ABSTRACT
Living organisms have the ability to self-shape into complex structures appropriate for their function. The genetic and molecular mechanisms that enable cells to do this have been extensively studied in several model and non-model organisms. In contrast, the physical mechanisms that shape cells and tissues have only recently started to emerge, in part thanks to new quantitative in vivo measurements of the physical quantities guiding morphogenesis. These data, combined with indirect inferences of physical characteristics, are starting to reveal similarities in the physical mechanisms underlying morphogenesis across different organisms. Here, we review how physics contributes to shape cells and tissues in a simple, yet ubiquitous, morphogenetic transformation: elongation. Drawing from observed similarities across species, we propose the existence of conserved physical mechanisms of morphogenesis.
Introduction
Throughout the tree of life, organisms exhibit a remarkable diversity of structures with complex morphologies directly linked to their function (Carroll, 2001; Shubin et al., 2009). Single-celled organisms, such as bacteria, come in cell shapes and sizes tailored to specific physiological or environmental conditions (Young, 2003; 2006; Shi et al., 2018). In multicellular organisms, large numbers of cells work together to shape functional structures, including tissues and organs, into complex 3D morphologies. Trichomes (Levin, 1973), roots (Hodge et al., 2009), meristems (Mathur, 2004; Ha et al., 2010; Trinh et al., 2021) or epidermal cells (Bidhendi et al., 2023) in plants, as well as bird beaks (Shoval et al., 2012; Navalón et al., 2019), vertebrate limbs (Wagner, 2007), mammalian teeth (Jernvall and Thesleff, 2012; Calamari et al., 2018), craniofacial structures (Young et al., 2017) or branching organs (Metzger et al., 2008; Costantini and Kopan, 2010; Shih et al., 2012; Palmer et al., 2021) in animals, all have morphologies and material characteristics that enable the organism to perform specific vital functions. Although the diversity of morphologies across species is vast (Carroll, 2001; Piersma and Drent, 2003), the variation of shape of a particular structure within a given species is typically very constrained and its formation is under tight genetic control, highlighting the functional relevance of these structures (Young, 2006). How are all these functional structures physically sculpted in a robust manner?
Despite the impressive complexity and diversity of shapes across organisms (Young et al., 2017; Metzger et al., 2008; Costantini and Kopan, 2010; Shih et al., 2012; Palmer et al., 2021; Mathur, 2004; Ha et al., 2010; Trinh et al., 2021), in many cases these structures are formed by a combination of simpler morphogenetic events. One of the most widely observed morphogenetic transformations, and perhaps also the simplest, is elongation. In this process, a cell, a tissue, or a material in general, extends preferentially in one spatial direction. Although simple, this morphogenetic process is observed across scales and throughout the entire tree of life, playing a key role in shaping both single-celled and multicellular organisms (Fig. 1). In some cases, the elongation process has been studied from a physical or mechanical perspective in addition to a molecular one, providing new insights into how elongating structures are built (Fig. 1 and Table S1).
Cell and tissue elongation across species. Examples of cell and tissue elongation where material properties (orange), growth (green) and/or active stresses (magenta) have been either directly measured or indirectly inferred. Organisms are organized according to their position on the phylogenetic tree. Black arrows indicate the direction of cell or tissue elongation. Filled circles indicate that the physical quantity has been quantitatively measured and is relevant for elongation. Empty circles indicate that the physical quantity has not been directly measured, but has been either indirectly estimated or inferred and is involved in elongation. Question marks indicate that that physical quantity has been neither measured nor inferred. Crosses indicate that the physical quantity has been either measured or inferred and does not contribute to elongation. The specific physical quantities measured or inferred in each organism, as well as information about the stages and techniques used, can be found in Table S1.
Cell and tissue elongation across species. Examples of cell and tissue elongation where material properties (orange), growth (green) and/or active stresses (magenta) have been either directly measured or indirectly inferred. Organisms are organized according to their position on the phylogenetic tree. Black arrows indicate the direction of cell or tissue elongation. Filled circles indicate that the physical quantity has been quantitatively measured and is relevant for elongation. Empty circles indicate that the physical quantity has not been directly measured, but has been either indirectly estimated or inferred and is involved in elongation. Question marks indicate that that physical quantity has been neither measured nor inferred. Crosses indicate that the physical quantity has been either measured or inferred and does not contribute to elongation. The specific physical quantities measured or inferred in each organism, as well as information about the stages and techniques used, can be found in Table S1.
At the single-cell level, many bacteria, including Escherichia coli, are shaped as rods that elongate longitudinally. Rod-like (or cylindrical) cells are common across organisms with cell walls because this geometry keeps the surface-to-volume ratio constant during growth (Harold, 2007; Chang and Huang, 2014), facilitating proper metabolism. Indeed, walled cells of many organisms grow as tubes that elongate only at their tips, a widespread process known as tip-growth (Hepler et al., 2001; Harold, 2002; Baskin, 2005; Cole and Fowler, 2006) that is used by plant cells [pollen tubes (Krichevsky et al., 2007; Geitmann, 2010) and root hairs (Carol and Dolan, 2002)], fungal species [filamentous hyphal growth (Harold, 1997; Heath and Geitmann, 2000; Lew, 2011), fission yeast (Chang and Martin, 2009; Davì and Minc, 2015) and mating projections in budding yeast (Cabib and Arroyo, 2013; Banavar et al., 2018)], water molds (Campàs et al., 2012), bacteria (Brown et al., 2011), and more (Fig. 1). At the multicellular level, plant roots elongate unidirectionally (Fig. 1) thanks to the coordinated anisotropic elongation of cells and regional softening of cell walls (Bibikova et al., 1999; Milani et al., 2011; Petricka et al., 2012; Barrada et al., 2015; Liu et al., 2022). In animal species, tissue elongation also plays an important role in shaping many tissues and organs. Body axis elongation is a hallmark example that has been studied in many organisms from a physical viewpoint (Fig. 1), including sea anemones (Nematostella) (Stokkermans et al., 2022), worms (Caenorhabditis elegans) (Vuong-Brender et al., 2017; Lardennois et al., 2019), insects (Drosophila) (Bertet et al., 2004; Kasza et al., 2014) and multiple vertebrates [fish (Mongera et al., 2018), frogs (Adams et al., 1990) and chick (Bénazéraf et al., 2010). Several tissues also elongate to acquire their shapes (Fig. 1), with notable examples including bird beaks (Wu et al., 2006), vertebrate limb buds (Zeller et al., 2009; Wyngaarden et al., 2010), worm gonads (Agarwal et al., 2022), egg chambers in insects (He et al., 2010; Haigo and Bilder, 2011; Horne-Badovinac, 2014) and the notochord in sea squirts (Dong et al., 2009) and fish (Glickman et al., 2003). Hence, cell/tissue elongation is an essential morphogenetic process that has been studied across a range of species from both physical and molecular perspectives, allowing a comparative study of physical mechanics of morphogenesis.
As for any inherited trait, the shape of many biological structures is genetically encoded, at least partially (Shubin et al., 2009). However, the genetic and molecular processes controlling the formation of specific structures, even homologous structures, can strongly differ across species. Bird beaks in closely related species, such as in Caribbean bullfinches, may be morphologically akin, but their shapes are controlled by distinct developmental programs involving different signaling molecules (Wu et al., 2006; Campàs et al., 2010; Mallarino et al., 2012). Similarly, the shapes of individual walled cells may be very similar despite differences in the molecular mechanisms underpinning cellular morphogenesis (Harold, 2005; Campàs et al., 2012). Convergent evolution can also lead to strong morphological similarities through distinct molecular and genetic mechanisms, as for anoles lizards (Corbett-Detig et al., 2020). Such observations show that similar structures can be built using widely different genetic or molecular mechanisms across species, highlighting a substantial flexibility in the encoding of morphogenesis.
Beyond the genetic or molecular aspects of morphogenesis, the immediate control of shape in biological structures is necessarily physical. Indeed, spatiotemporal changes in cell or tissue mechanics and growth control how a structure deforms, flows or moves in specific directions. These concepts were emphasized more than a century ago by D'Arcy Thompson, who highlighted similarities between the morphologies of living and non-living systems and suggested that some common underlying physical principles may exist (Thompson, 1917). Understanding the physical mechanisms of morphogenesis remains a challenge today, in part owing to difficulties in measuring many essential physical quantities as biological structures emerge during morphogenesis. Over the past decade, technological developments in microscopy (Ntziachristos, 2010) and physical measurements within developing organisms (Campàs, 2016; Sugimura et al., 2016) have started to reveal how physical quantities are controlled in space and time to shape complex structures. This new information suggests that, although there can be large differences in the molecular and genetic mechanisms controlling cell and tissue elongation across species, the physical mechanisms of morphogenesis share important similarities, raising the question of whether there exist conserved physical mechanisms of morphogenesis (Newman and Comper, 1990).
In this Review, we focus on the physical mechanisms underlying cell and tissue elongation and discuss the key physical factors controlling the elongation process in the specific cases for which we have more information about the physical process of elongation. Comparing different organisms, we propose the existence of a small number of conserved physical mechanisms of morphogenesis that occur across organisms and scales.
Physical quantities controlling shape changes
From a physical perspective, cells and tissues can be thought of as self-shaping complex materials. With some notable exceptions, such as the emergence of periodic patterns through instabilities (Cross and Hohenberg, 1993), shaping any material, living or non-living, requires multiple physical quantities to be controlled in space and time within the material being shaped. For living materials, these physical quantities are growth, active stresses and material properties (Stooke-Vaughan and Campàs, 2018) (Fig. 2A). Growth, either positive (addition of material) or negative (removal of material), can drive changes in volume and shape. Both cell proliferation (and cell death) or extracellular matrix (ECM) production (and degradation) can affect the volume and, potentially, the shape of the structure (Baena-López et al., 2005; Kalson et al., 2015; Pérez-Garijo and Steller, 2015; Fox et al., 2018). Beyond growth, internal active stresses have been one of the most studied physical quantities controlling cell and tissue shape changes. Unlike mechanical stresses in non-living materials, active stresses are generated within the material (cell or tissue) through internal energy consumption (Ramaswamy, 2010; Marchetti et al., 2013). Actomyosin force generation at the cell cortex (Murrell et al., 2015; Clarke and Martin, 2021), traction forces (Galbraith and Sheetz, 1998; Maruthamuthu et al., 2011; Patel et al., 2020), cell divisions (Nia et al., 2016; Nam et al., 2021; Agarwal et al., 2022) or osmotic pressure (Harold, 2002) are examples of processes that generate internal (active) stresses. Finally, the material properties of the structure also play a key role in morphogenesis, as they control how the forces within the structure translate into the deformations and/or flows that shape it. For instance, gradients in ECM composition (Harunaga et al., 2014; Agarwal et al., 2022) or in the amount of extracellular space between cells (Mongera et al., 2018, 2023) in a tissue affect the material properties and, consequently, the shape of the tissue. Many different types of material properties exist, from the simplest elastic (solid) or fluid states, to more complex behaviors, such as viscoelasticity and viscoplasticity, or anisotropy (Janmey et al., 2007; Lou, 2023). Consequently, the exact same force or growth pattern in different materials (cells or tissues) can translate into completely different deformations and shapes (Fig. 2A). Given that growth, active stresses and material properties all play a role in shaping living structures, understanding the physical mechanisms underpinning morphogenesis requires the collection of information about all three of these quantities as structures form.
Physical quantities controlling cell and tissue elongation. (A) The spatiotemporal variations in three physical quantities, namely growth (green), active stresses (magenta) and material properties (orange), guide morphogenetic flows and control tissue morphogenesis, including elongation. (B) Elongation corresponds to the extension (ΔL) of the length (L) of a cell or a tissue in one preferential spatial direction over time. In order for a material to change shape and, in particular, elongate, some of the physical quantities must be either inhomogeneous or anisotropic. Inhomogeneities in a physical quantity occur when such quantity varies in space, generating gradients (or differential values of the quantity). Anisotropy occurs when a physical quantity has different values along different spatial directions, but the values do not vary with the spatial position along these directions. We include examples of both inhomogeneous growth (differential cell proliferation; dividing cells in green) and anisotropic growth (oriented cell division), inhomogeneous active stresses (graded isotropic contractility; magenta bundles correspond to actomyosin) and anisotropic active stresses (anisotropic cell tensions; magenta arrows represent higher tension along a spatial direction), as well as inhomogeneous material properties (gradients in tissue fluidity or spatially controlled fluid–solid transitions; orange dashed lines represent active cellular rearrangements) and anisotropic material properties (oriented or anisotropic structural elements; orange bundles represent oriented fibers of ECM or cytoskeleton).
Physical quantities controlling cell and tissue elongation. (A) The spatiotemporal variations in three physical quantities, namely growth (green), active stresses (magenta) and material properties (orange), guide morphogenetic flows and control tissue morphogenesis, including elongation. (B) Elongation corresponds to the extension (ΔL) of the length (L) of a cell or a tissue in one preferential spatial direction over time. In order for a material to change shape and, in particular, elongate, some of the physical quantities must be either inhomogeneous or anisotropic. Inhomogeneities in a physical quantity occur when such quantity varies in space, generating gradients (or differential values of the quantity). Anisotropy occurs when a physical quantity has different values along different spatial directions, but the values do not vary with the spatial position along these directions. We include examples of both inhomogeneous growth (differential cell proliferation; dividing cells in green) and anisotropic growth (oriented cell division), inhomogeneous active stresses (graded isotropic contractility; magenta bundles correspond to actomyosin) and anisotropic active stresses (anisotropic cell tensions; magenta arrows represent higher tension along a spatial direction), as well as inhomogeneous material properties (gradients in tissue fluidity or spatially controlled fluid–solid transitions; orange dashed lines represent active cellular rearrangements) and anisotropic material properties (oriented or anisotropic structural elements; orange bundles represent oriented fibers of ECM or cytoskeleton).
For a cell or tissue to change shape, some of these physical quantities must either be inhomogeneous and/or anisotropic (Fig. 2B). Spatial inhomogeneities occur when the values of a physical quantity change with spatial location. For instance, a gradient in cell proliferation is a case of inhomogeneous growth. In contrast, anisotropy occurs when a physical quantity has different values along different spatial directions, but the values do not change with position along these different directions. A tissue with homogeneous (uniform) cell proliferation but with cell divisions oriented along a specific spatial direction is an example of growth anisotropy (Fig. 2B). Both single-cell and multicellular organisms control the anisotropy and/or inhomogeneity of one or several of the physical quantities described above. Although growth and active stresses have the potential to drive morphogenetic transformations, spatiotemporal changes in material properties control how internal forces translate into flows or deformations in the structure, thereby guiding morphogenesis. Therefore, spatiotemporal variations (inhomogeneities) or anisotropy in each of these three physical quantities within the material being shaped can affect the resulting morphology of the structure (Fig. 2A). However, although the three of them may be regulated to shape a given structure, some combinations seem to appear regularly. In some cases, structures are shaped in the absence of growth, with the organism controlling active stresses and material properties. In others, only control of growth and material properties is necessary to shape structures. Despite the small number of physical quantities available for control, the resulting morphologies are virtually endless (within physical limits) because the physical quantities can be controlled in space and time in many different ways.
Several techniques exist to quantify mechanical stresses, material properties (Campàs, 2016; Sugimura et al., 2016; Gómez-González et al., 2020) and growth in vivo, with multiple recent reviews detailing their capabilities (Campàs, 2016; Sugimura et al., 2016; Eastman and Guo, 2020; Gómez-González et al., 2020). In the absence of direct physical measurements of active stresses or material properties, indirect inferences of physical characteristics exist. Unlike quantitative measurements, which employ calibrated probes, inferences rely on fitting physical (theoretical) models to experimental data to obtain values of physical quantities. The obtained values are meaningful only if the physical model used is correct; therefore, although inference methods are very useful, care must be taken in the interpretation of inferred values. Finally, observations of tissue structure and/or molecular organization can sometimes provide indirect information about the mechanical state of the system.
There are very few examples of morphogenesis for which each of the physical quantities mentioned above has been quantitatively measured (Fig. 1 and Table S1), so in most cases it is unclear how many physical quantities are being spatiotemporally controlled. However, there are several cases in which direct physical measurements have been achieved or, in their absence, indirect inferences of physical characteristics exist (Fig. 1 and Table S1), allowing us to identify the physical quantities being controlled and, in some cases, the molecular and/or cellular processes regulating the physical state of the system. We focus on these best documented cases and show that some physical mechanisms of cell/tissue elongation emerge repeatedly across species, suggesting the existence of conserved physical principles of morphogenesis.
Conserved physical mechanisms of elongation
Control of active stresses and material properties
Perhaps the most intuitive way to shape structures, including cells and tissues, is by controlling the location, timing and direction of force generation within a material. This is one of the reasons why studies of morphogenesis focused for a long time on active stresses. These are generally associated with actomyosin contractility, although cell divisions, traction forces, osmotic pressure and other cellular processes also generate them (Goeckeler and Wysolmerski, 1995; Salbreux et al., 2012; Mammoto et al., 2013). In particular, actomyosin-driven active stresses have been extensively studied during embryogenesis and tissue elongation.
A hallmark case of tissue elongation in animal species is convergent extension (Tada and Heisenberg, 2012; Shindo, 2018), which is characterized by the thinning of the tissue along one spatial direction and its concomitant elongation along a perpendicular direction. Despite being important for many examples of morphogenesis (Fig. 1), convergent extension has been extensively studied in the context of embryonic axis elongation in amphibians (Xenopus laevis) (Keller et al., 2000; Davidson et al., 2010; Zhou et al., 2010; Shook et al., 2018; Shindo et al., 2019; Huebner et al., 2021; 2022; Weng et al., 2022) and arthropods (Drosophila melanogaster) (Bertet et al., 2004; Rauzi et al., 2008; Levayer and Lecuit, 2013; Kasza et al., 2014; Kong et al., 2017; Kale et al., 2018).
During germband extension in fruit fly embryos, adherent epithelial cells display a preferential apical accumulation of non-muscle myosin II on junctions oriented along the dorsoventral axis (Bertet et al., 2004; Rauzi et al., 2008; Kasza et al., 2014) (Fig. 3A, panel 1). This anisotropy, controlled by Toll-mediated planar cell polarity signaling (Irvine and Wieschaus, 1994; Zallen and Wieschaus, 2004; Blankenship et al., 2006; Paré et al., 2014), generates tissue-scale anisotropic active stress (Fig. 3A), with higher tensions along the dorsoventral junctions (Rauzi et al., 2008; Kasza et al., 2014; Bambardekar et al., 2015; Collinet et al., 2015). Repeated myosin pulses from a medial pool to the dorsoventral junctions (Fig. 3A, panel 2) drive a ratchet-like contraction of the dorsoventral junction via periodic increases in junctional tension (Levayer and Lecuit, 2013; Clément et al., 2017). As a consequence, dorsoventral junctions contract, eventually driving polarized cell intercalations (irreversible tissue remodeling; Fig. 3A, panel 3), with cells away from the embryo midline progressively approaching it and displacing the cells there along the anteroposterior axis (Fig. 3A, panel 4), thereby elongating the tissue in this direction.
Elongation controlled by active stresses and material properties. (A,B) Examples of tissue elongation by convergent extension in Drosophila melanogaster (germband extension; A) and Xenopus laevis (body axis elongation; B). In both cases, active anisotropic stresses cause oriented cell rearrangements and subsequent tissue elongation. During Drosophila germband extension (A), myosin is enriched along dorsoventral (D-V) junctions (panel 1), generating anisotropic stress. Myosin pulses between a medial pool and D-V junctions (panel 2; magenta arrows), leading to temporal changes in D-V junctional tensions (panel 3). When myosin-generated force crosses a threshold (orange dashed line), irreversible plastic deformation happens, leading to junction shortening (panel 3). This ultimately produces cell rearrangements in the form of polarized cell intercalation (panel 4). Cells of the body axis in Xenopus (B) are oriented perpendicular to the direction of elongation, forming lamellipodia at their mediolateral extremities and accumulating actomyosin at their anterior and posterior junctions. The traction forces of the lamellipodia, combined with cortical contractility from the actomyosin, generate an anisotropic stress perpendicular to direction of extension, leading to cell rearrangements and tissue elongation. (C) Elongation of the Caenorhabditis elegans body axis. The body (panel 1) has a cylindrical shape comprising a dorsal epidermis and a ventral epidermis (light gray) that each contain circumferential actin bundles (orange). The dorsal and ventral epidermis are connected laterally by seam cells (dark gray) that have a contractile cortex (actin, dark gray rods; myosin, magenta dots). Four bundles of muscles (magenta rods) are attached to the inside of the body cylinder. The first phase of elongation relies on the isotropic contraction of seam cells (panel 2) being resisted by anisotropic (circumferential) actin bundles (orange) in the dorsal and ventral epidermis (panel 3). During a second elongation phase, elongation is driven by rhythmic muscle contractions leading to irreversible reorganization of the actin bundles (panel 4). The four muscles that run below the epidermis contract in a rhythmic fashion, leading to oscillation of tension. When the actively generated forces are above a threshold (dashed orange line in panel 5), actin bundles break and are reassembled by the formin FHOD-1 (panel 4), thus becoming shorter and resulting in irreversible plastic deformation (panel 5). Together, these two phases of elongation result in circumferential shortening of the body and concomitant anteroposterior elongation. (D) Body axis elongation of Nematostella vectensis. Muscles in the body are arranged in a circumferential fashion, forming rings along the body axis (panel 1). Rhythmic contraction of these muscles (panel 2) drives transient hydrostatic pressure increases in the body cavity (panel 3; represented by P surrounded by arrows in panel 1). This pressure increase is resisted by the arrangement of muscle fibers that resist in the circumferential direction, leading to irreversible, plastic deformation when pressure reaches a threshold, ultimately driving elongation along the anteroposterior direction. (E) Conceptual sketch of the conserved features associated with the mechanism of tissue elongation relying on active stresses and material properties. Anisotropy in stress orientation, either due to oriented force generation or anisotropic material properties (magenta and orange arrows and lines, respectively, in the box), leads to oriented deformation. Dynamic active stresses (magenta curve) transiently overcome the yield stress (orange dashed line) of the material, driving (irreversible) viscoplastic flows along specific directions as a result of the anisotropic distribution of either active stresses and/or material properties, causing tissue elongation. A, anterior; D, dorsal; L, left; P, posterior; R, right; V, ventral.
Elongation controlled by active stresses and material properties. (A,B) Examples of tissue elongation by convergent extension in Drosophila melanogaster (germband extension; A) and Xenopus laevis (body axis elongation; B). In both cases, active anisotropic stresses cause oriented cell rearrangements and subsequent tissue elongation. During Drosophila germband extension (A), myosin is enriched along dorsoventral (D-V) junctions (panel 1), generating anisotropic stress. Myosin pulses between a medial pool and D-V junctions (panel 2; magenta arrows), leading to temporal changes in D-V junctional tensions (panel 3). When myosin-generated force crosses a threshold (orange dashed line), irreversible plastic deformation happens, leading to junction shortening (panel 3). This ultimately produces cell rearrangements in the form of polarized cell intercalation (panel 4). Cells of the body axis in Xenopus (B) are oriented perpendicular to the direction of elongation, forming lamellipodia at their mediolateral extremities and accumulating actomyosin at their anterior and posterior junctions. The traction forces of the lamellipodia, combined with cortical contractility from the actomyosin, generate an anisotropic stress perpendicular to direction of extension, leading to cell rearrangements and tissue elongation. (C) Elongation of the Caenorhabditis elegans body axis. The body (panel 1) has a cylindrical shape comprising a dorsal epidermis and a ventral epidermis (light gray) that each contain circumferential actin bundles (orange). The dorsal and ventral epidermis are connected laterally by seam cells (dark gray) that have a contractile cortex (actin, dark gray rods; myosin, magenta dots). Four bundles of muscles (magenta rods) are attached to the inside of the body cylinder. The first phase of elongation relies on the isotropic contraction of seam cells (panel 2) being resisted by anisotropic (circumferential) actin bundles (orange) in the dorsal and ventral epidermis (panel 3). During a second elongation phase, elongation is driven by rhythmic muscle contractions leading to irreversible reorganization of the actin bundles (panel 4). The four muscles that run below the epidermis contract in a rhythmic fashion, leading to oscillation of tension. When the actively generated forces are above a threshold (dashed orange line in panel 5), actin bundles break and are reassembled by the formin FHOD-1 (panel 4), thus becoming shorter and resulting in irreversible plastic deformation (panel 5). Together, these two phases of elongation result in circumferential shortening of the body and concomitant anteroposterior elongation. (D) Body axis elongation of Nematostella vectensis. Muscles in the body are arranged in a circumferential fashion, forming rings along the body axis (panel 1). Rhythmic contraction of these muscles (panel 2) drives transient hydrostatic pressure increases in the body cavity (panel 3; represented by P surrounded by arrows in panel 1). This pressure increase is resisted by the arrangement of muscle fibers that resist in the circumferential direction, leading to irreversible, plastic deformation when pressure reaches a threshold, ultimately driving elongation along the anteroposterior direction. (E) Conceptual sketch of the conserved features associated with the mechanism of tissue elongation relying on active stresses and material properties. Anisotropy in stress orientation, either due to oriented force generation or anisotropic material properties (magenta and orange arrows and lines, respectively, in the box), leads to oriented deformation. Dynamic active stresses (magenta curve) transiently overcome the yield stress (orange dashed line) of the material, driving (irreversible) viscoplastic flows along specific directions as a result of the anisotropic distribution of either active stresses and/or material properties, causing tissue elongation. A, anterior; D, dorsal; L, left; P, posterior; R, right; V, ventral.
In Xenopus, in which convergent extension was first reported (Vogt, 1925; Keller, 1975), mesenchymal cells adopt a Wnt-PCP-dependent bipolar shape with actin-rich protrusions along the mediolateral axis that establish connections between cells and generate anisotropic active stresses (traction forces directed along the mediolateral direction (Keller, 1984; Keller and Tibbetts, 1989; Wallingford et al., 2000, 2002; Shindo, 2018) (Fig. 3B). In addition to these traction forces, actomyosin accumulation and pulsatile dynamics at mediolateral cell–cell contacts generate an additional mechanical anisotropy and facilitate tissue contraction along the mediolateral direction (Shindo et al., 2019; Weng et al., 2022). Together, these processes drive cell intercalation along the dorsoventral axis, displacing cells in the midline along the anteroposterior direction and elongating the axis. Other vertebrates, such as zebrafish, display similar convergent-extension movements and cell behaviors during gastrulation (Glickman et al., 2003; Heisenberg et al., 2000; Roszko et al., 2015; Steventon et al., 2016; Williams and Solnica-Krezel, 2020).
Beyond convergent extension, other organisms also employ mechanical anisotropy to elongate their body axis. The C. elegans embryo undergoes a 4-fold elongation along the anteroposterior axis without cell proliferation (Fig. 3C) (Sulston et al., 1983; Priess and Hirsh, 1986; Fang et al., 2021). At the start of this process, the embryo resembles a tube with a fluid-filled cavity, surrounded by dorsal and ventral epidermal cells at the surface that connect to lateral (seam) cells (Priess and Hirsh, 1986) via long circumferential actin cables (Fig. 3C, panel 1). In the first elongation phase, seam cells, which display a disorganized actomyosin cortex (Fig. 3C, panel 2), contract and pull on dorsal and ventral cells, increasing the pressure in the lumen inside the embryo (Ciarletta et al., 2009; Fang et al., 2021). The actin corset in ventral and dorsal cells creates an anisotropy in material properties that mechanically reinforces the embryo along the circumferential direction (Fig. 3C, panel 3), suppressing radial deformations and thus causing tissue deformations arising from transient pressure increases to occur along the anteroposterior axis, ultimately leading to the extension of the body axis (Ciarletta et al., 2009; Vuong-Brender et al., 2017a,b, 2018; Amar et al., 2018). After this initial phase, elongation mainly relies on the contraction of four muscle fibers running along the anteroposterior axis and attached to the epidermis; these contractions bend, and eventually break, the circumferential actin fibers in the overlying epidermal cells (Fig. 3C, panel 4) (Lardennois et al., 2019). A molecular machinery relying on the formin FHOD-1 repairs the broken fibers, causing irreversible structural changes in the anisotropic actin bundles that enable local narrowing of the actin corset in a ratchet-like manner (Fig. 3C, panel 5) (Lardennois et al., 2019). Altogether, these processes cause a plastic deformation in the tissue that elongates the body axis (Lardennois et al., 2019).
Despite the phylogenetic distance between them, the physical mechanism of body axis elongation in the sea anemone Nematostella vectensis is similar to the mechanism used by C. elegans. During the larva-to-polyp transition, the Nematostella body axis elongates 4- to 5-fold (Stokkermans et al., 2022) (Fig. 3D). The larva has a roughly cylindrical body composed of circumferentially oriented muscle fibers enclosing a fluid-filled cavity with a mouth at one end. The circumferential arrangement of the muscles is believed to create an anisotropy in material properties (Fig. 3D, panel 1), restricting circumferential expansion of the body (Stokkermans et al., 2022). Peristaltic contractions of these muscles generate periodic increases in hydrostatic pressure within the body cavity that are thought to physically remodel the muscle wall in a periodic fashion (Fig. 3D, panel 2), thereby causing an irreversible elongation of the body along its axis in a ratchet-like manner (Fig. 3D, panel 3) (Stokkermans et al., 2022).
At a conceptual level, all the mechanisms of axis elongation described above involve the following features (Fig. 3E): first, a mechanical anisotropy (either in active stresses or material properties) that causes deformations to occur preferentially along the anteroposterior body axis; second, a pulsatile (either periodic or stochastic) increase in active stress that causes a transient and irreversible remodeling of tissue material, either by driving cellular rearrangements, cytoskeletal remodeling or other structural changes. The fact that the irreversible structural changes occur during periods of increased active stresses, as well as the lack of observed shape changes at low stresses, strongly points to the existence of a yield stress: a minimal mechanical stress required to cause irreversible structural changes in the tissue material (represented by the orange dashed line in Fig. 3E). When mechanical stresses in the tissue are below the yield stress, the tissue behaves as a (visco)elastic material and large tissue deformations are reversible, meaning that permanent tissue elongation is not possible. However, when the stresses in the tissue overcome the yield stress, these stresses drive irreversible structural changes (such as cellular rearrangements, cytoskeletal remodeling, etc.) that allow the tissue material to flow and the tissue to elongate. These irreversible structural changes occurring when the yield stress is surpassed, and associated material flows, are known as plastic behavior and viscoplastic flows, respectively. Although yield stress has not yet been measured directly in any of the systems described above, the observations of irreversible tissue or cytoskeletal remodeling following transient increases in active stress constitute indirect evidence for it, as suggested in several of the studies illustrated in Fig. 3 (Lardennois et al., 2019; Stokkermans et al., 2022). Indeed, the existence of a yield stress in tissues and the ability of active stresses to overcome it and cause irreversible tissue remodeling has been demonstrated in 3D cell aggregates (Marmottant et al., 2009) and in living zebrafish tissues (Mongera et al., 2018; 2023), as well as in systems with abundant ECM (Nam et al., 2016). These studies indicate that yield stress is an important mechanical quantity that is regulated during embryonic development.
Although tissues behave as viscoelastic materials for small deformations (with elastic behavior over long timescales) (Bambardekar et al., 2015; Mongera et al., 2023), and can display fluid-like behavior at long timescales or for large applied deformations (Forgacs et al., 1998; Marmottant et al., 2009), these are behaviors consistent with the mechanical description above. Indeed, the yield stress can be tuned by active turnover (or remodeling) of some mechanical structures in the tissues [active cell rearrangements (Marmottant et al., 2009; Kim et al., 2021), actin turnover (Salbreux et al., 2012; Wyatt et al., 2016), ECM remodeling (Nam et al., 2016; Elosegui-Artola, 2021), etc.], and can vanish at timescales longer than the turnover timescale. These turnover timescales, which are controlled by several cellular or molecular processes (Campàs et al., 2023), are key to understanding the mechanical behavior of the tissue. Similarly, because inducing irreversible structural changes in the tissue requires large enough deformations, the timescale (duration) of the active stress pulses is also an important parameter to control the material state of the tissue (Wyatt et al., 2016; Campàs et al., 2023) and its ability to elongate.
All the observations described above (Fig. 3) indicate that organisms using this mechanism of morphogenesis (Fig. 3E) must control active stress dynamics (magnitude and duration of pulsatile behavior), the value of the yield stress (material properties) and the anisotropy of either active stresses or material properties (or both). As the different examples above show, the molecular/cellular mechanisms that control these physical quantities can be strikingly different in distinct species, yet the physical mechanism of tissue elongation is conceptually analogous in all of them.
Control of material properties and growth during cell and tissue elongation
One of the most salient examples of cell elongation occurs in the morphogenesis of walled cells. Tip-growth is a morphogenetic process characterized by the unidirectional elongation of the cell at one end (Hepler et al., 2001; Harold, 2002; Cole and Fowler, 2006) (Fig. 4A). Cells from a wide range of organisms, including bacteria (such as Corynebacterium and Caulobacter; Scheffers and Pinho, 2005; Cameron et al., 2015; Egan et al., 2017), plants (Cosgrove, 2000; 2005; Harold, 2002; Rounds and Bezanilla, 2013) [which elongate structures including pollen tubes (Krichevsky et al., 2007; Geitmann, 2010) and root hairs (Carol and Dolan, 2002)], fungi (Bartnicki-García, 1999; Riquelme, 2012; Merlini et al., 2013; Chang, 2017; Chevalier et al., 2023) [such as filamentous fungi, fission yeast (Chang and Martin, 2009; Davì and Minc, 2015) and mating projections in budding yeast (Cabib and Arroyo, 2013; Banavar et al., 2018)] and other eukaryotic groups (Campas et al., 2012), elongate using tip-growth (Hepler et al., 2001; Baskin, 2005; Cole and Fowler, 2006).
Elongation controlled by growth and material properties. (A) Tip growth in walled cells is driven by an isotropic turgor pressure (represented by P surrounded by arrows) inside the cell. The otherwise isotropic force of turgor pressure leads to elongation due to the localized addition of cell wall (CW) polysaccharides (green arrows) and remodeling of the cell wall at the tip of the elongating cell. CW-modifying enzymes modulate the material properties of the CW by altering its crosslinking state, with the CW being fluid-like (dark orange) at the tip of the elongating cell and solid (yellow) away from the tip. The specific molecular players used to achieve the spatiotemporal control of these physical quantities differ across species. The panels on the right illustrate the molecular differences between elongating pollen tubes (top) and budding yeast (bottom). (B) Elongation of the gonads in Caenorhabditis elegans. The tissue is composed of dividing germ cells and a distal tip cell, all surrounded by a basement membrane (BM). Gonad elongation is a consequence of increased tissue pressure caused by germ cell proliferation, coupled with the fluidization (dark orange) of the BM by metalloproteases, which are secreted by the distal tip cell and locally digest the BM at the elongating tip. Local fluidization of the BM allows localized dissipation of the stress generated by tissue pressure, resulting in directed elongation. (C) Body axis elongation in zebrafish requires the movement of cells from dorsal tissues into the ventral tissues (panels 1, 2 and 3) to maintain elongation. It also involves a transition in the tissue physical state, with the posterior mesodermal progenitor zone (MPZ) maintained in a fluid-like state (dark orange, panels 1 and 3) via actively induced cell rearrangements (panel 3), and the anterior presomitic mesoderm (PSM) tissues rigidified into a solid-like (yellow, panels 1 and 3) state, as cells stop rearranging and reduce extracellular spaces (panel 3). (D) Conceptual sketch of the conserved features associated with the mechanism of tissue elongation relying on growth and material properties. New material (either cells or ECM) is constantly added to a fluid-like region located at the elongating tip. The material progressively rigidifies away from the tip, providing a solid support for further elongation. A, anterior; D, dorsal; P, posterior; V, ventral.
Elongation controlled by growth and material properties. (A) Tip growth in walled cells is driven by an isotropic turgor pressure (represented by P surrounded by arrows) inside the cell. The otherwise isotropic force of turgor pressure leads to elongation due to the localized addition of cell wall (CW) polysaccharides (green arrows) and remodeling of the cell wall at the tip of the elongating cell. CW-modifying enzymes modulate the material properties of the CW by altering its crosslinking state, with the CW being fluid-like (dark orange) at the tip of the elongating cell and solid (yellow) away from the tip. The specific molecular players used to achieve the spatiotemporal control of these physical quantities differ across species. The panels on the right illustrate the molecular differences between elongating pollen tubes (top) and budding yeast (bottom). (B) Elongation of the gonads in Caenorhabditis elegans. The tissue is composed of dividing germ cells and a distal tip cell, all surrounded by a basement membrane (BM). Gonad elongation is a consequence of increased tissue pressure caused by germ cell proliferation, coupled with the fluidization (dark orange) of the BM by metalloproteases, which are secreted by the distal tip cell and locally digest the BM at the elongating tip. Local fluidization of the BM allows localized dissipation of the stress generated by tissue pressure, resulting in directed elongation. (C) Body axis elongation in zebrafish requires the movement of cells from dorsal tissues into the ventral tissues (panels 1, 2 and 3) to maintain elongation. It also involves a transition in the tissue physical state, with the posterior mesodermal progenitor zone (MPZ) maintained in a fluid-like state (dark orange, panels 1 and 3) via actively induced cell rearrangements (panel 3), and the anterior presomitic mesoderm (PSM) tissues rigidified into a solid-like (yellow, panels 1 and 3) state, as cells stop rearranging and reduce extracellular spaces (panel 3). (D) Conceptual sketch of the conserved features associated with the mechanism of tissue elongation relying on growth and material properties. New material (either cells or ECM) is constantly added to a fluid-like region located at the elongating tip. The material progressively rigidifies away from the tip, providing a solid support for further elongation. A, anterior; D, dorsal; P, posterior; V, ventral.
Unlike animal cells, walled cells feature a high internal (turgor) pressure that is mechanically resisted by a cell wall, which defines the cell surface and its shape (Harold, 2002; Cosgrove, 2023). At a physical level (Harold, 1990; Geitmann and Ortega, 2009; Riquelme, 2012; Rounds and Bezanilla, 2013), tip growth is characterized by the localized expansion of the cell wall at the tip (apex) of the cell (Fig. 4A). In order to elongate, cells polarize and reorganize the cytoskeleton to transport specific molecular machinery to the region of the cell surface where elongation will proceed (Harold, 1990; 2005; Ayscough and Drubin, 1998; Geitmann and Emons, 2000; Merlini et al., 2013). Enzymes that degrade the cell wall are secreted at this location, locally fluidizing the cell wall by substantially lowering its yield stress (well below the turgor pressure), thus enabling cell wall expansion under the force of turgor pressure (Cappellaro et al., 1998; Cosgrove, 2000; Huberman and Murray, 2014; Chebli and Geitmann, 2017). Although not directly measured, the transition from a fluid-like state at the tip to a solid-like state away from it suggests that the cell wall undergoes a gelation transition (a fluid-to-solid transition caused by overcoming a threshold density of crosslinks between cell wall polymers; Axelos and Kolb, 1990) as its crosslinking state increases in regions that are further away from the tip (Campàs and Mahadevan, 2009). Indeed, measurements of cell wall crosslinking state in pollen tubes show a sharp transition that correlates well with these different mechanical states of the cell wall (Bosch and Hepler, 2005; Röckel et al., 2008). To sustain tip growth over time, the cell also secretes new cell wall material into the apical expanding region (Fig. 4A) (Cabib et al., 1982; Cosgrove, 2005). Away from the expanding tip region, there is no secretion and the cell wall rigidifies, resisting turgor pressure and maintaining cell wall integrity and shape (Hepler et al., 2013). Although turgor pressure is the underlying force (active stress) enabling cell wall expansion, it is uniform and isotropic and does not control the shape of the cell. Instead, the shape is defined by the spatiotemporal changes in the material properties and the growth of the cell wall.
Different organisms use distinct molecular mechanisms to modulate the inhomogeneities in cell wall growth and material properties. In plant pollen tubes, pectins are secreted to the pre-existing cell wall by exocytic vesicles (Chebli et al., 2012, 2013), which also carry enzymes (pectin methylesterase inhibitors) that prevent the rigidification of the new cell wall (Bosch and Hepler, 2005; Röckel et al., 2008), directly coupling the control of cell wall growth to its material properties (Fayant et al., 2010; Chebli et al., 2012) (Fig. 4A, top-right panel). Indeed, if secretion ceases, the cell wall rigidifies and elongation stops, ensuring cell integrity and viability (Bove et al., 2008; Banavar et al., 2018). Some rod-shaped bacteria [Agrobacterium tumefaciens (Brown et al., 2011) and Corynebacterium glutamicum (Letek et al., 2008)] grow by inserting peptidoglycans at either one or both poles of the cell, in contrast to the more widely studied mechanism of inserting the material into the side walls as seen in E. coli and Bacillus subtilis (Wang et al., 2012). In fungi, rod-shaped fission yeast cells (Schizosaccharomyces pombe) elongate when new cell wall polysaccharides are secreted by cell wall synthases such as Bgs4 (Hochstenbach et al., 1998; Cortés et al., 2004), which are transmembrane proteins localized at the growing tip (Hochstenbach et al., 1998; Cortés et al., 2004), and enzymes that remodel the cell wall, including glucan-degrading enzymes, such as Exg2 (Dueñas-Santero et al., 2010), are also secreted at the tip (Dueñas-Santero et al., 2010).
In budding yeast (Saccharomyces cerevisiae) mating projections, the ability to sustain unidirectional elongation of the cell via tip-growth relies on mechanical feedback between cell wall mechanics and growth (Banavar et al., 2018). Mechanical sensors respond to regions of the cell wall that are expanding at high rates and locally activate the cell wall synthases Fks1/2 (Utsugi et al., 2002) via Rho GTPases (Philip and Levin, 2001), enhancing the secretion of new cell wall material in thinner cell wall regions to stop their further thinning and prevent the eventual piercing of the cell wall (Fig. 4A, bottom-right panel). Similar mechanical feedback mechanisms (albeit encoded by distinct molecular players) have recently been identified in fission yeast tip-growth (Davì et al., 2018) and may also be involved in plant pollen tube growth (Mecchia et al., 2017).
The spatiotemporal control of material properties in polymeric scaffolds, such as cell walls, is a widespread strategy to control elongation. In multicellular animal species, spatial and temporal variations in the material properties of the ECM (Díaz-de-la-Loza and Stramer, 2023) are thought to contribute to the shaping of tissues, from branching morphogenesis (Sakai et al., 2003; Walma and Yamada, 2020) to wing folding (Harmansa et al., 2023). Recent studies of gonad morphogenesis in C. elegans show that this strategy is also used to control elongation of multicellular structures (Agarwal et al., 2022) (Fig. 4B). During the larval stages, each of the two gonads forms a small, straight tube made of germ cells, surrounded by a basal lamina and covered at one end by a distal tip cell, which acts as a niche for germ cell proliferation. Although it was previously proposed that this distal tip cell drives elongation through migration (Cecchetelli and Cram, 2017), it was recently shown that these cells exhibit no sign of migratory activity (Agarwal et al., 2022). Instead, germ cell proliferation is thought to increase the tissue pressure on the basal lamina (Agarwal et al., 2022). Concomitantly, the distal tip cell secretes metalloproteases that locally degrade the ECM at the extending end, likely fluidizing the basal lamina at this point, as suggested by fluorescence recovery after photobleaching (FRAP) measurements (Agarwal et al., 2022). Similar to tip-growth in walled cells, this local fluidization allows the pressure generated by cell proliferation to drive elongation of the tissue in one preferential direction.
Zebrafish also use the combined control of growth and material properties to elongate tissues during embryogenesis (Fig. 4C). In this species, posterior axis elongation occurs without significant cell proliferation before tail eversion (Zhang et al., 2008; Riley et al., 2010). Instead, cells in dorsal tissues move toward the posterior end of the body, eventually entering the ventral tissues there and providing the necessary ‘material’ to sustain the progressive elongation of the body axis (Fig. 4C, panels 1 and 2) (Lawton et al., 2013; Banavar et al., 2021). Direct in vivo mechanical measurements have shown that the tissue transitions from a fluid state at the posterior end of the embryo (the mesodermal progenitor zone; MPZ) to a solid state in the presomitic mesoderm (PSM) (Fig. 4C, panel 3) (Mongera et al., 2018; Kim et al., 2021). Unlike convergent extension, tissue-scale active stresses in ventral tissues do not contribute to their posterior elongation (Mongera et al., 2018); instead, elongation occurs via a combination of the addition of new cells into the posterior-most fluid-like region of the tissue and the subsequent rigidification of the PSM (Banavar et al., 2021). The fluidization of posterior tissues is due to both the presence of more extracellular spaces between cells in the MPZ region (Mongera et al., 2018, 2023) and actomyosin-driven tension fluctuations at cell–cell boundaries (Mongera et al., 2018; Kim et al., 2021), which drive cell rearrangements that relax stresses in the tissue, thereby fluidizing it (Fig. 4C, panel 3). As cells transition from the MPZ to the PSM, extracellular spaces are strongly reduced and cells exhibit fewer cell–cell contact fluctuations, decreasing cell rearrangements and thus rigidifying the tissue in a solid-like state (Mongera et al., 2018; Banavar et al., 2021; Kim et al., 2021).
Posterior axis elongation in chick embryos involves both ECM production and cell addition in the tailbud. Cells exhibit random (diffusive) movements with respect to the ECM, with cellular diffusion decreasing as cells move away from the posterior-most tailbud region until movements are arrested in the anterior PSM, reminiscent of the fluid-to-solid transition observed in zebrafish (Bénazéraf et al., 2010; 2017; Xiong et al., 2020; Regev et al., 2022). Recent measurements show an increase in tissue viscosity away from the elongating end of the body, confirming that, similar to the zebrafish embryo, material properties are graded along the anteroposterior axis (Michaut et al., 2022 preprint). Much less is known about the mechanics of axis elongation in mouse embryos, but some studies suggest that FGF signaling-dependent incorporation of new cells at the posterior end of the primitive streak is also required for elongation (Rossant et al., 1997; Ciruna and Rossant, 2001; Naiche et al., 2011). Altogether, observations in chick and fish suggest that key features of the physical mechanism of body axis elongation are likely shared across vertebrate species.
Remarkably, tip-growth in individual walled cells, posterior body axis elongation in multicellular organisms (such as zebrafish), and even organ elongation (in the case of the C. elegans gonad) share a common physical mechanism of elongation (Fig. 4D): first, the tip end of the elongating structure is actively fluidized to enable shape changes, whereas the structure away from the tip is progressively rigidified, ensuring its mechanical integrity; second, new material is simultaneously incorporated in the fluid-like region to promote elongation. This mechanism requires cells or tissues to control addition of new material (or growth) and its fluidity (material properties) at the tip of the elongating structure. The molecular/cellular mechanisms that control these physical quantities are very different, especially considering the differences in scales and the vast phylogenetic distance between species. However, at a conceptual level, the physical mechanism of elongation is conserved among them.
Controlling active stresses, growth and material properties
So far, we described examples in which either growth or active stresses did not play an important role in elongation. However, organisms can simultaneously control growth, active stresses and material properties to guide morphogenesis. There are very few examples for which information about all three of these physical quantities (let alone direct measurements) is known for a given morphogenetic process (Table S1). Here, we describe two examples of systems in which the three physical quantities seem to be spatially controlled during elongation.
During mammalian embryogenesis, nascent digits elongate from the limb bud surface by a morphogenetic process that involves convergent extension, with the tissue thinning along the anteroposterior axis and elongating along the proximo-distal axis (Parada et al., 2022) (Fig. 5A). Direct measurements of mechanical stresses in the developing digits have shown the existence of Wnt5a-dependent anisotropic active stresses generated by actomyosin cables spanning several cells and oriented along the anteroposterior axis (Parada et al., 2022). These stresses cause the tissue to contract along the anteroposterior direction and elongate along the proximodistal direction. In addition, cell proliferation is necessary to sustain the volumetric growth involved in digit elongation (Parada et al., 2022). Chondrogenic progenitors located close to the tissue surface proliferate and move with respect to each other, creating a growing fluid-like tissue region (Parada et al., 2022). The central region of the tissue is characterized by a solid-like tissue core, composed of non-proliferative and largely immobile chondrocytes surrounded by abundant collagen ECM (Parada et al., 2022). The combination of active stresses, tissue growth and the spatial variations in material properties generate a localized mechanical compression zone in the tissue that drives chondrogenic differentiation (activin/p-SMAD/Sox9 expression), enabling the tissue to coordinate morphogenesis and patterning while self-sustaining its elongation (Parada et al., 2022). In this case, the physical mechanism of digit elongation is essentially a combination of the previously described mechanisms, merging the existence of a fluid-like, growing tissue region with the presence of anisotropic active stresses.
Elongation involving control of active stresses, growth and material properties. (A) The elongation of digits from mouse (Mus musculus) limb buds relies on the spatiotemporal control of the three physical quantities. Cell proliferation (tissue growth; green) happens at the periphery, where the tissue is maintained fluid by numerous cell rearrangements and absence of collagen. At the core, away from the surface, a solid-like (or very viscous) tissue (yellow) is formed by increased deposition of collagen, with anisotropic stresses leading to convergent-extension-like cell rearrangements. Anisotropic stress is generated by actomyosin cables (magenta) spanning several cells and preferentially perpendicular to digit elongation direction, which occurs along the proximo-distal axis. The combination of localized growth, rigidification and convergent extension result in digit elongation. (B) Although less well characterized, the elongation of the primitive streak (dashed black line) in avian embryos also relies on the simultaneous control of growth, material properties and active stresses. A gradient of contractility (magenta) at the posterior side of the embryo drives tissue flows (black arrows) in a counter-rotating vortex pattern that elongates the tissue. The tissue is believed to be maintained in fluid-like state by uniform cell divisions (green). This combination of physical quantities leads to the elongation of the primitive streak. A, anterior; D, dorsal; P, posterior; V, ventral.
Elongation involving control of active stresses, growth and material properties. (A) The elongation of digits from mouse (Mus musculus) limb buds relies on the spatiotemporal control of the three physical quantities. Cell proliferation (tissue growth; green) happens at the periphery, where the tissue is maintained fluid by numerous cell rearrangements and absence of collagen. At the core, away from the surface, a solid-like (or very viscous) tissue (yellow) is formed by increased deposition of collagen, with anisotropic stresses leading to convergent-extension-like cell rearrangements. Anisotropic stress is generated by actomyosin cables (magenta) spanning several cells and preferentially perpendicular to digit elongation direction, which occurs along the proximo-distal axis. The combination of localized growth, rigidification and convergent extension result in digit elongation. (B) Although less well characterized, the elongation of the primitive streak (dashed black line) in avian embryos also relies on the simultaneous control of growth, material properties and active stresses. A gradient of contractility (magenta) at the posterior side of the embryo drives tissue flows (black arrows) in a counter-rotating vortex pattern that elongates the tissue. The tissue is believed to be maintained in fluid-like state by uniform cell divisions (green). This combination of physical quantities leads to the elongation of the primitive streak. A, anterior; D, dorsal; P, posterior; V, ventral.
In some cases, however, the physical mechanism of tissue elongation may be more complex than the combination of simpler mechanisms. Before gastrulation, chick and quail embryos consist of an epithelial layer of epiblast cells arranged as a flat disk (Fig. 5B). As the embryo starts gastrulating, the primitive streak, which defines the future midline of the embryo body axis, elongates along the anteroposterior axis of the embryo (Cui et al., 2005; Chuai et al., 2006). Although quantitative measurements of active forces, growth and mechanical properties during this process are still missing, several studies point toward a plausible mechanism for primitive streak elongation that involves the control of the three physical quantities. In quail (Coturnix japonica) (Saadaoui et al., 2020; Caldarelli et al., 2021 preprint) and chick (Chuai et al., 2006; Rozbicki et al., 2015; Serra et al., 2023) embryos, a contractile ring around the blastoderm, composed of circumferential supracellular actomyosin cables, generates a decreasing gradient in contractility from the posterior end of the embryo (Saadaoui et al., 2020; Caldarelli et al., 2021 preprint). This contractility gradient drives tissue flows that, constrained by the circular geometry of the embryo, lead to tissue elongation along the midline (Saadaoui et al., 2020; Caldarelli et al., 2021 preprint). In addition to enabling tissue growth, cell proliferation is believed to maintain the tissue in a fluid state, thereby allowing tissue flows to occur (Firmino et al., 2016). Although in this example the physical mechanism of primitive streak formation involves the control of active stresses, growth and material properties, neither growth nor material properties seem to be spatially graded to guide tissue elongation (Chuai et al., 2006). In the future, direct measurements of these three physical fields will help define the roles of each of these physical quantities in the morphogenesis process.
Discussion
Understanding how complex 3D structures are formed in living systems remains a major challenge. Thanks to new quantitative physical measurements, as well as indirect evidence or inference of physical quantities in some living systems, it is now possible to explore how different species physically shape themselves. Here, we focused on the physical mechanisms that different species use to elongate structures, identifying along the way some conserved physical mechanisms of elongation that are shared across species and scales. Two distinct strategies to control elongation physically are: (1) the control of the tissue mechanical anisotropy and the dynamics of active stresses (Fig. 3) and (2) the simultaneous control of material properties and growth (Fig. 4). It is remarkable that such a diverse range of organisms employ conceptually equivalent physical mechanisms to elongate, despite the large differences in length scales and structures involved in the process. In other cases, such as in digit elongation, a combination of the two mechanisms seems to be used, with all three physical quantities (growth, active stresses and material properties) being spatially controlled and coordinated to elongate a digit. This classification is based on our limited, current knowledge of the physical quantities controlled during morphogenesis, and will likely change as we learn more about the physics of morphogenesis in other species. It is unclear how many conceptually different physical mechanisms of morphogenesis exist, how conserved each one of them is, whether or not these same physical mechanisms are used to shape more complex 3D structures (beyond elongation), and why these specific physical mechanisms seem to have emerged repeatedly during evolution. Studies that quantify growth, active stresses and material properties in the same structure as it forms remain rare, but performing such measurements in different structures and organisms will help answer these fundamental questions.
It is unclear why different species control different combinations of physical quantities to achieve the same physical transformation, elongation. Answering this question will likely require an understanding of how molecular processes and their evolution are connected to the physical control of morphogenesis. However, species that share a physical mechanism of morphogenesis can employ different molecular players and mechanisms to control physical quantities. This indicates that there exist many possible molecular mechanisms able to encode the same spatiotemporal variations in physical quantities associated with a given conserved physical mechanism of morphogenesis. More systematic studies of the connection between physical and molecular mechanisms of morphogenesis across species are necessary to reveal why these conserved physical mechanisms emerge and why different species employ distinct ones.
Understanding the physical mechanisms that shape cells and tissues is a complex and fundamental problem in science. Although it is clear that morphogenesis of cells and tissues depends on myriad molecular processes, the study of its physical underpinnings is as important as understanding its molecular aspects and will provide new insights into how living systems build themselves, perhaps even helping us construct a much-needed conceptual framework. And yet, the spatiotemporal variations in physical fields that shape living systems are controlled at the cellular and/or molecular levels. Connecting the physics of morphogenesis to its underlying cellular and molecular control, as well as identifying the feedback loops that coordinate physical and molecular variations, remains a major challenge.
Acknowledgements
We thank Dr Sandy Westermann for help with the figures.
Footnotes
Funding
A.B. is supported by a postdoctoral fellowship of the Alexander von Humboldt-Stiftung. S.P.B. is supported by a Shurl and Kay Curci Foundation Award of the Life Sciences Research Foundation. This work was supported by the Eunice Kennedy Shriver National Institute of Child Health and Human Development of the National Institutes of Health (R01HD095797 to O.C.), and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy – EXC 2068–390729961 – Cluster of Excellence Physics of Life of TU Dresden. Deposited in PMC for release after 12 months.
References
Competing interests
The authors declare no competing or financial interests.