From genes to neural tube defects (NTDs): insights from multiscale computational modeling

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.

Hinge point emergence in mammalian spinal neurulation

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

From heterogeneous morphogenetic fields to homogeneous regions as a step towards understanding complex tissue dynamics

Within developing tissues, cell proliferation, cell motility and other cell behaviors vary spatially, and this variability gives a complexity to the morphogenesis. Recently, novel formalisms have been developed to quantify tissue deformation and underlying cellular processes. A major challenge for the study of morphogenesis now is to objectively define tissue sub-regions exhibiting different dynamics. Here, we propose a method to automatically divide a tissue into regions where the local deformation rate is homogeneous. This was achieved by several steps including image segmentation, clustering and region boundary smoothing. We illustrate the use of the pipeline using a large dataset obtained during the metamorphosis of the Drosophila pupal notum. We also adapt it to determine regions in which the time evolution of the local deformation rate is homogeneous. Finally, we generalize its use to find homogeneous regions for cellular processes such as cell division, cell rearrangement, or cell size and shape changes. We also illustrate it on wing blade morphogenesis. This pipeline will contribute substantially to the analysis of complex tissue shaping, and the biochemical and biomechanical regulations driving tissue morphogenesis.

French flag gradients and Turing reaction-diffusion versus differentiation waves as models of morphogenesis

The Turing reaction-diffusion model and the French Flag Model are widely accepted in the field of development as the best models for explaining embryogenesis. Virtually all current attempts to understand cell differentiation in embryos begin and end with the assumption that some combination of these two models works. The result may become a bias in embryogenesis in assuming the problem has been solved by these two-chemical substance-based models. Neither model is applied consistently. We review the differences between the French Flag, Turing reaction-diffusion model, and a mechanochemical model called the differentiation wave/cell state splitter model. The cytoskeletal cell state splitter and the embryonic differentiation waves was first proposed in 1987 as a combined physics and chemistry model for cell differentiation in embryos, based on empirical observations on urodele amphibian embryos. We hope that the development of theory can be advanced and observations relevant to distinguishing the embryonic differentiation wave model from the French Flag model and reaction-diffusion equations will be taken up by experimentalists. Experimentalists rely on mathematical biologists for theory, and therefore depend on them for what parameters they choose to measure and ignore. Therefore, mathematical biologists need to fully understand the distinctions between these three models.

Towards organogenesis and morphogenesis in vitro: harnessing engineered microenvironment and autonomous behaviors of pluripotent stem cells

Recently, researchers have been attempting to control pluripotent stem cell fate or generate self-organized tissues from stem cells. Advances in bioengineering enable generation of organotypic structures, which capture the cellular components, spatial cell organization and even some functions of tissues or organs in development. However, only a few engineering tools have been utilized to regulate the formation and organization of spatially complex tissues derived from stem cells. Here, we provide a review of recent progress in the culture of organotypic structures in vitro, focusing on how microengineering approaches including geometric confinement, extracellular matrix (ECM) property modulation, spatially controlled biochemical factors, and external forces, can be utilized to generate organotypic structures. Moreover, we will discuss potential technologies that can be applied to further control both soluble and insoluble factors spatiotemporally in vitro. In summary, advanced engineered approaches have a great promise in generating miniaturized tissues and organs in a reproducible fashion, facilitating the cellular and molecular understanding of embryogenesis and morphogenesis processes.

Inferring cellular forces from image stacks

Although the importance of cellular forces to a wide range of embryogenesis and disease processes is widely recognized, measuring these forces is challenging, especially in three dimensions. Here, we introduce CellFIT-3D, a force inference technique that allows tension maps for three-dimensional cellular systems to be estimated from image stacks. Like its predecessors, video force microscopy and CellFIT, this cell mechanics technique assumes boundary-specific interfacial tensions to be the primary drivers, and it constructs force-balance equations based on triple junction (TJ) dihedral angles. The technique involves image processing, segmenting of cells, grouping of cell outlines, calculation of dihedral planes, averaging along three-dimensional TJs, and matrix equation assembly and solution. The equations tend to be strongly overdetermined, allowing indistinct TJs to be ignored and solution error estimates to be determined. Application to clean and noisy synthetic data generated using Surface Evolver gave tension errors of 1.6-7%, and analyses of eight-cell murine embryos gave estimated errors smaller than the 10% uncertainty of companion aspiration experiments. Other possible areas of application include morphogenesis, cancer metastasis and tissue engineering.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

Mechanocellular models of epithelial morphogenesis

Embryonic epithelia achieve complex morphogenetic movements, including in-plane reshaping, bending and folding, through the coordinated action and rearrangement of individual cells. Technical advances in molecular and live-imaging studies of epithelial dynamics provide a very real opportunity to understand how cell-level processes facilitate these large-scale tissue rearrangements. However, the large datasets that we are now able to generate require careful interpretation. In combination with experimental approaches, computational modelling allows us to challenge and refine our current understanding of epithelial morphogenesis and to explore experimentally intractable questions. To this end, a variety of cell-based modelling approaches have been developed to describe cell-cell mechanical interactions, ranging from vertex and 'finite-element' models that approximate each cell geometrically by a polygon representing the cell's membrane, to immersed boundary and subcellular element models that allow for more arbitrary cell shapes. Here, we review how these models have been used to provide insights into epithelial morphogenesis and describe how such models could help future efforts to decipher the forces and mechanical and biochemical feedbacks that guide cell and tissue-level behaviour. In addition, we discuss current challenges associated with using computational models of morphogenetic processes in a quantitative and predictive way.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

Neural tube closure: cellular, molecular and biomechanical mechanisms

Neural tube closure has been studied for many decades, across a range of vertebrates, as a paradigm of embryonic morphogenesis. Neurulation is of particular interest in view of the severe congenital malformations - 'neural tube defects' - that result when closure fails. The process of neural tube closure is complex and involves cellular events such as convergent extension, apical constriction and interkinetic nuclear migration, as well as precise molecular control via the non-canonical Wnt/planar cell polarity pathway, Shh/BMP signalling, and the transcription factors Grhl2/3, Pax3, Cdx2 and Zic2. More recently, biomechanical inputs into neural tube morphogenesis have also been identified. Here, we review these cellular, molecular and biomechanical mechanisms involved in neural tube closure, based on studies of various vertebrate species, focusing on the most recent advances in the field.

Biomechanical coupling facilitates spinal neural tube closure in mouse embryos

Neural tube (NT) formation in the spinal region of the mammalian embryo involves a wave of "zippering" that passes down the elongating spinal axis, uniting the neural fold tips in the dorsal midline. Failure of this closure process leads to open spina bifida, a common cause of severe neurologic disability in humans. Here, we combined a tissue-level strain-mapping workflow with laser ablation of live-imaged mouse embryos to investigate the biomechanics of mammalian spinal closure. Ablation of the zippering point at the embryonic dorsal midline causes far-reaching, rapid separation of the elevating neural folds. Strain analysis revealed tissue expansion around the zippering point after ablation, but predominant tissue constriction in the caudal and ventral neural plate zone. This zone is biomechanically coupled to the zippering point by a supracellular F-actin network, which includes an actin cable running along the neural fold tips. Pharmacologic inhibition of F-actin or laser ablation of the cable causes neural fold separation. At the most advanced somite stages, when completion of spinal closure is imminent, the cable forms a continuous ring around the neuropore, and simultaneously, a new caudal-to-rostral zippering point arises. Laser ablation of this new closure initiation point causes neural fold separation, demonstrating its biomechanical activity. Failure of spinal closure in pre-spina bifida Zic2Ku mutant embryos is associated with altered tissue biomechanics, as indicated by greater neuropore widening after ablation. Thus, this study identifies biomechanical coupling of the entire region of active spinal neurulation in the mouse embryo as a prerequisite for successful NT closure.

Wide and high resolution tension measurement using FRET in embryo

During embryonic development, physical force plays an important role in morphogenesis and differentiation. Stretch sensitive fluorescence resonance energy transfer (FRET) has the potential to provide non-invasive tension measurements inside living tissue. In this study, we introduced a FRET-based actinin tension sensor into Xenopus laevis embryos and demonstrated that this sensor captures variation of tension across differentiating ectoderm. The actinin tension sensor, containing mCherry and EGFP connected by spider silk protein, was validated in human embryonic kidney (HEK) cells and embryos. It co-localized with actin filaments and changed FRET efficiencies in response to actin filament destruction, myosin deactivation, and osmotic perturbation. Time-lapse FRET analysis showed that the prospective neural ectoderm bears higher tension than the epidermal ectoderm during gastrulation and neurulation, and cells morphogenetic behavior correlated with the tension difference. These data confirmed that the sensor enables us to measure tension across tissues concurrently and with high resolution.

Non-straight cell edges are important to invasion and engulfment as demonstrated by cell mechanics model

Computational models of cell–cell mechanical interactions typically simulate sorting and certain other motions well, but as demands on these models continue to grow, discrepancies between the cell shapes, contact angles and behaviours they predict and those that occur in real cells have come under increased scrutiny. To investigate whether these discrepancies are a direct result of the straight cell–cell edges generally assumed in these models, we developed a finite element model that approximates cell boundaries using polylines with an arbitrary number of segments. We then compared the predictions of otherwise identical polyline and monoline (straight-edge) models in a variety of scenarios, including annealing, single- and multi-cell engulfment, sorting, and two forms of mixing—invasion and checkerboard pattern formation. Keeping cell–cell edges straight influences cell motion, cell shape, contact angle, and boundary length, especially in cases where one cell type is pulled between or around cells of a different type, as in engulfment or invasion. These differences arise because monoline cells have restricted deformation modes. Polyline cells do not face these restrictions, and with as few as three segments per edge yielded realistic edge shapes and contact angle errors one-tenth of those produced by monoline models, making them considerably more suitable for situations where angles and shapes matter, such as validation of cellular force–inference techniques. The findings suggest that non-straight cell edges are important both in modelling and in nature.

Colloquium: Mechanical formalisms for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progress in experimental techniques that provide access to cell scale, quantitative information both on the shapes of cells within tissues and on the genes being expressed. This information suggests that our understanding of the respective contributions of gene expression and mechanics, and of their crucial entanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assist the design and interpretation of experiments, point out the main ingredients and assumptions, and ultimately lead to predictions. The newly accessible local information thus calls for a reflection on how to select suitable classes of mechanical models. We review both mechanical ingredients suggested by the current knowledge of tissue behaviour, and modelling methods that can help generate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell") and tissue scale ("inter-cell") contributions. We recall the mathematical framework developed for continuum materials and explain how to transform a constitutive equation into a set of partial differential equations amenable to numerical resolution. We show that when plastic behaviour is relevant, the dissipation function formalism appears appropriate to generate constitutive equations; its variational nature facilitates numerical implementation, and we discuss adaptations needed in the case of large deformations. The present article gathers theoretical methods that can readily enhance the significance of the data to be extracted from recent or future high throughput biomechanical experiments.

Practical aspects of the cellular force inference toolkit (CellFIT)

If we are to fully understand the reasons that cells and tissues move and acquire their distinctive geometries during processes such as embryogenesis and wound healing, we will need detailed maps of the forces involved. One of the best current prospects for obtaining this information is noninvasive force-from-images techniques such as CellFIT, the Cellular Force Inference Toolkit, whose various steps are discussed here. Like other current quasistatic approaches, this one assumes that cell shapes are produced by interactions between interfacial tensions and intracellular pressures. CellFIT, however, allows cells to have curvilinear boundaries, which can significantly improve inference accuracy and reduce noise sensitivity. The quality of a CellFIT analysis depends on how accurately the junction angles and edge curvatures are measured, and a software tool we describe facilitates determination and evaluation of this information. Special attention is required when edges are crenulated or significantly different in shape from a circular arc. Because the tension and pressure equations are overdetermined, a select number of edges can be removed from the analysis, and these might include edges that are poorly defined in the source image, too short to provide accurate angles or curvatures, or noncircular. The approach works well for aggregates with as many as 1000 cells, and introduced errors have significant effects on only a few adjacent cells. An understanding of these considerations will help CellFIT users to get the most out of this promising new technique.

CellFIT: a cellular force-inference toolkit using curvilinear cell boundaries

Mechanical forces play a key role in a wide range of biological processes, from embryogenesis to cancer metastasis, and there is considerable interest in the intuitive question, "Can cellular forces be inferred from cell shapes?" Although several groups have posited affirmative answers to this stimulating question, nagging issues remained regarding equation structure, solution uniqueness and noise sensitivity. Here we show that the mechanical and mathematical factors behind these issues can be resolved by using curved cell edges rather than straight ones. We present a new package of force-inference equations and assessment tools and denote this new package CellFIT, the Cellular Force Inference Toolkit. In this approach, cells in an image are segmented and equilibrium equations are constructed for each triple junction based solely on edge tensions and the limiting angles at which edges approach each junction. The resulting system of tension equations is generally overdetermined. As a result, solutions can be obtained even when a modest number of edges need to be removed from the analysis due to short length, poor definition, image clarity or other factors. Solving these equations yields a set of relative edge tensions whose scaling must be determined from data external to the image. In cases where intracellular pressures are also of interest, Laplace equations are constructed to relate the edge tensions, curvatures and cellular pressure differences. That system is also generally overdetermined and its solution yields a set of pressures whose offset requires reference to the surrounding medium, an open wound, or information external to the image. We show that condition numbers, residual analyses and standard errors can provide confidence information about the inferred forces and pressures. Application of CellFIT to several live and fixed biological tissues reveals considerable force variability within a cell population, significant differences between populations and elevated tensions along heterotypic boundaries.

Quantitative approaches to uncover physical mechanisms of tissue morphogenesis

Morphogenesis, the creation of tissue and organ architecture, is a series of complex and dynamic processes driven by genetic programs, microenvironmental cues, and intercellular interactions. Elucidating the physical mechanisms that generate tissue form is key to understanding development, disease, and the strategies needed for regenerative therapies. Advancements in imaging technologies, genetic recombination techniques, laser ablation, and microfabricated tissue models have enabled quantitative descriptions of the cellular motions and tissue deformations and stresses with unprecedented temporal and spatial resolution. Using these data synergistically with increasingly more sophisticated physical, mathematical, and computational models will unveil the physical mechanisms that drive morphogenesis.

Multiscale computational models of complex biological systems

Integration of data across spatial, temporal, and functional scales is a primary focus of biomedical engineering efforts. The advent of powerful computing platforms, coupled with quantitative data from high-throughput experimental methodologies, has allowed multiscale modeling to expand as a means to more comprehensively investigate biological phenomena in experimentally relevant ways. This review aims to highlight recently published multiscale models of biological systems, using their successes to propose the best practices for future model development. We demonstrate that coupling continuous and discrete systems best captures biological information across spatial scales by selecting modeling techniques that are suited to the task. Further, we suggest how to leverage these multiscale models to gain insight into biological systems using quantitative biomedical engineering methods to analyze data in nonintuitive ways. These topics are discussed with a focus on the future of the field, current challenges encountered, and opportunities yet to be realized.

Computational models for mechanics of morphogenesis

In the developing embryo, tissues differentiate, deform, and move in an orchestrated manner to generate various biological shapes driven by the complex interplay between genetic, epigenetic, and environmental factors. Mechanics plays a key role in regulating and controlling morphogenesis, and quantitative models help us understand how various mechanical forces combine to shape the embryo. Models allow for the quantitative, unbiased testing of physical mechanisms, and when used appropriately, can motivate new experimentaldirections. This knowledge benefits biomedical researchers who aim to prevent and treat congenital malformations, as well as engineers working to create replacement tissues in the laboratory. In this review, we first give an overview of fundamental mechanical theories for morphogenesis, and then focus on models for specific processes, including pattern formation, gastrulation, neurulation, organogenesis, and wound healing. The role of mechanical feedback in development is also discussed. Finally, some perspectives aregiven on the emerging challenges in morphomechanics and mechanobiology.

The mechanics of metastasis: insights from a computational model

Although it may seem obvious that mechanical forces are required to drive metastatic cell movements, understanding of the mechanical aspects of metastasis has lagged far behind genetic and biochemical knowledge. The goal of this study is to learn about the mechanics of metastasis using a cell-based finite element model that proved useful for advancing knowledge about the forces that drive embryonic cell and tissue movements. Metastasis, the predominant cause of cancer-related deaths, involves a series of mechanical events in which one or more cells dissociate from a primary tumour, migrate through normal tissue, traverse in and out of a multi-layer circulatory system vessel and resettle. The present work focuses on the dissemination steps, from dissociation to circulation. The model shows that certain surface tension relationships must be satisfied for cancerous cells to dissociate from a primary tumour and that these equations are analogous to those that govern dissociation of embryonic cells. For a dissociated cell to then migrate by invadopodium extension and contraction and exhibit the shapes seen in experiments, the invadopodium must generate a contraction equal to approximately twice that produced by the interfacial tension associated with surrounding cells. Intravasation through the wall of a vessel is governed by relationships akin to those in the previous two steps, while release from the vessel wall is governed by equations that involve surface and interfacial tensions. The model raises a number of potential research questions. It also identifies how specific mechanical properties and the sub-cellular structural components that give rise to them might be changed so as to thwart particular metastatic steps and thereby block the spread of cancer.