Indentation of ellipsoidal and cylindrical elastic shells

Force measurements on natural membrane nanovesicles reveal a composition-independent, high Young's modulus

Mechanical properties of nano-sized vesicles made up of natural membranes are crucial to the development of stable, biocompatible nanocontainers with enhanced functional, recognition and sensing capabilities. Here we measure and compare the mechanical properties of plasma and inner membrane nanovesicles ∼80 nm in diameter obtained from disrupted yeast Saccharomyces cerevisiae cells. We provide evidence of a highly deformable behaviour for these vesicles, able to support repeated wall-to-wall compressions without irreversible deformations, accompanied by a noticeably high Young's modulus (∼300 MPa) compared to that obtained for reconstituted artificial liposomes of similar size and approaching that of some virus particles. Surprisingly enough, the results are approximately similar for plasma and inner membrane nanovesicles, in spite of their different lipid compositions, especially on what concerns the ergosterol content. These results point towards an important structural role of membrane proteins in the mechanical response of natural membrane vesicles and open the perspective to their potential use as robust nanocontainers for bioapplications.

Shrinking the hammer: micromechanical approaches to morphogenesis

Morphogenesis, the remarkable process by which a developing organism achieves its shape, relies on the coordinated growth of cells, tissues, and organs. While the molecular and genetic basis of morphogenesis is starting to be unravelled, understanding shape changes is lagging behind. Actually, shape is imposed by the structural elements of the organism, and the translation of cellular activity into morphogenesis must go through these elements. Therefore, many methods have been developed recently to quantify, at cellular resolution, the properties of the main structural element in plants, the cell wall. As plant cell growth is restrained by the cell wall and powered by turgor pressure, such methods also address the quantification of turgor. These different micromechanical approaches are reviewed here, with a critical assessment of their strengths and weaknesses, and a discussion of how they can help us understand the regulation of growth and morphogenesis.

Reflection and refraction of flexural waves at geometric boundaries

We present a theory of flexural wave propagation on elastic shells having nontrivial geometry and develop an analogy to geometric optics. The transport of momentum within the shell itself is anisotropic due to the curvature, and as such complex classical effects such as birefringence are generically found. We determine the equations of reflection and refraction of such waves at boundaries between different local geometries, showing that waves are totally internally reflected, especially at boundaries between regions of positive and negative Gaussian curvature. We verify these effects by using finite element simulations and discuss the ramifications of these effects for the statistical mechanics of thin curved materials.

Geometry-induced rigidity in nonspherical pressurized elastic shells

We present results from an experimental investigation of the indentation of nonspherical pressurized elastic shells with a positive Gauss curvature. A predictive framework is proposed that rationalizes the dependence of the local rigidity of an indented shell on the curvature in the neighborhood of the locus of indentation, the in-out pressure differential, and the material properties. In our approach, we combine classic theory for spherical shells with recent analytical developments for the pressurized case, and proceed, for the most part, by analogy, guided by our own experiments. By way of example, our results elucidate why an eggshell is significantly stiffer when compressed along its major axis, as compared to doing so along its minor axis. The prominence of geometry in this class of problems points to the relevance and applicability of our findings over a wide range of length scales.