Adhesion-regulated junction slippage controls cell intercalation dynamics in an Apposed-Cortex Adhesion Model

Cell intercalation is a key cell behaviour of morphogenesis and wound healing, where local cell neighbour exchanges can cause dramatic tissue deformations such as body axis extension. Substantial experimental work has identified the key molecular players facilitating intercalation, but there remains a lack of consensus and understanding of their physical roles. Existing biophysical models that represent cell-cell contacts with single edges cannot study cell neighbour exchange as a continuous process, where neighbouring cell cortices must uncouple. Here, we develop an Apposed-Cortex Adhesion Model (ACAM) to understand active cell intercalation behaviours in the context of a 2D epithelial tissue. The junctional actomyosin cortex of every cell is modelled as a continuous viscoelastic rope-loop, explicitly representing cortices facing each other at bicellular junctions and the adhesion molecules that couple them. The model parameters relate directly to the properties of the key subcellular players that drive dynamics, providing a multi-scale understanding of cell behaviours. We show that active cell neighbour exchanges can be driven by purely junctional mechanisms. Active contractility and cortical turnover in a single bicellular junction are sufficient to shrink and remove a junction. Next, a new, orthogonal junction extends passively. The ACAM reveals how the turnover of adhesion molecules regulates tension transmission and junction deformation rates by controlling slippage between apposed cell cortices. The model additionally predicts that rosettes, which form when a vertex becomes common to many cells, are more likely to occur in actively intercalating tissues with strong friction from adhesion molecules.     

Mechanical roles of apical constriction,cell elongation,and cell migration during neural tube formation in Xenopus

Neural tube closure is an important and necessary process during the development of the central nervous system. The formation of the neural tube structure from a flat sheet of neural epithelium requires several cell morphogenetic events and tissue dynamics to account for the mechanics of tissue deformation. Cell elongation changes cuboidal cells into columnar cells, and apical constriction then causes them to adopt apically narrow, wedge-like shapes. In addition, the neural plate in Xenopus is stratified, and the non-neural cells in the deep layer (deep cells) pull the overlying superficial cells, eventually bringing the two layers of cells to the midline. Thus, neural tube closure appears to be a complex event in which these three physical events are considered to play key mechanical roles. To test whether these three physical events are mechanically sufficient to drive neural tube formation, we employed a three-dimensional vertex model and used it to simulate the process of neural tube closure. The results suggest that apical constriction cued the bending of the neural plate by pursing the circumference of the apical surface of the neural cells. Neural cell elongation in concert with apical constriction further narrowed the apical surface of the cells and drove the rapid folding of the neural plate, but was insufficient for complete neural tube closure. Migration of the deep cells provided the additional tissue deformation necessary for closure. To validate the model, apical constriction and cell elongation were inhibited in Xenopus laevis embryos. The resulting cell and tissue shapes resembled the corresponding simulation results.

     

Using optogenetics to link myosin patterns to contractile cell behaviors during convergent extension

Distinct patterns of actomyosin contractility are often associated with particular epithelial tissue shape changes during development. For example, a planar-polarized pattern of myosin II localization regulated by Rho1 signaling during Drosophila body axis elongation is thought to drive cell behaviors that contribute to convergent extension. However, it is not well understood how specific aspects of a myosin pattern influence the multiple cell behaviors, including cell intercalation, cell shape changes, and apical cell area fluctuations, that simultaneously occur during morphogenesis. Here, we developed two optogenetic tools, optoGEF and optoGAP, to activate or deactivate Rho1 signaling, respectively. We used these tools to manipulate myosin patterns at the apical side of the germband epithelium during Drosophila axis elongation and analyzed the effects on contractile cell behaviors. We show that uniform activation or inactivation of Rho1 signaling across the apical surface of the germband is sufficient to disrupt the planar-polarized pattern of myosin at cell junctions on the timescale of 3–5 min, leading to distinct changes in junctional and medial myosin patterns in optoGEF and optoGAP embryos. These two perturbations to Rho1 activity both disrupt axis elongation and cell intercalation but have distinct effects on cell area fluctuations and cell packings that are linked with changes in the medial and junctional myosin pools. These studies demonstrate that acute optogenetic perturbations to Rho1 activity are sufficient to rapidly override the endogenous planar-polarized myosin pattern in the germband during axis elongation. Moreover, our results reveal that the levels of Rho1 activity and the balance between medial and junctional myosin play key roles not only in organizing the cell rearrangements that are known to directly contribute to axis elongation but also in regulating cell area fluctuations and cell packings, which have been proposed to be important factors influencing the mechanics of tissue deformation and flow.     

MDP25, a novel calcium regulatory protein, mediates hypocotyl cell elongation by destabilizing cortical microtubules in Arabidopsis

The regulation of hypocotyl elongation is important for plant growth. Microtubules play a crucial role during hypocotyl cell elongation. However, the molecular mechanism underlying this process is not well understood. In this study, we describe a novel Arabidopsis thaliana microtubule-destabilizing protein 25 (MDP25) as a negative regulator of hypocotyl cell elongation. We found that MDP25 directly bound to and destabilized microtubules to enhance microtubule depolymerization in vitro. The seedlings of mdp25 mutant Arabidopsis lines had longer etiolated hypocotyls. In addition, MDP25 overexpression resulted in significant overall shortening of hypocotyl cells, which exhibited destabilized cortical microtubules and abnormal cortical microtubule orientation, suggesting that MDP25 plays a crucial role in the negative regulation of hypocotyl cell elongation. Although MDP25 localized to the plasma membrane under normal conditions, increased calcium levels in cells caused MDP25 to partially dissociate from the plasma membrane and move into the cytosol. Cellular MDP25 bound to and destabilized cortical microtubules, resulting in their reorientation, and subsequently inhibited hypocotyl cell elongation. Our results suggest that MDP25 exerts its function on cortical microtubules by responding to cytoplasmic calcium levels to mediate hypocotyl cell elongation.     

Apical Junctional Fluctuations Lead to Cell Flow while Maintaining Epithelial Integrity

Epithelial sheet integrity is robustly maintained during morphogenesis, which is essential to shape organs and embryos. While maintaining the planar monolayer in three-dimensional space, cells dynamically flow via rearranging their connections between each other. However, little is known about how cells maintain the plane sheet integrity in three-dimensional space and provide cell flow in the in-plane sheet. In this study, using a three-dimensional vertex model, we demonstrate that apical junctional fluctuations allow stable cell rearrangements while ensuring monolayer integrity. In addition to the fluctuations, direction-dependent contraction on the apical cell boundaries, which corresponds to forces from adherens junctions, induces cell flow in a definite direction. We compared the kinematic behaviors of this apical-force-driven cell flow with those of typical cell flow that is driven by forces generated on basal regions and revealed the characteristic differences between them. These differences can be used to distinguish the mechanism of epithelial cell flow observed in experiments, i.e., whether it is apical- or basal-force-driven. Our numerical simulations suggest that cells actively generate fluctuations and use them to regulate both epithelial integrity and plasticity during morphogenesis.     

Mechanical Coupling between Endoderm Invagination and Axis Extension in Drosophila

How genetic programs generate cell-intrinsic forces to shape embryos is actively studied, but less so how tissue-scale physical forces impact morphogenesis. Here we address the role of the latter during axis extension, using Drosophila germband extension (GBE) as a model. We found previously that cells elongate in the anteroposterior (AP) axis in the extending germband, suggesting that an extrinsic tensile force contributed to body axis extension. Here we further characterized the AP cell elongation patterns during GBE, by tracking cells and quantifying their apical cell deformation over time. AP cell elongation forms a gradient culminating at the posterior of the embryo, consistent with an AP-oriented tensile force propagating from there. To identify the morphogenetic movements that could be the source of this extrinsic force, we mapped gastrulation movements temporally using light sheet microscopy to image whole Drosophila embryos. We found that both mesoderm and endoderm invaginations are synchronous with the onset of GBE. The AP cell elongation gradient remains when mesoderm invagination is blocked but is abolished in the absence of endoderm invagination. This suggested that endoderm invagination is the source of the tensile force. We next looked for evidence of this force in a simplified system without polarized cell intercalation, in acellular embryos. Using Particle Image Velocimetry, we identify posteriorwards Myosin II flows towards the presumptive posterior endoderm, which still undergoes apical constriction in acellular embryos as in wildtype. We probed this posterior region using laser ablation and showed that tension is increased in the AP orientation, compared to dorsoventral orientation or to either orientations more anteriorly in the embryo. We propose that apical constriction leading to endoderm invagination is the source of the extrinsic force contributing to germband extension. This highlights the importance of physical interactions between tissues during morphogenesis.     

The mechanism of cell elongation during lens fiber cell differentiation

Lens fiber formation is characterized by extensive cell elongation. Earlier studies have shown that lens cell elongation in vitro can occur in the absence of microtubules and is associated with a proportional increase in cell volume. We have previously suggested that lens fiber cell elongation is directly caused by an increase in cell volume. In this report, lenses from 3- and 6-day-old chicken embryos were three-dimensionally reconstructed from serial sections to provide a measure of cell volume and length during various stages of primary and secondary lens fiber formation. In both cases, cell volume was highly correlated with cell length during lens cell elongation. In addition, during primary lens fiber formation, large intercellular spaces between lens vesicle cells disappeared as these cells began to elongate to form lens fibers. Loss of intercellular spaces would be expected if increasing cell volume were responsible for cell elongation. Finally, results of experiments in which the lens capsule was cut with a fine tungsten needle suggested that the capsule was elastic and normally under tension. These findings were used to formulate a model which accounts for the major events in lens morphogenesis based on (1) the regulation of cell volume, (2) the junctions present between lens cells, and (3) the constraint provided by the elasticity of the lens capsule.     

Oriented cell divisions in the extending germband of Drosophila

Tissue elongation is a general feature of morphogenesis. One example is the extension of the germband, which occurs during early embryogenesis in Drosophila. In the anterior part of the embryo, elongation follows from a process of cell intercalation. In this study, we follow cell behaviour at the posterior of the extending germband. We find that, in this region, cell divisions are mostly oriented longitudinally during the fast phase of elongation. Inhibiting cell divisions prevents longitudinal deformation of the posterior region and leads to an overall reduction in the rate and extent of elongation. Thus, as in zebrafish embryos, cell intercalation and oriented cell division together contribute to tissue elongation. We also show that the proportion of longitudinal divisions is reduced when segmental patterning is compromised, as, for example, in even skipped (eve) mutants. Because polarised cell intercalation at the anterior germband also requires segmental patterning, a common polarising cue might be used for both processes. Even though, in fish embryos, both mechanisms require the classical planar cell polarity (PCP) pathway, germband extension and oriented cell divisions proceed normally in embryos lacking dishevelled (dsh), a key component of the PCP pathway. An alternative means of planar polarisation must therefore be at work in the embryonic epidermis.     

Polarized interfacial tension induces collective migration of cells,as a cluster,in a 3D tissue

In embryogenesis and cancer invasion, cells collectively migrate as a cluster in 3D tissues. Many studies have elucidated mechanisms of either individual or collective cell migration on 2D substrates; however, it remains unclear how cells collectively migrate as a cluster through 3D tissues. To address this issue, we considered the interfacial tension at cell-cell boundaries expressing cortical actomyosin contractions and cell-cell adhesive interactions. The strength of this tension is polarized; i.e., spatially biased within each cell according to a chemoattractant gradient. Using a 3D vertex model, we performed numerical simulations of multicellular dynamics in 3D space. The simulations revealed that the polarized interfacial tension enables cells to migrate collectively as a cluster through a 3D tissue. In this mechanism, interfacial tension induces unidirectional flow of each cell surface from the front to the rear along the cluster surface. Importantly, this mechanism does not necessarily require convection of cells, i.e., cell rearrangement, within the cluster. Moreover, several migratory modes were induced, depending on the strengths of polarity, adhesion, and noise; i.e., cells migrate either as single cells, as a cluster, or aligned like beads on a string, as occurs in embryogenesis and cancer invasion. These results indicate that the simple expansion and contraction of cell-cell boundaries enables cells to move directionally forward and to produce the variety of collective migratory movements observed in living systems.     

Lamellipodium-driven tissue reshaping: a parametric study

We recently showed that lamellipodia are able to generate forces of the right type to drive convergent extension (CE), an important class of tissue reshaping, in early stage embryos. The purpose of the present work is to quantify the mechanics of this process using parametric analyses. We use finite elements to implement a gamma-mu model in which a net interfacial tension gamma acts along each cell boundary and the cytoplasm exhibits an effective viscosity mu. The stress-strain characteristics of a rectangular patch of model tissue are investigated in terms of the rate r at which lamellipodia form and the relative strength q of their contractions. In tissues that are not constrained in-plane by adjacent tissues, the rate of tissue reshaping is proportional to r the rate of lamellipodium formation and its dependence on q is nonlinear and, near its expected value of 2 highly sensitive to q. Cell elongation, a central characteristic of CE, and stress is found to vary linearly with e the degree of kinematic restraint. Relevant "mechanical pathways" are also identified.     

Cytomechanics of cell deformations and migration: from models to experiments

A cytomechanical model bas been proposed to analyse cell-cell interactions and cell migration through chemotaxis. We consider as the leading assumption that the cell cortical tension is locally modified by the protrusive activity of neighbour cells and binding of chemoattractant molecules to membrane receptors respectively. The model derives from the one initially proposed by Alt and Tranquillo (1995), which successfully describes experimentally observed cyclic autonomous cell shape changes. It is based on force balance equations coupling intracellular hydrostatic pressure and cell cortex contraction. Considering the protrusive dynamics of L929 fibroblats observed by videomicroscopy, we simulated the influence of neighbouring protrusions on a cell spontaneous pulsating behaviour. We further investigated the role of an extracellular gradient as another kind of external stimulus. The model illustrates how binding of chemoattractant molecules can induce a cell morphological instability that, above an intracellular stress threshold, will break the cell-substratum attachment. As a result, realistic cell chemotaxis can be simulated.     

Oscillatory behaviors and hierarchical assembly of contractile structures in intercalating cells

Fluctuations in the size of the apical cell surface have been associated with apical constriction and tissue invagination. However, it is currently not known if apical oscillatory behaviors are a unique property of constricting cells or if they constitute a universal feature of the force balance between cells in multicellular tissues. Here, we set out to determine whether oscillatory cell behaviors occur in parallel with cell intercalation during the morphogenetic process of axis elongation in the Drosophila embryo. We applied multi-color, time-lapse imaging of living embryos and SIESTA, an integrated tool for automated and semi-automated cell segmentation, tracking, and analysis of image sequences. Using SIESTA, we identified cycles of contraction and expansion of the apical surface in intercalating cells and characterized them at the molecular, cellular, and tissue scales. We demonstrate that apical oscillations are anisotropic, and this anisotropy depends on the presence of intact cell-cell junctions and spatial cues provided by the anterior-posterior patterning system. Oscillatory cell behaviors during axis elongation are associated with the hierarchical assembly and disassembly of contractile actomyosin structures at the medial cortex of the cell, with actin localization preceding myosin II and with the localization of both proteins preceding changes in cell shape. We discuss models to explain how the architecture of cytoskeletal networks regulates their contractile behavior and the mechanisms that give rise to oscillatory cell behaviors in intercalating cells.     

A semianalytical model to study the effect of cortical tension on cell rolling

Cell rolling on the vascular endothelium plays an important role in trafficking of leukocytes, stem cells, and cancer cells. We describe a semianalytical model of cell rolling that focuses on the microvillus as the unit of cell-substrate interaction and integrates microvillus mechanics, receptor clustering, force-dependent receptor-ligand kinetics, and cortical tension that enables incorporation of cell body deformation. Using parameters obtained from independent experiments, the model showed excellent agreement with experimental studies of neutrophil rolling on P-selectin and predicted different regimes of cell rolling, including spreading of the cells on the substrate under high shear. The cortical tension affected the cell-surface contact area and influenced the rolling velocity, and modulated the dependence of rolling velocity on microvillus stiffness. Moreover, at the same shear stress, microvilli of cells with higher cortical tension carried a greater load compared to those with lower cortical tension. We also used the model to obtain a scaling dependence of the contact radius and cell rolling velocity under different conditions of shear stress, cortical tension, and ligand density. This model advances theoretical understanding of cell rolling by incorporating cortical tension and microvillus extension into a versatile, semianalytical framework.     

Alteration of oriented deposition of cellulose microfibrils by mutation of a katanin-like microtubule-severing protein

It has long been hypothesized that cortical microtubules (MTs) control the orientation of cellulose microfibril deposition, but no mutants with alterations of MT orientation have been shown to affect this process. We have shown previously that in Arabidopsis, the fra2 mutation causes aberrant cortical MT orientation and reduced cell elongation, and the gene responsible for the fra2 mutation encodes a katanin-like protein. In this study, using field emission scanning electron microscopy, we found that the fra2 mutation altered the normal orientation of cellulose microfibrils in walls of expanding cells. Although cellulose microfibrils in walls of wild-type cells were oriented transversely along the elongation axis, cellulose microfibrils in walls of fra2 cells often formed bands and ran in different directions. The fra2 mutation also caused aberrant deposition of cellulose microfibrils in secondary walls of fiber cells. The aberrant orientation of cellulose microfibrils was shown to be correlated with disorganized cortical MTs in several cell types examined. In addition, the thickness of both primary and secondary cell walls was reduced significantly in the fra2 mutant. These results indicate that the katanin-like protein is essential for oriented cellulose microfibril deposition and normal cell wall biosynthesis. We further demonstrated that the Arabidopsis katanin-like protein possessed MT-severing activity in vitro; thus, it is an ortholog of animal katanin. We propose that the aberrant MT orientation caused by the mutation of katanin results in the distorted deposition of cellulose microfibrils, which in turn leads to a defect in cell elongation. These findings strongly support the hypothesis that cortical MTs regulate the oriented deposition of cellulose microfibrils that determines the direction of cell elongation.     

FAK is required for tension-dependent organization of collective cell movements in Xenopus mesendoderm

Collective cell movements are integral to biological processes such as embryonic development and wound healing and also have a prominent role in some metastatic cancers. In migrating Xenopus mesendoderm, traction forces are generated by cells through integrin-based adhesions and tension transmitted across cadherin adhesions. This is accompanied by assembly of a mechanoresponsive cadherin adhesion complex containing keratin intermediate filaments and the catenin-family member plakoglobin. We demonstrate that focal adhesion kinase (FAK), a major component of integrin adhesion complexes, is required for normal morphogenesis at gastrulation, closure of the anterior neural tube, axial elongation and somitogenesis. Depletion of zygotically expressed FAK results in disruption of mesendoderm tissue polarity similar to that observed when expression of keratin or plakoglobin is inhibited. Both individual and collective migrations of mesendoderm cells from FAK depleted embryos are slowed, cell protrusions are disordered, and cell spreading and traction forces are decreased. Additionally, keratin filaments fail to organize at the rear of cells in the tissue and association of plakoglobin with cadherin is diminished. These findings suggest that FAK is required for the tension-dependent assembly of the cadherin adhesion complex that guides collective mesendoderm migration, perhaps by modulating the dynamic balance of substrate traction forces and cell cohesion needed to establish cell polarity.     

Emergent properties during dorsal closure in Drosophila morphogenesis

Dorsal closure is an essential stage of Drosophila development that is a model system for research in morphogenesis and biological physics. Dorsal closure involves an orchestrated interplay between gene expression and cell activities that produce shape changes, exert forces and mediate tissue dynamics. We investigate the dynamics of dorsal closure based on confocal microscopic measurements of cell shortening in living embryos. During the mid-stages of dorsal closure we find that there are fluctuations in the width of the leading edge cells but the time-averaged analysis of measurements indicate that there is essentially no net shortening of cells in the bulk of the leading edge, that contraction predominantly occurs at the canthi as part of the process for zipping together the two leading edges of epidermis and that the rate constant for zipping correlates with the rate of movement of the leading edges. We characterize emergent properties that regulate dorsal closure, i.e., a velocity governor and the coordination and synchronization of tissue dynamics.     

Patterned cell adhesion associated with tissue deformations during dorsal closure in Drosophila

Cell shape changes within epithelia require the regulation of adhesive molecules that maintain tissue integrity. How remodelling of cell contacts is achieved while tissue integrity is maintained remains a fundamental question in morphogenesis. Dorsal Closure is a good system to study the dynamics of DE-Cadherin during morphogenesis. It relies on concerted cell shape changes of two epithelial sheets: amnioserosa cell contraction and epidermal cell elongation. To investigate the modulation of DE-Cadherin we performed antibody uptake experiments in live embryos during Dorsal Closure. We found that some antibodies access certain epitopes of the extracellular domain of native DE-Cadherin only in the amnioserosa and epidermal cells attached to the amnioserosa, which has never been observed in fixed DE-Cadherin in Drosophila embryos. These differences correlate with the different cell behaviour of these regions and therefore we suggest that DE-Cadherin exists in different forms that confer different adhesive strengths. We propose this to be a widespread mechanism for the differential modulation of adhesion during morphogenesis.     

The SPIRAL genes are required for directional control of cell elongation in Aarabidopsis thaliana

Cells at the elongation zone expand longitudinally to form the straight central axis of plant stems, hypocotyls and roots, and transverse cortical microtubule arrays are generally recognized to be important for the anisotropic growth. Recessive mutations in either of two Arabidopsis thaliana SPIRAL loci, SPR1 or SPR2, reduce anisotropic growth of endodermal and cortical cells in roots and etiolated hypocotyls, and induce right-handed helical growth in epidermal cell files of these organs. spr2 mutants additionally show right-handed twisting in petioles and petals. The spr1spr2 double mutant's phenotype is synergistic, suggesting that SPR1 and SPR2 act on a similar process but in separate pathways in controlling cell elongation. Interestingly, addition of a low dose of either of the microtubule-interacting drugs propyzamide or taxol in the agar medium was found to reduce anisotropic expansion of endodermal and cortical cells at the root elongation zone of wild-type seedlings, resulting in left-handed helical growth. In both spiral mutants, exogenous application of these drugs reverted the direction of the epidermal helix, in a dose-dependent manner, from right-handed to left-handed; propyzamide at 1 microM and taxol at 0.2-0.3 microM effectively suppressed the cell elongation defects of spiral seedlings. The spr1 phenotype is more pronounced at low temperatures and is nearly suppressed at high temperatures. Cortical microtubules in elongating epidermal cells of spr1 roots were arranged in left-handed helical arrays, whereas the highly isotropic cortical cells of etiolated spr1 hypocotyls showed microtubule arrays with irregular orientations. We propose that a microtubule-dependent process and SPR1/SPR2 act antagonistically to control directional cell elongation by preventing elongating cells from potential twisting. Our model may have implicit bearing on the circumnutation mechanism.     

Furrow Constriction in Animal Cell Cytokinesis

Cytokinesis is the process of physical cleavage at the end of cell division; it proceeds by ingression of an acto-myosin furrow at the equator of the cell. Its failure leads to multinucleated cells and is a possible cause of tumorigenesis. Here, we calculate the full dynamics of furrow ingression and predict cytokinesis completion above a well-defined threshold of equatorial contractility. The cortical acto-myosin is identified as the main source of mechanical dissipation and active forces. Thereupon, we propose a viscous active nonlinear membrane theory of the cortex that explicitly includes actin turnover and where the active RhoA signal leads to an equatorial band of myosin overactivity. The resulting cortex deformation is calculated numerically, and reproduces well the features of cytokinesis such as cell shape and cortical flows toward the equator. Our theory gives a physical explanation of the independence of cytokinesis duration on cell size in embryos. It also predicts a critical role of turnover on the rate and success of furrow constriction. Scaling arguments allow for a simple interpretation of the numerical results and unveil the key mechanism that generates the threshold for cytokinesis completion: cytoplasmic incompressibility results in a competition between the furrow line tension and the cell poles’ surface tension.     

Furrow Constriction in Animal Cell Cytokinesis

Cytokinesis is the process of physical cleavage at the end of cell division; it proceeds by ingression of an acto-myosin furrow at the equator of the cell. Its failure leads to multinucleated cells and is a possible cause of tumorigenesis. Here, we calculate the full dynamics of furrow ingression and predict cytokinesis completion above a well-defined threshold of equatorial contractility. The cortical acto-myosin is identified as the main source of mechanical dissipation and active forces. Thereupon, we propose a viscous active nonlinear membrane theory of the cortex that explicitly includes actin turnover and where the active RhoA signal leads to an equatorial band of myosin overactivity. The resulting cortex deformation is calculated numerically, and reproduces well the features of cytokinesis such as cell shape and cortical flows toward the equator. Our theory gives a physical explanation of the independence of cytokinesis duration on cell size in embryos. It also predicts a critical role of turnover on the rate and success of furrow constriction. Scaling arguments allow for a simple interpretation of the numerical results and unveil the key mechanism that generates the threshold for cytokinesis completion: cytoplasmic incompressibility results in a competition between the furrow line tension and the cell poles’ surface tension.