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1. Nonuniform growth and surface friction determine bacterial biofilm morphology on soft substrates

   https://doi.org/10.1073/pnas.1919607117  

   Fei, Chenyi ; Mao, Sheng ; Yan, Jing ; Alert, Ricard ; Stone, Howard A. ; Bassler, Bonnie L. ; Wingreen, Ned S. ; Košmrlj, Andrej ( March 2020 , Proceedings of the National Academy of Sciences)

   During development, organisms acquire three-dimensional (3D) shapes with important physiological consequences. While basic mechanisms underlying morphogenesis are known in eukaryotes, it is often difficult to manipulate them in vivo. To circumvent this issue, here we present a study of developingVibrio choleraebiofilms grown on agar substrates in which the spatiotemporal morphological patterns were altered by varying the agar concentration. Expanding biofilms are initially flat but later undergo a mechanical instability and become wrinkled. To gain mechanistic insights into this dynamic pattern-formation process, we developed a model that considers diffusion of nutrients and their uptake by bacteria, bacterial growth/biofilm matrix production, mechanicalmore »deformation of both the biofilm and the substrate, and the friction between them. Our model shows quantitative agreement with experimental measurements of biofilm expansion dynamics, and it accurately predicts two distinct spatiotemporal patterns observed in the experiments—the wrinkles initially appear either in the peripheral region and propagate inward (soft substrate/low friction) or in the central region and propagate outward (stiff substrate/high friction). Our results, which establish that nonuniform growth and friction are fundamental determinants of stress anisotropy and hence biofilm morphology, are broadly applicable to bacterial biofilms with similar morphologies and also provide insight into how other bacterial biofilms form distinct wrinkle patterns. We discuss the implications of forming undulated biofilm morphologies, which may enhance the availability of nutrients and signaling molecules and serve as a “bet hedging” strategy.

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2. Van der Waals interaction affects wrinkle formation in two-dimensional materials

   https://doi.org/10.1073/pnas.2025870118  

   Ares, Pablo ; Wang, Yi Bo ; Woods, Colin R. ; Dougherty, James ; Fumagalli, Laura ; Guinea, Francisco ; Davidovitch, Benny ; Novoselov, Kostya S. ( March 2021 , Proceedings of the National Academy of Sciences)

   Nonlinear mechanics of solids is an exciting field that encompasses both beautiful mathematics, such as the emergence of instabilities and the formation of complex patterns, as well as multiple applications. Two-dimensional crystals and van der Waals (vdW) heterostructures allow revisiting this field on the atomic level, allowing much finer control over the parameters and offering atomistic interpretation of experimental observations. In this work, we consider the formation of instabilities consisting of radially oriented wrinkles around mono- and few-layer “bubbles” in two-dimensional vdW heterostructures. Interestingly, the shape and wavelength of the wrinkles depend not only on the thickness of the two-dimensionalmore »crystal forming the bubble, but also on the atomistic structure of the interface between the bubble and the substrate, which can be controlled by their relative orientation. We argue that the periodic nature of these patterns emanates from an energetic balance between the resistance of the top membrane to bending, which favors large wavelength of wrinkles, and the membrane-substrate vdW attraction, which favors small wrinkle amplitude. Employing the classical “Winkler foundation” model of elasticity theory, we show that the number of radial wrinkles conveys a valuable relationship between the bending rigidity of the top membrane and the strength of the vdW interaction. Armed with this relationship, we use our data to demonstrate a nontrivial dependence of the bending rigidity on the number of layers in the top membrane, which shows two different regimes driven by slippage between the layers, and a high sensitivity of the vdW force to the alignment between the substrate and the membrane.« less
3. Programming emergent symmetries with saddle-splay elasticity

   https://doi.org/10.1038/s41467-019-13012-9  

   Xia, Yu ; DeBenedictis, Andrew A. ; Kim, Dae Seok ; Chen, Shenglan ; Kim, Se-Um ; Cleaver, Douglas J. ; Atherton, Timothy J. ; Yang, Shu ( November 2019 , Nature Communications)

   The director field adopted by a confined liquid crystal is controlled by a balance between the externally imposed interactions and the liquid’s internal orientational elasticity. While the latter is usually considered to resist all deformations, liquid crystals actually have an intrinsic propensity to adopt saddle-splay arrangements, characterised by the elastic constant$${K}_{24}$$$K_{24}$. In most realisations, dominant surface anchoring treatments suppress such deformations, rendering$${K}_{24}$$$K_{24}$immeasurable. Here we identify regimes where more subtle, patterned surfaces enable saddle-splay effects to be both observed and exploited. Utilising theory and continuum calculations, we determine experimental regimes where generic, achiral liquid crystals exhibit spontaneously broken surface symmetries.more »These provide a new route to measuring$${K}_{24}$$$K_{24}$. We further demonstrate a multistable device in which weak, but directional, fields switch between saddle-splay-motivated, spontaneously-polar surface states. Generalising beyond simple confinement, our highly scalable approach offers exciting opportunities for low-field, fast-switching optoelectronic devices which go beyond current technologies.

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4. Constant spacing in filament bundles

   https://doi.org/10.1088/1367-2630/ab1c2d  

   Atkinson, Daria W. ; Santangelo, Christian D. ; Grason, Gregory M. ( June 2019 , New Journal of Physics)

   Assemblies of one-dimensional filaments appear in a wide range of physical systems: from biopolymer bundles, columnar liquid crystals, and superconductor vortex arrays; to familiar macroscopic materials, like ropes, cables, and textiles. Interactions between the constituent filaments in such systems are most sensitive to thedistance of closest approachbetween the central curves which approximate their configuration, subjecting these distinct assemblies to common geometric constraints. In this paper, we consider two distinct notions of constant spacing in multi-filament packings in${\mathbb{R}}^3$:equidistance, where the distance of closest approach is constant along the length of filament pairs; andisometry, where the distancesmore »of closest approach between all neighboring filaments are constant and equal. We show that, although any smooth curve in${\mathbb{R}}^3$permits one dimensional families of collinear equidistant curves belonging to a ruled surface, there are only two families of tangent fields with mutually equidistant integral curves in${\mathbb{R}}^3$. The relative shapes and configurations of curves in these families are highly constrained: they must be either (isometric) developable domains, which can bend, but not twist; or (non-isometric) constant-pitch helical bundles, which can twist, but not bend. Thus, filament textures that are simultaneously bent and twisted, such as twisted toroids of condensed DNA plasmids or wire ropes, are doubly frustrated: twist frustrates constant neighbor spacing in the cross-section, while non-equidistance requires additional longitudinal variations of spacing along the filaments. To illustrate the consequences of the failure of equidistance, we compare spacing in three ‘almost equidistant’ ansatzes for twisted toroidal bundles and use our formulation of equidistance to construct upper bounds on the growth of longitudinal variations of spacing with bundle thickness.

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5. Rods in a lyotropic chromonic liquid crystal: emergence of chirality, symmetry-breaking alignment, and caged angular diffusion

   https://doi.org/10.1039/D1SM01209F  

   Ettinger, Sophie ; Dietrich, Clarissa F. ; Mishra, Chandan K. ; Miksch, Cornelia ; Beller, Daniel A. ; Collings, Peter J. ; Yodh, A. G. ( January 2022 , Soft Matter)

   In lyotropic chromonic liquid crystals (LCLCs), twist distortion of the nematic director costs much less energy than splay or bend distortion. This feature leads to novel mirror-symmetry breaking director configurations when the LCLCs are confined by interfaces or contain suspended particles. Spherical colloids in an aligned LCLC nematic phase, for example, induce chiral director perturbations (“twisted tails”). The asymmetry of rod-like particles in an aligned LCLC offer a richer set of possibilities due to their aspect ratio ( α ) and mean orientation angle (〈 θ 〉) between their long axis and the uniform far-field director. Here we report onmore »the director configuration, equilibrium orientation, and angular diffusion of rod-like particles with planar anchoring suspended in an aligned LCLC. Video microscopy reveals, counterintuitively, that two-thirds of the rods have an angled equilibrium orientation (〈 θ 〉 ≠ 0) that decreases with increasing α , while only one-third of the rods are aligned (〈 θ 〉 = 0). Polarized optical video-microscopy and Landau–de Gennes numerical modeling demonstrate that the angled and aligned rods are accompanied by distinct chiral director configurations. Angled rods have a longitudinal mirror plane (LMP) parallel to their long axis and approximately parallel to the substrate walls. Aligned rods have a transverse and longitudinal mirror plane (TLMP), where the transverse mirror plane is perpendicular to the rod's long axis. Effectively, the small twist elastic constant of LCLCs promotes chiral director configurations that modify the natural tendency of rods to orient along the far-field director. Additional diffusion experiments confirm that rods are angularly confined with strength that depends on α .« less