SimuCell3D: three-dimensional simulation of tissue mechanics with cell polarization

The three-dimensional (3D) organization of cells determines tissue function and integrity, and changes markedly in development and disease. Cell-based simulations have long been used to define the underlying mechanical principles. However, high computational costs have so far limited simulations to either simplified cell geometries or small tissue patches. Here, we present SimuCell3D, an efficient open-source program to simulate large tissues in three dimensions with subcellular resolution, growth, proliferation, extracellular matrix, fluid cavities, nuclei and non-uniform mechanical properties, as found in polarized epithelia. Spheroids, vesicles, sheets, tubes and other tissue geometries can readily be imported from microscopy images and simulated to infer biomechanical parameters. Doing so, we show that 3D cell shapes in layered and pseudostratified epithelia are largely governed by a competition between surface tension and intercellular adhesion. SimuCell3D enables the large-scale in silico study of 3D tissue organization in development and disease at a great level of detail.

Geometric effects position renal vesicles during kidney development

During kidney development, reciprocal signaling between the epithelium and the mesenchyme coordinates nephrogenesis with branching morphogenesis of the collecting ducts. The mechanism that positions the renal vesicles, and thus the nephrons, relative to the branching ureteric buds has remained elusive. By combining computational modeling and experiments, we show that geometric effects concentrate the key regulator, WNT9b, at the junctions between parent and daughter branches where renal vesicles emerge, even when uniformly expressed in the ureteric epithelium. This curvature effect might be a general paradigm to create non-uniform signaling in development.

2D effects enhance precision of gradient-based tissue patterning

Robust embryonic development requires pattern formation with high spatial accuracy. In epithelial tissues that are patterned by morphogen gradients, the emerging patterns achieve levels of precision that have recently been explained by a simple one-dimensional reaction-diffusion model with kinetic noise. Here, we show that patterning precision is even greater if transverse diffusion effects are at play in such tissues. The positional error, a measure for spatial patterning accuracy, decreases in wider tissues but then saturates beyond a width of about ten cells. This demonstrates that the precision of gradient-based patterning in two- or higher-dimensional systems can be even greater than predicted by 1D models, and further attests to the potential of noisy morphogen gradients for high-precision tissue patterning.

Impact of cell size on morphogen gradient precision

Tissue patterning during embryonic development is remarkably precise. In this paper, we numerically determine the impact of the cell diameter, gradient length, and the morphogen source on the variability of morphogen gradients. In this way, we show that the positional error increases with the gradient length relative to the size of the morphogen source, and with the square root of the cell diameter and the readout position. We provide theoretical explanations for these relationships, and show thatthey enable high patterning precision over developmental time for readouts that scale with expanding tissue domains, as observed in the Drosophila wing disc. Our analysis suggests that epithelial tissues generally achieve higher patterning precision with small cross-sectional cell areas. An extensive survey of measured apical cell areas shows that they are indeed small in developing tissues that are patterned by morphogen gradients. Enhanced precision may thus have led to the emergence of pseudostratification in epithelia, a phenomenon for which the evolutionary benefit had so far remained elusive.

Patterning precision under non-linear morphogen decay and molecular noise

Morphogen gradients can instruct cells about their position in a patterned tissue. Non-linear morphogen decay has been suggested to increase gradient precision by reducing the sensitivity to variability in the morphogen source. Here, we use cell-based simulations to quantitatively compare the positional error of gradients for linear and non-linear morphogen decay. While we confirm that non-linear decay reduces the positional error close to the source, the reduction is very small for physiological noise levels. Far from the source, the positional error is much larger for non-linear decay in tissues that pose a flux barrier to the morphogen at the boundary. In light of this new data, a physiological role of morphogen decay dynamics in patterning precision appears unlikely.

Time-lapse and cleared imaging of mouse embryonic lung explants to study three-dimensional cell morphology and topology dynamics

Here, we present a protocol for collecting high-spatiotemporal-resolution datasets of undisturbed mouse embryonic epithelial rudiments using light-sheet fluorescence microscopy. We describe steps for rudiment dissection, clearing, and embedding for cleared and live imaging. We then detail procedures for light-sheet imaging followed by image processing and morphometric analysis. We provide protocol variations for imaging both growing and optically cleared lung explants to encourage the quantitative exploration of three-dimensional cell shapes, cell organization, and complex cell-cell dynamics. For complete details on the use and execution of this protocol, please refer to Gómez et al. (2021).¹.

Temporal and sequential transcriptional dynamics define lineage shifts in corticogenesis

The cerebral cortex contains billions of neurons, and their disorganization or misspecification leads to neurodevelopmental disorders. Understanding how the plethora of projection neuron subtypes are generated by cortical neural stem cells (NSCs) is a major challenge. Here, we focused on elucidating the transcriptional landscape of murine embryonic NSCs, basal progenitors (BPs), and newborn neurons (NBNs) throughout cortical development. We uncover dynamic shifts in transcriptional space over time and heterogeneity within each progenitor population. We identified signature hallmarks of NSC, BP, and NBN clusters and predict active transcriptional nodes and networks that contribute to neural fate specification. We find that the expression of receptors, ligands, and downstream pathway components is highly dynamic over time and throughout the lineage implying differential responsiveness to signals. Thus, we provide an expansive compendium of gene expression during cortical development that will be an invaluable resource for studying neural developmental processes and neurodevelopmental disorders.

FGF8 induces chemokinesis and regulates condensation of mouse nephron progenitor cells

Kidneys develop via iterative branching of the ureteric epithelial tree and subsequent nephrogenesis at the branch points. Nephrons form in the cap mesenchyme as the metanephric mesenchyme (MM) condenses around the epithelial ureteric buds (UBs). Previous work has demonstrated that FGF8 is important for the survival of nephron progenitor cells (NPCs), and early deletion of Fgf8 leads to the cessation of nephron formation, which results in post-natal lethality. We now reveal a previously unreported function of FGF8. By combining transgenic mouse models, quantitative imaging assays and data-driven computational modelling, we show that FGF8 has a strong chemokinetic effect and that this chemokinetic effect is important for the condensation of NPCs to the UB. The computational model shows that the motility must be lower close to the UB to achieve NPC attachment. We conclude that the FGF8 signalling pathway is crucial for the coordination of NPC condensation at the UB. Chemokinetic effects have also been described for other FGFs and may be generally important for the formation of mesenchymal condensates.

Abstract 3073: Bladder cancer patient-derived organoids to decipher cellular plasticity and cancer progression

Introduction: Muscular Invasive Bladder Cancer (MIBC) is a highly heterogeneous disease. A consensus classification, based on gene expression profiling, has identified six MIBC subgroups, ranging from basal/squamous (Ba/Sq) to luminal papillary (LumP). This classification is a static representation of the disease and does not account for cellular plasticity, which may induce phenotype switch and cancer progression. Here, we aimed at identifying factors involved in cellular plasticity using bladder cancer patient-derived organoids (PDO) models.

Methods: Bladder cancer RNA sequencing data from bulk and single cell experiments were downloaded from public repositories. Samples from both datasets were classified using the consensus molecular classification. Pathway activation scores and cell-cell interaction scores were calculated for each subtype. Differential gene expression analysis was performed with the R packages edgeR and Seurat. MIBC samples were collected from bladder cancer patients undergoing surgical treatment. The samples were mechanically and enzymatically digested to generate a cell suspension which was seeded in Matrigel and immersed in growth-factor supplemented medium. Phenotypical characterization of long-term PDO lines was performed through immunofluorescence (IF). The PDOs were classified as Luminal, Basal or Mixed, based on the number of cells expressing the luminal marker CK8 or the basal marker CK5. Three selected organoids lines were cultured in alginate, immersed in a serum-free chemically-defined medium.

Results: Long-term PDO lines were successfully generated from 6 out of 13 MIBC samples. Organoids from the same line showed a consistent expression of basal and luminal markers. One line was classified as Basal, 2 lines as Mixed and 3 lines as Luminal. Exploring bulk RNAseq and scRNAseq datasets, we identified several genes whose expression was significantly altered in Ba/Sq and LumP MIBC subtypes. In particular, SHH and related BMP genes were significantly less expressed in Ba/Sq samples than in LumP. In addition, we observed an overexpression of BMP3 in LumP samples and of TGFβ2 in Ba/Sq samples. As preliminary test, we formulated a chemically-defined medium containing inhibitors of the proteins encoded by the identified genes (TGFβ inhibitor and Noggin); using this medium, we were able to maintain organoids from a Luminal, Basal and Mixed subtype in culture for up to two weeks. Interestingly, after two weeks of culture, IF analysis highlighted the presence of cells expressing luminal markers in the basal organoid line, suggesting culture-induced change of phenotype.

Conclusions: Bladder cancer PDOs represent promising models to study MIBC plasticity. The integration of RNA sequencing data and the successful culture of PDOs in chemically-defined culture conditions may allow to identify candidate factors impacting the phenotype of bladder cancer cells.

Citation Format: Michele Garioni, Luca Roma, Renaud Mével, Tatjana Vlajnic, Heike Pueschel, Dagmar Iber, Hans-Helge Seifert, Cyrill A. Rentsch, Lukas Bubendorf, Clémentine Le Magnen. Bladder cancer patient-derived organoids to decipher cellular plasticity and cancer progression [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 3073.

Relationship between epithelial organization and morphogen interpretation

Despite molecular noise and genetic differences between individuals, developmental outcomes are remarkably constant. Decades of research has focused on the underlying mechanisms that ensure this precision and robustness. Recent quantifications of chemical gradients and epithelial cell shapes provide novel insights into the basis of precise development. In this review, we argue that these two aspects may be linked in epithelial morphogenesis.

Hinge point emergence in mammalian spinal neurulation

Neurulation is the process in early vertebrate embryonic development during which the neural plate folds to form the neural tube. Spinal neural tube folding in the posterior neuropore changes over time, first showing a median hinge point, then both the median hinge point and dorsolateral hinge points, followed by dorsolateral hinge points only. The biomechanical mechanism of hinge point formation in the mammalian neural tube is poorly understood. Here we employ a mechanical finite element model to study neural tube formation. The computational model mimics the mammalian neural tube using microscopy data from mouse and human embryos. While intrinsic curvature at the neural plate midline has been hypothesized to drive neural tube folding, intrinsic curvature was not sufficient for tube closure in our simulations. We achieved neural tube closure with an alternative model combining mesoderm expansion, nonneural ectoderm expansion, and neural plate adhesion to the notochord. Dorsolateral hinge points emerged in simulations with low mesoderm expansion and zippering. We propose that zippering provides the biomechanical force for dorsolateral hinge point formation in settings where the neural plate lateral sides extend above the mesoderm. Together, these results provide a perspective on the biomechanical and molecular mechanism of mammalian spinal neurulation.

Tracheal Ring Formation

The trachea is a long tube that enables air passage between the larynx and the bronchi. C-shaped cartilage rings on the ventral side stabilise the structure. On its esophagus-facing dorsal side, deformable smooth muscle facilitates the passage of food in the esophagus. While the symmetry break along the dorsal-ventral axis is well understood, the molecular mechanism that results in the periodic Sox9 expression pattern that translates into the cartilage rings has remained elusive. Here, we review the molecular regulatory interactions that have been elucidated, and discuss possible patterning mechanisms. Understanding the principles of self-organisation is important, both to define biomedical interventions and to enable tissue engineering.

Precision of morphogen gradients in neural tube development

Morphogen gradients encode positional information during development. How high patterning precision is achieved despite natural variation in both the morphogen gradients and in the readout process, is still largely elusive. Here, we show that the positional error of gradients in the mouse neural tube has previously been overestimated, and that the reported accuracy of the central progenitor domain boundaries in the mouse neural tube can be achieved with a single gradient, rather than requiring the simultaneous readout of opposing gradients. Consistently and independently, numerical simulations based on measured molecular noise levels likewise result in lower gradient variabilities than reported. Finally, we show that the patterning mechanism yields progenitor cell numbers with even greater precision than boundary positions, as gradient amplitude changes do not affect interior progenitor domain sizes. We conclude that single gradients can yield the observed developmental precision, which provides prospects for tissue engineering.

Development of a 3D atlas of the embryonic pancreas for topological and quantitative analysis of heterologous cell interactions

Generating comprehensive image maps, while preserving spatial three-dimensional (3D) context, is essential in order to locate and assess quantitatively specific cellular features and cell-cell interactions during organ development. Despite recent advances in 3D imaging approaches, our current knowledge of the spatial organization of distinct cell types in the embryonic pancreatic tissue is still largely based on two-dimensional histological sections. Here, we present a light-sheet fluorescence microscopy approach to image the pancreas in three dimensions and map tissue interactions at key time points in the mouse embryo. We demonstrate the utility of the approach by providing volumetric data, 3D distribution of three main cellular components (epithelial, mesenchymal and endothelial cells) within the developing pancreas, and quantification of their relative cellular abundance within the tissue. Interestingly, our 3D images show that endocrine cells are constantly and increasingly in contact with endothelial cells forming small vessels, whereas the interactions with mesenchymal cells decrease over time. These findings suggest distinct cell-cell interaction requirements for early endocrine cell specification and late differentiation. Lastly, we combine our image data in an open-source online repository (referred to as the Pancreas Embryonic Cell Atlas).

Summary: A light-sheet fluorescence microscopy approach is used for 3D imaging of the pancreas and to quantitatively map its interactions with surrounding tissues at key development time points in the mouse embryo.

3D cell neighbour dynamics in growing pseudostratified epithelia

During morphogenesis, epithelial sheets remodel into complex geometries. How cells dynamically organise their contact with neighbouring cells in these tightly packed tissues is poorly understood. We have used light-sheet microscopy of growing mouse embryonic lung explants, three-dimensional cell segmentation, and physical theory to unravel the principles behind 3D cell organisation in growing pseudostratified epithelia. We find that cells have highly irregular 3D shapes and exhibit numerous neighbour intercalations along the apical-basal axis as well as over time. Despite the fluidic nature, the cell packing configurations follow fundamental relationships previously described for apical epithelial layers, that is, Euler's polyhedron formula, Lewis' law, and Aboav-Weaire's law, at all times and across the entire tissue thickness. This arrangement minimises the lateral cell-cell surface energy for a given cross-sectional area variability, generated primarily by the distribution and movement of nuclei. We conclude that the complex 3D cell organisation in growing epithelia emerges from simple physical principles.

Positional information encoded in the dynamic differences between neighboring oscillators during vertebrate segmentation

A central problem in developmental biology is to understand how cells interpret their positional information to give rise to spatial patterns, such as the process of periodic segmentation of the vertebrate embryo into somites. For decades, somite formation has been interpreted according to the clock-and-wavefront model. In this conceptual framework, molecular oscillators set the frequency of somite formation while the positional information is encoded in signaling gradients. Recent experiments using ex vivo explants have challenged this interpretation, suggesting that positional information is encoded in the properties of the oscillators, independent of long-range modulations such as signaling gradients. Here, we propose that positional information is encoded in the difference in the levels of neighboring oscillators. The differences gradually increase because both the amplitude and the period of the oscillators increase with time. When this difference exceeds a certain threshold, the segmentation program starts. Using this framework, we quantitatively fit experimental data from in vivo and ex vivo mouse segmentation, and propose mechanisms of somite scaling. Our results suggest a novel mechanism of spatial pattern formation based on the local interactions between dynamic molecular oscillators.

Organ-Specific Branching Morphogenesis

A common developmental process, called branching morphogenesis, generates the epithelial trees in a variety of organs, including the lungs, kidneys, and glands. How branching morphogenesis can create epithelial architectures of very different shapes and functions remains elusive. In this review, we compare branching morphogenesis and its regulation in lungs and kidneys and discuss the role of signaling pathways, the mesenchyme, the extracellular matrix, and the cytoskeleton as potential organ-specific determinants of branch position, orientation, and shape. Identifying the determinants of branch and organ shape and their adaptation in different organs may reveal how a highly conserved developmental process can be adapted to different structural and functional frameworks and should provide important insights into epithelial morphogenesis and developmental disorders.

The biomechanical basis of biased epithelial tube elongation in lung and kidney development

During lung development, epithelial branches expand preferentially in a longitudinal direction. This bias in outgrowth has been linked to a bias in cell shape and in the cell division plane. How this bias arises is unknown. Here, we show that biased epithelial outgrowth occurs independent of the surrounding mesenchyme, of preferential turnover of the extracellular matrix at the bud tips and of FGF signalling. There is also no evidence for actin-rich filopodia at the bud tips. Rather, we find epithelial tubes to be collapsed during early lung and kidney development, and we observe fluid flow in the narrow tubes. By simulating the measured fluid flow inside segmented narrow epithelial tubes, we show that the shear stress levels on the apical surface are sufficient to explain the reported bias in cell shape and outgrowth. We use a cell-based vertex model to confirm that apical shear forces, unlike constricting forces, can give rise to both the observed bias in cell shapes and tube elongation. We conclude that shear stress may be a more general driver of biased tube elongation beyond its established role in angiogenesis. This article has an associated 'The people behind the papers' interview.

The control of lung branching morphogenesis

Branching morphogenesis generates epithelial trees which facilitate gas exchange, filtering, as well as secretion processes with their large surface to volume ratio. In this review, we focus on the developmental mechanisms that control the early stages of lung branching morphogenesis. Lung branching morphogenesis involves the stereotypic, recurrent definition of new branch points, subsequent epithelial budding, and lung tube elongation. We discuss current models and experimental evidence for each of these steps. Finally, we discuss the role of the mesenchyme in determining the organ-specific shape.

Id4 Downstream of Notch2 Maintains Neural Stem Cell Quiescence in the Adult Hippocampus

Neural stem cells (NSCs) in the adult mouse hippocampal dentate gyrus (DG) are mostly quiescent, and only a few are in cell cycle at any point in time. DG NSCs become increasingly dormant with age and enter mitosis less frequently, which impinges on neurogenesis. How NSC inactivity is maintained is largely unknown. Here, we found that Id4 is a downstream target of Notch2 signaling and maintains DG NSC quiescence by blocking cell-cycle entry. Id4 expression is sufficient to promote DG NSC quiescence and Id4 knockdown rescues Notch2-induced inhibition of NSC proliferation. Id4 deletion activates NSC proliferation in the DG without evoking neuron generation, and overexpression increases NSC maintenance while promoting astrogliogenesis at the expense of neurogenesis. Together, our findings indicate that Id4 is a major effector of Notch2 signaling in NSCs and a Notch2-Id4 axis promotes NSC quiescence in the adult DG, uncoupling NSC activation from neuronal differentiation.

A Shh/Gli-driven three-node timer motif controls temporal identity and fate of neural stem cells

How time is measured by neural stem cells during temporal neurogenesis has remained unresolved. By combining experiments and computational modeling, we define a Shh/Gli-driven three-node timer underlying the sequential generation of motor neurons (MNs) and serotonergic neurons in the brainstem. The timer is founded on temporal decline of Gli-activator and Gli-repressor activities established through down-regulation of Gli transcription. The circuitry conforms an incoherent feed-forward loop, whereby Gli proteins not only promote expression of Phox2b and thereby MN-fate but also account for a delayed activation of a self-promoting transforming growth factor-β (Tgfβ) node triggering a fate switch by repressing Phox2b. Hysteresis and spatial averaging by diffusion of Tgfβ counteract noise and increase temporal accuracy at the population level, providing a functional rationale for the intrinsically programmed activation of extrinsic switch signals in temporal patterning. Our study defines how time is reliably encoded during the sequential specification of neurons.

Cell-based simulations of biased epithelial lung growth

During morphogenesis, epithelial tubes elongate. In the case of the mammalian lung, biased elongation has been linked to a bias in cell shape and cell division, but it has remained unclear whether a bias in cell shape along the axis of outgrowth is sufficient for biased outgrowth and how it arises. Here, we use our 2D cell-based tissue simulation software [Formula: see text] to investigate the conditions for biased epithelial outgrowth. We show that the observed bias in cell shape and cell division can result in the observed bias in outgrowth only in the case of strong cortical tension, and comparison to biological data suggests that the cortical tension in epithelia is likely sufficient. We explore mechanisms that may result in the observed bias in cell division and cell shapes. To this end, we test the possibility that the surrounding tissue or extracellular matrix acts as a mechanical constraint that biases growth in the longitudinal direction. While external compressive forces can result in the observed bias in outgrowth, we find that they do not result in the observed bias in cell shapes. We conclude that other mechanisms must exist that generate the bias in lung epithelial outgrowth.

Systems NMR: single-sample quantification of RNA, proteins and metabolites for biomolecular network analysis

Cellular behavior is controlled by the interplay of diverse biomolecules. Most experimental methods, however, can monitor only a single molecule class or reaction type at a time. We developed an in vitro Nuclear Magnetic Resonance spectroscopy (NMR) approach, which permitted dynamic quantification of an entire “heterotypic” network – simultaneously monitoring three distinct molecule classes (metabolites, proteins, RNA) and all elementary reaction types (bimolecular interactions, catalysis, unimolecular changes). Focusing on an 8-reaction co-transcriptional RNA folding network, in a single sample we recorded over 35 time-points with over 170 observables each, and accurately determined 5 core reaction constants in multiplex. This reconstruction revealed unexpected cross-talk between the different reactions. We further observed dynamic phase-separation in a system of five distinct RNA binding domains in the course of the RNA transcription reaction. Our Systems NMR approach provides a deeper understanding of biological network dynamics by combining the dynamic resolution of biochemical assays and the multiplexing ability of “omics”.

Generation of 3D Soluble Signal Gradients in Cell-Laden Hydrogels Using Passive Diffusion

Soluble signal gradients play an important role in organ patterning, cell migration, and differentiation. Currently, signal gradients in 2D cell culture are realized using microfluidics and here cells are exposed to high and nonphysiological shear stress. Tissue morphogenesis (organogenesis) however occurs in 3D and therefore there is a need for simple and practical systems to impose gradients to cells dispersed in 3D matrix. Herein, a 3D gradient generator based on passive diffusion elements that recapitulates interstitial flow and is capable of imposing predictable gradients over long length scales (6 mm) lasting up to 48 h to cells dispersed in a hydrogel environment is reported. Using recombinant human WNT3A (rhWNT3A), the spatiotemporal activation of the canonical WNT pathway in human epithelial kidney cells and human mesenchymal stems cells expressing a green fluorescence protein reporter on a transcription factor/lymphoid enhancer-binding factor (TCF/LEF) promoter is demonstrated. By refining computation models based on experimental findings, the diffusion coefficient of rhWNT3A in presence of human cells in 3D is determined. Furthermore, the formation of rhBMP4 gradients is visualized using immunohistochemistry by staining for phospho-SMAD1/5, the downstream targets of the bone morphogenetic protein (BMP) pathway. The simplicity of the gradient generator is expected to spur its adoption in studying developmental biology paradigms in vitro.

Growth and size control during development

The size and shape of organs are characteristic for each species. Even when organisms develop to different sizes due to varying environmental conditions, such as nutrition, organ size follows species-specific rules of proportionality to the rest of the body, a phenomenon referred to as allometry. Therefore, for a given environment, organs stop growth at a predictable size set by the species's genotype. How do organs stop growth? How can related species give rise to organs of strikingly different size? No definitive answer has been given to date. One of the major models for the studies of growth termination is the vinegar fly Drosophila melanogaster. Therefore, this review will focus mostly on work carried out in Drosophila to try to tease apart potential mechanisms and identify routes for further investigation. One general rule, found across the animal kingdom, is that the rate of growth declines with developmental time. Therefore, answers to the problem of growth termination should explain this seemingly universal fact. In addition, growth termination is intimately related to the problems of robustness (i.e. precision) and plasticity in organ size, symmetric and asymmetric organ development, and of how the ‘target’ size depends on extrinsic, environmental factors.

Travelling waves in somitogenesis: Collective cellular properties emerge from time-delayed juxtacrine oscillation coupling

The sculpturing of the vertebrate body plan into segments begins with the sequential formation of somites in the presomitic mesoderm (PSM). The rhythmicity of this process is controlled by travelling waves of gene expression. These kinetic waves emerge from coupled cellular oscillators and sweep across the PSM. In zebrafish, the oscillations are driven by autorepression of her genes and are synchronized via Notch signalling. Mathematical modelling has played an important role in explaining how collective properties emerge from the molecular interactions. Increasingly more quantitative experimental data permits the validation of those mathematical models, yet leads to increasingly more complex model formulations that hamper an intuitive understanding of the underlying mechanisms. Here, we review previous efforts, and design a mechanistic model of the her1 oscillator, which represents the experimentally viable her7;hes6 double mutant. This genetically simplified system is ideally suited to conceptually recapitulate oscillatory entrainment and travelling wave formation, and to highlight open questions. It shows that three key parameters, the autorepression delay, the juxtacrine coupling delay, and the coupling strength, are sufficient to understand the emergence of the collective period, the collective amplitude, and the synchronization of neighbouring Her1 oscillators. Moreover, two spatiotemporal time delay gradients, in the autorepression and in the juxtacrine signalling, are required to explain the collective oscillatory dynamics and synchrony of PSM cells. The highlighted developmental principles likely apply more generally to other developmental processes, including neurogenesis and angiogenesis.

Simulation of Morphogen and Tissue Dynamics

Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modeling this process can provide novel insights into development and the principles that orchestrate the developmental processes. This chapter focuses on the mathematical description and numerical simulation of developmental processes. In particular, we discuss the mathematical representation of morphogen and tissue dynamics on static and growing domains, as well as the corresponding tissue mechanics. In addition, we give an overview of numerical methods that are routinely used to solve the resulting systems of partial differential equations. These include the finite element method and the Lattice Boltzmann method for the discretization as well as the arbitrary Lagrangian-Eulerian method and the Diffuse-Domain method to numerically treat deforming domains.

Differential interactions between Notch and ID factors control neurogenesis by modulating Hes factor autoregulation

During embryonic and adult neurogenesis, neural stem cells (NSCs) generate the correct number and types of neurons in a temporospatial fashion. Control of NSC activity and fate is crucial for brain formation and homeostasis. Neurogenesis in the embryonic and adult brain differ considerably, but Notch signaling and inhibitor of DNA-binding (ID) factors are pivotal in both. Notch and ID factors regulate NSC maintenance; however, it has been difficult to evaluate how these pathways potentially interact. Here, we combined mathematical modeling with analysis of single-cell transcriptomic data to elucidate unforeseen interactions between the Notch and ID factor pathways. During brain development, Notch signaling dominates and directly regulates Id4 expression, preventing other ID factors from inducing NSC quiescence. Conversely, during adult neurogenesis, Notch signaling and Id2/3 regulate neurogenesis in a complementary manner and ID factors can induce NSC maintenance and quiescence in the absence of Notch. Our analyses unveil key molecular interactions underlying NSC maintenance and mechanistic differences between embryonic and adult neurogenesis. Similar Notch and ID factor interactions may be crucial in other stem cell systems.

Summary: Computational analysis of transcriptome data from neural stem cells reveals key differences in the synergistic interactions between Notch and inhibitor of DNA-binding factors during embryonic and adult neurogenesis.

Growth control in the Drosophila eye disc by the cytokine Unpaired

A fundamental question in developmental biology is how organ size is controlled. We have previously shown that the area growth rate in the Drosophila eye primordium declines inversely proportionally to the increase in its area. How the observed reduction in the growth rate is achieved is unknown. Here, we explore the dilution of the cytokine Unpaired (Upd) as a possible candidate mechanism. In the developing eye, upd expression is transient, ceasing at the time when the morphogenetic furrow first emerges. We confirm experimentally that the diffusion and stability of the JAK/STAT ligand Upd are sufficient to control eye disc growth via a dilution mechanism. We further show that sequestration of Upd by ectopic expression of an inactive form of the receptor Domeless (Dome) results in a substantially lower growth rate, but the area growth rate still declines inversely proportionally to the area increase. This growth rate-to-area relationship is no longer observed when Upd dilution is prevented by the continuous, ectopic expression of Upd. We conclude that a mechanism based on the dilution of the growth modulator Upd can explain how growth termination is controlled in the eye disc.

An Unbiased Analysis of Candidate Mechanisms for the Regulation of Drosophila Wing Disc Growth

The control of organ size presents a fundamental open problem in biology. A declining growth rate is observed in all studied higher animals, and the growth limiting mechanism may therefore be evolutionary conserved. Most studies of organ growth control have been carried out in Drosophila imaginal discs. We have previously shown that the area growth rate in the Drosophila eye primordium declines inversely proportional to the increase in its area, which is consistent with a dilution mechanism for growth control. Here, we show that a dilution mechanism cannot explain growth control in the Drosophila wing disc. We computationally evaluate a range of alternative candidate mechanisms and show that the experimental data can be best explained by a biphasic growth law. However, also logistic growth and an exponentially declining growth rate fit the data very well. The three growth laws correspond to fundamentally different growth mechanisms that we discuss. Since, as we show, a fit to the available experimental growth kinetics is insufficient to define the underlying mechanism of growth control, future experimental studies must focus on the molecular mechanisms to define the mechanism of growth control.

A Model of the Spatio-temporal Dynamics of Drosophila Eye Disc Development

Patterning and growth are linked during early development and have to be tightly controlled to result in a functional tissue or organ. During the development of the Drosophila eye, this linkage is particularly clear: the growth of the eye primordium mainly results from proliferating cells ahead of the morphogenetic furrow (MF), a moving signaling wave that sweeps across the tissue from the posterior to the anterior side, that induces proliferating cells anterior to it to differentiate and become cell cycle quiescent in its wake. Therefore, final eye disc size depends on the proliferation rate of undifferentiated cells and on the speed with which the MF sweeps across the eye disc. We developed a spatio-temporal model of the growing eye disc based on the regulatory interactions controlled by the signals Decapentaplegic (Dpp), Hedgehog (Hh) and the transcription factor Homothorax (Hth) and explored how the signaling patterns affect the movement of the MF and impact on eye disc growth. We used published and new quantitative data to parameterize the model. In particular, two crucial parameter values, the degradation rate of Hth and the diffusion coefficient of Hh, were measured. The model is able to reproduce the linear movement of the MF and the termination of growth of the primordium. We further show that the model can explain several mutant phenotypes, but fails to reproduce the previously observed scaling of the Dpp gradient in the anterior compartment.

MOCCASIN: converting MATLAB ODE models to SBML

Summary: MATLAB is popular in biological research for creating and simulating models that use ordinary differential equations (ODEs). However, sharing or using these models outside of MATLAB is often problematic. A community standard such as Systems Biology Markup Language (SBML) can serve as a neutral exchange format, but translating models from MATLAB to SBML can be challenging—especially for legacy models not written with translation in mind. We developed MOCCASIN (Model ODE Converter for Creating Automated SBML INteroperability) to help. MOCCASIN can convert ODE-based MATLAB models of biochemical reaction networks into the SBML format.

Availability and implementation: MOCCASIN is available under the terms of the LGPL 2.1 license (http://www.gnu.org/licenses/lgpl-2.1.html). Source code, binaries and test cases can be freely obtained from https://github.com/sbmlteam/moccasin.

Contact: mhucka@caltech.edu

Supplementary information: More information is available at https://github.com/sbmlteam/moccasin.

A quantitative analysis of growth control in the Drosophila eye disc

The size and shape of organs is species specific, and even in species in which organ size is strongly influenced by environmental cues, such as nutrition or temperature, it follows defined rules. Therefore, mechanisms must exist to ensure a tight control of organ size within a given species, while being flexible enough to allow for the evolution of different organ sizes in different species. We combined computational modeling and quantitative measurements to analyze growth control in the Drosophila eye disc. We find that the area growth rate declines inversely proportional to the increasing total eye disc area. We identify two growth laws that are consistent with the growth data and that would explain the extraordinary robustness and evolutionary plasticity of the growth process and thus of the final adult eye size. These two growth laws correspond to very different control mechanisms and we discuss how each of these laws constrains the set of candidate biological mechanisms for growth control in the Drosophila eye disc.

Read-Out of Dynamic Morphogen Gradients on Growing Domains

Quantitative data from the Drosophila wing imaginal disc reveals that the amplitude of the Decapentaplegic (Dpp) morphogen gradient increases continuously. It is an open question how cells can determine their relative position within a domain based on a continuously increasing gradient. Here we show that pre-steady state diffusion-based dispersal of morphogens results in a zone within the growing domain where the concentration remains constant over the patterning period. The position of the zone that is predicted based on quantitative data for the Dpp morphogen corresponds to where the Dpp-dependent gene expression boundaries of spalt (sal) and daughters against dpp (dad) emerge. The model also suggests that genes that are scaling and are expressed at lateral positions are either under the control of a different read-out mechanism or under the control of a different morphogen. The patterning mechanism explains the extraordinary robustness that is observed for variations in Dpp production, and offers an explanation for the dual role of Dpp in controlling patterning and growth. Pre-steady-state dynamics are pervasive in morphogen-controlled systems, thus making this a probable general mechanism for the scaled read-out of morphogen gradients in growing developmental systems.

Axis Patterning by BMPs: Cnidarian Network Reveals Evolutionary Constraints

BMP signaling plays a crucial role in the establishment of the dorso-ventral body axis in bilaterally symmetric animals. However, the topologies of the bone morphogenetic protein (BMP) signaling networks vary drastically in different animal groups, raising questions about the evolutionary constraints and evolvability of BMP signaling systems. Using loss-of-function analysis and mathematical modeling, we show that two signaling centers expressing different BMPs and BMP antagonists maintain the secondary axis of the sea anemone Nematostella. We demonstrate that BMP signaling is required for asymmetric Hox gene expression and mesentery formation. Computational analysis reveals that network parameters related to BMP4 and Chordin are constrained both in Nematostella and Xenopus, while those describing the BMP signaling modulators can vary significantly. Notably, only chordin, but not bmp4 expression needs to be spatially restricted for robust signaling gradient formation. Our data provide an explanation of the evolvability of BMP signaling systems in axis formation throughout Eumetazoa.

LBIBCell: a cell-based simulation environment for morphogenetic problems

MOTIVATION

The simulation of morphogenetic problems requires the simultaneous and coupled simulation of signalling and tissue dynamics. A cellular resolution of the tissue domain is important to adequately describe the impact of cell-based events, such as cell division, cell-cell interactions and spatially restricted signalling events. A tightly coupled cell-based mechano-regulatory simulation tool is therefore required.

RESULTS

We developed an open-source software framework for morphogenetic problems. The environment offers core functionalities for the tissue and signalling models. In addition, the software offers great flexibility to add custom extensions and biologically motivated processes. Cells are represented as highly resolved, massless elastic polygons; the viscous properties of the tissue are modelled by a Newtonian fluid. The Immersed Boundary method is used to model the interaction between the viscous and elastic properties of the cells, thus extending on the IBCell model. The fluid and signalling processes are solved using the Lattice Boltzmann method. As application examples we simulate signalling-dependent tissue dynamics.

AVAILABILITY AND IMPLEMENTATION

The documentation and source code are available on http://tanakas.bitbucket.org/lbibcell/index.html

An interplay of geometry and signaling enables robust lung branching morphogenesis

Early branching events during lung development are stereotyped. Although key regulatory components have been defined, the branching mechanism remains elusive. We have now used a developmental series of 3D geometric datasets of mouse embryonic lungs as well as time-lapse movies of cultured lungs to obtain physiological geometries and displacement fields. We find that only a ligand-receptor-based Turing model in combination with a particular geometry effect that arises from the distinct expression domains of ligands and receptors successfully predicts the embryonic areas of outgrowth and supports robust branch outgrowth. The geometry effect alone does not support bifurcating outgrowth, while the Turing mechanism alone is not robust to noisy initial conditions. The negative feedback between the individual Turing modules formed by fibroblast growth factor 10 (FGF10) and sonic hedgehog (SHH) enlarges the parameter space for which the embryonic growth field is reproduced. We therefore propose that a signaling mechanism based on FGF10 and SHH directs outgrowth of the lung bud via a ligand-receptor-based Turing mechanism and a geometry effect.

Feedback, receptor clustering, and receptor restriction to single cells yield large Turing spaces for ligand-receptor-based Turing models

Turing mechanisms can yield a large variety of patterns from noisy, homogenous initial conditions and have been proposed as patterning mechanism for many developmental processes. However, the molecular components that give rise to Turing patterns have remained elusive, and the small size of the parameter space that permits Turing patterns to emerge makes it difficult to explain how Turing patterns could evolve. We have recently shown that Turing patterns can be obtained with a single ligand if the ligand-receptor interaction is taken into account. Here we show that the general properties of ligand-receptor systems result in very large Turing spaces. Thus, the restriction of receptors to single cells, negative feedbacks, regulatory interactions among different ligand-receptor systems, and the clustering of receptors on the cell surface all greatly enlarge the Turing space. We further show that the feedbacks that occur in the FGF10-SHH network that controls lung branching morphogenesis are sufficient to result in large Turing spaces. We conclude that the cellular restriction of receptors provides a mechanism to sufficiently increase the size of the Turing space to make the evolution of Turing patterns likely. Additional feedbacks may then have further enlarged the Turing space. Given their robustness and flexibility, we propose that receptor-ligand-based Turing mechanisms present a general mechanism for patterning in biology.

Inter-dependent tissue growth and Turing patterning in a model for long bone development

The development of long bones requires a sophisticated spatial organization of cellular signalling, proliferation, and differentiation programs. How such spatial organization emerges on the growing long bone domain is still unresolved. Based on the reported biochemical interactions we developed a regulatory model for the core signalling factors IHH, PTCH1, and PTHrP and included two cell types, proliferating/resting chondrocytes and (pre-)hypertrophic chondrocytes. We show that the reported IHH-PTCH1 interaction gives rise to a Schnakenberg-type Turing kinetics, and that inclusion of PTHrP is important to achieve robust patterning when coupling patterning and tissue dynamics. The model reproduces relevant spatiotemporal gene expression patterns, as well as a number of relevant mutant phenotypes. In summary, we propose that a ligand-receptor based Turing mechanism may control the emergence of patterns during long bone development, with PTHrP as an important mediator to confer patterning robustness when the sensitive Turing system is coupled to the dynamics of a growing and differentiating tissue. We have previously shown that ligand-receptor based Turing mechanisms can also result from BMP-receptor, SHH-receptor, and GDNF-receptor interactions, and that these reproduce the wildtype and mutant patterns during digit formation in limbs and branching morphogenesis in lung and kidneys. Receptor-ligand interactions may thus constitute a general mechanism to generate Turing patterns in nature.

Studies of morphogens: keep calm and carry on

Morphogens are signaling factors that direct cell fate and tissue development at a distance from their source, and various modes of transport and interpretation have been suggested for morphogens. The recent EMBO Workshop on 'Morphogen gradients', which took place in Oxford, UK in June 2013, centered on the formation and interpretation of such morphogen gradients during development. This meeting allowed an exchange of views in light of recent results. Here, we provide a brief overview of the talks, organized in relation to several major themes of discussion at the meeting: (1) morphogen gradient formation; (2) morphogen gradient interpretation; (3) signaling networks and feedback in morphogenesis; (4) emergence of patterns; (5) scaling of patterns; (6) the control of growth; and (7) new techniques in the field.

The control of branching morphogenesis

Many organs of higher organisms are heavily branched structures and arise by an apparently similar process of branching morphogenesis. Yet the regulatory components and local interactions that have been identified differ greatly in these organs. It is an open question whether the regulatory processes work according to a common principle and how far physical and geometrical constraints determine the branching process. Here, we review the known regulatory factors and physical constraints in lung, kidney, pancreas, prostate, mammary gland and salivary gland branching morphogenesis, and describe the models that have been formulated to analyse their impacts.

Computational modelling of bovine ovarian follicle development

Background

The development of ovarian follicles hinges on the timely exposure to the appropriate combination of hormones. Follicle stimulating hormone (FSH) and luteinizing hormone (LH) are both produced in the pituitary gland and are transported via the blood circulation to the thecal layer surrounding the follicle. From there both hormones are transported into the follicle by diffusion. FSH-receptors are expressed mainly in the granulosa while LH-receptors are expressed in a gradient with highest expression in the theca. How this spatial organization is achieved is not known. Equally it is not understood whether LH and FSH trigger distinct signalling programs or whether the distinct spatial localization of their G-protein coupled receptors is sufficient to convey their distinct biological function.

Results

We have developed a data-based computational model of the spatio-temporal signalling processes within the follicle and (i) predict that FSH and LH form a gradient inside the follicle, (ii) show that the spatial distribution of FSH- and LH-receptors can arise from the well known regulatory interactions, and (iii) find that the differential activity of FSH and LH may well result from the distinct spatial localisation of their receptors, even when both receptors respond with the same intracellular signalling cascade to their ligand.

Conclusion

The model integrates the large amount of published data into a consistent framework that can now be used to better understand how observed defects translate into failed follicle maturation.