Falsifying computational models of endothelial cell network formation through quantitative comparison with in vitro models

During angiogenesis, endothelial cells expand the vasculature by migrating from existing blood vessels, proliferating and collectively organizing into new capillaries. In vitro and in vivo experimentation is instrumental for identifying the molecular players and cell behaviour that regulate angiogenesis. Alongside experimental work, computational and mathematical models of endothelial cell network formation have helped to analyse if the current molecular and cellular understanding of endothelial cell behaviour is sufficient to explain the formation of endothelial cell networks. As input, the models take (a subset of) the current knowledge or hypotheses of single cell behaviour and capture it into a dynamical, mathematical description. As output, they predict the multicellular behaviour following from the actions of many individual cells, i.e., formation of a vascular-like network. Paradoxically, computational modelling based on different assumptions, i.e., completely different, sometimes non-intersecting sets of observed single cell behaviour, can reproduce the same angiogenesis-like multicellular behaviour, making it practically impossible to decide which, if any, of these models is correct. Here we present dynamical analyses of time-lapses of in vitro endothelial cell network formation experiments and compare these with dynamic analyses of three mathematical models: (1) the cell elongation model; (2) the contact-inhibited chemotaxis model; and (3) the mechanical cell-cell communication model. We extract a variety of dynamical characteristics of endothelial cell network formation using a custom time-lapse video analysis pipeline in ImageJ. We compare the dynamical network characteristics of the in vitro experiments to those of the cellular networks produced by the computational models. We test the response of the in silico dynamical cell network characteristics to changes in cell density and make related changes in the in vitro experiments. Of the three computational models that we have considered, the cell elongation model best captures the remodelling phase of in vitro endothelial cell network formation. Furthermore, in the in vitro model, the final size and number of lacunae in the network are independent of the initial cell density. This observation is also reproduced in the cell elongation model, but not in the other two models that we have considered. Altogether, we present an approach to model validation based on comparisons of time-resolved data and variations of model conditions.

Development necessitates evolutionarily conserved factors

Early-stage generalised transcription factors in biological development are often evolutionarily conserved across species. Here, we find for the first time that similar factors functionally emerge in an alternative medium of development. Through comprehensively analysing a Neural Cellular Automata (NCA) model of morphogenesis, we find multiple properties of the hidden units that are functionally analogous to early factors in biological development. We test the generalisation abilities of our model through transfer learning of other morphologies and find that developmental strategies learnt by the model are reused to grow new body forms by conserving its early generalised factors. Our paper therefore provides evidence that nature did not become locked into one arbitrary method of developing multicellular organisms: the use of early generalised factors as fundamental control mechanisms and the resulting necessity for evolutionary conservation of those factors may be fundamental to development, regardless of the details of how development is implemented.

Emergent Tissue Shapes from the Regulatory Feedback between Morphogens and Cell Growth

Patterning and morphogenesis in multicellular organisms require precise dynamic coordination between cellular behaviors and mechano-chemical signals. However, the mechanisms underlying the pathways that coordinate and integrate these signals into emergent cellular behaviors and tissue shapes remain poorly understood. Here, we present a cell-centered agent-based mathematical approach to shed light on the feedback mechanisms underlying tissue growth and pattern formation. The model includes cell size dynamics governed by both intercellular diffusible morphogen concentrations and mechanical stress between cells to control their spatial organization, and does not require the use of any superimposed lattice, increasing its applicability and performance. The results show how the precise integration of the feedback loop between cellular behaviors and mechano-chemical signaling is essential for the regulation of shape and spatial patterns across the tissue scale. Furthermore, the regulation of cellular dynamics by patterning processes, such as Turing activator-inhibitor systems, can drive the formation of emergent stable tissue shapes, which, in turn, specify the domain for morphogen patterning-closing the self-regulated loop between tissue shape and morphogenetic signals. Overall, this study highlights the importance of the feedback loop between morphogen patterning and cellular behaviors in regulating tissue growth dynamics and stable shape formation. Moreover, this study establishes a framework for further experiments to understand the regulatory dynamics of whole-body development and regeneration using high spatiotemporal resolution models.

Deciphering the interplay between biology and physics with a finite element method-implemented vertex organoid model: A tool for the mechanical analysis of cell behavior on a spherical organoid shell

Understanding the interplay between biology and mechanics in tissue architecture is challenging, particularly in terms of 3D tissue organization. Addressing this challenge requires a biological model enabling observations at multiple levels from cell to tissue, as well as theoretical and computational approaches enabling the generation of a synthetic model that is relevant to the biological model and allowing for investigation of the mechanical stresses experienced by the tissue. Using a monolayer human colon epithelium organoid as a biological model, freely available tools (Fiji, Cellpose, Napari, Morphonet, or Tyssue library), and the commercially available Abaqus FEM solver, we combined vertex and FEM approaches to generate a comprehensive viscoelastic finite element model of the human colon organoid and demonstrated its flexibility. We imaged human colon organoid development for 120 hours, following the evolution of the organoids from an immature to a mature morphology. According to the extracted architectural/geometric parameters of human colon organoids at various stages of tissue architecture establishment, we generated organoid active vertex models. However, this approach did not consider the mechanical aspects involved in the organoids' morphological evolution. Therefore, we applied a finite element method considering mechanical loads mimicking osmotic pressure, external solicitation, or active contraction in the vertex model by using the Abaqus FEM solver. Integration of finite element analysis (FEA) into the vertex model achieved a better fit with the biological model. Therefore, the FEM model provides a basis for depicting cell shape, tissue deformation, and cellular-level strain due to imposed stresses. In conclusion, we demonstrated that a combination of vertex and FEM approaches, combining geometrical and mechanical parameters, improves modeling of alterations in organoid morphology over time and enables better assessment of the mechanical cues involved in establishing the architecture of the human colon epithelium.

The legacy and evolvability of Pere Alberch's ideas

Pere Alberch played a pivotal role in shaping the field of evolutionary developmental biology during the 1980s and 1990s. Whereas initially his contributions were sidelined by the empirical advancements of the molecular revolution in developmental and evolutionary biology, his theoretical insights have left a lasting impact on the discipline. This article provides a comprehensive review of the legacy and evolvability of Alberch's ideas in contemporary evo-devo, which included the study of morphogenesis as the proper level of developmental causation, the interplay between developmental constraints and natural selection, the epistemic role of teratologies, the origin of evolutionary novelties and the concept of evolvability.

Mechanistic regulation of planarian shape during growth and degrowth

Adult planarians can grow when fed and degrow (shrink) when starved while maintaining their whole-body shape. It is unknown how the morphogens patterning the planarian axes are coordinated during feeding and starvation or how they modulate the necessary differential tissue growth or degrowth. Here, we investigate the dynamics of planarian shape together with a theoretical study of the mechanisms regulating whole-body proportions and shape. We found that the planarian body proportions scale isometrically following similar linear rates during growth and degrowth, but that fed worms are significantly wider than starved worms. By combining a descriptive model of planarian shape and size with a mechanistic model of anterior-posterior and medio-lateral signaling calibrated with a novel parameter optimization methodology, we theoretically demonstrate that the feedback loop between these positional information signals and the shape they control can regulate the planarian whole-body shape during growth. Furthermore, the computational model produced the correct shape and size dynamics during degrowth as a result of a predicted increase in apoptosis rate and pole signal during starvation. These results offer mechanistic insights into the dynamic regulation of whole-body morphologies.

Integrating mechanical cues with engineered platforms to explore cardiopulmonary development and disease

Mechanical forces provide critical biological signals to cells during healthy and aberrant organ development as well as during disease processes in adults. Within the cardiopulmonary system, mechanical forces, such as shear, compressive, and tensile forces, act across various length scales, and dysregulated forces are often a leading cause of disease initiation and progression such as in bronchopulmonary dysplasia and cardiomyopathies. Engineered in vitro models have supported studies of mechanical forces in a number of tissue and disease-specific contexts, thus enabling new mechanistic insights into cardiopulmonary development and disease. This review first provides fundamental examples where mechanical forces operate at multiple length scales to ensure precise lung and heart function. Next, we survey recent engineering platforms and tools that have provided new means to probe and modulate mechanical forces across in vitro and in vivo settings. Finally, the potential for interdisciplinary collaborations to inform novel therapeutic approaches for a number of cardiopulmonary diseases are discussed.

A hybrid physics-based and data-driven framework for cellular biological systems: Application to the morphogenesis of organoids

How cells orchestrate their cellular functions remains a crucial question to unravel how they organize in different patterns. We present a framework based on artificial intelligence to advance the understanding of how cell functions are coordinated spatially and temporally in biological systems. It consists of a hybrid physics-based model that integrates both mechanical interactions and cell functions with a data-driven model that regulates the cellular decision-making process through a deep learning algorithm trained on image data metrics. To illustrate our approach, we used data from 3D cultures of murine pancreatic ductal adenocarcinoma cells (PDAC) grown in Matrigel as tumor organoids. Our approach allowed us to find the underlying principles through which cells activate different cell processes to self-organize in different patterns according to the specific microenvironmental conditions. The framework proposed here expands the tools for simulating biological systems at the cellular level, providing a novel perspective to unravel morphogenetic patterns.

Julia for biologists

Major computational challenges exist in relation to the collection, curation, processing and analysis of large genomic and imaging datasets, as well as the simulation of larger and more realistic models in systems biology. Here we discuss how a relative newcomer among programming languages-Julia-is poised to meet the current and emerging demands in the computational biosciences and beyond. Speed, flexibility, a thriving package ecosystem and readability are major factors that make high-performance computing and data analysis available to an unprecedented degree. We highlight how Julia's design is already enabling new ways of analyzing biological data and systems, and we provide a list of resources that can facilitate the transition into Julian computing.

Cell state transitions: catch them if you can

The Company of Biologists' 2022 workshop on 'Cell State Transitions: Approaches, Experimental Systems and Models' brought together an international and interdisciplinary team of investigators spanning the fields of cell and developmental biology, stem cell biology, physics, mathematics and engineering to tackle the question of how cells precisely navigate between distinct identities and do so in a dynamic manner. This second edition of the workshop was organized after a successful virtual workshop on the same topic that took place in 2021.

Coordination of non-professional efferocytosis and actomyosin contractility during epithelial tissue morphogenesis

In developing embryos, specific cell populations are often removed to remodel tissue architecture for organogenesis. During urinary tract development, an epithelial duct called the common nephric duct (CND) gets shortened and eventually eliminated to remodel the entry point of the ureter into the bladder. Here we show that non-professional efferocytosis (the process in which epithelial cells engulf apoptotic bodies) is the main mechanism that contributes to CND shortening. Combining biological metrics and computational modeling, we show that efferocytosis with actomyosin contractility are essential factors that drive the CND shortening without compromising the ureter-bladder structural connection. The disruption of either apoptosis, non-professional efferocytosis, or actomyosin results in contractile tension reduction and deficient CND shortening. Actomyosin activity helps to maintain tissue architecture while non-professional efferocytosis removes cellular volume. Together our results demonstrate that non-professional efferocytosis with actomyosin contractility are important morphogenetic factors controlling CND morphogenesis.

Tissue interplay during morphogenesis

The process by which biological systems such as cells, tissues and organisms acquire shape has been named as morphogenesis and it is central to a plethora of biological contexts including embryo development, wound healing, or even cancer. Morphogenesis relies in both self-organising properties of the system and in environmental inputs (biochemical and biophysical). The classical view of morphogenesis is based on the study of external biochemical molecules, such as morphogens. However, recent studies are establishing that the mechanical environment is also used by cells to communicate within tissues, suggesting that this mechanical crosstalk is essential to synchronise morphogenetic transitions and self-organisation. In this article we discuss how tissue interaction drive robust morphogenesis, starting from a classical biochemical view, to finalise with more recent advances on how the biophysical properties of a tissue feedback with their surroundings to allow form acquisition. We also comment on how in silico models aid to integrate and predict changes in cell and tissue behaviour. Finally, considering recent advances from the developmental biomechanics field showing that mechanical inputs work as cues that promote morphogenesis, we invite to revisit the concept of morphogen.

Concentration-Dependent Domain Evolution in Reaction-Diffusion Systems

Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic modelling in developmental biology. Most work to date has considered prescribed domains evolving as given functions of time, but not the scenario of concentration-dependent dynamics, which is also highly relevant in a developmental setting. Here, we study such concentration-dependent domain evolution for reaction-diffusion systems to elucidate fundamental aspects of these more complex models. We pose a general form of one-dimensional domain evolution and extend this to N-dimensional manifolds under mild constitutive assumptions in lieu of developing a full tissue-mechanical model. In the 1D case, we are able to extend linear stability analysis around homogeneous equilibria, though this is of limited utility in understanding complex pattern dynamics in fast growth regimes. We numerically demonstrate a variety of dynamical behaviours in 1D and 2D planar geometries, giving rise to several new phenomena, especially near regimes of critical bifurcation boundaries such as peak-splitting instabilities. For sufficiently fast growth and contraction, concentration-dependence can have an enormous impact on the nonlinear dynamics of the system both qualitatively and quantitatively. We highlight crucial differences between 1D evolution and higher-dimensional models, explaining obstructions for linear analysis and underscoring the importance of careful constitutive choices in defining domain evolution in higher dimensions. We raise important questions in the modelling and analysis of biological systems, in addition to numerous mathematical questions that appear tractable in the one-dimensional setting, but are vastly more difficult for higher-dimensional models.

Modelling the evolution of novelty: a review

Evolution has been an inventive process since its inception, about 4 billion years ago. It has generated an astounding diversity of novel mechanisms and structures for adaptation to the environment, for competition and cooperation, and for organisation of the internal and external dynamics of the organism. How does this novelty come about? Evolution builds with the tools available, and on top of what it has already built - therefore, much novelty consists in repurposing old functions in a different context. In the process, the tools themselves evolve, allowing yet more novelty to arise. Despite evolutionary novelty being the most striking observable of evolution, it is not accounted for in classical evolutionary theory. Nevertheless, mathematical and computational models that illustrate mechanisms of evolutionary innovation have been developed. In the present review, we present and compare several examples of computational evo-devo models that capture two aspects of novelty: 'between-level novelty' and 'constructive novelty.' Novelty can evolve between predefined levels of organisation to dynamically transcode biological information across these levels - as occurs during development. Constructive novelty instead generates a level of biological organisation by exploiting the lower level as an informational scaffold to open a new space of possibilities - an example being the evolution of multicellularity. We propose that the field of computational evo-devo is well-poised to reveal many more exciting mechanisms for the evolution of novelty. A broader theory of evolutionary novelty may well be attainable in the near future.

Pseudodynamic analysis of heart tube formation in the mouse reveals strong regional variability and early left-right asymmetry

Understanding organ morphogenesis requires a precise geometrical description of the tissues involved in the process. The high morphological variability in mammalian embryos hinders the quantitative analysis of organogenesis. In particular, the study of early heart development in mammals remains a challenging problem due to imaging limitations and complexity. Here, we provide a complete morphological description of mammalian heart tube formation based on detailed imaging of a temporally dense collection of mouse embryonic hearts. We develop strategies for morphometric staging and quantification of local morphological variations between specimens. We identify hot spots of regionalized variability and identify Nodal-controlled left-right asymmetry of the inflow tracts as the earliest signs of organ left-right asymmetry in the mammalian embryo. Finally, we generate a three-dimensional+t digital model that allows co-representation of data from different sources and provides a framework for the computer modeling of heart tube formation.

The unappreciated generative role of cell movements in pattern formation

The mechanisms underpinning the formation of patterned cellular landscapes has been the subject of extensive study as a fundamental problem of developmental biology. In most cases, attention has been given to situations in which cell movements are negligible, allowing researchers to focus on the cell-extrinsic signalling mechanisms, and intrinsic gene regulatory interactions that lead to pattern emergence at the tissue level. However, in many scenarios during development, cells rapidly change their neighbour relationships in order to drive tissue morphogenesis, while also undergoing patterning. To draw attention to the ubiquity of this problem and propose methodologies that will accommodate morphogenesis into the study of pattern formation, we review the current approaches to studying pattern formation in both static and motile cellular environments. We then consider how the cell movements themselves may contribute to the generation of pattern, rather than hinder it, with both a species specific and evolutionary viewpoint.

Interactive, Visual Simulation of a Spatio-Temporal Model of Gas Exchange in the Human Alveolus

In interdisciplinary fields such as systems biology, good communication between experimentalists and theorists is crucial for the success of a project. Theoretical modeling in physiology usually describes complex systems with many interdependencies. On one hand, these models have to be grounded on experimental data. On the other hand, experimenters must be able to understand the interdependent complexities of the theoretical model in order to interpret the model's results in the physiological context. We promote interactive, visual simulations as an engaging way to present theoretical models in physiology and to make complex processes tangible. Based on a requirements analysis, we developed a new model for gas exchange in the human alveolus in combination with an interactive simulation software named Alvin. Alvin exceeds the current standard with its spatio-temporal resolution and a combination of visual and quantitative feedback. In Alvin, the course of the simulation can be traced in a three-dimensional rendering of an alveolus and dynamic plots. The user can interact by configuring essential model parameters. Alvin allows to run and compare multiple simulation instances simultaneously. We exemplified the use of Alvin for research by identifying unknown dependencies in published experimental data. Employing a detailed questionnaire, we showed the benefits of Alvin for education. We postulate that interactive, visual simulation of theoretical models, as we have implemented with Alvin on respiratory processes in the alveolus, can be of great help for communication between specialists and thereby advancing research.

An integrative multiscale view of early cardiac looping

The heart is the first organ to form and function during the development of an embryo. Heart development consists of a series of events believed to be highly conserved in vertebrates. Development of heart begins with the formation of the cardiac fields followed by a linear heart tube formation. The straight heart tube then undergoes a ventral bending prior to further bending and helical torsion to form a looped heart. The looping phase is then followed by ballooning, septation, and valve formation giving rise to a four-chambered heart in avians and mammals. The looping phase plays a central role in heart development. Successful looping is essential for proper alignment of the future cardiac chambers and tracts. As aberrant looping results in various congenital heart diseases, the mechanisms of cardiac looping have been studied for several decades by various disciplines. Many groups have studied anatomy, biology, genetics, and mechanical processes during heart looping, and have proposed multiple mechanisms. Computational modeling approaches have been utilized to examine the proposed mechanisms of the looping process. Still, the exact underlying mechanism(s) controlling the looping phase remain poorly understood. Although further experimental measurements are obviously still required, the need for more integrative computational modeling approaches is also apparent in order to make sense of the vast amount of experimental data and the complexity of multiscale developmental systems. Indeed, there needs to be an iterative interaction between experimentation and modeling in order to properly find the gap in the existing data and to validate proposed hypotheses. This article is categorized under: Cardiovascular Diseases > Genetics/Genomics/Epigenetics Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiology.

Minimal Developmental Computation: A Causal Network Approach to Understand Morphogenetic Pattern Formation

What information-processing strategies and general principles are sufficient to enable self-organized morphogenesis in embryogenesis and regeneration? We designed and analyzed a minimal model of self-scaling axial patterning consisting of a cellular network that develops activity patterns within implicitly set bounds. The properties of the cells are determined by internal 'genetic' networks with an architecture shared across all cells. We used machine-learning to identify models that enable this virtual mini-embryo to pattern a typical axial gradient while simultaneously sensing the set boundaries within which to develop it from homogeneous conditions-a setting that captures the essence of early embryogenesis. Interestingly, the model revealed several features (such as planar polarity and regenerative re-scaling capacity) for which it was not directly selected, showing how these common biological design principles can emerge as a consequence of simple patterning modes. A novel "causal network" analysis of the best model furthermore revealed that the originally symmetric model dynamically integrates into intercellular causal networks characterized by broken-symmetry, long-range influence and modularity, offering an interpretable macroscale-circuit-based explanation for phenotypic patterning. This work shows how computation could occur in biological development and how machine learning approaches can generate hypotheses and deepen our understanding of how featureless tissues might develop sophisticated patterns-an essential step towards predictive control of morphogenesis in regenerative medicine or synthetic bioengineering contexts. The tools developed here also have the potential to benefit machine learning via new forms of backpropagation and by leveraging the novel distributed self-representation mechanisms to improve robustness and generalization.

Computational Systems Biology of Morphogenesis

Extracting mechanistic knowledge from the spatial and temporal phenotypes of morphogenesis is a current challenge due to the complexity of biological regulation and their feedback loops. Furthermore, these regulatory interactions are also linked to the biophysical forces that shape a developing tissue, creating complex interactions responsible for emergent patterns and forms. Here we show how a computational systems biology approach can aid in the understanding of morphogenesis from a mechanistic perspective. This methodology integrates the modeling of tissues and whole-embryos with dynamical systems, the reverse engineering of parameters or even whole equations with machine learning, and the generation of precise computational predictions that can be tested at the bench. To implement and perform the computational steps in the methodology, we present user-friendly tools, computer code, and guidelines. The principles of this methodology are general and can be adapted to other model organisms to extract mechanistic knowledge of their morphogenesis.

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.

Sculpting with stem cells: how models of embryo development take shape

During embryogenesis, organisms acquire their shape given boundary conditions that impose geometrical, mechanical and biochemical constraints. A detailed integrative understanding how these morphogenetic information modules pattern and shape the mammalian embryo is still lacking, mostly owing to the inaccessibility of the embryo in vivo for direct observation and manipulation. These impediments are circumvented by the developmental engineering of embryo-like structures (stembryos) from pluripotent stem cells that are easy to access, track, manipulate and scale. Here, we explain how unlocking distinct levels of embryo-like architecture through controlled modulations of the cellular environment enables the identification of minimal sets of mechanical and biochemical inputs necessary to pattern and shape the mammalian embryo. We detail how this can be complemented with precise measurements and manipulations of tissue biochemistry, mechanics and geometry across spatial and temporal scales to provide insights into the mechanochemical feedback loops governing embryo morphogenesis. Finally, we discuss how, even in the absence of active manipulations, stembryos display intrinsic phenotypic variability that can be leveraged to define the constraints that ensure reproducible morphogenesis in vivo.

Forced into shape: Mechanical forces in Drosophila development and homeostasis

Mechanical forces play a central role in shaping tissues during development and maintaining epithelial integrity in homeostasis. In this review, we discuss the roles of mechanical forces in Drosophila development and homeostasis, starting from the interplay of mechanics with cell growth and division. We then discuss several examples of morphogenetic processes where complex 3D structures are shaped by mechanical forces, followed by a closer look at patterning processes. We also review the role of forces in homeostatic processes, including cell elimination and wound healing. Finally, we look at the interplay of mechanics and developmental robustness and discuss open questions in the field, as well as novel approaches that will help tackle them in the future.

Mechanobiology of the female reproductive system

BACKGROUND

Mechanobiology in the field of human female reproduction has been extremely challenging technically and ethically.

METHODS

The present review provides the current knowledge on mechanobiology of the female reproductive system. This review focuses on the early phases of reproduction from oocyte development to early embryonic development, with an emphasis on current progress.

MAIN FINDINGS RESULTS

Optimal, well-controlled mechanical cues are required for female reproductive system physiology. Many important questions remain unanswered; whether and how mechanical imbalances among the embryo, decidua, and uterine muscle contractions affect early human embryonic development, whether the biomechanical properties of oocytes/embryos are potential biomarkers for selecting high-quality oocytes/embryos, whether mechanical properties differ between the two major compartments of the ovary (cortex and medulla) in normally ovulating human ovaries, whether durotaxis is involved in several processes in addition to embryonic development. Progress in mechanobiology is dependent on development of technologies that enable precise physical measurements.

CONCLUSION

More studies are needed to understand the roles of forces and changes in the mechanical properties of female reproductive system physiology. Recent and future technological advancements in mechanobiology research will help us understand the role of mechanical forces in female reproductive system disorders/diseases.

Size scaling in collective cell growth

Size is a fundamental feature of living entities and is intimately tied to their function. Scaling laws, which can be traced to D'Arcy Thompson and Julian Huxley, have emerged as a powerful tool for studying regulation of the growth dynamics of organisms and their constituent parts. Yet, throughout the 20th century, as scaling laws were established for single cells, quantitative studies of the coordinated growth of multicellular structures have lagged, largely owing to technical challenges associated with imaging and image processing. Here, we present a supervised learning approach for quantifying the growth dynamics of germline cysts during oogenesis. Our analysis uncovers growth patterns induced by the groupwise developmental dynamics among connected cells, and differential growth rates of their organelles. We also identify inter-organelle volumetric scaling laws, finding that nurse cell growth is linear over several orders of magnitude. Our approach leverages the ever-increasing quantity and quality of imaging data, and is readily amenable for studies of collective cell growth in other developmental contexts, including early mammalian embryogenesis and germline development.

Computational modelling unveils how epiblast remodelling and positioning rely on trophectoderm morphogenesis during mouse implantation

Understanding the processes by which the mammalian embryo implants in the maternal uterus is a long-standing challenge in embryology. New insights into this morphogenetic event could be of great importance in helping, for example, to reduce human infertility. During implantation the blastocyst, composed of epiblast, trophectoderm and primitive endoderm, undergoes significant remodelling from an oval ball to an egg cylinder. A main feature of this transformation is symmetry breaking and reshaping of the epiblast into a “cup”. Based on previous studies, we hypothesise that this event is the result of mechanical constraints originating from the trophectoderm, which is also significantly transformed during this process. In order to investigate this hypothesis we propose MG# (MechanoGenetic Sharp), an original computational model of biomechanics able to reproduce key cell shape changes and tissue level behaviours in silico. With this model, we simulate epiblast and trophectoderm morphogenesis during implantation. First, our results uphold experimental findings that repulsion at the apical surface of the epiblast is essential to drive lumenogenesis. Then, we provide new theoretical evidence that trophectoderm morphogenesis indeed can dictate the cup shape of the epiblast and fosters its movement towards the uterine tissue. Our results offer novel mechanical insights into mouse peri-implantation and highlight the usefulness of agent-based modelling methods in the study of embryogenesis.

A comprehensive survey of developmental programs reveals a dearth of tree-like lineage graphs and ubiquitous regeneration

Background

Multicellular organisms are characterized by a wide diversity of forms and complexity despite a restricted set of key molecules and mechanisms at the base of organismal development. Development combines three basic processes—asymmetric cell division, signaling, and gene regulation—in a multitude of ways to create this overwhelming diversity of multicellular life forms. Here, we use a generative model to test the limits to which such processes can be combined to generate multiple differentiation paths during development, and attempt to chart the diversity of multicellular organisms generated.

Results

We sample millions of biologically feasible developmental schemes, allowing us to comment on the statistical properties of cell differentiation trajectories they produce. We characterize model-generated “organisms” using the graph topology of their cell type lineage maps. Remarkably, tree-type lineage differentiation maps are the rarest in our data. Additionally, a majority of the “organisms” generated by our model appear to be endowed with the ability to regenerate using pluripotent cells.

Conclusions

Our results indicate that, in contrast to common views, cell type lineage graphs are unlikely to be tree-like. Instead, they are more likely to be directed acyclic graphs, with multiple lineages converging on the same terminal cell type. Furthermore, the high incidence of pluripotent cells in model-generated organisms stands in line with the long-standing hypothesis that whole body regeneration is an epiphenomenon of development. We discuss experimentally testable predictions of our model and some ways to adapt the generative framework to test additional hypotheses about general features of development.

Supplementary Information

The online version contains supplementary material available at (10.1186/s12915-021-01013-4).

Mathematical modeling of the interaction between yolk utilization and fish growth in zebrafish, Danio rerio

Optimal embryonic development plays a major role in the health of an individual beyond the developmental stage. Nutritional perturbation during development is associated with cardiovascular and metabolic disease later in life. With both nutritional uptake and overall growth being risk factors for eventual health, it is necessary to understand not only the behavior of the processes during development but also their interactions. In this study, we used differential equations, image analyses, curve fittings, parameter estimation and laboratory experiments to quantify the rate of yolk absorption and its effect on early development of a vertebrate model (Danio rerio). Findings from this study establish a nonlinear functional relationship between nutrient absorption and early fish growth. We found that the rate of change in fish length and yolk utilization is logistic, that is the yolk decays rapidly for a period of time before leveling out. An interesting finding from this study is that yolk utilization reaches its maximum at 84 h post-fertilization. We validated our mathematical models against experimental observations, making them powerful tools for replication and future simulations.

Mechanical control of tissue shape and morphogenetic flows during vertebrate body axis elongation

Shaping embryonic tissues into their functional morphologies requires cells to control the physical state of the tissue in space and time. While regional variations in cellular forces or cell proliferation have been typically assumed to be the main physical factors controlling tissue morphogenesis, recent experiments have revealed that spatial variations in the tissue physical (fluid/solid) state play a key role in shaping embryonic tissues. Here we theoretically study how the regional control of fluid and solid tissue states guides morphogenetic flows to shape the extending vertebrate body axis. Our results show that both the existence of a fluid-to-solid tissue transition along the anteroposterior axis and the tissue surface tension determine the shape of the tissue and its ability to elongate unidirectionally, with large tissue tensions preventing unidirectional elongation and promoting blob-like tissue expansions. We predict both the tissue morphogenetic flows and stresses that enable unidirectional axis elongation. Our results show the existence of a sharp transition in the structure of morphogenetic flows, from a flow with no vortices to a flow with two counter-rotating vortices, caused by a transition in the number and location of topological defects in the flow field. Finally, comparing the theoretical predictions to quantitative measurements of both tissue flows and shape during zebrafish body axis elongation, we show that the observed morphogenetic events can be explained by the existence of a fluid-to-solid tissue transition along the anteroposterior axis. These results highlight the role of spatiotemporally-controlled fluid-to-solid transitions in the tissue state as a physical mechanism of embryonic morphogenesis.

Regenerative medicine meets mathematical modelling: developing symbiotic relationships

Successful progression from bench to bedside for regenerative medicine products is challenging and requires a multidisciplinary approach. What has not yet been fully recognised is the potential for quantitative data analysis and mathematical modelling approaches to support this process. In this review, we highlight the wealth of opportunities for embedding mathematical and computational approaches within all stages of the regenerative medicine pipeline. We explore how exploiting quantitative mathematical and computational approaches, alongside state-of-the-art regenerative medicine research, can lead to therapies that potentially can be more rapidly translated into the clinic.

Computational Stem Cell Biology: Open Questions and Guiding Principles

Computational biology is enabling an explosive growth in our understanding of stem cells and our ability to use them for disease modeling, regenerative medicine, and drug discovery. We discuss four topics that exemplify applications of computation to stem cell biology: cell typing, lineage tracing, trajectory inference, and regulatory networks. We use these examples to articulate principles that have guided computational biology broadly and call for renewed attention to these principles as computation becomes increasingly important in stem cell biology. We also discuss important challenges for this field with the hope that it will inspire more to join this exciting area.

A Life Cycle for Modeling Biology at Different Scales

Modeling has become a popular tool for inquiry and discovery across biological disciplines. Models allow biologists to probe complex questions and to guide experimentation. Modeling literacy among biologists, however, has not always kept pace with the rise in popularity of these techniques and the relevant advances in modeling theory. The result is a lack of understanding that inhibits communication and ultimately, progress in data gathering and analysis. In an effort to help bridge this gap, we present a blueprint that will empower biologists to interrogate and apply models in their field. We demonstrate the applicability of this blueprint in two case studies from distinct subdisciplines of biology; developmental-biomechanics and evolutionary biology. The models used in these fields vary from summarizing dynamical mechanisms to making statistical inferences, demonstrating the breadth of the utility of models to explore biological phenomena.

Self-organized multicellular structures from simple cell signaling: a computational model

Recent synthetic biology experiments reveal that signaling modules designed to target cell-cell adhesion enable self-organization of multicellular structures Toda et al (2018 Science 361 156-162). Changes in homotypic adhesion that arise through contact-dependent signaling networks result in sorting of an aggregate into two- or three-layered structures. Here we investigate the formation, maintenance, and robustness of such self-organization in the context of a computational model. To do so, we use an established model for Notch/ligand signaling within cells to set up differential E-cadherin expression. This signaling model is integrated with the cellular Potts model to track state changes, adhesion, and cell sorting in a group of cells. The resulting multicellular structures are in accordance with those observed in the experimental reference. In addition to reproducing these experimental results, we track the dynamics of the evolving structures and cell states to understand how such morphologies are dynamically maintained. This appears to be an important developmental principle that was not emphasized in previous models. Our computational model facilitates more detailed understanding of the link between intra- and intercellular signaling, spatio-temporal rearrangement, and emergent behavior at the scale of hundred(s) of cells.

The transition from local to global patterns governs the differentiation of mouse blastocysts

During mammalian blastocyst development, inner cell mass (ICM) cells differentiate into epiblast (Epi) or primitive endoderm (PrE). These two fates are characterized by the expression of the transcription factors NANOG and GATA6, respectively. Here, we investigate the spatio-temporal distribution of NANOG and GATA6 expressing cells in the ICM of the mouse blastocysts with quantitative three-dimensional single cell-based neighbourhood analyses. We define the cell neighbourhood by local features, which include the expression levels of both fate markers expressed in each cell and its neighbours, and the number of neighbouring cells. We further include the position of a cell relative to the centre of the ICM as a global positional feature. Our analyses reveal a local three-dimensional pattern that is already present in early blastocysts: 1) Cells expressing the highest NANOG levels are surrounded by approximately nine neighbours, while 2) cells expressing GATA6 cluster according to their GATA6 levels. This local pattern evolves into a global pattern in the ICM that starts to emerge in mid blastocysts. We show that FGF/MAPK signalling is involved in the three-dimensional distribution of the cells and, using a mutant background, we further show that the GATA6 neighbourhood is regulated by NANOG. Our quantitative study suggests that the three-dimensional cell neighbourhood plays a role in Epi and PrE precursor specification. Our results highlight the importance of analysing the three-dimensional cell neighbourhood while investigating cell fate decisions during early mouse embryonic development.

Multi-scale cellular engineering: From molecules to organ-on-a-chip

Recent technological advances in cellular and molecular engineering have provided new insights into biology and enabled the design, manufacturing, and manipulation of complex living systems. Here, we summarize the state of advances at the molecular, cellular, and multi-cellular levels using experimental and computational tools. The areas of focus include intrinsically disordered proteins, synthetic proteins, spatiotemporally dynamic extracellular matrices, organ-on-a-chip approaches, and computational modeling, which all have tremendous potential for advancing fundamental and translational science. Perspectives on the current limitations and future directions are also described, with the goal of stimulating interest to overcome these hurdles using multi-disciplinary approaches.

A GPU Algorithm for Agent-Based Models to Simulate the Integration of Cell Membrane Signals

Simulation of complex biological systems with agent-based models is becoming more relevant with the increase in Graphics Processing Unit (GPU) power. In those simulations, up to millions of virtual cells are individually computed, involving daunting processing times. An important part of computational models is the algorithm that manages how agents perceive their surroundings. This can be particularly problematic in three-dimensional environments where agents have deformable virtual membranes. This article presents a GPU algorithm that gives the possibility for agents to integrate the signals scattered on their virtual membrane. It is detailed to be coded in languages like OpenCL or Cuda. Its performances are tested to show its speed with current GPU devices. Finally, it was implemented inside an existing software to test and illustrate the possibilities it offers.

PhysiBoSS: a multi-scale agent-based modelling framework integrating physical dimension and cell signalling

MOTIVATION

Due to the complexity and heterogeneity of multicellular biological systems, mathematical models that take into account cell signalling, cell population behaviour and the extracellular environment are particularly helpful. We present PhysiBoSS, an open source software which combines intracellular signalling using Boolean modelling (MaBoSS) and multicellular behaviour using agent-based modelling (PhysiCell).

RESULTS

PhysiBoSS provides a flexible and computationally efficient framework to explore the effect of environmental and genetic alterations of individual cells at the population level, bridging the critical gap from single-cell genotype to single-cell phenotype and emergent multicellular behaviour. PhysiBoSS thus becomes very useful when studying heterogeneous population response to treatment, mutation effects, different modes of invasion or isomorphic morphogenesis events. To concretely illustrate a potential use of PhysiBoSS, we studied heterogeneous cell fate decisions in response to TNF treatment. We explored the effect of different treatments and the behaviour of several resistant mutants. We highlighted the importance of spatial information on the population dynamics by considering the effect of competition for resources like oxygen.

AVAILABILITY AND IMPLEMENTATION

PhysiBoSS is freely available on GitHub (https://github.com/sysbio-curie/PhysiBoSS), with a Docker image (https://hub.docker.com/r/gletort/physiboss/). It is distributed as open source under the BSD 3-clause license.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Curation and annotation of planarian gene expression patterns with segmented reference morphologies

Motivation

Morphological and genetic spatial data from functional experiments based on genetic, surgical and pharmacological perturbations are being produced at an extraordinary pace in developmental and regenerative biology. However, our ability to extract knowledge from these large datasets are hindered due to the lack of formalization methods and tools able to unambiguously describe, centralize and interpret them. Formalizing spatial phenotypes and gene expression patterns is especially challenging in organisms with highly variable morphologies such as planarian worms, which due to their extraordinary regenerative capability can experimentally result in phenotypes with almost any combination of body regions or parts.

Results

Here, we present a computational methodology and mathematical formalism to encode and curate the morphological outcomes and gene expression patterns in planaria. Worm morphologies are encoded with mathematical graphs based on anatomical ontology terms to automatically generate reference morphologies. Gene expression patterns are registered to these standard reference morphologies, which can then be annotated automatically with anatomical ontology terms by analyzing the spatial expression patterns and their textual descriptions. This methodology enables the curation and annotation of complex experimental morphologies together with their gene expression patterns in a centralized standardized dataset, paving the way for the extraction of knowledge and reverse-engineering of the much sought-after mechanistic models in planaria and other regenerative organisms.

Availability and implementation

We implemented this methodology in a user-friendly graphical software tool, PlanGexQ, freely available together with the data in the manuscript at https://lobolab.umbc.edu/plangexq.

Supplementary information

Supplementary data are available at Bioinformatics online.

The Physics of Cellular Decision Making During Epithelial-Mesenchymal Transition

The epithelial-mesenchymal transition (EMT) is a process by which cells lose epithelial traits, such as cell-cell adhesion and apico-basal polarity, and acquire migratory and invasive traits. EMT is crucial to embryonic development and wound healing. Misregulated EMT has been implicated in processes associated with cancer aggressiveness, including metastasis. Recent experimental advances such as single-cell analysis and temporal phenotypic characterization have established that EMT is a multistable process wherein cells exhibit and switch among multiple phenotypic states. This is in contrast to the classical perception of EMT as leading to a binary choice. Mathematical modeling has been at the forefront of this transformation for the field, not only providing a conceptual framework to integrate and analyze experimental data, but also making testable predictions. In this article, we review the key features and characteristics of EMT dynamics, with a focus on the mathematical modeling approaches that have been instrumental to obtaining various useful insights.

Turing-like patterns in an asymmetric dynamic Ising model

To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in Ising models always relies on infinite-range interactions, this mapping allows us to design a finite-range-interactions Ising model that can produce patterns observed in reaction-diffusion systems including Turing patterns with a tunable typical length scale. This model has asymmetric interactions and several spin types coexisting at a site. While we use the example of genetic regulation during embryogenesis to build our model, it can be used to study the behavior of other complex systems of interacting agents.

Automated Design of Pluripotent Stem Cell Self-Organization

Human pluripotent stem cells (hPSCs) have the intrinsic ability to self-organize into complex multicellular organoids that recapitulate many aspects of tissue development. However, robustly directing morphogenesis of hPSC-derived organoids requires novel approaches to accurately control self-directed pattern formation. Here, we combined genetic engineering with computational modeling, machine learning, and mathematical pattern optimization to create a data-driven approach to control hPSC self-organization by knock down of genes previously shown to affect stem cell colony organization, CDH1 and ROCK1. Computational replication of the in vitro system in silico using an extended cellular Potts model enabled machine learning-driven optimization of parameters that yielded emergence of desired patterns. Furthermore, in vitro the predicted experimental parameters quantitatively recapitulated the in silico patterns. These results demonstrate that morphogenic dynamics can be accurately predicted through model-driven exploration of hPSC behaviors via machine learning, thereby enabling spatial control of multicellular patterning to engineer human organoids and tissues. A record of this paper's Transparent Peer Review process is included in the Supplemental Information.

Probing the Functional Role of Physical Motion in Development

Spatiotemporal organization during development has frequently been proposed to be explainable by reaction-transport models, where biochemical reactions couple to physical motion. However, whereas genetic tools allow causality of molecular players to be dissected via perturbation experiments, the functional role of physical transport processes, such as diffusion and cytoplasmic streaming, frequently remains untestable. This Perspective explores the challenges of validating reaction-transport hypotheses and highlights new opportunities provided by perturbation approaches that specifically target physical transport mechanisms. Using these methods, experimental physics may begin to catch up with molecular biology and find ways to test roles of diffusion and flows in development.

Arthropod segmentation

There is now compelling evidence that many arthropods pattern their segments using a clock-and-wavefront mechanism, analogous to that operating during vertebrate somitogenesis. In this Review, we discuss how the arthropod segmentation clock generates a repeating sequence of pair-rule gene expression, and how this is converted into a segment-polarity pattern by ‘timing factor’ wavefronts associated with axial extension. We argue that the gene regulatory network that patterns segments may be relatively conserved, although the timing of segmentation varies widely, and double-segment periodicity appears to have evolved at least twice. Finally, we describe how the repeated evolution of a simultaneous (Drosophila-like) mode of segmentation within holometabolan insects can be explained by heterochronic shifts in timing factor expression plus extensive pre-patterning of the pair-rule genes.

Mathematical models of dorsal closure

Dorsal closure is a model cell sheet movement that occurs midway through Drosophila embryogenesis. A dorsal hole, filled with amnioserosa, closes through the dorsalward elongation of lateral epidermal cell sheets. Closure requires contributions from 5 distinct tissues and well over 140 genes (see Mortensen et al., 2018, reviewed in Kiehart et al., 2017 and Hayes and Solon, 2017). In spite of this biological complexity, the movements (kinematics) of closure are geometrically simple at tissue, and in certain cases, at cellular scales. This simplicity has made closure the target of a number of mathematical models that seek to explain and quantify the processes that underlie closure's kinematics. The first (purely kinematic) modeling approach recapitulated well the time-evolving geometry of closure even though the underlying physical principles were not known. Almost all subsequent models delve into the forces of closure (i.e. the dynamics of closure). Models assign elastic, contractile and viscous forces which impact tissue and/or cell mechanics. They write rate equations which relate the forces to one another and to other variables, including those which represent geometric, kinematic, and or signaling characteristics. The time evolution of the variables is obtained by computing the solution of the model's system of equations, with optimized model parameters. The basis of the equations range from the phenomenological to biophysical first principles. We review various models and present their contribution to our understanding of the molecular mechanisms and biophysics of closure. Models of closure will contribute to our understanding of similar movements that characterize vertebrate morphogenesis.

Microbial multicellular development: mechanical forces in action

Multicellular development occurs in diverse microbial lineages and involves the complex interaction among biochemical, physical and ecological factors. We focus on the mechanical forces that appear to be relevant for the scale and material qualities of individual cells and small cellular conglomerates. We review the effects of such forces on the development of some paradigmatic microorganisms, as well as their overall consequences in multicellular structures. Microbes exhibiting multicellular development have been considered models for the evolutionary transition to multicellularity. Therefore, we discuss how comparative, integrative and dynamic approaches to the mechanical effects involved in microbial development can provide valuable insights into some of the principles behind the evolutionary transition to multicellularity.