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Roffay C, Chan CJ, Guirao B, Hiiragi T, Graner F. Inferring cell junction tension and pressure from cell geometry. Development 2021; 148:148/18/dev192773. [PMID: 33712442 DOI: 10.1242/dev.192773] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Recognizing the crucial role of mechanical regulation and forces in tissue development and homeostasis has stirred a demand for in situ measurement of forces and stresses. Among emerging techniques, the use of cell geometry to infer cell junction tensions, cell pressures and tissue stress has gained popularity owing to the development of computational analyses. This approach is non-destructive and fast, and statistically validated based on comparisons with other techniques. However, its qualitative and quantitative limitations, in theory as well as in practice, should be examined with care. In this Primer, we summarize the underlying principles and assumptions behind stress inference, discuss its validity criteria and provide guidance to help beginners make the appropriate choice of its variants. We extend our discussion from two-dimensional stress inference to three dimensional, using the early mouse embryo as an example, and list a few possible extensions. We hope to make stress inference more accessible to the scientific community and trigger a broader interest in using this technique to study mechanics in development.
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Affiliation(s)
- Chloé Roffay
- Matière et Systèmes Complexes, Université de Paris - Diderot, CNRS UMR7057, 10 rue Alice Domon et Léonie Duquet, F-75205 Paris Cedex 13, France.,Polarity, Division and Morphogenesis Team, Genetics and Developmental Biology Unit, (CNRS UMR3215/Inserm U934), Institut Curie, F-75248 Paris Cedex 05, France
| | - Chii J Chan
- European Molecular Biology Laboratory, 69117 Heidelberg, Germany
| | - Boris Guirao
- Polarity, Division and Morphogenesis Team, Genetics and Developmental Biology Unit, (CNRS UMR3215/Inserm U934), Institut Curie, F-75248 Paris Cedex 05, France
| | - Takashi Hiiragi
- European Molecular Biology Laboratory, 69117 Heidelberg, Germany.,Institute for the Advanced Study of Human Biology (WPI-ASHBi), Kyoto University, Kyoto 606-8501, Japan
| | - François Graner
- Matière et Systèmes Complexes, Université de Paris - Diderot, CNRS UMR7057, 10 rue Alice Domon et Léonie Duquet, F-75205 Paris Cedex 13, France
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Crawford-Young SJ, Dittapongpitch S, Gordon R, Harrington KI. Acquisition and reconstruction of 4D surfaces of axolotl embryos with the flipping stage robotic microscope. Biosystems 2018; 173:214-220. [DOI: 10.1016/j.biosystems.2018.10.006] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2018] [Revised: 10/02/2018] [Accepted: 10/04/2018] [Indexed: 10/28/2022]
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Merkel M, Manning ML. Using cell deformation and motion to predict forces and collective behavior in morphogenesis. Semin Cell Dev Biol 2017; 67:161-169. [PMID: 27496334 PMCID: PMC5290285 DOI: 10.1016/j.semcdb.2016.07.029] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2016] [Revised: 07/05/2016] [Accepted: 07/27/2016] [Indexed: 12/20/2022]
Abstract
In multi-cellular organisms, morphogenesis translates processes at the cellular scale into tissue deformation at the scale of organs and organisms. To understand how biochemical signaling regulates tissue form and function, we must understand the mechanical forces that shape cells and tissues. Recent progress in developing mechanical models for tissues has led to quantitative predictions for how cell shape changes and polarized cell motility generate forces and collective behavior on the tissue scale. In particular, much insight has been gained by thinking about biological tissues as physical materials composed of cells. Here we review these advances and discuss how they might help shape future experiments in developmental biology.
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Affiliation(s)
- Matthias Merkel
- Department of Physics, Syracuse University, Syracuse, NY 13244, United States
| | - M Lisa Manning
- Department of Physics, Syracuse University, Syracuse, NY 13244, United States.
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4
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Gordon NK, Gordon R. The organelle of differentiation in embryos: the cell state splitter. Theor Biol Med Model 2016; 13:11. [PMID: 26965444 PMCID: PMC4785624 DOI: 10.1186/s12976-016-0037-2] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2015] [Accepted: 02/27/2016] [Indexed: 12/16/2022] Open
Abstract
The cell state splitter is a membraneless organelle at the apical end of each epithelial cell in a developing embryo. It consists of a microfilament ring and an intermediate filament ring subtending a microtubule mat. The microtubules and microfilament ring are in mechanical opposition as in a tensegrity structure. The cell state splitter is bistable, perturbations causing it to contract or expand radially. The intermediate filament ring provides metastability against small perturbations. Once this snap-through organelle is triggered, it initiates signal transduction to the nucleus, which changes gene expression in one of two readied manners, causing its cell to undergo a step of determination and subsequent differentiation. The cell state splitter also triggers the cell state splitters of adjacent cells to respond, resulting in a differentiation wave. Embryogenesis may be represented then as a bifurcating differentiation tree, each edge representing one cell type. In combination with the differentiation waves they propagate, cell state splitters explain the spatiotemporal course of differentiation in the developing embryo. This review is excerpted from and elaborates on "Embryogenesis Explained" (World Scientific Publishing, Singapore, 2016).
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Affiliation(s)
| | - Richard Gordon
- />Retired, University of Manitoba, Winnipeg, Canada
- />Embryogenesis Center, Gulf Specimen Aquarium & Marine Laboratory, 222 Clark Drive, Panacea, FL 32346 USA
- />C.S. Mott Center for Human Growth & Development, Department of Obstetrics & Gynecology, Wayne State University, 275 E. Hancock, Detroit, MI 48201 USA
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Hussan JR, Hunter PJ. Inferring intra-cellular mechanics using geometric metamorphosis: A preliminary study. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2016; 2015:901-4. [PMID: 26736408 DOI: 10.1109/embc.2015.7318508] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Mechanotransduction plays an important role in sub-cellular processes and is an active area of research. Determining the forces/strains that the intra-cellular structures experience is vital for developing quantitative models of cellular behavior. Established techniques such as traction force microscopy, digital image correlation etc. track surface forces and kinematics of intra-cellular structures. However, difficulties arise when cells cannot be seeded on micro-patterned substrates or the intra-cellular structures vary (unstable landmarks). Here, we applied geometric metamorphosis, a global image registration method, to determine the kinematic profile of a cell during cell division. The method does not require stable landmarks, the registration is non-local in nature and constraints such as volume conservation can be enforced. The cell wall was tracked over time and a sequence of transformations relating the cell wall at the start of cytokinesis to the configuration prior to the daughters completely separate was determined. These transformations are associated with a scalar metric and a statistical atlas describing the wall kinematics from multiple tracking's of the wall shape is constructed. Using these transformations, the cellular kinematics can be described using a Lagrangian frame of reference and the evolution of a material point property can be easily modeled. To demonstrate this, we use the kinematic data derived from the atlas along with a model of stress-fiber (de)formation dynamics to simulate the stress-fiber configuration as the cell domain deforms.
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Perrone MC, Veldhuis JH, Brodland GW. Non-straight cell edges are important to invasion and engulfment as demonstrated by cell mechanics model. Biomech Model Mechanobiol 2015; 15:405-18. [PMID: 26148533 PMCID: PMC4792343 DOI: 10.1007/s10237-015-0697-6] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2014] [Accepted: 06/23/2015] [Indexed: 11/28/2022]
Abstract
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.
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Affiliation(s)
- Matthew C Perrone
- Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
| | - Jim H Veldhuis
- Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
| | - G Wayne Brodland
- Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada.
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Abstract
Cell-generated forces produce a variety of tissue movements and tissue shape changes. The cytoskeletal elements that underlie these dynamics act at cell-cell and cell-ECM contacts to apply local forces on adhesive structures. In epithelia, force imbalance at cell contacts induces cell shape changes, such as apical constriction or polarized junction remodeling, driving tissue morphogenesis. The dynamics of these processes are well-characterized; however, the mechanical basis of cell shape changes is largely unknown because of a lack of mechanical measurements in vivo. We have developed an approach combining optical tweezers with light-sheet microscopy to probe the mechanical properties of epithelial cell junctions in the early Drosophila embryo. We show that optical trapping can efficiently deform cell-cell interfaces and measure tension at cell junctions, which is on the order of 100 pN. We show that tension at cell junctions equilibrates over a few seconds, a short timescale compared with the contractile events that drive morphogenetic movements. We also show that tension increases along cell interfaces during early tissue morphogenesis and becomes anisotropic as cells intercalate during germ-band extension. By performing pull-and-release experiments, we identify time-dependent properties of junctional mechanics consistent with a simple viscoelastic model. Integrating this constitutive law into a tissue-scale model, we predict quantitatively how local deformations propagate throughout the tissue.
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Brodland GW, Veldhuis JH, Kim S, Perrone M, Mashburn D, Hutson MS. CellFIT: a cellular force-inference toolkit using curvilinear cell boundaries. PLoS One 2014; 9:e99116. [PMID: 24921257 PMCID: PMC4055627 DOI: 10.1371/journal.pone.0099116] [Citation(s) in RCA: 71] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2014] [Accepted: 05/11/2014] [Indexed: 11/19/2022] Open
Abstract
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.
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Affiliation(s)
- G. Wayne Brodland
- Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario, Canada
- * E-mail:
| | - Jim H. Veldhuis
- Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario, Canada
| | - Steven Kim
- Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario, Canada
| | - Matthew Perrone
- Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario, Canada
| | - David Mashburn
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee, United States of America
| | - M. Shane Hutson
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee, United States of America
- Department of Biological Sciences, Vanderbilt University, Nashville, Tennessee, United States of America
- Vanderbilt Institute for Integrative Biosystem Research & Education, Vanderbilt University, Nashville, Tennessee, United States of America
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Lu K, Gordon R, Cao T. Reverse engineering the mechanical and molecular pathways in stem cell morphogenesis. J Tissue Eng Regen Med 2013; 9:169-73. [DOI: 10.1002/term.1672] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2011] [Revised: 10/05/2012] [Accepted: 11/05/2012] [Indexed: 01/28/2023]
Affiliation(s)
- Kai Lu
- Institute for Integrated Cell-Material Sciences; Kyoto University; Japan
| | - Richard Gordon
- Embryogenesis Center; Gulf Specimen Marine Laboratory; Panacea FL 32346 USA
| | - Tong Cao
- Stem Cell Laboratory, Faculty of Dentistry; National University of Singapore
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A biomechanical analysis of ventral furrow formation in the Drosophila melanogaster embryo. PLoS One 2012; 7:e34473. [PMID: 22511944 PMCID: PMC3325263 DOI: 10.1371/journal.pone.0034473] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2011] [Accepted: 03/02/2012] [Indexed: 11/19/2022] Open
Abstract
The article provides a biomechanical analysis of ventral furrow formation in the Drosophila melanogaster embryo. Ventral furrow formation is the first large-scale morphogenetic movement in the fly embryo. It involves deformation of a uniform cellular monolayer formed following cellularisation, and has therefore long been used as a simple system in which to explore the role of mechanics in force generation. Here we use a quantitative framework to carry out a systematic perturbation analysis to determine the role of each of the active forces observed. The analysis confirms that ventral furrow invagination arises from a combination of apical constriction and apical–basal shortening forces in the mesoderm, together with a combination of ectodermal forces. We show that the mesodermal forces are crucial for invagination: the loss of apical constriction leads to a loss of the furrow, while the mesodermal radial shortening forces are the primary cause of the internalisation of the future mesoderm as the furrow rises. Ectodermal forces play a minor but significant role in furrow formation: without ectodermal forces the furrow is slower to form, does not close properly and has an aberrant morphology. Nevertheless, despite changes in the active mesodermal and ectodermal forces lead to changes in the timing and extent of furrow, invagination is eventually achieved in most cases, implying that the system is robust to perturbation and therefore over-determined.
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Abstract
Intercellular surface tension is a key variable in understanding cellular mechanics. However, conventional methods are not well suited for measuring the absolute magnitude of intercellular surface tension because these methods require determination of the effective viscosity of the whole cell, a quantity that is difficult to measure. In this study, we present a novel method for estimating the intercellular surface tension at single-cell resolution. This method exploits the cytoplasmic flow that accompanies laser-induced cell fusion when the pressure difference between cells is large. Because the cytoplasmic viscosity can be measured using well-established technology, this method can be used to estimate the absolute magnitudes of tension. We applied this method to two-cell-stage embryos of the nematode Caenorhabditis elegans and estimated the intercellular surface tension to be in the 30-90 µN m(-1) range. Our estimate was in close agreement with cell-medium surface tensions measured at single-cell resolution.
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Affiliation(s)
- Masashi Fujita
- Laboratory for Developmental Dynamics, RIKEN Quantitative Biology Center, 2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
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Micromechanical regulation in cardiac myocytes and fibroblasts: implications for tissue remodeling. Pflugers Arch 2011; 462:105-17. [PMID: 21308471 DOI: 10.1007/s00424-011-0931-8] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2010] [Revised: 01/25/2011] [Accepted: 01/25/2011] [Indexed: 10/18/2022]
Abstract
Cells of the myocardium are at home in one of the most mechanically dynamic environments in the body. At the cellular level, pulsatile stimuli of chamber filling and emptying are experienced as cyclic strains (relative deformation) and stresses (force per unit area). The intrinsic characteristics of tension-generating myocytes and fibroblasts thus have a continuous mechanical interplay with their extrinsic surroundings. This review explores the ways that the micromechanics at the scale of single cardiac myocytes and fibroblasts have been measured, modeled, and recapitulated in vitro in the context of adaptation. Both types of cardiac cells respond to externally applied strain, and many of the intracellular mechanosensing pathways have been identified with the careful manipulation of experimental variables. In addition to strain, the extent of loading in myocytes and fibroblasts is also regulated by cues from the microenvironment such as substrate surface chemistry, stiffness, and topography. Combinations of these structural cues in three dimensions are needed to mimic the micromechanical complexity derived from the extracellular matrix of the developing, healthy, or pathophysiologic heart. An understanding of cardiac cell micromechanics can therefore inform the design and composition of tissue engineering scaffolds or stem cell niches for future applications in regenerative medicine.
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Video force microscopy reveals the mechanics of ventral furrow invagination in Drosophila. Proc Natl Acad Sci U S A 2010; 107:22111-6. [PMID: 21127270 DOI: 10.1073/pnas.1006591107] [Citation(s) in RCA: 121] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The absence of tools for mapping the forces that drive morphogenetic movements in embryos has impeded our understanding of animal development. Here we describe a unique approach, video force microscopy (VFM), that allows detailed, dynamic force maps to be produced from time-lapse images. The forces at work in an embryo are considered to be decomposed into active and passive elements, where active forces originate from contributions (e.g., actomyosin contraction) that do mechanical work to the system and passive ones (e.g., viscous cytoplasm) that dissipate energy. In the present analysis, the effects of all passive components are considered to be subsumed by an effective cytoplasmic viscosity, and the driving forces are resolved into equivalent forces along the edges of the polygonal boundaries into which the region of interest is divided. Advanced mathematical inverse methods are used to determine these driving forces. When applied to multiphoton sections of wild-type and mutant Drosophila melanogaster embryos, VFM is able to calculate the equivalent driving forces acting along individual cell edges and to do so with subminute temporal resolution. In the wild type, forces along the apical surface of the presumptive mesoderm are found to be large and to vary parabolically with time and angular position, whereas forces along the basal surface of the ectoderm, for example, are found to be smaller and nearly uniform with position. VFM shows that in mutants with reduced junction integrity and myosin II activity, the driving forces are reduced, thus accounting for ventral furrow failure.
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