Wrinkling in the deflation of elastic bubbles

The protein hydrophobin HFBII self-assembles into very elastic films at the surface of water; these films wrinkle readily upon compression. We demonstrate and study this wrinkling instability in the context of non-planar interfaces by forming HFBII layers at the surface of bubbles; the interfaces are then compressed by deflating the bubble. By varying the initial concentration of the hydrophobin solutions, we are able to show that buckling occurs at a critical packing fraction of protein molecules on the surface. Independent experiments show that at this packing fraction the interface has a finite positive surface tension, and not zero surface tension as is usually assumed at buckling. We attribute this non-zero wrinkling tension to the finite elasticity of these interfaces. We develop a simple geometrical model for the evolution of the wrinkle length with further deflation, and show that wrinkles start close to the needle used for deflation and grow rapidly towards the mid-plane of the bubble. This geometrical model yields predictions for the length of wrinkles in good agreement with experiments, independently of the rheological properties of the adsorbed layer

The Influence of high pressure on the bending rigidity of model membranes

Curvature is a fundamental lipid membrane property that influences many membrane-mediated biological processes and dynamic soft materials. One of the key parameters that determines the energetics of curvature change is the membrane bending rigidity. Understanding the intrinsic effect of pressure on membrane bending is critical to understanding the adaptation and structural behavior of biomembranes in deep-sea organisms as well as soft material processing. However, it has not previously been possible to measure the influence of high hydrostatic pressure on membrane bending energetics, and this bottleneck has primarily been due to a lack of technology platforms for performing such measurements. We have developed a new high-pressure microscopy cell which, combined with vesicle fluctuation analysis, has allowed us to make the first measurements of membrane bending rigidity as a function of pressure. Our results show a significant increase in bending rigidity at pressures up to 40 MPa. Above 40 MPa, the membrane mechanics become more complex. Corresponding small and wide-angle X-ray diffraction shows an increase in density and thickness of the bilayer with increasing pressure which correlates with the micromechanical measurements. These results are consistent with recent theoretical predictions of the bending rigidity as a function of hydrocarbon chain density. This technology has the potential to transform our quantitative understanding of the role of pressure in soft material processing, the structural behavior of biomembranes, and the adaptation mechanisms employed by deep-sea organisms

Elastometry of deflated capsules elastic moduli from shape and wrinkle analysis

Elastic capsules, prepared from droplets or bubbles attached to a capillary (as in a pendant drop tensiometer), can be deflated by suction through the capillary. We study this deflation and show that a combined analysis of the shape and wrinkling characteristics enables us to determine the elastic properties in situ. Shape contours are analyzed and fitted using shape equations derived from nonlinear membrane-shell theory to give the elastic modulus, Poisson ratio and stress distribution of the membrane. We include wrinkles, which generically form upon deflation, within the shape analysis. Measuring the wavelength of wrinkles and using the calculated stress distribution gives the bending stiffness of the membrane. We illustrate this method on two very different capsule materials: polymerized octadecyltrichlorosilane (OTS) capsules and hydrophobin (HFBII) coated bubbles. Our results are in agreement with the available rheological data. For hydrophobin coated bubbles the method reveals an interesting nonlinear behavior consistent with the hydrophobin molecules having\ud a rigid core surrounded by a softer shell

Photonic gaps in cholesteric elastomers under deformation

Cholesteric liquid crystal elastomers have interesting and potentially very useful photonic properties. In an ideal monodomain configuration of these materials, one finds a Bragg-reflection of light in a narrow wavelength range and a particular circular polarization. This is due to the periodic structure of the material along one dimension. In many practical cases, the cholesteric rubber possesses a sufficient degree of quenched disorder, which makes the selective reflection broadband. We investigate experimentally the problem of how the transmittance of light is affected by mechanical deformation of the elastomer, and the relation to changes in liquid crystalline structure. We explore a series of samples which have been synthesized with photonic stop-gaps across the visible range. This allows us to compare results with detailed theoretical predictions regarding the evolution of stop-gaps in cholesteric elastomers

Direct measurement of DNA-mediated adhesion between lipid bilayers

Multivalent interactions between deformable mesoscopic units are ubiquitous in biology, where membrane macromolecules mediate the interactions between neighbouring living cells and between cells and solid substrates. Lately, analogous artificial materials have been synthesised by functionalising the outer surface of compliant Brownian units, for example emulsion droplets and lipid vesicles, with selective linkers, in particular short DNA sequences. This development extended the range of applicability of DNA as a selective glue, originally applied to solid nano and colloidal particles. On very deformable lipid vesicles, the coupling between statistical effects of multivalent interactions and mechanical deformation of the membranes gives rise to complex emergent behaviours, as we recently contributed to demonstrate [Parolini et al., Nature Communications, 2015, 6, 5948]. Several aspects of the complex phenomenology observed in these systems still lack a quantitative experimental characterisation and fundamental understanding. Here we focus on the DNA-mediated multivalent interactions of a single liposome adhering to a flat supported bilayer. This simplified geometry enables the estimate of the membrane tension induced by the DNA-mediated adhesive forces acting on the liposome. Our experimental investigation is completed by morphological measurements and the characterisation of the DNA-melting transition, probed by in-situ F\"{o}rster Resonant Energy Transfer spectroscopy. Experimental results are compared with the predictions of an analytical theory that couples the deformation of the vesicle to a full description of the statistical mechanics of mobile linkers. With at most one fitting parameter, our theory is capable of semi-quantitatively matching experimental data, confirming the quality of the underlying assumptions.Comment: 16 pages, 7 figure

Real symmetric random matrices and paths counting

Exact evaluation of $$ is here performed for real symmetric matrices $S$ of arbitrary order $n$, up to some integer $p$, where the matrix entries are independent identically distributed random variables, with an arbitrary probability distribution. These expectations are polynomials in the moments of the matrix entries ; they provide useful information on the spectral density of the ensemble in the large $n$ limit. They also are a straightforward tool to examine a variety of rescalings of the entries in the large $n$ limit.Comment: 23 pages, 10 figures, revised pape

Compact support probability distributions in random matrix theory

We consider a generalization of the fixed and bounded trace ensembles introduced by Bronk and Rosenzweig up to an arbitrary polynomial potential. In the large-N limit we prove that the two are equivalent and that their eigenvalue distribution coincides with that of the "canonical" ensemble with measure exp[-$n$Tr V(M)]. The mapping of the corresponding phase boundaries is illuminated in an explicit example. In the case of a Gaussian potential we are able to derive exact expressions for the one- and two-point correlator for finite $n$, having finite support

Long-range interactions, wobbles, and phase defects in chains of model cilia

Eukaryotic cilia and flagella are chemo-mechanical oscillators capable of generating long-range coordinated motions known as metachronal waves. Pair synchronization is a fundamental requirement for these collective dynamics, but it is generally not sufficient for collective phase-locking, chiefly due to the effect of long-range interactions. Here we explore experimentally and numerically a minimal model for a ciliated surface: hydrodynamically coupled oscillators rotating above a no-slip plane. Increasing their distance from the wall profoundly affects the global dynamics, due to variations in hydrodynamic interaction range. The array undergoes a transition from a traveling wave to either a steady chevron pattern or one punctuated by periodic phase defects. Within the transition between these regimes the system displays behavior reminiscent of chimera states.Human Frontier Science Program; Wellcome Trust; EU ERC CoG Hydrosyn

Volume and porosity thermal regulation in lipid mesophases by coupling mobile ligands to soft membranes

Short DNA linkers are increasingly being exploited for driving specific self-assembly of Brownian objects. DNA-functionalised colloids can assemble into ordered or amorphous materials with tailored morphology. Recently, the same approach has been applied to compliant units, including emulsion droplets and lipid vesicles. The liquid structure of these substrates introduces new degrees of freedom: the tethers can diffuse and rearrange, radically changing the physics of the interactions. Unlike droplets, vesicles are extremely deformable and DNA-mediated adhesion causes significant shape adjustments. We investigate experimentally the thermal response of pairs and networks of DNA-tethered liposomes and observe two intriguing and possibly useful collective properties: negative thermal expansion and tuneable porosity of the liposome networks. A model providing a thorough understanding of this unexpected phenomenon is developed, explaining the emergent properties out of the interplay between the temperature-dependent deformability of the vesicles and the DNA-mediated adhesive forces.Funding was provided by the Ernest Oppenheimer Fund and Emmanuel College Cambridge (L.D.M.), EPSRC Programme Grant CAPITALS number EP/J017566/1 (L.P., J.K., P.C. and L.D.M.) and the Winton Fund for Physics of Sustainability (E.E.).This article was originally published in Nature Communications (L Parolini, BM Mognetti, J Kotar, E Eiser, P Cicuta, L Di Michele, Nature Communications 2015, 6, 5948