMB-NET, 2D gene expression patterns taken from images are mapped into a standard morphological framework, the ‘morphomovie’, covering the developmental stages E9.5 to E12.5 of mouse hindlimb bud. LIMB-NET’s customisable models are based on a reaction-diffusion framework simulated using finite-volume techniques on a moving finite element mesh. The models can use the experimental data stored in morphomovies as inputs. Expression patterns predicted by a given computational model can be visualised in the same morphomovie framework as experimentally acquired data, permitting a direct comparison to be made between the two, or indeed between outputs of different models. Most importantly, all this functionality will be accessible through a standard web browser, avoiding the need for any special software, and thus opening the field of image-driven modelling to the full diversity of the scientific community.