Interplay of mechanical deformation and patterned gene expression in developing embryos

Hedgehog morphogen gradient is robust towards variations in tissue morphology in Drosophila

During tissue development, gradients of secreted signaling molecules known as morphogens provide cells with positional information. The mechanisms underlying morphogen spreading have been widely studied, however, it remains largely unexplored whether the shape of morphogen gradients is influenced by tissue morphology. Here, we developed an analysis pipeline to quantify the distribution of proteins within a curved tissue. We applied it to the Hedgehog morphogen gradient in the Drosophila wing and eye-antennal imaginal discs, which are flat and curved tissues, respectively. Despite a different expression profile, the slope of the Hedgehog gradient was comparable between the two tissues. Moreover, inducing ectopic folds in wing imaginal discs did not affect the slope of the Hedgehog gradient. Suppressing curvature in the eye-antennal imaginal disc also did not alter the Hedgehog gradient slope but led to ectopic Hedgehog expression. In conclusion, through the development of an analysis pipeline that allows quantifying protein distribution in curved tissues, we show that the Hedgehog gradient is robust towards variations in tissue morphology.

Mechano-biochemical marine stimulation of inversion, gastrulation, and endomesoderm specification in multicellular Eukaryota

The evolutionary emergence of the primitive gut in Metazoa is one of the decisive events that conditioned the major evolutionary transition, leading to the origin of animal development. It is thought to have been induced by the specification of the endomesoderm (EM) into the multicellular tissue and its invagination (i.e., gastrulation). However, the biochemical signals underlying the evolutionary emergence of EM specification and gastrulation remain unknown. Herein, we find that hydrodynamic mechanical strains, reminiscent of soft marine flow, trigger active tissue invagination/gastrulation or curvature reversal via a Myo-II-dependent mechanotransductive process in both the metazoan Nematostella vectensis (cnidaria) and the multicellular choanoflagellate Choanoeca flexa. In the latter, our data suggest that the curvature reversal is associated with a sensory-behavioral feeding response. Additionally, like in bilaterian animals, gastrulation in the cnidarian Nematostella vectensis is shown to participate in the biochemical specification of the EM through mechanical activation of the β-catenin pathway via the phosphorylation of Y654-βcatenin. Choanoflagellates are considered the closest living relative to metazoans, and the common ancestor of choanoflagellates and metazoans dates back at least 700 million years. Therefore, the present findings using these evolutionarily distant species suggest that the primitive emergence of the gut in Metazoa may have been initiated in response to marine mechanical stress already in multicellular pre-Metazoa. Then, the evolutionary transition may have been achieved by specifying the EM via a mechanosensitive Y654-βcatenin dependent mechanism, which appeared during early Metazoa evolution and is specifically conserved in all animals.

Biomimetic Hydrogels in the Study of Cancer Mechanobiology: Overview, Biomedical Applications, and Future Perspectives

Hydrogels are biocompatible polymers that are tunable to the system under study, allowing them to be widely used in medicine, bioprinting, tissue engineering, and biomechanics. Hydrogels are used to mimic the three-dimensional microenvironment of tissues, which is essential to understanding cell–cell interactions and intracellular signaling pathways (e.g., proliferation, apoptosis, growth, and survival). Emerging evidence suggests that the malignant properties of cancer cells depend on mechanical cues that arise from changes in their microenvironment. These mechanobiological cues include stiffness, shear stress, and pressure, and have an impact on cancer proliferation and invasion. The hydrogels can be tuned to simulate these mechanobiological tissue properties. Although interest in and research on the biomedical applications of hydrogels has increased in the past 25 years, there is still much to learn about the development of biomimetic hydrogels and their potential applications in biomedical and clinical settings. This review highlights the application of hydrogels in developing pre-clinical cancer models and their potential for translation to human disease with a focus on reviewing the utility of such models in studying glioblastoma progression.

Beyond Turing: far-from-equilibrium patterns and mechano-chemical feedback

Turing patterns are commonly understood as specific instabilities of a spatially homogeneous steady state, resulting from activator-inhibitor interaction destabilized by diffusion. We argue that this view is restrictive and its agreement with biological observations is problematic. We present two alternatives to the classical Turing analysis of patterns. First, we employ the abstract framework of evolution equations to enable the study of far-from-equilibrium patterns. Second, we introduce a mechano-chemical model, with the surface on which the pattern forms being dynamic and playing an active role in the pattern formation, effectively replacing the inhibitor. We highlight the advantages of these two alternatives vis-à-vis the classical Turing analysis, and give an overview of recent results and future challenges for both approaches. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Mechanical feedback and robustness of apical constrictions in Drosophila embryo ventral furrow formation

Formation of the ventral furrow in the Drosophila embryo relies on the apical constriction of cells in the ventral region to produce bending forces that drive tissue invagination. In our recent paper we observed that apical constrictions during the initial phase of ventral furrow formation produce elongated patterns of cellular constriction chains prior to invagination and argued that these are indicative of tensile stress feedback. Here, we quantitatively analyze the constriction patterns preceding ventral furrow formation and find that they are consistent with the predictions of our active-granular-fluid model of a monolayer of mechanically coupled stress-sensitive constricting particles. Our model shows that tensile feedback causes constriction chains to develop along underlying precursor tensile stress chains that gradually strengthen with subsequent cellular constrictions. As seen in both our model and available optogenetic experiments, this mechanism allows constriction chains to penetrate or circumvent zones of reduced cell contractility, thus increasing the robustness of ventral furrow formation to spatial variation of cell contractility by rescuing cellular constrictions in the disrupted regions.

Mechanochemical induction of wrinkling morphogenesis on elastic shells

Morphogenetic dynamics of tissue sheets require coordinated cell shape changes regulated by global patterning of mechanical forces. Inspired by such biological phenomena, we propose a minimal mechanochemical model based on the notion that cell shape changes are induced by diffusible biomolecules that influence tissue contractility in a concentration-dependent manner - and whose concentration is in turn affected by the macroscopic tissue shape. We perform computational simulations of thin shell elastic dynamics to reveal propagating chemical and three-dimensional deformation patterns arising due to a sequence of buckling instabilities. Depending on the concentration threshold that actuates cell shape change, we find qualitatively different patterns. The mechanochemically coupled patterning dynamics are distinct from those driven by purely mechanical or purely chemical factors, and emerge even without diffusion. Using numerical simulations and theoretical arguments, we analyze the elastic instabilities that result from our model and provide simple scaling laws to identify wrinkling morphologies.

High-throughput mechanotransduction in Drosophila embryos with mesofluidics

Developing embryos create complexity by expressing genes to coordinate movement which generates mechanical force. An emerging theory is that mechanical force can also serve as an input signal to regulate developmental gene expression. Experimental methods to apply mechanical stimulation to whole embryos have been limited, mainly to aspiration, indentation, or moving a coverslip; these approaches stimulate only a few embryos at a time and require manual alignment. A powerful approach for automation is microfluidic devices, which can precisely manipulate hundreds of samples. However, using microfluidics to apply mechanical stimulation has been limited to small cellular systems, with fewer applications for larger scale whole embryos. We developed a mesofluidic device that applies the precision and automation of microfluidics to the Drosophila embryo: high-throughput automatic alignment, immobilization, compression, real-time imaging, and recovery of hundreds of live embryos. We then use twist:eGFP embryos to show that the mechanical induction of twist depends on the dose and duration of compression. This device allows us to quantify responses to compression, map the distribution of ectopic twist, and measure embryo stiffness. For building mesofluidic devices, we describe modifications on ultra-thick photolithography, derive an analytical model that predicts the deflection of sidewalls, and discuss parametric calibration. This "mesomechanics" approach combines the high-throughput automation and precision of microfluidics with the biological relevance of live embryos to examine mechanotransduction. These analytical models facilitate the design of future devices to process multicellular organisms such as larvae, organoids, and mesoscale tissue samples.

The major β-catenin/E-cadherin junctional binding site is a primary molecular mechano-transductor of differentiation in vivo

In vivo, the primary molecular mechanotransductive events mechanically initiating cell differentiation remain unknown. Here we find the molecular stretching of the highly conserved Y654-β-catenin-D665-E-cadherin binding site as mechanically induced by tissue strain. It triggers the increase of accessibility of the Y654 site, target of the Src42A kinase phosphorylation leading to irreversible unbinding. Molecular dynamics simulations of the β-catenin/E-cadherin complex under a force mimicking a 6 pN physiological mechanical strain predict a local 45% stretching between the two α-helices linked by the site and a 15% increase in accessibility of the phosphorylation site. Both are quantitatively observed using FRET lifetime imaging and non-phospho Y654 specific antibody labelling, in response to the mechanical strains developed by endogenous and magnetically mimicked early mesoderm invagination of gastrulating Drosophila embryos. This is followed by the predicted release of 16% of β-catenin from junctions, observed in FRAP, which initiates the mechanical activation of the β-catenin pathway process.

Post-Turing tissue pattern formation: Advent of mechanochemistry

Chemical and mechanical pattern formation is fundamental during embryogenesis and tissue development. Yet, the underlying molecular and cellular mechanisms are still elusive in many cases. Most current theories assume that tissue development is driven by chemical processes: either as a sequence of chemical patterns each depending on the previous one, or by patterns spontaneously arising from specific chemical interactions (such as “Turing-patterns”). Within both theories, mechanical patterns are usually regarded as passive by-products of chemical pre-patters. However, several experiments question these theories, and an increasing number of studies shows that tissue mechanics can actively influence chemical patterns during development. In this study, we thus focus on the interplay between chemical and mechanical processes during tissue development. On one hand, based on recent experimental data, we develop new mechanochemical simulation models of evolving tissues, in which the full 3D representation of the tissue appears to be critical for obtaining a realistic mechanochemical behaviour. The presented modelling approach is flexible and numerically studied using state of the art finite element methods. Thus, it may serve as a basis to combine simulations with new experimental methods in tissue development. On the other hand, we apply the developed approach and demonstrate that even simple interactions between tissue mechanics and chemistry spontaneously lead to robust and complex mechanochemical patterns. Especially, we demonstrate that the main contradictions arising in the framework of purely chemical theories are naturally and automatically resolved using the mechanochemical patterning theory.

During embryogenesis, biological tissues gradually increase their complexity by self-organised creation of diverse chemical and mechanical patterns. Detailed mechanisms driving and controlling these patterns are not well understood. Previous theories mostly assume that these patterns are driven by chemical processes. Based on these theories, mechanical patterns are usually considered being mainly determined by chemical pre-patterns. However, experimental evidence for these theories is sparse, and several inconsistencies have been discovered. Furthermore, an increasing amount of data shows that tissue mechanics plays an important role in pattern formation. In this study, we present 3D computer simulations of evolving tissues to investigate the capacity of mechanochemical interactions for pattern formation. We show that even simple interactions between tissue mechanics and tissue chemistry spontaneously lead to robust chemical and mechanical pattern formation. We additionally demonstrate that main contradictions arising in the framework of purely chemical theories are naturally and automatically resolved using the mechanochemical patterning theory. The presented modelling approach can be used to combine simulations with recent experimental developments, to help unravel one of the big mysteries in biology: The mechanisms of self-organised pattern formation during embryogenesis.

Mechanotransduction in tumor progression: The dark side of the force

Broders-Bondon et al. review the pathological mechanical properties of tumor tissues and how abnormal mechanical signals result in oncogenic biochemical signals during tumor progression.

Cancer has been characterized as a genetic disease, associated with mutations that cause pathological alterations of the cell cycle, adhesion, or invasive motility. Recently, the importance of the anomalous mechanical properties of tumor tissues, which activate tumorigenic biochemical pathways, has become apparent. This mechanical induction in tumors appears to consist of the destabilization of adult tissue homeostasis as a result of the reactivation of embryonic developmental mechanosensitive pathways in response to pathological mechanical strains. These strains occur in many forms, for example, hypervascularization in late tumors leads to high static hydrodynamic pressure that can promote malignant progression through hypoxia or anomalous interstitial liquid and blood flow. The high stiffness of tumors directly induces the mechanical activation of biochemical pathways enhancing the cell cycle, epithelial–mesenchymal transition, and cell motility. Furthermore, increases in solid-stress pressure associated with cell hyperproliferation activate tumorigenic pathways in the healthy epithelial cells compressed by the neighboring tumor. The underlying molecular mechanisms of the translation of a mechanical signal into a tumor inducing biochemical signal are based on mechanically induced protein conformational changes that activate classical tumorigenic signaling pathways. Understanding these mechanisms will be important for the development of innovative treatments to target such mechanical anomalies in cancer.

Top-down models in biology: explanation and control of complex living systems above the molecular level

It is widely assumed in developmental biology and bioengineering that optimal understanding and control of complex living systems follows from models of molecular events. The success of reductionism has overshadowed attempts at top-down models and control policies in biological systems. However, other fields, including physics, engineering and neuroscience, have successfully used the explanations and models at higher levels of organization, including least-action principles in physics and control-theoretic models in computational neuroscience. Exploiting the dynamic regulation of pattern formation in embryogenesis and regeneration requires new approaches to understand how cells cooperate towards large-scale anatomical goal states. Here, we argue that top-down models of pattern homeostasis serve as proof of principle for extending the current paradigm beyond emergence and molecule-level rules. We define top-down control in a biological context, discuss the examples of how cognitive neuroscience and physics exploit these strategies, and illustrate areas in which they may offer significant advantages as complements to the mainstream paradigm. By targeting system controls at multiple levels of organization and demystifying goal-directed (cybernetic) processes, top-down strategies represent a roadmap for using the deep insights of other fields for transformative advances in regenerative medicine and systems bioengineering.

Coupling between chromosome intermingling and gene regulation during cellular differentiation

In this article, we summarize current findings for the emergence of biophysical properties such as nuclear stiffness, chromatin compaction, chromosome positioning, and chromosome intermingling during stem cell differentiation, which eventually correlated with the changes of gene expression profiles during cellular differentiation. An overview is first provided to link stem cell differentiation with alterations in nuclear architecture, chromatin compaction, along with nuclear and chromatin dynamics. Further, we highlight the recent biophysical and molecular approaches, imaging methods and computational developments in characterizing transcription-related chromosome organization especially chromosome intermingling and nano-scale chromosomal contacts. Finally, the article ends with an outlook towards the emergence of a functional roadmap in setting up chromosome positioning and intermingling in a cell type specific manner during cellular differentiation.

Biophysical Regulation of Cancer Stem/Initiating Cells: Implications for Disease Mechanisms and Translation

Cancer stem/initiating cells (CSCs) are a subset of tumor cells proposed to play privileged roles in seeding tumors and driving metastasis. CSCs have emerged as an increasingly important target of interest in cancer biology and therapy. Recent work has suggested that CSC maintenance and metastatic potential may be modulated by physical inputs within the tissue microenvironment, including interstitial pressure and extracellular matrix stiffness. Here we review recent progress in our understanding of CSC regulation by biophysical signals within the tumor microenvironment. While the mechanistic basis of this signaling remains incompletely understood, we discuss emerging evidence that mechanical inputs can epigenetically regulate CSC behavior and that some CSCs can evade mechanotransductive signals to more efficiently infiltrate tissue. We also describe efforts to leverage these findings to engineer culture platforms for the characterization of CSC mechanics for discovery and screening.

Micro- and nano-technologies to probe the mechano-biology of the brain

Biomechanical forces have been demonstrated to influence a plethora of neuronal functions across scales including gene expression, mechano-sensitive ion channels, neurite outgrowth and folding of the cortices in the brain. However, the detailed roles biomechanical forces may play in brain development and disorders has seen limited study, partly due to a lack of effective methods to probe the mechano-biology of the brain. Current techniques to apply biomechanical forces on neurons often suffer from low throughput and poor spatiotemporal resolution. On the other hand, newly developed micro- and nano-technologies can overcome these aforementioned limitations and offer advantages such as lower cost and possibility of non-invasive control of neuronal circuits. This review compares the range of conventional, micro- and nano-technological techniques that have been developed and how they have been or can be used to understand the effect of biomechanical forces on neuronal development and homeostasis.

Looking Beyond the Genes: The Interplay Between Signaling Pathways and Mechanics in the Shaping and Diversification of Epithelial Tissues

The core of Evo-Devo lies in the intuition that the way tissues grow during embryonic development, the way they sustain their structure and function throughout lifetime, and the way they evolve are closely linked. Epithelial tissues are ubiquitous in metazoans, covering the gut and internal branched organs, as well as the skin and its derivatives (ie, teeth). Here, we discuss in vitro, in vivo, and in silico studies on epithelial tissues to illustrate the conserved, dynamical, and complex aspects of their development. We then explore the implications of the dynamical and nonlinear nature of development on the evolution of their size and shape at the phenotypic and genetic levels. In rare cases, when the interplay between signaling and mechanics is well understood at the cell level, it is becoming clear that the structure of development leads to covariation of characters, an integration which in turn provides some predictable structure to evolutionary changes. We suggest that such nonlinear systems are prone to genetic drift, cryptic genetic variation, and context-dependent mutational effects. We argue that experimental and theoretical studies at the cell level are critical to our understanding of the phenotypic and genetic evolution of epithelial tissues, including carcinomas.

Beyond Turing: mechanochemical pattern formation in biological tissues

Background

During embryogenesis, chemical (morphogen) and mechanical patterns develop within tissues in a self-organized way. More than 60 years ago, Turing proposed his famous reaction-diffusion model for such processes, assuming chemical interactions as the main driving force in tissue patterning. However, experimental identification of corresponding molecular candidates is still incomplete. Recent results suggest that beside morphogens, also tissue mechanics play a significant role in these patterning processes.

Results

Combining continuous finite strain with discrete cellular tissue models, we present and numerically investigate mechanochemical processes, in which morphogen dynamics and tissue mechanics are coupled by feedback loops. We consider three different mechanical cues involved in such feedbacks: strain, stress, and compression. Based on experimental results, for each case, we present a feedback loop spontaneously creating robust mechanochemical patterns. In contrast to Turing-type models, simple mechanochemical interaction terms are sufficient to create de novo patterns.

Conclusions

Our results emphasize mechanochemical processes as possible candidates controlling different steps of embryogenesis. To motivate further experimental research discovering related mechanisms in living tissues, we also present predictive in silicio experiments.

Reviewers

Reviewer 1 - Marek Kimmel; Reviewer 2 - Konstantin Doubrovinski (nominated by Ned Wingreen); Reviewer 3 - Jun Allard (nominated by William Hlavacek).

Characterization of Hemodynamics in Great Arteries of Wild-Type Mouse Using Computational Fluid Dynamics Based on Ultrasound Images

Hemodynamic factors in cardiovascular system are hypothesized to play a significant role in causing structural heart development. It is thus important to improve our understanding of velocity characteristics and parameters. We present such a study on wild-type mouse to characterize the vessel geometry, flow pattern, and wall shear stress in great arteries. Microultrasound imaging for small animals was used to measure blood boundary and velocity of the great arteries. Subsequently, specimens' flow boundary conditions were used for 3-dimensional reconstructions of the great artery and aortic arch dimensions, and blood flow velocity data were input into subject-specific computational fluid dynamics for modeling hemodynamics. Measurement by microultrasound imaging showed that blood velocities in the great artery and aortic arch had strong correlations with vascular sizes, whereas blood pressure had a weak trend in relation to vascular size. Wall shear stress magnitude increased when closer to arterial branches and reduced proximally in the aortic root and distally in the descending aorta, and the parameters were related to the fluid mechanics in branches in some degree. We developed a method to investigate fluid mechanics in mouse arteries, using a combination of microultrasound and computational fluid dynamics, and demonstrated its ability to reveal detailed geometric, kinematic, and fluid mechanics parameters.

Mechanochemical symmetry breaking in Hydra aggregates

Tissue morphogenesis comprises the self-organized creation of various patterns and shapes. Although detailed underlying mechanisms are still elusive in many cases, an increasing amount of experimental data suggests that chemical morphogen and mechanical processes are strongly coupled. Here, we develop and test a minimal model of the axis-defining step (i.e., symmetry breaking) in aggregates of the Hydra polyp. Based on previous findings, we combine osmotically driven shape oscillations with tissue mechanics and morphogen dynamics. We show that the model incorporating a simple feedback loop between morphogen patterning and tissue stretch reproduces a wide range of experimental data. Finally, we compare different hypothetical morphogen patterning mechanisms (Turing, tissue-curvature, and self-organized criticality). Our results suggest the experimental investigation of bigger (i.e., multiple head) aggregates as a key step for a deeper understanding of mechanochemical symmetry breaking in Hydra.

How Tissue Mechanical Properties Affect Enteric Neural Crest Cell Migration

Neural crest cells (NCCs) are a population of multipotent cells that migrate extensively during vertebrate development. Alterations to neural crest ontogenesis cause several diseases, including cancers and congenital defects, such as Hirschprung disease, which results from incomplete colonization of the colon by enteric NCCs (ENCCs). We investigated the influence of the stiffness and structure of the environment on ENCC migration in vitro and during colonization of the gastrointestinal tract in chicken and mouse embryos. We showed using tensile stretching and atomic force microscopy (AFM) that the mesenchyme of the gut was initially soft but gradually stiffened during the period of ENCC colonization. Second-harmonic generation (SHG) microscopy revealed that this stiffening was associated with a gradual organization and enrichment of collagen fibers in the developing gut. Ex-vivo 2D cell migration assays showed that ENCCs migrated on substrates with very low levels of stiffness. In 3D collagen gels, the speed of the ENCC migratory front decreased with increasing gel stiffness, whereas no correlation was found between porosity and ENCC migration behavior. Metalloprotease inhibition experiments showed that ENCCs actively degraded collagen in order to progress. These results shed light on the role of the mechanical properties of tissues in ENCC migration during development.

Re-membering the body: applications of computational neuroscience to the top-down control of regeneration of limbs and other complex organs

A major goal of regenerative medicine and bioengineering is the regeneration of complex organs, such as limbs, and the capability to create artificial constructs (so-called biobots) with defined morphologies and robust self-repair capabilities. Developmental biology presents remarkable examples of systems that self-assemble and regenerate complex structures toward their correct shape despite significant perturbations. A fundamental challenge is to translate progress in molecular genetics into control of large-scale organismal anatomy, and the field is still searching for an appropriate theoretical paradigm for facilitating control of pattern homeostasis. However, computational neuroscience provides many examples in which cell networks - brains - store memories (e.g., of geometric configurations, rules, and patterns) and coordinate their activity towards proximal and distant goals. In this Perspective, we propose that programming large-scale morphogenesis requires exploiting the information processing by which cellular structures work toward specific shapes. In non-neural cells, as in the brain, bioelectric signaling implements information processing, decision-making, and memory in regulating pattern and its remodeling. Thus, approaches used in computational neuroscience to understand goal-seeking neural systems offer a toolbox of techniques to model and control regenerative pattern formation. Here, we review recent data on developmental bioelectricity as a regulator of patterning, and propose that target morphology could be encoded within tissues as a kind of memory, using the same molecular mechanisms and algorithms so successfully exploited by the brain. We highlight the next steps of an unconventional research program, which may allow top-down control of growth and form for numerous applications in regenerative medicine and synthetic bioengineering.

Monitoring developmental force distributions in reconstituted embryonic epithelia

The way cells are organized within a tissue dictates how they sense and respond to extracellular signals, as cues are received and interpreted based on expression and organization of receptors, downstream signaling proteins, and transcription factors. Part of this microenvironmental context is the result of forces acting on the cell, including forces from other cells or from the cellular substrate or basement membrane. However, measuring forces exerted on and by cells is difficult, particularly in an in vivo context, and interpreting how forces affect downstream cellular processes poses an even greater challenge. Here, we present a simple method for monitoring and analyzing forces generated from cell collectives. We demonstrate the ability to generate traction force data from human embryonic stem cells grown in large organized epithelial sheets to determine the magnitude and organization of cell-ECM and cell-cell forces within a self-renewing colony. We show that this method can be used to measure forces in a dynamic hESC system and demonstrate the ability to map intracolony protein localization to force organization.

Inelastic mechanics: A unifying principle in biomechanics

Many soft materials are classified as viscoelastic. They behave mechanically neither quite fluid-like nor quite solid-like - rather a bit of both. Biomaterials are often said to fall into this class. Here, we argue that this misses a crucial aspect, and that biomechanics is essentially damage mechanics, at heart. When deforming an animal cell or tissue, one can hardly avoid inducing the unfolding of protein domains, the unbinding of cytoskeletal crosslinkers, the breaking of weak sacrificial bonds, and the disruption of transient adhesions. We classify these activated structural changes as inelastic. They are often to a large degree reversible and are therefore not plastic in the proper sense, but they dissipate substantial amounts of elastic energy by structural damping. We review recent experiments involving biological materials on all scales, from single biopolymers over cells to model tissues, to illustrate the unifying power of this paradigm. A deliberately minimalistic yet phenomenologically very rich mathematical modeling framework for inelastic biomechanics is proposed. It transcends the conventional viscoelastic paradigm and suggests itself as a promising candidate for a unified description and interpretation of a wide range of experimental data. This article is part of a Special Issue entitled: Mechanobiology.

Characterization of the vessel geometry, flow mechanics and wall shear stress in the great arteries of wildtype prenatal mouse

Introduction

Abnormal fluid mechanical environment in the pre-natal cardiovascular system is hypothesized to play a significant role in causing structural heart malformations. It is thus important to improve our understanding of the prenatal cardiovascular fluid mechanical environment at multiple developmental time-points and vascular morphologies. We present such a study on fetal great arteries on the wildtype mouse from embryonic day 14.5 (E14.5) to near-term (E18.5).

Methods

Ultrasound bio-microscopy (UBM) was used to measure blood velocity of the great arteries. Subsequently, specimens were cryo-embedded and sectioned using episcopic fluorescent image capture (EFIC) to obtain high-resolution 2D serial image stacks, which were used for 3D reconstructions and quantitative measurement of great artery and aortic arch dimensions. EFIC and UBM data were input into subject-specific computational fluid dynamics (CFD) for modeling hemodynamics.

Results

In normal mouse fetuses between E14.5–18.5, ultrasound imaging showed gradual but statistically significant increase in blood velocity in the aorta, pulmonary trunk (with the ductus arteriosus), and descending aorta. Measurement by EFIC imaging displayed a similar increase in cross sectional area of these vessels. However, CFD modeling showed great artery average wall shear stress and wall shear rate remain relatively constant with age and with vessel size, indicating that hemodynamic shear had a relative constancy over gestational period considered here.

Conclusion

Our EFIC-UBM-CFD method allowed reasonably detailed characterization of fetal mouse vascular geometry and fluid mechanics. Our results suggest that a homeostatic mechanism for restoring vascular wall shear magnitudes may exist during normal embryonic development. We speculate that this mechanism regulates the growth of the great vessels.

A mechanochemical model for embryonic pattern formation: coupling tissue mechanics and morphogen expression

Motivated by recent experimental findings, we propose a novel mechanism of embryonic pattern formation based on coupling of tissue curvature with diffusive signaling by a chemical factor. We derive a new mathematical model using energy minimization approach and show that the model generates a variety of morphogen and curvature patterns agreeing with experimentally observed structures. The mechanism proposed transcends the classical Turing concept which requires interactions between two morphogens with a significantly different diffusivity. Our studies show how biomechanical forces may replace the elusive long-range inhibitor and lead to formation of stable spatially heterogeneous structures without existence of chemical prepatterns. We propose new experimental approaches to decisively test our central hypothesis that tissue curvature and morphogen expression are coupled in a positive feedback loop.

Towards 3D in silico modeling of the sea urchin embryonic development

Embryogenesis is a dynamic process with an intrinsic variability whose understanding requires the integration of molecular, genetic, and cellular dynamics. Biological circuits function over time at the level of single cells and require a precise analysis of the topology, temporality, and probability of events. Integrative developmental biology is currently looking for the appropriate strategies to capture the intrinsic properties of biological systems. The "-omic" approaches require disruption of the function of the biological circuit; they provide static information, with low temporal resolution and usually with population averaging that masks fast or variable features at the cellular scale and in a single individual. This data should be correlated with cell behavior as cells are the integrators of biological activity. Cellular dynamics are captured by the in vivo microscopy observation of live organisms. This can be used to reconstruct the 3D + time cell lineage tree to serve as the basis for modeling the organism's multiscale dynamics. We discuss here the progress that has been made in this direction, starting with the reconstruction over time of three-dimensional digital embryos from in toto time-lapse imaging. Digital specimens provide the means for a quantitative description of the development of model organisms that can be stored, shared, and compared. They open the way to in silico experimentation and to a more theoretical approach to biological processes. We show, with some unpublished results, how the proposed methodology can be applied to sea urchin species that have been model organisms in the field of classical embryology and modern developmental biology for over a century.

On the evolution of morphogenetic models: mechano-chemical interactions and an integrated view of cell differentiation, growth, pattern formation and morphogenesis

In the 1950s, embryology was conceptualized as four relatively independent problems: cell differentiation, growth, pattern formation and morphogenesis. The mechanisms underlying the first three traditionally have been viewed as being chemical in nature, whereas those underlying morphogenesis have usually been discussed in terms of mechanics. Often, morphogenesis and its mechanical processes have been regarded as subordinate to chemical ones. However, a growing body of evidence indicates that the biomechanics of cells and tissues affect in striking ways those phenomena often thought of as mainly under the control of cell-cell signalling. This accumulation of data has led to a revival of the mechano-transduction concept in particular, and of complexity in general, causing us now to consider whether we should retain the traditional conceptualization of development. The researchers' semantic preferences for the terms 'patterning', 'pattern formation' or 'morphogenesis' can be used to describe three main 'schools of thought' which emerged in the late 1970s. In the 'molecular school', the term patterning is deeply tied to the positional information concept. In the 'chemical school', the term 'pattern formation' regularly implies reaction-diffusion models. In the 'mechanical school', the term 'morphogenesis' is more frequently used in relation to mechanical instabilities. Major differences among these three schools pertain to the concept of self-organization, and models can be classified as morphostatic or morphodynamic. Various examples illustrate the distorted picture that arises from the distinction among differentiation, growth, pattern formation and morphogenesis, based on the idea that the underlying mechanisms are respectively chemical or mechanical. Emerging quantitative approaches integrate the concepts and methods of complex sciences and emphasize the interplay between hierarchical levels of organization via mechano-chemical interactions. They draw upon recent improvements in mathematical and numerical morphogenetic models and upon considerable progress in collecting new quantitative data. This review highlights a variety of such models, which exhibit important advances, such as hybrid, stochastic and multiscale simulations.

Exploring the link between human embryonic stem cell organization and fate using tension-calibrated extracellular matrix functionalized polyacrylamide gels

Human embryonic stem cell (hESc) lines are likely the in vitro equivalent of the pluripotent epiblast. hESc express high levels of the extracellular matrix (ECM) laminin integrin receptor α6β1 and consequently can adhere robustly and be propagated in an undifferentiated state on tissue culture plastic coated with the laminin rich basement membrane preparation, Matrigel, even in the absence of supporting fibroblasts. Such cultures represent a critical step in the development of more defined feeder free cultures of hESc; a goal deemed necessary for regenerative medical applications and have been used as the starting point in some differentiation protocols. However, on standard non-deformable tissue culture plastic hESc either fail or inadequately develop the structural/morphological organization of the epiblast in vivo. By contrast, growth of hESc on appropriately defined mechanically deformable polyacrylamide substrates permits recapitulation of many of these in vivo features. These likely herald differences in the precise nature of the integration of signal transduction pathways from soluble morphogens and represent an unexplored variable in hESc (fate) state space. In this chapter we describe how to establish viable hESc colonies on these functionalized polyacrylamide gels. We suggest this strategy as a prospective in vitro model of the genetics, biochemistry, and cell biology of pre- and early-gastrulation stage human embryos and the permissive and instructive roles that cellular and substrate mechanics might play in early embryonic cell fate decisions. Such knowledge should inform regenerative medical applications aimed at enabling or improving the differentiation of specific cell types from embryonic or induced embryonic stem cells.

Diffusion-reaction model for Drosophila embryo development

During the early stages of gastrulation in Drosophila embryo, the epithelial cells composing the single tissue layer of the egg undergo large strains and displacements. These movements have been usually modelled by decomposing the total deformation gradient in an (imposed or strain/stress dependent) active part and a passive response. Although the influence of the chemical and genetic activity in the mechanical response of the cell has been experimentally observed, the effects of the mechanical deformation on the latter have been far less studied, and much less modelled. Here, we propose a model that couples morphogen transport and the cell mechanics during embryogenesis. A diffusion-reaction equation is introduced as an additional mechanical regulator of morphogenesis. Consequently, the active deformations are not directly imposed in the analytical formulation, but they rather depend on the morphogen concentration, which is introduced as a new variable. In this study, we show that strain patterns similar to those observed during biological experiments can be reproduced by properly combining the two phenomena. In addition, we use a novel technique to parameterise the embryo geometry by solving two Laplace problems with specific boundary conditions. We apply the method to two morphogenetic movements: ventral furrow invagination and germ band extension. The matching between our results and the observed experimental deformations confirms that diffusion-reaction of morphogens can actually be controlling large morphogenetic movements.

Mechanosignaling to the cell nucleus and gene regulation

Cells integrate physicochemical signals on the nanoscale from the local microenvironment, resulting in altered functional nuclear landscape and gene expression. These alterations regulate diverse biological processes including stem cell differentiation, establishing robust developmental genetic programs and cellular homeostatic control systems. The mechanisms by which these signals are integrated into the 3D spatiotemporal organization of the cell nucleus to elicit differential gene expression programs are poorly understood. In this review I analyze our current understanding of mechanosignal transduction mechanisms to the cell nucleus to induce differential gene regulation. A description of both physical and chemical coupling, resulting in a prestressed nuclear organization, is emphasized. I also highlight the importance of spatial dimension in chromosome assembly, as well as the temporal filtering and stochastic processes at gene promoters that may be important in understanding the biophysical design principles underlying mechanoregulation of gene transcription.

Tension and epithelial morphogenesis in Drosophila early embryos

During morphogenesis, tissues are shaped by cell behaviors such as apical cell constriction and cell intercalation, which are the result of cell intrinsic forces, but are also shaped passively by forces acting on the cells. The latter extrinsic forces can be produced either within the deforming tissue by the tissue-scale integration of intrinsic forces, or outside the tissue by other tissue movements or by fluid flows. Here we review the intrinsic and extrinsic forces that sculpt the epithelium of early Drosophila embryos, focusing on three conserved morphogenetic processes: tissue internalization, axis extension, and segment boundary formation. Finally, we look at how the actomyosin cytoskeleton forms force-generating structures that power these three morphogenetic events at the cell and the tissue scales.

Mechanotransduction in development

Biochemical patterning and morphogenetic movements coordinate the design of embryonic development. The molecular processes that pattern and closely control morphogenetic movements are today becoming well understood. Recent experimental evidence demonstrates that mechanical cues generated by morphogenesis activate mechanotransduction pathways, which in turn regulate cytoskeleton remodeling, cell proliferation, tissue differentiation. From Drosophila oocytes and embryos to Xenopus and mouse embryos and Arabidopsis meristem, here we review the developmental processes known to be activated in vivo by the mechanical strains associated to embryonic multicellular tissue morphogenesis. We describe the genetic, mechanical, and magnetic tools that have allowed the testing of mechanical induction in development by a step-by-step uncoupling of genetic inputs from mechanical inputs in embryogenesis. We discuss the known underlying molecular mechanisms involved in such mechanotransduction processes, including the Armadillo/β-catenin activation of Twist and the Fog-dependent stabilization of Myosin-II. These mechanotransduction processes are associated with a variety of physiological functions, such as mid-gut differentiation, mesoderm invagination and skeletal joint differentiation in embryogenesis, cell migration and internal pressure regulation during oogenesis, and meristem morphogenesis. We describe how the conservation of associated mechanosensitive pathways in embryonic and adult tissues opens new perspectives on mechanical involvement, potentially in evolution, and in cancer progression.

Osteopathy and (hatha) yoga

Differences and points of contact between osteopathy and yoga as regards their history and practical application are outlined. Both seek to promote healing. Yoga seeks the attainment of consciousness; osteopathy aims for providing support to health. One fundamental difference is the personal involvement of the individual in yoga. Teacher and student alike are challenged to re-examine the attitudes of mind they have adopted toward their lives. Osteopathy generally involves a relatively passive patient while the osteopath is active in providing treatment. Practical examples are used to highlight points of contact between yoga and osteopathy. The text includes a discussion of the importance of physicality and a description of ways of using it in healing processes. Furthermore, processes of attaining consciousness are outlined. Possible reductionist misconceptions in yoga and osteopathy are also pointed out. Fundamental attitudes and focus that complement each other are presented, taking the concept of stillness as a particular example.

Mechanical induction in embryonic development and tumor growth integrative cues through molecular to multicellular interplay and evolutionary perspectives

Embryonic development is a coordination of multicellular biochemical patterning and morphogenetic movements. Last decades revealed the close control of myosin-II-dependent biomechanical morphogenesis by patterning gene expression, with constant progress in the understanding of the underlying molecular mechanisms. Reversed control of developmental gene expression and of myosin-II patterning by the mechanical strains developed by morphogenetic movements was recently revealed at Drosophila gastrulation, through mechanotransduction processes involving the Armadillo/beta-catenin and the downstream of Fog Rho pathways. Here, we present the theoretical (simulations integrating the accumulated knowledge in the genetics of early embryonic development and morphogenesis) and the experimental (genetic and biophysical control of morphogenetic movements) tools having allowed the uncoupling of pure genetic inputs from pure mechanical inputs in the regulation of gene expression and myosin-II patterning. Specifically, we describe the innovative magnetic tweezers tools we have set up to measure and apply physiological strains and forces in vivo, from the inside of the tissue, to modulate and mimic morphogenetic movements in living embryos. We discuss mechanical induction incidence in tumor development and perspective in evolution.

Multiscale modeling of form and function

Topobiology posits that morphogenesis is driven by differential adhesive interactions among heterogeneous cell populations. This paradigm has been revised to include force-dependent molecular switches, cell and tissue tension, and reciprocal interactions with the microenvironment. It is now appreciated that tissue development is executed through conserved decision-making modules that operate on multiple length scales from the molecular and subcellular level through to the cell and tissue level and that these regulatory mechanisms specify cell and tissue fate by modifying the context of cellular signaling and gene expression. Here, we discuss the origin of these decision-making modules and illustrate how emergent properties of adhesion-directed multicellular structures sculpt the tissue, promote its functionality, and maintain its homeostasis through spatial segregation and organization of anchored proteins and secreted factors and through emergent properties of tissues, including tension fields and energy optimization.

Mechanogenetic coupling of Hydra symmetry breaking and driven Turing instability model

The freshwater polyp Hydra can regenerate from tissue fragments or random cell aggregates. We show that the axis-defining step ("symmetry breaking") of regeneration requires mechanical inflation-collapse oscillations of the initial cell ball. We present experimental evidence that axis definition is retarded if these oscillations are slowed down mechanically. When biochemical signaling related to axis formation is perturbed, the oscillation phase is extended and axis formation is retarded as well. We suggest that mechanical oscillations play a triggering role in axis definition. We extend earlier reaction-diffusion models for Hydra regrowth by coupling morphogen transport to mechanical stress caused by the oscillations. The modified reaction-diffusion model reproduces well two important experimental observations: 1), the existence of an optimum size for regeneration, and 2), the dependence of the symmetry breaking time on the properties of the mechanical oscillations.

Emergence of patterned stem cell differentiation within multicellular structures

The ability of stem cells to differentiate into specified lineages in the appropriate locations is vital to morphogenesis and adult tissue regeneration. Although soluble signals are important regulators of patterned differentiation, here we show that gradients of mechanical forces can also drive patterning of lineages. In the presence of soluble factors permitting osteogenic and adipogenic differentiation, human mesenchymal stem cells at the edge of multicellular islands differentiate into the osteogenic lineage, whereas those in the center became adipocytes. Interestingly, changing the shape of the multicellular sheet modulated the locations of osteogenic versus adipogenic differentiation. Measuring traction forces revealed gradients of stress that preceded and mirrored the patterns of differentiation, where regions of high stress resulted in osteogenesis, whereas stem cells in regions of low stress differentiated to adipocytes. Inhibiting cytoskeletal tension suppressed the relative degree of osteogenesis versus adipogenesis, and this spatial patterning of differentiation was also present in three-dimensional multicellular clusters. These findings demonstrate a role for mechanical forces in linking multicellular organization to spatial differentials of cell differentiation, and they represent an important guiding principle in tissue patterning that could be exploited in stem cell-based therapies. Disclosure of potential conflicts of interest is found at the end of this article.

Phyllotaxis as an example of the symbiosis of mechanical forces and biochemical processes in living tissue

Phyllotaxis, the arrangement of a plant's phylla (flowers, bracts, stickers) near its shoot apical meristem (SAM), has intrigued natural scientists for centuries. Even today, the reasons for the observed patterns and their special properties, the physical and chemical mechanisms which give rise to strikingly similar configurations in a wide variety of plants, the almost-constant golden divergence angle, the almost constant plastichrone ratio, the choices of parastichy numbers and the prevalence of Fibonacci sequences to which these numbers belong, are at best only partially understood. Our goals in this Addendum are: To give a brief overview of current thinking on possible mechanisms for primordia (the bumps on the plant surface which eventually mature into fully developed structures such as leaves or florets) formation and give a descriptive narrative of the mathematical models which encode various hypotheses.To emphasize the point that patterns, whether they be phyllotactic configurations on plant surfaces or convection cells on the sun's surface, are macroscopic objects whose behaviors are determined more by symmetries of the proposed model and less by microscopic details. Because of this, the identification of observations with the predications of a particular model can only be made with confidence when the match coincides over a range of circumstances and parameters.To discuss some of the key results of the proposed models and, in particular, introduce the prediction of a new and, in principle, measurable invariant in plant phyllotaxis.To introduce a new model of primordia formation which is more in keeping with the pictures and paradigms of Hofmeister,1 Snow & Snow,2 and Douady and Couder3,4 which see primordia as forming in a fairly narrow annular zone surrounding the plant's SAM separating a region of undifferentiated cells from a fully developed patterned state.To consider the challenge of phyllotaxis in the broader context of pattern formation in biological tissue which responds to both mechanical and biochemical processes.