How bees and foams respond to curved confinement:Level set boundary representations in the Surface Evolver

We investigate the equilibrium properties of a single area-minimising bubble trapped between two narrowly-separated parallel curved plates. We begin with the simple case of a bubble trapped between concentric spherical plates. We develop a model that shows that the surface tension energy of the bubble is lower when confined between spherical plates as compared to a bubble trapped between flat plates. We confirm our findings by comparing against Surface Evolver simulations. Next, we derive a simple model for a bubble between arbitrarily curved parallel plates. The energy is found to be higher when the local Gaussian curvature of the plates is negative and lower when the curvature is positive. To check the validity of the model we consider a bubble trapped between concentric tori. In the toroidal case we find that the sensitivity of the bubble's energy to the local curvature acts as a geometric potential capable of driving bubbles from regions with negative to positive curvature

Curvature driven motion of a bubble in a toroidal Hele-Shaw cell

We investigate the equilibrium properties of a single area-minimizing bubble trapped between two narrowly separated parallel curved plates. We begin with the case of a bubble trapped between concentric spherical plates. We develop a model which shows that the surface energy of the bubble is lower when confined between spherical plates than between flat plates. We confirm our findings by comparing against Surface Evolver simulations. We then derive a simple model for a bubble between arbitrarily curved parallel plates. The energy is found to be higher when the local Gaussian curvature of the plates is negative and lower when the curvature is positive. To check the validity of the model, we consider a bubble trapped between concentric tori. In the toroidal case, we find that the sensitivity of the bubble’s energy to the local curvature acts as a geometric potential capable of driving bubbles from regions with negative to positive curvature

Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

Local Anisotropy of Fluids using Minkowski Tensors

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0\leq \beta_\nu^{a,b}\leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from $\beta_\nu^{a,b}\approx 0.3$ for vapor phases to $\beta_\nu^{a,b}\to 1$ for ordered solids. We find that for fluids, local anisotropy decreases monotonously with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices $\beta_\nu^{a,b}$ are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs

Bicontinuous minimal surface nanostructures for polymer blend solar cells

This paper presents the first examination of the potential for bicontinuous structures such as the gyroid structure to produce high efficiency solar cells based on conjugated polymers. The solar cell characteristics are predicted by a simulation model that shows how the morphology influences device performance through integration of all the processes occurring in organic photocells in a specified morphology. In bicontinuous phases, the surface de. ning the interface between the electron and hole transporting phases divides the volume into two disjoint subvolumes. Exciton loss is reduced because the interface at which charge separation occurs permeates the device so excitons have only a short distance to reach the interface. As each of the component phases is connected, charges will be able to reach the electrodes more easily. In simulations of the current-voltage characteristics of organic cells with gyroid, disordered blend and vertical rod (rods normal to the electrodes) morphologies, we find that gyroids have a lower than anticipated performance advantage over disordered blends, and that vertical rods are superior. These results are explored thoroughly, with geminate recombination, i.e. recombination of charges originating from the same exciton, identified as the primary source of loss. Thus, if an appropriate materials choice could reduce geminate recombination, gyroids show great promise for future research and applications

Minkowski tensors and local structure metrics: Amorphous and crystalline sphere packings

Robust and sensitive tools to characterise local structure are essential for investigations of granular or particulate matter. Often local structure metrics derived from the bond network are used for this purpose, in particular Steinhardt's bond-orientational order parameters ql . Here we discuss an alternative method, based on the robust characterisation of the shape of the particles' Voronoi cells, by Minkowski tensors and derived anisotropy measures. We have successfully applied these metrics to quantify structural changes and the onset of crystallisation in random sphere packs. Here we specifically discuss the expectation values of these metrics for simple crystalline unimodal packings of spheres, consisting of single spheres on the points of a Bravais lattice. These data provide an important reference for the discussion of anisotropy values of disordered structures that are typically of relevance in granular systems. This analysis demonstrates that, at least for sufficiently high packing fractions above φ > 0.61, crystalline sphere packs exist whose Voronoi cells are more anisotropic with respect to a volumetric moment tensor than the average value of Voronoi cell anisotropy in random sphere packs

Butterfly gyroid nanostructures as a time-frozen glimpse of intracellular membrane development

The formation of the biophotonic gyroid material in butterflywing scales is an exceptional feat of evolutionary engineering of functional nanostructures. It is hypothesized that this nanostructure forms by chitin polymerization inside a convolutedmembrane of corresponding shape in the endoplasmic reticulum. However, this dynamic formation process, including whether membrane folding and chitin expression are simultaneous or sequential processes, cannot yet be elucidated by in vivo imaging. We report an unusual hierarchical ultrastructure in the butterfly Thecla opisena that, as a solid material, allows high-resolution three-dimensional microscopy. Rather than the conventional polycrystalline spacefilling arrangement, a gyroid occurs in isolated facetted crystallites with a pronounced size gradient.When interpreted as a sequence of time-frozen snapshots of the morphogenesis, this arrangement provides insight into the formation mechanisms of the nanoporous gyroid material as well as of the intracellular organelle membrane that acts as the template

Bioassays to Monitor Taspase1 Function for the Identification of Pharmacogenetic Inhibitors

Background: Threonine Aspartase 1 (Taspase1) mediates cleavage of the mixed lineage leukemia (MLL) protein and leukemia provoking MLL-fusions. In contrast to other proteases, the understanding of Taspase1's (patho)biological relevance and function is limited, since neither small molecule inhibitors nor cell based functional assays for Taspase1 are currently available. Methodology/Findings: Efficient cell-based assays to probe Taspase1 function in vivo are presented here. These are composed of glutathione S-transferase, autofluorescent protein variants, Taspase1 cleavage sites and rational combinations of nuclear import and export signals. The biosensors localize predominantly to the cytoplasm, whereas expression of biologically active Taspase1 but not of inactive Taspase1 mutants or of the protease Caspase3 triggers their proteolytic cleavage and nuclear accumulation. Compared to in vitro assays using recombinant components the in vivo assay was highly efficient. Employing an optimized nuclear translocation algorithm, the triple-color assay could be adapted to a high-throughput microscopy platform (Z'factor = 0.63). Automated high-content data analysis was used to screen a focused compound library, selected by an in silico pharmacophor screening approach, as well as a collection of fungal extracts. Screening identified two compounds, N-[2-[(4-amino-6-oxo-3H-pyrimidin-2-yl)sulfanyl]ethyl]benzenesulfonamideand 2-benzyltriazole-4,5-dicarboxylic acid, which partially inhibited Taspase1 cleavage in living cells. Additionally, the assay was exploited to probe endogenous Taspase1 in solid tumor cell models and to identify an improved consensus sequence for efficient Taspase1 cleavage. This allowed the in silico identification of novel putative Taspase1 targets. Those include the FERM Domain-Containing Protein 4B, the Tyrosine-Protein Phosphatase Zeta, and DNA Polymerase Zeta. Cleavage site recognition and proteolytic processing of these substrates were verified in the context of the biosensor. Conclusions: The assay not only allows to genetically probe Taspase1 structure function in vivo, but is also applicable for high-content screening to identify Taspase1 inhibitors. Such tools will provide novel insights into Taspase1's function and its potential therapeutic relevance

Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales

© 2023 The Authors. Advanced Materials published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.A.P.G.C. and P.R.F. acknowledge the funding from Fundação para a Ciência e Tecnologia (Portugal), through IDMEC, under LAETA project UIDB/50022/2020. T.H.V.P. acknowledges the funding from Fundação para a Ciência e Tecnologia (Portugal), through Ph.D. Grant 2020.04417.BD. A.S. acknowledges that this work was partially supported by the ATTRACT Investigator Grant (no. A17/MS/11572821/MBRACE, to A.S.) from the Luxembourg National Research Fund. The author thanks Gerardo Ceada for his help in the graphical representations. N.A.K. acknowledges support from the European Research Council (grant 851960) and the Gravitation Program “Materials Driven Regeneration,” funded by the Netherlands Organization for Scientific Research (024.003.013). M.B.A. acknowledges support from the French National Research Agency (grant ANR-201-8-CE1-3-0008 for the project “Epimorph”). G.E.S.T. acknowledges funding by the Australian Research Council through project DP200102593. A.C. acknowledges the funding from the Deutsche Forschungsgemeinschaft (DFG) Emmy Noether Grant CI 203/-2 1, the Spanish Ministry of Science and Innovation (PID2021-123013O-BI00) and the IKERBASQUE Basque Foundation for Science.Peer reviewe