The mechanical influence of densification on epithelial architecture.

Epithelial tissues are the most abundant tissue type in animals, lining body cavities and generating compartment barriers. The function of a monolayered epithelial tissue-whether protective, secretory, absorptive, or filtrative-relies on the side-by-side arrangement of its component cells. The mechanical parameters that determine the shape of epithelial cells in the apical-basal plane are not well-understood. Epithelial tissue architecture in culture is intimately connected to cell density, and cultured layers transition between architectures as they proliferate. This prompted us to ask to what extent epithelial architecture emerges from two mechanical considerations: A) the constraints of densification and B) cell-cell adhesion, a hallmark feature of epithelial cells. To address these questions, we developed a novel polyline cell-based computational model and used it to make theoretical predictions about epithelial architecture upon changes to density and cell-cell adhesion. We tested these predictions using cultured cell experiments. Our results show that the appearance of extended lateral cell-cell borders in culture arises as a consequence of crowding-independent of cell-cell adhesion. However, cadherin-mediated cell-cell adhesion is associated with a novel architectural transition. Our results suggest that this transition represents the initial appearance of a distinctive epithelial architecture. Together our work reveals the distinct mechanical roles of densification and adhesion to epithelial layer formation and provides a novel theoretical framework to understand the less well-studied apical-basal plane of epithelial tissues.

Accurate staging of chick embryonic tissues via deep learning of salient features.

Recent work shows that the developmental potential of progenitor cells in the HH10 chick brain changes rapidly, accompanied by subtle changes in morphology. This demands increased temporal resolution for studies of the brain at this stage, necessitating precise and unbiased staging. Here, we investigated whether we could train a deep convolutional neural network to sub-stage HH10 chick brains using a small dataset of 151 expertly labelled images. By augmenting our images with biologically informed transformations and data-driven preprocessing steps, we successfully trained a classifier to sub-stage HH10 brains to 87.1% test accuracy. To determine whether our classifier could be generally applied, we re-trained it using images (269) of randomised control and experimental chick wings, and obtained similarly high test accuracy (86.1%). Saliency analyses revealed that biologically relevant features are used for classification. Our strategy enables training of image classifiers for various applications in developmental biology with limited microscopy data.

insideOutside: an accessible algorithm for classifying interior and exterior points, with applications in embryology.

A crucial aspect of embryology is relating the position of individual cells to the broader geometry of the embryo. A classic example of this is the first cell-fate decision of the mouse embryo, where interior cells become inner cell mass and exterior cells become trophectoderm. Fluorescent labelling, imaging, and quantification of tissue-specific proteins have advanced our understanding of this dynamic process. However, instances arise where these markers are either not available, or not reliable, and we are left only with the cells' spatial locations. Therefore, a simple, robust method for classifying interior and exterior cells of an embryo using spatial information is required. Here, we describe a simple mathematical framework and an unsupervised machine learning approach, termed insideOutside, for classifying interior and exterior points of a three-dimensional point-cloud, a common output from imaged cells within the early mouse embryo. We benchmark our method against other published methods to demonstrate that it yields greater accuracy in classification of nuclei from the pre-implantation mouse embryos and greater accuracy when challenged with local surface concavities. We have made MATLAB and Python implementations of the method freely available. This method should prove useful for embryology, with broader applications to similar data arising in the life sciences.

In-silico and in-vitro morphometric analysis of intestinal organoids.

Organoids offer a powerful model to study cellular self-organisation, the growth of specific tissue morphologies in-vitro, and to assess potential medical therapies. However, the intrinsic mechanisms of these systems are not entirely understood yet, which can result in variability of organoids due to differences in culture conditions and basement membrane extracts used. Improving the standardisation of organoid cultures is essential for their implementation in clinical protocols. Developing tools to assess and predict the behaviour of these systems may produce a more robust and standardised biological model to perform accurate clinical studies. Here, we developed an algorithm to automate crypt-like structure counting on intestinal organoids in both in-vitro and in-silico images. In addition, we modified an existing two-dimensional agent-based mathematical model of intestinal organoids to better describe the system physiology, and evaluated its ability to replicate budding structures compared to new experimental data we generated. The crypt-counting algorithm proved useful in approximating the average number of budding structures found in our in-vitro intestinal organoid culture images on days 3 and 7 after seeding. Our changes to the in-silico model maintain the potential to produce simulations that replicate the number of budding structures found on days 5 and 7 of in-vitro data. The present study aims to aid in quantifying key morphological structures and provide a method to compare both in-vitro and in-silico experiments. Our results could be extended later to 3D in-silico models.

Polychaetoid/ZO-1 strengthens cell junctions under tension while localizing differently than core adherens junction proteins.

During embryonic development, dramatic cell shape changes and movements reshape the embryonic body plan. These require robust but dynamic linkage between the cell-cell adherens junctions and the force-generating actomyosin cytoskeleton. Our view of this linkage has evolved, and we now realize linkage is mediated by mechanosensitive multiprotein complexes assembled via multivalent connections. Here we combine genetic, cell biological, and modeling approaches to define the mechanism of action and functions of an important player, Drosophila polychaetoid, homologue of mammalian ZO-1. Our data reveal that Pyd reinforces cell junctions under elevated tension, and facilitates cell rearrangements. Pyd is important to maintain junctional contractility and in its absence cell rearrangements stall. We next use structured illumination microscopy to define the molecular architecture of cell-cell junctions during these events. The cadherin-catenin complex and Cno both localize to puncta along the junctional membrane, but are differentially enriched in different puncta. Pyd, in contrast, exhibits a distinct localization to strands that extend out from the region occupied by core junction proteins. We then discuss the implications for the protein network at the junction-cytoskeletal interface, suggesting different proteins localize and function in distinct ways, perhaps in distinct subcomplexes, but combine to produce robust connections.

The Mechanical Influence of Densification on Initial Epithelial Architecture.

Epithelial tissues are the most abundant tissue type in animals, lining body cavities and generating compartment barriers. The function of a monolayer epithelium - whether protective, secretory, absorptive, or filtrative -relies on regular tissue architecture with respect to the apical-basal axis. Using an unbiased 3D analysis pipeline developed in our lab, we previously showed that epithelial tissue architectures in culture can be divided into distinct developmental categories, and that these are intimately connected to cell density: at sparse densities, cultured epithelial cell layers have a squamous morphology (Immature); at intermediate densities, these layers develop lateral cell-cell borders and rounded cell apices (Intermediate); cells at the highest densities reach their full height and demonstrate flattened apices (Mature). These observations prompted us to ask whether epithelial architecture emerges from the mechanical constraints of densification, and to what extent a hallmark feature of epithelial cells, namely cell-cell adhesion, contributes. In other words, to what extent is the shape of cells in an epithelial layer a simple matter of sticky, deformable objects squeezing together? We addressed this problem using a combination of computational modeling and experimental manipulations. Our results show that the first morphological transition, from Immature to Intermediate, can be explained simply by cell crowding. Additionally, we identify a new division (and thus transition) within the Intermediate category, and find that this second morphology relies on cell-cell adhesion.

Polychaetoid/ZO-1 strengthens cell junctions under tension while localizing differently than core adherens junction proteins.

During embryonic development dramatic cell shape changes and movements re-shape the embryonic body plan. These require robust but dynamic linkage between the cell-cell adherens junctions and the force-generating actomyosin cytoskeleton. Our view of this linkage has evolved, and we now realize linkage is mediated by a mechanosensitive multiprotein complex assembled via multivalent connections. Here we combine genetic, cell biological and modeling approaches to define the mechanism of action and functions of an important player, Drosophila Polychaetoid, homolog of mammalian ZO-1. Our data reveal that Pyd reinforces cell junctions under elevated tension, and facilitates cell rearrangements. Pyd is important to maintain junctional contractility and in its absence cell rearrangements stall. We next use structured illumination microscopy to define the molecular architecture of cell-cell junctions during these events. The cadherin-catenin complex and Cno both localize to puncta along the junctional membrane, but are differentially enriched in different puncta. Pyd, in contrast, exhibits a distinct localization to strands that extend out from the region occupied by core junction proteins. We then discuss the implications for the protein network at the junction-cytoskeletal interface, suggesting different proteins localize and function in distinct ways but combine to produce robust connections.

ChemChaste: Simulating spatially inhomogeneous biochemical reaction-diffusion systems for modeling cell-environment feedbacks.

BACKGROUND: Spatial organization plays an important role in the function of many biological systems, from cell fate specification in animal development to multistep metabolic conversions in microbial communities. The study of such systems benefits from the use of spatially explicit computational models that combine a discrete description of cells with a continuum description of one or more chemicals diffusing within a surrounding bulk medium. These models allow the in silico testing and refinement of mechanistic hypotheses. However, most existing models of this type do not account for concurrent bulk and intracellular biochemical reactions and their possible coupling. CONCLUSIONS: Here, we describe ChemChaste, an extension for the open-source C++ computational biology library Chaste. ChemChaste enables the spatial simulation of both multicellular and bulk biochemistry by expanding on Chaste's existing capabilities. In particular, ChemChaste enables (i) simulation of an arbitrary number of spatially diffusing chemicals, (ii) spatially heterogeneous chemical diffusion coefficients, and (iii) inclusion of both bulk and intracellular biochemical reactions and their coupling. ChemChaste also introduces a file-based interface that allows users to define the parameters relating to these functional features without the need to interact directly with Chaste's core C++ code. We describe ChemChaste and demonstrate its functionality using a selection of chemical and biochemical exemplars, with a focus on demonstrating increased ability in modeling bulk chemical reactions and their coupling with intracellular reactions. AVAILABILITY AND IMPLEMENTATION: ChemChaste version 1.0 is a free, open-source C++ library, available via GitHub at https://github.com/OSS-Lab/ChemChaste under the BSD license, on the Zenodo archive at zendodo doi, as well as on BioTools (biotools:chemchaste) and SciCrunch (RRID:SCR022208) databases.

Seven challenges in the multiscale modeling of multicellular tissues.

The growth and dynamics of multicellular tissues involve tightly regulated and coordinated morphogenetic cell behaviors, such as shape changes, movement, and division, which are governed by subcellular machinery and involve coupling through short- and long-range signals. A key challenge in the fields of developmental biology, tissue engineering and regenerative medicine is to understand how relationships between scales produce emergent tissue-scale behaviors. Recent advances in molecular biology, live-imaging and ex vivo techniques have revolutionized our ability to study these processes experimentally. To fully leverage these techniques and obtain a more comprehensive understanding of the causal relationships underlying tissue dynamics, computational modeling approaches are increasingly spanning multiple spatial and temporal scales, and are coupling cell shape, growth, mechanics, and signaling. Yet such models remain challenging: modeling at each scale requires different areas of technical skills, while integration across scales necessitates the solution to novel mathematical and computational problems. This review aims to summarize recent progress in multiscale modeling of multicellular tissues and to highlight ongoing challenges associated with the construction, implementation, interrogation, and validation of such models. This article is categorized under: Reproductive System Diseases > Computational Models Metabolic Diseases > Computational Models Cancer > Computational Models.

Adhesion-regulated junction slippage controls cell intercalation dynamics in an Apposed-Cortex Adhesion Model.

Cell intercalation is a key cell behaviour of morphogenesis and wound healing, where local cell neighbour exchanges can cause dramatic tissue deformations such as body axis extension. Substantial experimental work has identified the key molecular players facilitating intercalation, but there remains a lack of consensus and understanding of their physical roles. Existing biophysical models that represent cell-cell contacts with single edges cannot study cell neighbour exchange as a continuous process, where neighbouring cell cortices must uncouple. Here, we develop an Apposed-Cortex Adhesion Model (ACAM) to understand active cell intercalation behaviours in the context of a 2D epithelial tissue. The junctional actomyosin cortex of every cell is modelled as a continuous viscoelastic rope-loop, explicitly representing cortices facing each other at bicellular junctions and the adhesion molecules that couple them. The model parameters relate directly to the properties of the key subcellular players that drive dynamics, providing a multi-scale understanding of cell behaviours. We show that active cell neighbour exchanges can be driven by purely junctional mechanisms. Active contractility and cortical turnover in a single bicellular junction are sufficient to shrink and remove a junction. Next, a new, orthogonal junction extends passively. The ACAM reveals how the turnover of adhesion molecules regulates tension transmission and junction deformation rates by controlling slippage between apposed cell cortices. The model additionally predicts that rosettes, which form when a vertex becomes common to many cells, are more likely to occur in actively intercalating tissues with strong friction from adhesion molecules.

The evolution of strategy in bacterial warfare via the regulation of bacteriocins and antibiotics.

Bacteria inhibit and kill one another with a diverse array of compounds, including bacteriocins and antibiotics. These attacks are highly regulated, but we lack a clear understanding of the evolutionary logic underlying this regulation. Here, we combine a detailed dynamic model of bacterial competition with evolutionary game theory to study the rules of bacterial warfare. We model a large range of possible combat strategies based upon the molecular biology of bacterial regulatory networks. Our model predicts that regulated strategies, which use quorum sensing or stress responses to regulate toxin production, will readily evolve as they outcompete constitutive toxin production. Amongst regulated strategies, we show that a particularly successful strategy is to upregulate toxin production in response to an incoming competitor's toxin, which can be achieved via stress responses that detect cell damage (competition sensing). Mirroring classical game theory, our work suggests a fundamental advantage to reciprocation. However, in contrast to classical results, we argue that reciprocation in bacteria serves not to promote peaceful outcomes but to enable efficient and effective attacks.

Modelling of Epithelial Growth, Fission and Lumen Formation During Embryonic Thyroid Development: A Combination of Computational and Experimental Approaches.

Organogenesis is the phase of embryonic development leading to the formation of fully functional organs. In the case of the thyroid, organogenesis starts from the endoderm and generates a multitude of closely packed independent spherical follicular units surrounded by a dense network of capillaries. Follicular organisation is unique and essential for thyroid function, i.e. thyroid hormone production. Previous in vivo studies showed that, besides their nutritive function, endothelial cells play a central role during thyroid gland morphogenesis. However, the precise mechanisms and biological parameters controlling the transformation of the multi-layered thyroid epithelial primordium into a multitude of single-layered follicles are mostly unknown. Animal studies used to improve understanding of organogenesis are costly and time-consuming, with recognised limitations. Here, we developed and used a 2-D vertex model of thyroid growth, angiogenesis and folliculogenesis, within the open-source Chaste framework. Our in silico model, based on in vivo images, correctly simulates the differential growth and proliferation of central and peripheral epithelial cells, as well as the morphogen-driven migration of endothelial cells, consistently with our experimental data. Our simulations further showed that reduced epithelial cell adhesion was critical to allow endothelial invasion and fission of the multi-layered epithelial mass. Finally, our model also allowed epithelial cell polarisation and follicular lumen formation by endothelial cell abundance and proximity. Our study illustrates how constant discussion between theoretical and experimental approaches can help us to better understand the roles of cellular movement, adhesion and polarisation during thyroid embryonic development. We anticipate that the use of in silico models like the one we describe can push forward the fields of developmental biology and regenerative medicine.

Of mitogens and morphogens: modelling Sonic Hedgehog mechanisms in vertebrate development.

Sonic Hedgehog (Shh) Is a critical protein in vertebrate development, orchestrating patterning and growth in many developing systems. First described as a classic morphogen that patterns tissues through a spatial concentration gradient, subsequent studies have revealed a more complex mechanism, in which Shh can also regulate proliferation and differentiation. While the mechanism of action of Shh as a morphogen is well understood, it remains less clear how Shh might integrate patterning, proliferation and differentiation in a given tissue, to ultimately direct its morphogenesis. In tandem with experimental studies, mathematical modelling can help gain mechanistic insights into these processes and bridge the gap between Shh-regulated patterning and growth, by integrating these processes into a common theoretical framework. Here, we briefly review the roles of Shh in vertebrate development, focusing on its functions as a morphogen, mitogen and regulator of differentiation. We then discuss the contributions that modelling has made to our understanding of the action of Shh and highlight current challenges in using mathematical models in a quantitative and predictive way. This article is part of a discussion meeting issue 'Contemporary morphogenesis'.

Toward Engineering Biosystems With Emergent Collective Functions.

Many complex behaviors in biological systems emerge from large populations of interacting molecules or cells, generating functions that go beyond the capabilities of the individual parts. Such collective phenomena are of great interest to bioengineers due to their robustness and scalability. However, engineering emergent collective functions is difficult because they arise as a consequence of complex multi-level feedback, which often spans many length-scales. Here, we present a perspective on how some of these challenges could be overcome by using multi-agent modeling as a design framework within synthetic biology. Using case studies covering the construction of synthetic ecologies to biological computation and synthetic cellularity, we show how multi-agent modeling can capture the core features of complex multi-scale systems and provide novel insights into the underlying mechanisms which guide emergent functionalities across scales. The ability to unravel design rules underpinning these behaviors offers a means to take synthetic biology beyond single molecules or cells and toward the creation of systems with functions that can only emerge from collectives at multiple scales.

Coupled differentiation and division of embryonic stem cells inferred from clonal snapshots.

The deluge of single-cell data obtained by sequencing, imaging and epigenetic markers has led to an increasingly detailed description of cell state. However, it remains challenging to identify how cells transition between different states, in part because data are typically limited to snapshots in time. A prerequisite for inferring cell state transitions from such snapshots is to distinguish whether transitions are coupled to cell divisions. To address this, we present two minimal branching process models of cell division and differentiation in a well-mixed population. These models describe dynamics where differentiation and division are coupled or uncoupled. For each model, we derive analytic expressions for each subpopulation's mean and variance and for the likelihood, allowing exact Bayesian parameter inference and model selection in the idealised case of fully observed trajectories of differentiation and division events. In the case of snapshots, we present a sample path algorithm and use this to predict optimal temporal spacing of measurements for experimental design. We then apply this methodology to an in vitro dataset assaying the clonal growth of epiblast stem cells in culture conditions promoting self-renewal or differentiation. Here, the larger number of cell states necessitates approximate Bayesian computation. For both culture conditions, our inference supports the model where cell state transitions are coupled to division. For culture conditions promoting differentiation, our analysis indicates a possible shift in dynamics, with these processes becoming more coupled over time.

Close Encounters of the Cell Kind: The Impact of Contact Inhibition on Tumour Growth and Cancer Models.

Cancer is a complex phenomenon, and the sheer variation in behaviour across different types renders it difficult to ascertain underlying biological mechanisms. Experimental approaches frequently yield conflicting results for myriad reasons, and mathematical modelling of cancer is a vital tool to explore what we cannot readily measure, and ultimately improve treatment and prognosis. Like experiments, models are underpinned by certain biological assumptions, variation of which can lead to divergent predictions. An outstanding and important question concerns contact inhibition of proliferation (CIP), the observation that proliferation ceases when cells are spatially confined by their neighbours. CIP is a characteristic of many healthy adult tissues, but it remains unclear to which extent it holds in solid tumours, which exhibit regions of hyper-proliferation, and apparent breakdown of CIP. What precisely occurs in tumour tissue remains an open question, which mathematical modelling can help shed light on. In this perspective piece, we explore the implications of different hypotheses and available experimental evidence to elucidate the implications of these scenarios. We also outline how erroneous conclusions about the nature of tumour growth may be arrived at by looking selectively at biological data in isolation, and how this might be circumvented.

Chaste: Cancer, Heart and Soft Tissue Environment.

Chaste (Cancer, Heart And Soft Tissue Environment) is an open source simulation package for the numerical solution of mathematical models arising in physiology and biology. To date, Chaste development has been driven primarily by applications that include continuum modelling of cardiac electrophysiology ('Cardiac Chaste'), discrete cell-based modelling of soft tissues ('Cell-based Chaste'), and modelling of ventilation in lungs ('Lung Chaste'). Cardiac Chaste addresses the need for a high-performance, generic, and verified simulation framework for cardiac electrophysiology that is freely available to the scientific community. Cardiac chaste provides a software package capable of realistic heart simulations that is efficient, rigorously tested, and runs on HPC platforms. Cell-based Chaste addresses the need for efficient and verified implementations of cell-based modelling frameworks, providing a set of extensible tools for simulating biological tissues. Computational modelling, along with live imaging techniques, plays an important role in understanding the processes of tissue growth and repair. A wide range of cell-based modelling frameworks have been developed that have each been successfully applied in a range of biological applications. Cell-based Chaste includes implementations of the cellular automaton model, the cellular Potts model, cell-centre models with cell representations as overlapping spheres or Voronoi tessellations, and the vertex model. Lung Chaste addresses the need for a novel, generic and efficient lung modelling software package that is both tested and verified. It aims to couple biophysically-detailed models of airway mechanics with organ-scale ventilation models in a package that is freely available to the scientific community. Chaste is designed to be modular and extensible, providing libraries for common scientific computing infrastructure such as linear algebra operations, finite element meshes, and ordinary and partial differential equation solvers. This infrastructure is used by libraries for specific applications, such as continuum mechanics, cardiac models, and cell-based models. The software engineering techniques used to develop Chaste are intended to ensure code quality, re-usability and reliability. Primary applications of the software include cardiac and respiratory physiology, cancer and developmental biology.

Inferring Tumor Proliferative Organization from Phylogenetic Tree Measures in a Computational Model.

We use a computational modeling approach to explore whether it is possible to infer a solid tumor's cellular proliferative hierarchy under the assumptions of the cancer stem cell hypothesis and neutral evolution. We work towards inferring the symmetric division probability for cancer stem cells, since this is believed to be a key driver of progression and therapeutic response. Motivated by the advent of multiregion sampling and resulting opportunities to infer tumor evolutionary history, we focus on a suite of statistical measures of the phylogenetic trees resulting from the tumor's evolution in different regions of parameter space and through time. We find strikingly different patterns in these measures for changing symmetric division probability which hinge on the inclusion of spatial constraints. These results give us a starting point to begin stratifying tumors by this biological parameter and also generate a number of actionable clinical and biological hypotheses regarding changes during therapy, and through tumor evolutionary time. [Cancer; evolution; phylogenetics.].

The tricellular vertex-specific adhesion molecule Sidekick facilitates polarised cell intercalation during Drosophila axis extension.

In epithelia, tricellular vertices are emerging as important sites for the regulation of epithelial integrity and function. Compared to bicellular contacts, however, much less is known. In particular, resident proteins at tricellular vertices were identified only at occluding junctions, with none known at adherens junctions (AJs). In a previous study, we discovered that in Drosophila embryos, the adhesion molecule Sidekick (Sdk), well-known in invertebrates and vertebrates for its role in the visual system, localises at tricellular vertices at the level of AJs. Here, we survey a wide range of Drosophila epithelia and establish that Sdk is a resident protein at tricellular AJs (tAJs), the first of its kind. Clonal analysis showed that two cells, rather than three cells, contributing Sdk are sufficient for tAJ localisation. Super-resolution imaging using structured illumination reveals that Sdk proteins form string-like structures at vertices. Postulating that Sdk may have a role in epithelia where AJs are actively remodelled, we analysed the phenotype of sdk null mutant embryos during Drosophila axis extension using quantitative methods. We find that apical cell shapes are abnormal in sdk mutants, suggesting a defect in tissue remodelling during convergence and extension. Moreover, adhesion at apical vertices is compromised in rearranging cells, with apical tears in the cortex forming and persisting throughout axis extension, especially at the centres of rosettes. Finally, we show that polarised cell intercalation is decreased in sdk mutants. Mathematical modelling of the cell behaviours supports the notion that the T1 transitions of polarised cell intercalation are delayed in sdk mutants, in particular in rosettes. We propose that this delay, in combination with a change in the mechanical properties of the converging and extending tissue, causes the abnormal apical cell shapes in sdk mutant embryos.