The crucial role of elasticity in regulating liquid-liquid phase separation in cells.

Liquid-liquid phase separation has emerged as a fundamental mechanism underlying intracellular organization, with evidence for it being reported in numerous different systems. However, there is a growing concern regarding the lack of quantitative rigor in the techniques employed to study phase separation, and their ability to account for the complex nature of the cellular milieu, which affects key experimentally observable measures, such as the shape, size and transport dynamics of liquid droplets. Here, we bridge this gap by combining recent experimental data with theoretical predictions that capture the subtleties of nonlinear elasticity and fluid transport. We show that within a biologically accessible range of material parameters, phase separation is highly sensitive to elastic properties and can thus be used as a mechanical switch to rapidly transition between different states in cellular systems. Furthermore, we show that this active mechanically mediated mechanism can drive transport across cells at biologically relevant timescales and could play a crucial role in promoting spatial localization of condensates; whether cells exploit such mechanisms for transport of their constituents remains an open question.

Biofilms as self-shaping growing nematics.

Active nematics are the nonequilibrium analogue of passive liquid crystals. They consist of anisotropic units that consume free energy to drive emergent behaviour. Like liquid crystal molecules in displays, ordering and dynamics in active nematics are sensitive to boundary conditions. However, unlike passive liquid crystals, active nematics have the potential to regulate their boundaries through self-generated stresses. Here, we show how a three-dimensional, living nematic can actively shape itself and its boundary to regulate its internal architecture through growth-induced stresses, using bacterial biofilms confined by a hydrogel as a model system. We show that biofilms exhibit a sharp transition in shape from domes to lenses upon changing environmental stiffness or cell-substrate friction, which is explained by a theoretical model that considers the competition between confinement and interfacial forces. The growth mode defines the progression of the boundary, which in turn determines the trajectories and spatial distribution of cell lineages. We further demonstrate that the evolving boundary and corresponding stress anisotropy define the orientational ordering of cells and the emergence of topological defects in the biofilm interior. Our findings may provide strategies for the development of programmed microbial consortia with emergent material properties.

Morphogenesis and cell ordering in confined bacterial biofilms.

Biofilms are aggregates of bacterial cells surrounded by an extracellular matrix. Much progress has been made in studying biofilm growth on solid substrates; however, little is known about the biophysical mechanisms underlying biofilm development in three-dimensional confined environments in which the biofilm-dwelling cells must push against and even damage the surrounding environment to proliferate. Here, combining single-cell imaging, mutagenesis, and rheological measurement, we reveal the key morphogenesis steps of Vibrio cholerae biofilms embedded in hydrogels as they grow by four orders of magnitude from their initial size. We show that the morphodynamics and cell ordering in embedded biofilms are fundamentally different from those of biofilms on flat surfaces. Treating embedded biofilms as inclusions growing in an elastic medium, we quantitatively show that the stiffness contrast between the biofilm and its environment determines biofilm morphology and internal architecture, selecting between spherical biofilms with no cell ordering and oblate ellipsoidal biofilms with high cell ordering. When embedded in stiff gels, cells self-organize into a bipolar structure that resembles the molecular ordering in nematic liquid crystal droplets. In vitro biomechanical analysis shows that cell ordering arises from stress transmission across the biofilm-environment interface, mediated by specific matrix components. Our imaging technique and theoretical approach are generalizable to other biofilm-forming species and potentially to biofilms embedded in mucus or host tissues as during infection. Our results open an avenue to understand how confined cell communities grow by means of a compromise between their inherent developmental program and the mechanical constraints imposed by the environment.

Controlled propagation and jamming of a delamination front.

We study the birth and propagation of a delamination front in the peeling of a soft, weakly adhesive layer. In a controlled-displacement setting, the layer partially detaches via a subcritical instability and the motion continues until arrested, by jamming of the two lobes. Using numerical solutions and scaling analysis, we quantitatively describe the equilibrium shapes and obtain constitutive sensitivities of jamming process to material and interface properties. We conclude with a way to delay or avoid jamming altogether by tunable interface properties.

Critical curvature localization in graphene. II. Non-local flexoelectricity-dielectricity coupling.

As a sequel of part I (Kothari et al. 2018 Proc. R. Soc. A 474, 20180054), we present a general thermodynamic framework of flexoelectric constitutive laws for multi-layered graphene (MLG), and apply these laws to explain the role of crinkles in peculiar molecular adsorption characteristics of highly oriented pyrolytic graphite (HOPG) surfaces. The thermodynamically consistent constitutive laws lead to a non-local interaction model of polarization induced by electromechanical deformation with flexoelectricity-dielectricity coupling. The non-local model predicts curvature and polarization localization along crinkle valleys and ridges very close to those calculated by density functional theory (DFT). Our analysis reveals that the non-local model can be reduced to a simplified uc-local or e-local model (Kothari et al. 2018 Proc. R. Soc. A 474, 20180054) only when the curvature distribution is uniform or highly localized. For the non-local model, we calibrated and formulated the layer-number-dependent dielectric and intrinsic flexoelectric coefficients of MLGs. In addition, we also obtained layer-number dependent flexoelectric coefficients for uc-local and e-local models. Our DFT analysis shows that polarization-induced adsorption of neutral molecules at crinkle ridges depends on the molecular weight of the molecule. Furthermore, our detailed study of polarization localization in graphene crinkles enables us to understand previously unexplained self-organized adsorption of C60 buckyballs in a linear array on an HOPG surface.

Critical curvature localization in graphene. I. Quantum-flexoelectricity effect.

Here, we report the discovery of a new, curvature-localizing, subcritical buckling mode that produces shallow-kink corrugation in multi-layer graphene. Our density functional theory (DFT) analysis reveals the mode configuration-an approximately 2 nm wide boundary layer of highly localized curvature that connects two regions of uniformly but oppositely sheared stacks of flat atomic sheets. The kink angle between the two regions is limited to a few degrees, ensuring elastic deformation. By contrast, a purely mechanical model of sandwich structures shows progressive supercritical curvature localization spread over a 50-100 nm wide boundary layer. Our effective-locality model of electromechanics reveals that coupling between atomic-layer curvature and electric-charge polarization, i.e. quantum flexoelectricity, leads to emergence of a boundary layer in which curvature is focused primarily within a 0.86 nm fixed band width. Both DFT and the model analyses show focused distributions of curvature and polarization exhibiting oscillating decay within the approximately 2 nm wide boundary layer. The results show that dipole-dipole interaction lowers the potential energy with such a distribution. Furthermore, this model predicts peak-polarization density approximately 0.12 e- nm-1 for 3° tilt angle. This high polarization concentration can be controlled by macroscopic deformation and is expected to be useful in studies of selective graphene-surface functionalization for various applications.