Basolateral Mechanics Prevents Rigidity Transition in Epithelial Monolayers.

The mechanics of epithelial tissues, which is governed by forces generated in various cell regions, is often investigated using two-dimensional models that account for the apically positioned actomyosin structures but neglect basolateral mechanics. We employ a more detailed three-dimensional model to study how lateral surface tensions affect the structure and rigidity of such tissues. We find that cells are apicobasally asymmetric, with one side appearing more ordered than the other depending on target cell apical perimeter.

A mechanical wave travels along a genetic guide to drive the formation of an epithelial furrow during Drosophila gastrulation.

Epithelial furrowing is a fundamental morphogenetic process during gastrulation, neurulation, and body shaping. A furrow often results from a fold that propagates along a line. How fold formation and propagation are controlled and driven is poorly understood.

Morphology of vesicle triplets: shape transformation at weak and strong adhesion limits.

We investigate the morphologies of adhering vesicle triplets as a function of volume-to-area ratio encoded by the reduced volume in strong and weak adhesion regimes. In the strong adhesion regime, the morphology change of the vesicle triplet depends on the arrangement of vesicles. By decreasing the reduced volume, a triangular triplet composed of three spherical caps with a trifurcated flat contact zone deformed to a compact spherical shape with a sigmoidal contact zone, whereas a linear vesicle triplet composed of pancake-shaped vesicles sandwiched between two spherical-cap vesicles with a flat contact zone deformed into a compact spherical shape with biconvex interfaces.

Wrinkling Instability in Unsupported Epithelial Sheets.

We investigate the elasticity of an unsupported epithelial monolayer and we discover that unlike a thin solid plate, which wrinkles if geometrically incompatible with the underlying substrate, the epithelium may do so even in the absence of the substrate. From a cell-based model, we derive an exact elasticity theory and discover wrinkling driven by the differential apico-basal surface tension. Our theory is mapped onto that for supported plates by introducing a phantom substrate whose stiffness is finite beyond a critical differential tension.

Intrinsic lipid curvatures of mammalian plasma membrane outer leaflet lipids and ceramides.

We developed a global X-ray data analysis method to determine the intrinsic curvatures of lipids hosted in inverted hexagonal phases. In particular, we combined compositional modelling with molecular shape-based arguments to account for non-linear mixing effects of guest-in-host lipids on intrinsic curvature. The technique was verified by all-atom molecular dynamics simulations and applied to sphingomyelin and a series of phosphatidylcholines and ceramides with differing composition of the hydrocarbon chains.

Morphologies of compressed active epithelial monolayers.

Using a three-dimensional active vertex model, we numerically study the shapes of strained unsupported epithelial monolayers subject to active junctional noise due to stochastic binding and unbinding of myosin. We find that while uniaxial, biaxial, and isotropic in-plane compressive strains do lead to the formation of longitudinal, herringbone pattern, and labyrinthine folds, respectively, the villus morphology characteristic of, e.g.

Morphologies of Vesicle Doublets: Competition among Bending Elasticity, Surface Tension, and Adhesion.

To study the mechanical laws governing the form of multicellular organisms, we examine the morphology of adhering vesicle doublets as the simplest model system. We monitor the morphological transformations of doublets induced by changes of adhesion strength and volume/area ratio, which are controlled by intermembrane interactions and thermal area expansion, respectively. When we increase the temperature in the weak adhesion regime, a dumbbell flat-contact doublet is transformed to a parallel-prolate doublet, whereas in the strong adhesion regime, heating transforms the dumbbell flat-contact doublet into a spherical sigmoid-contact doublet.

Collective cell mechanics of epithelial shells with organoid-like morphologies.

The study of organoids, artificially grown cell aggregates with the functionality and small-scale anatomy of real organs, is one of the most active areas of research in biology and biophysics, yet the basic physical origins of their different morphologies remain poorly understood. Here, we propose a mechanistic theory of epithelial shells which resemble small-organoid morphologies. Using a 3D surface tension-based vertex model, we reproduce the characteristic shapes from branched and budded to invaginated structures.

Metallic-mean quasicrystals as aperiodic approximants of periodic crystals.

Ever since the discovery of quasicrystals, periodic approximants of these aperiodic structures constitute a very useful experimental and theoretical device. Characterized by packing motifs typical for quasicrystals arranged in large unit cells, these approximants bridge the gap between periodic and aperiodic positional order. Here we propose a class of sequences of 2-D quasicrystals that consist of increasingly larger periodic domains and are marked by an ever more pronounced periodicity, thereby representing aperiodic approximants of a periodic crystal.

Fluidization of epithelial sheets by active cell rearrangements.

We theoretically explore fluidization of epithelial tissues by active T1 neighbor exchanges. We show that the geometry of cell-cell junctions encodes important information about the local features of the energy landscape, which we support by an elastic theory of T1 transformations. Using a 3D vertex model, we show that the degree of active noise driving forced cell rearrangements governs the stress-relaxation timescale of the tissue.

Bronze-mean hexagonal quasicrystal.

The most striking feature of conventional quasicrystals is their non-traditional symmetry characterized by icosahedral, dodecagonal, decagonal or octagonal axes. The symmetry and the aperiodicity of these materials stem from an irrational ratio of two or more length scales controlling their structure, the best-known examples being the Penrose and the Ammann-Beenker tiling as two-dimensional models related to the golden and the silver mean, respectively. Surprisingly, no other metallic-mean tilings have been discovered so far.

Role of Inverse-Cone-Shape Lipids in Temperature-Controlled Self-Reproduction of Binary Vesicles.

We investigate a temperature-driven recursive division of binary giant unilamellar vesicles (GUVs). During the heating step of the heating-cooling cycle, the spherical mother vesicle deforms to a budded limiting shape using up the excess area produced by the chain melting of the lipids and then splits off into two daughter vesicles. Upon cooling, the daughter vesicle opens a pore and recovers the spherical shape of the mother vesicle.

Quantitative Morphology of Epithelial Folds.

The shape of spatially modulated epithelial morphologies such as villi and crypts is usually associated with the epithelium-stroma area mismatch leading to buckling. We propose an alternative mechanical model based on intraepithelial stresses generated by differential tensions of apical, lateral, and basal sides of cells as well as on the elasticity of the basement membrane. We use it to theoretically study longitudinal folds in simple epithelia and we identify four types of corrugated morphologies: compact, invaginated, evaginated, and wavy.

Theory of epithelial elasticity.

We propose an elastic theory of epithelial monolayers based on a two-dimensional discrete model of dropletlike cells characterized by differential surface tensions of their apical, basal, and lateral sides. We show that the effective tissue bending modulus depends on the apicobasal differential tension and changes sign at the transition from the flat to the fold morphology. We discuss three mechanisms that stabilize the finite-wavelength fold structures: Physical constraint on cell geometry, hard-core interaction between non-neighboring cells, and bending elasticity of the basement membrane.

Elasticity of polymeric nanocolloidal particles.

Softness is an essential mechanical feature of macromolecular particles such as polymer-grafted nanocolloids, polyelectrolyte networks, cross-linked microgels as well as block copolymer and dendrimer micelles. Elasticity of individual particles directly controls their swelling, wetting, and adsorption behaviour, their aggregation and self-assembly as well as structural and rheological properties of suspensions. Here we use numerical simulations and self-consistent field theory to study the deformation behaviour of a single spherical polymer brush upon diametral compression.

Embryo-scale tissue mechanics during Drosophila gastrulation movements.

Morphogenesis of an organism requires the development of its parts to be coordinated in time and space. While past studies concentrated on defined cell populations, a synthetic view of the coordination of these events in a whole organism is needed for a full understanding. Drosophila gastrulation begins with the embryo forming a ventral furrow, which is eventually internalized.

Physical models of mesoderm invagination in Drosophila embryo.

The invagination of the mesoderm in the Drosophila melanogaster embryo is an intensely studied example of epithelial folding. Several theoretical studies have explored the conditions and mechanisms needed to reproduce the formation of the invagination in silico. Here we discuss the aspects of epithelial folding captured by these studies, and compare the questions addressed, the approaches used, and the answers provided.

A model of epithelial invagination driven by collective mechanics of identical cells.

We propose a 2D mechanical model of a tubular epithelium resembling the early Drosophila embryo. The model consists of a single layer of identical cells with energy associated with the tension of cell cortex. Depending on the relative tension of the apical, basal, and lateral sides of the cells, tissue thickness, and the degree of external constraint, the minimal-energy states of the epithelial cross section include circular shapes as well as a range of inward-buckled shapes.

Reaction kinetics and mechanical models of liposome adhesion at charged interface.

Dynamics of adhesion of single liposome at the charged mercury interface is analyzed through its amperometric signal using a reaction kinetics model and a mechanical model. We present analytical solutions of the reaction kinetics model for decoupling and identifying temporal evolution of three distinct states: i) the initial state corresponding to an intact liposome, ii) the intermediate state where the liposome is partly deformed, and iii) the final state of a lipid monolayer. The results obtained with this model indicate that all three states simultaneously evolve from the onset of the adhesion process.

Analysis of side chain rotational restrictions of membrane-embedded proteins by spin-label ESR spectroscopy.

Site-directed spin-labeling electron spin resonance (SDSL-ESR) is a promising tool for membrane protein structure determination. Here we propose a novel way to translate the local structural constraints gained by SDSL-ESR data into a low-resolution structure of a protein by simulating the restrictions of the local conformational spaces of the spin label attached at different protein sites along the primary structure of the membrane-embedded protein. We test the sensitivity of this approach for membrane-embedded M13 major coat protein decorated with a limited number of strategically placed spin labels employing high-throughput site-directed mutagenesis.

The cooperative role of membrane skeleton and bilayer in the mechanical behaviour of red blood cells.

Red blood cell (RBC) shape, behaviour and deformability can be consistently accounted for by a model for the elastic properties of the RBC membrane that includes the elasticity of the membrane skeleton in dilation and shear, and the local and nonlocal resistance of the bilayer to bending. The role of the corresponding energy terms in different RBC shape and deformation situations is analyzed. RBC shape transformations are compared to the shape transformations of phospholipid vesicles that are driven by the difference between the equilibrium areas of the bilayer leaflets (DeltaA0).