Madhav Mani

Physical Ageing of the Contact Line on Colloidal Particles at Liquid Interfaces

Youngs law predicts that a colloidal sphere in equilibrium with a liquid interface will straddle the two fluids, its height above the interface defined by an equilibrium contact angle. This has been used to explain why colloids often bind to liquid interfaces, and has been exploited in emulsification, water purification, mineral recovery, encapsulation and the making of nanostructured materials. However, little is known about the dynamics of binding. Here we show that the adsorption of polystyrene microspheres to a water/oil interface is characterized by a sudden breach and an unexpectedly slow relaxation. The relaxation appears logarithmic in time, indicating that complete equilibration may take months. Surprisingly, viscous dissipation appears to play little role. Instead, the observed dynamics, which bear strong resemblance to ageing in glassy systems, agree well with a model describing activated hopping of the contact line over nanoscale surface heterogeneities. These results may provide clues to longstanding questions on colloidal interactions at an interface.

Events before droplet splashing on a solid surface

A high-velocity (≈1 m s ―1 ) impact between a liquid droplet (≈1 mm) and a solid surface produces a splash. Classical observations traced the origin of this splash to a thin sheet of fluid ejected near the impact point, though the fluid mechanical mechanism leading to the sheet is not known. Mechanisms of sheet formation have heretofore relied on initial contact of the droplet and the surface. In this paper, we theoretically and numerically study the events within the time scale of about 1 μs over which the coupled dynamics between the gas and the droplet becomes important. The droplet initially tries to contact the substrate by either draining gas out of a thin layer or compressing it, with the local behaviour described by a self-similar solution of the governing equations. This similarity solution is not asymptotically consistent: forces that were initially negligible become relevant and dramatically change the behaviour. Depending on the radius and impact velocity of the droplet, we show that the solution is overtaken by initially subdominant physical effects such as the surface tension of the liquid―gas interface or viscous forces in the liquid. At low impact velocities surface tension stops the droplet from impacting the surface, whereas at higher velocities viscous forces become important before surface tension. The ultimate dynamics of the interface once droplet viscosity cannot be neglected is not yet known.

Principles of E-Cadherin Supramolecular Organization In Vivo

BACKGROUND E-cadherin plays a pivotal role in tissue morphogenesis by forming clusters that support intercellular adhesion and transmit tension. What controls E-cadherin mesoscopic organization in clusters is unclear. RESULTS We use 3D superresolution quantitative microscopy in Drosophila embryos to characterize the size distribution of E-cadherin nanometric clusters. The cluster size follows power-law distributions over three orders of magnitude with exponential decay at large cluster sizes. By exploring the predictions of a general theoretical framework including cluster fusion and fission events and recycling of E-cadherin, we identify two distinct active mechanisms setting the cluster-size distribution. Dynamin-dependent endocytosis targets large clusters only, thereby imposing a cutoff size. Moreover, interactions between E-cadherin clusters and actin filaments control the fission in a size-dependent manner. CONCLUSIONS E-cadherin clustering depends on key cortical regulators, which provide tunable and local control over E-cadherin organization. Our data provide the foundation for a quantitative understanding of how E-cadherin distribution affects adhesion and might regulate force transmission in vivo.

Propagation of Dachsous-Fat planar cell polarity.

The Fat pathway controls both planar cell polarity (PCP) and organ growth. Fat signaling is regulated by the graded expression of the Fat ligand Dachsous (Ds) and the cadherin-domain kinase Four-jointed (Fj). The vectors of these gradients influence PCP, whereas their slope can influence growth. The Fj and Ds gradients direct the polarized membrane localization of the myosin Dachs, which is a crucial downstream component of Fat signaling. Here we show that repolarization of Dachs by differential expression of Fj or Ds can propagate through the wing disc, which indicates that Fj and Ds gradients can be measured over long range. Through characterization of tagged genomic constructs, we show that Ds and Fat are themselves partially polarized along the endogenous Fj and Ds gradients, providing a mechanism for propagation of PCP within the Fat pathway. We also identify a biochemical mechanism that might contribute to this polarization by showing that Ds is subject to endoproteolytic cleavage and that the relative levels of Ds isoforms are modulated by Fat.

Collective polarization model for gradient sensing via Dachsous-Fat intercellular signaling

Significance Morphogenesis is a biological process that generates the physical form and structure of multicellular organisms. Although many of the genes controlling morphogenesis are known, little is understood of the mechanisms that define tissue shape and size. Prominent among these mechanisms is the contact signaling between cells mediated by two cell adhesion-type proteins Dachsous and Fat, which regulate cell division in response to the spatially graded distribution of morphogens, factors governing tissue patterning and growth. Here, based on the known behavior of this signaling pathway, we develop a model of the underlying mechanism that relates signaling to the polarization of Dachsous/Fat heterodimers on cell interfaces. This model explains observed phenotypes, makes quantitative predictions, and provides a framework for further experimental studies. Dachsous-Fat signaling via the Hippo pathway influences proliferation during Drosophila development, and some of its mammalian homologs are tumor suppressors, highlighting its role as a universal growth regulator. The Fat/Hippo pathway responds to morphogen gradients and influences the in-plane polarization of cells and orientation of divisions, linking growth with tissue patterning. Remarkably, the Fat pathway transduces a growth signal through the polarization of transmembrane complexes that responds to both morphogen level and gradient. Dissection of these complex phenotypes requires a quantitative model that provides a systematic characterization of the pathway. In the absence of detailed knowledge of molecular interactions, we take a phenomenological approach that considers a broad class of simple models, which are sufficiently constrained by observations to enable insight into possible mechanisms. We predict two modes of local/cooperative interactions among Fat–Dachsous complexes, which are necessary for the collective polarization of tissues and enhanced sensitivity to weak gradients. Collective polarization convolves level and gradient of input signals, reproducing known phenotypes while generating falsifiable predictions. Our construction of a simplified signal transduction map allows a generalization of the positional value model and emphasizes the important role intercellular interactions play in growth and patterning of tissues.

Active tension network model suggests an exotic mechanical state realized in epithelial tissues

Mechanical interactions play a crucial role in epithelial morphogenesis, yet understanding the complex mechanisms through which stress and deformation affect cell behavior remains an open problem. Here we formulate and analyze the Active Tension Network (ATN) model, which assumes that the mechanical balance of cells within a tissue is dominated by cortical tension and introduces tension-dependent active remodeling of the cortex. We find that ATNs exhibit unusual mechanical properties. Specifically, an ATN behaves as a fluid at short times, but at long times supports external tension like a solid. Furthermore, an ATN has an extensively degenerate equilibrium mechanical state associated with a discrete conformal - “isogonal” - deformation of cells. The ATN model predicts a constraint on equilibrium cell geometries, which we demonstrate to approximately hold in certain epithelial tissues. We further show that isogonal modes are observed in the fruit y embryo, accounting for the striking variability of apical areas of ventral cells and helping understand the early phase of gastrulation. Living matter realizes new and exotic mechanical states, the study of which helps to understand biological phenomena.

Two contractile pools of actomyosin distinctly load and tune E-cadherin levels during morphogenesis

Epithelial tissues are highly dynamic. During embryonic morphogenesis cell contacts are constantly remodeled. This stems from active contractile forces that work against adhesive forces at cell interfaces. E-cadherin complexes play a pivotal role in this process as they both support inter-molecular adhesive forces and transmit mechanical tension due to their coupling to the cortical contractile actomyosin networks. In this context, it is unclear how tensile forces affect E-cadherin adhesion complexes and junction dynamics. Addressing this calls for methods to estimate the tensile forces (load) experienced by adhesion complexes themselves. We address this during the early morphogenesis of the Drosophila embryonic ectoderm. Tensile forces generated by Myosin-II in the apico-medial cortex (medial Myosin-II) and in the junctional cortex (junctional Myosin-II) are responsible for junction remodeling. We combined mechanical inference and laser ablations to map tension at cell junctions. We also established Vinculin as a force sensor whose enrichment with respect to E-cadherin measures the load on adhesion complexes within each junction. Combining these tools, we show that the tension generated in both medial and junction pools of Myosin-II imposes load on E-cadherin adhesion complexes. Medial Myosin-II loads adhesion complexes uniformly on all junctions of a cell and increases levels of E-cadherin. Junctional Myosin-II, on the other hand, biases the distribution of the load between junctions of the same cell and exerts shear forces, which correspond to a decrease in the levels of E-cadherin. This work highlights the difference between medial Myosin-II and junctional Myosin-II in regulating E-cadherin levels during junction remodeling and suggest opposite effects of shear versus tensile stresses on E-cadherin complexes and on the dynamics of adhesive cell contacts.Epithelial tissues are highly dynamic. During embryonic morphogenesis cell contacts are constantly remodeled. This stems from active contractile forces that work against adhesive forces at cell interfaces. E-cadherin complexes play a pivotal role in this process as they both support inter-molecular adhesive forces and transmit mechanical tension due to their coupling to the cortical contractile actomyosin networks. In this context, it is unclear how tensile forces affect E-cadherin adhesion complexes and junction dynamics. Addressing this calls for methods to estimate the tensile forces (load) experienced by adhesion complexes themselves. We address this during the early morphogenesis of the Drosophila embryonic ectoderm. Tensile forces generated by Myosin-II in the apico-medial cortex (medial Myosin-II) and in the junctional cortex (junctional Myosin-II) are responsible for junction remodeling. We combined mechanical inference and laser ablations to map tension at cell junctions. We also established the ratio between Vinculin and E-cadherin intensities as a ratiometric readout that measures the load at adhesion complexes. Combining these tools, we show that the tension generated in both medial and junction pools of Myosin-II imposes load on E-cadherin adhesion complexes. Medial Myosin-II loads adhesion complexes on all junctions of a cell and increases levels of E-cadherin. Junctional Myosin-II, on the other hand, biases the distribution of the load between junctions of the same cell and exerts shear forces, which decrease the levels of E-cadherin. This work highlights the difference between medial Myosin-II and junctional Myosin-II in regulating E-cadherin levels during junction remodeling and suggests distinct effects of shear versus tensile stresses on E-cadherin complexes and on the dynamics of adhesive cell contacts.

The Role of Cytoplasmic Interactions in the Collective Polarization of Tissues and its Interplay with Cellular Geometry.

Planar cell polarity (PCP), the ability of a tissue to polarize coherently over multicellular length scales, provides the directional information that guides a multitude of developmental processes at cellular and tissue levels. While it is manifest that cells utilize both intra-cellular and intercellular mechanisms, how they couple together to produce the collective response remains an active area of investigation. Exploring a phenomeno-logical reaction-diffusion model, we predict a crucial, and novel, role for cytoplasmic interactions in the large-scale correlations of cell polarities. We demonstrate that finite-range (i.e. nonlocal) cytoplasmic interactions are necessary and sufficient for the robust and long-range polarization of tissues — even in the absence of global cues — and are essential to the faithful detection of weak directional signals. Strikingly, our model re-capitulates an observed influence of anisotropic tissue geometries on the orientation of polarity. In order to facilitate a conversation between theory and experiments, we compare five distinct classes of in silico mutants with experimental observations. Within this context, we propose quantitative measures that can guide the search for the participant molecular components, and the identification of their roles in the collective polarization of tissues.

A mechanism for the proliferative control of tissue mechanics in the absence of growth

During the development of a multicellular organism, cells coordinate their activities to generate mechanical forces, which in turn drives tissue deformation and eventually defines the shape of the adult tissue. Broadly speaking, it is recognized that mechanical forces can be generated through differential growth and the activity of the cytoskeleton. Based on quantitative analyses of live imaging of the Drosophila dorsal thorax, we suggest a novel mechanism that can generate contractile forces within the plane of an epithelia - via cell proliferation in the absence of growth. Utilizing force inference techniques, we demonstrate that it is not the gradient of junction tension but the divergence of junction-tension associated stresses that induces the area constriction of the proliferating tissue. Using the vertex model simulations, we show that the local averaged stresses can be roughly elevated by a fold of p 2 per cell division without growth. Moreover, this mechanism is robust to disordered cell shapes and the division anisotropy, but can be dominated by growth. In competition with growth, we identify the parameter regime where this mechanism is effective and suggest experiments to test this new mechanism.

QuBiT: A quantitative tool for epithelial tubes reveals cell dynamics and unexpected patterns of organization during Drosophila tracheal morphogenesis

Biological tubes are essential for animal survival, and their functions are critically dependent on tube shape. Analyzing the contributions of cell shape and organization to the morphogenesis of small tubes has been hampered by the limitations of existing programs in quantifying cell geometry on highly curved tubular surfaces and calculating tube-specific parameters. We therefore developed QuBiT (Quantitative Tool for Biological Tubes) and used it to analyze morphogenesis during embryonic Drosophila tracheal (airway) development. We find that there are previously unknown anterior-to-posterior (A-P) gradients of cell orientation and aspect ratio, and that there is periodicity in the organization of cells in the main tube. Furthermore, cell intercalation during development dampens an A-P gradient of the number of the number of cells per cross-section of the tube, but these intercalation events do not change the patterns of cell connectivity. These unexpected findings demonstrate the importance of a computational tool for analyzing the morphogenesis of small diameter biological tubes.